Reconsidering Conceptual Change: Issues in Theory and Practice

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Reconsidering Conceptual Change: Issues in Theory and Practice

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Reconsidering Conceptual Change: Issues in Theory and Practice

Edited by

Margarita Limón Universidad Autónoma, Madrid, Spain

and

Lucia Mason University of Padova, Italy

KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

eBook ISBN: Print ISBN:

0-306-47637-1 1-4020-0494-X

©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2002 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at:

http://kluweronline.com http://ebooks.kluweronline.com

TABLE OF CONTENTS CONTRIBUTORS

ix

PREFACE

xiii

INTRODUCTION Margarita Limón & Lucia Mason

XV

PART I: THEORETICAL PERSPECTIVES THE PROCESSES AND CHALLENGES OF CONCEPTUAL CHANGE Michelene T. H. Chi & Rod D. Roscoe

3

WHY “CONCEPTUAL ECOLOGY” IS A GOOD IDEA Andrea A. diSessa

29

ON THE NATURE OF NAÏVE PHYSICS Stella Vosniadou

61

MAP READING VERSUS MIND READING: REVISITING CHILDREN’S UNDERSTANDING OF THE SHAPE OF THE EARTH Jonas Ivarsson, Jan Schoultz & Roger Säljö

77

UNDERSTANDING CONCEPTUAL CHANGE: A COMMENTARY Richard E. Mayer

101

PART II: MOTIVATIONAL, SOCIAL AND CONTEXTUAL ASPECTS THE ROLE OF MOTIVATIONAL BELIEFS IN CONCEPTUAL CHANGE Elizabeth A. Linnenbrink & Paul R. Pintrich v

115

vi

TABLE OF CONTENTS

SITUATING THE QUESTION OF CONCEPTUAL CHANGE

137

Ola Halldén, Gunilla Petersson, Max Scheja, Karin Ehrlén, Liza Haglund, Karolina Österlind & Agneta Stenlund PARTICIPATIVE LEARNING AND CONCEPTUAL CHANGE Malka Gorodetsky & Shoshana Keiny COGNITIVE VARIABILITY IN THE DEVELOPMENT OF THE CONCEPT OF FAMILY: A CONTEXTUALIST OR A GRADUALIST VIEW? María José Rodrigo, Beatriz Triana & María Isabel Simón MOTIVATIONAL, SOCIAL, AND CONTEXTUAL ASPECTS OF CONCEPTUAL CHANGE: A COMMENTARY

149

165

187

Gale M. Sinatra PART III: DOMAIN SPECIFICITY AND LEARNING THE ROLE OF STUDENTS’ EPISTEMOLOGICAL KNOWLEDGE IN THE PROCESS OF CONCEPTUAL CHANGE IN SCIENCE John Leach & Jenny Lewis INTUITIVE RULES: THE CASE OF “MORE A – MORE B” Ruth Stavy, Pessia Tsamir & Dina Tirosh CONCEPTUAL CHANGE IN MATHEMATICS: UNDERSTANDING THE REAL NUMBERS Kaarina Merenluoto & Erno Lehtinen

201

217

233

CONCEPTUAL CHANGE IN HISTORY Margarita Limón

259

CONTENT AND CONCEPTUAL CHANGE: A COMMENTARY

291

Richard White

TABLE OF CONTENTS

vii

PART IV: INSTRUCTIONAL PRACTICES TO PROMOTE CONCEPTUAL CHANGE IN CLASSROOM DEVELOPING EPISTEMOLOGICAL THINKING TO FOSTER CONCEPTUAL CHANGE IN DIFFERENT DOMAINS

301

Lucia Mason SCIENCE LEARNING THROUGH TEXT: THE EFFECT OF TEXT DESIGN AND TEXT COMPREHENSION SKILLS ON CONCEPTUAL CHANGE

337

Mirjamaija Mikkilä-Erdmann COMPUTER-BASED INTERACTIONS FOR CONCEPTUAL CHANGE IN SCIENCE

357

Marianne Wiser & Tamer G. Amin KNOWLEDGE ASSESSMENT AND CONCEPTUAL UNDERSTANDING Jesús Alonso-Tapia CHANGE AS A PROCESS AND A DISPOSITION: A COMMENTARY Pietro Boscolo

389

415

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CONTRIBUTORS

Ben Gurion University Beer Sheva Israel [email protected]

Tamer G. Amin Department of Psychology Clark University Worcester, MA 01610 USA [email protected]

Jonas Ivarsson Department of Education University of Göteborg Box 300 SE-40530 Göteborg Sweden [email protected]

Pietro Boscolo Department of Developmental and Socialization Psychology University of Padova Via Venezia 8 35131 Padova Italy [email protected]

Liza Haglund Department of Education Stockholm University Frescati Hagväg 24 S-10691 Stockholm Sweden

Michelene T. H. Chi Learning Research and Development Center University of Pittsburgh 3939 O’Hara Street Pittsburgh, PA 15260 USA [email protected]

Ola Halldén Department of Education Stockholm University Frescati Hagväg 24 S-10691 Stockholm Sweden [email protected]

Andrea A. diSessa Graduate School of Education University of California, Berkeley Tolman Hall Berkeley, CA 94720 USA [email protected]

Shoshana Keiny Department of Education and Chemistry Ben Gurion University Beer Sheva Israel [email protected]

Karin Ehrlén Department of Education Stockholm University Frescati Hagväg 24 S-10691 Stockholm Sweden

John Leach Centre for Studies in Science and Mathematics Education University of Leeds Leeds LS2 9JT UK [email protected]

Malka Gorodetsky Department of Education and Chemistry ix

x

Erno Lehtinen Department of Education University of Turku FIN-20014 Turku Finland [email protected] Jenny Lewis Centre for Studies in Science and Mathematics Education University of Leeds Leeds LS2 9JT UK [email protected] Margarita Limón Departamento de Psicología Básica Facultad de Psicología Universidad Autónoma de Madrid Cantoblanco, 28049 Madrid Spain [email protected] Elizabeth A. Linnenbrink School of Education The University of Michigan 610 E. University, 1225 SEB Ann Arbor, MI 48109-1259 USA [email protected] Lucia Mason Department of Developmental and Socialization Psychology University of Padova Via Venezia 8 35131 Padova Italy [email protected] Richard E. Mayer Department of Psychology University of California, Santa Barbara Santa Barbara, CA 93106

CONTRIBUTORS

USA [email protected]

Kaarina Merenluoto Department of Education University of Turku FIN-20014 Turku Finland [email protected] Mirjamaija Mikkilä-Erdmann Department of Education University of Turku FIN-20014 Turku Finland [email protected] Karolina Österlind Department of Education Stockholm University Frescati Hagväg 24 S-10691 Stockholm Sweden Günilla Petersson Department of Education Stockholm University Frescati Hagväg 24 S-10691 Stockholm Sweden Paul R. Pintrich Combined Program in Education and Psychology The University of Michigan 610 E. University, 1225 SEB Ann Arbor, MI 48109-1259 USA [email protected] María José Rodrigo Departamento de Psicología Educativa, Evolutiva y Psicobiología Facultad de Psicología Universidad de La Laguna Tenerife

CONTRIBUTORS

Spain [email protected] Rod D. Roscoe Learning Research and Development Center University of Pittsburgh 3939 O’Hara St. Pittsburgh, PA 15260 USA [email protected] Roger Säljö Department of Education University of Göteborg Box 300 SE-40530 Göteborg Sweden [email protected] Max Scheja Department of Education Stockholm University Frescati Hagväg 24 S-10691 Stockholm Sweden Jan Schoultz Department of Thematic Studies Linköping University Campus Norrköping SE 601 74 Norrköping Sweden [email protected] María Isabel Simón Departamento de Psicología Educativa, Evolutiva y Psicobiología Facultad de Psicología Universidad de la Laguna Tenerife Spain [email protected]

Gale M. Sinatra Department of Educational Psychology University of Nevada, Las Vegas 4505 Maryland Parkway Las Vegas, NV 89154-3003 USA [email protected] Ruth Stavy Department of Science Education School of Education Tel Aviv University Tel Aviv 69978 Israel [email protected] Agneta Stenlund Department of Education Stockholm University Frescati Hagväg 24 S-10691 Stockholm Sweden Jesus Alonso-Tapia Departamento de Psicología Biológica y de la Salud Facultad de Psicología Universidad Autónoma de Madrid Cantoblanco, 28049 Madrid Spain [email protected] Dina Tirosh

Department of Science Education School of Education Tel Aviv University Tel Aviv 69978 Israel [email protected] Beatriz Triana Departamento de Psicología Educativa, Evolutiva y Psicobiología Facultad de Psicología Universidad de la Laguna

xi

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CONTRIBUTORS

Tenerife Spain [email protected]

Gr-16121 Athens Greece [email protected]

Pessia Tsamir Department of Science Education School of Education Tel Aviv University Tel Aviv 69978 Israel [email protected]

Richard White Faculty of Education Monash University Monash 3800 Australia [email protected]

Stella Vosniadou Department of History and Philosophy of Science National and Kapodistrian University of Athens 8 Chersonos

Marianne Wiser Department of Psychology Clark University Worcester, MA 01610 USA [email protected]

PREFACE

The chapters in this volume derive from a symposium held in Madrid, Spain, from 6-8 November, 1998. Organized and supported by the Autónoma University of Madrid, the meeting was part of the activities of the Special Interest Group (SIG) on Conceptual Change of the European Association for Research on Learning and Instruction (EARLI), coordinated by the editors of this book. The volume brings together contributions from leading researchers investigating the role of conceptual change to enhance meaningful learning in the classroom. The aim of the volume is to present the state of the art on a topic that has become very relevant to explaining how students, and people in general, build their knowledge and incorporate new concepts and ideas. The volume keeps the four main sessions in which the symposium was articulated. They were structured around both theoretical and practical issues of conceptual change. Particular attention was paid to discussing the characteristics of individuals’ prior knowledge and to the more recent topic of how to integrate social, motivational and contextual aspects of learning within conceptual change research (Parts 1 and 2). Most research on conceptual change has been carried out about science. Thus, the open question of whether conceptual change models and findings about the science domain are valid for other subject-matter domains, such as mathematics or history, was addressed in the meeting (Part 3). Finally, implications for instructional practices to promote knowledge revision, as well as crucial aspects that emerge when considering conceptual understanding in the real and complex context of the classroom, were debated in the symposium (Part 4). Bringing to a wider audience the thorough treatment of the most significant questions on knowledge construction and revision, which were discussed during the SIG meeting in Madrid, this volume aims at contributing to stimulating further reflection and new research in the field of conceptual change. Enjoy reading! ACKNOWLEDGMENTS

The symposium on which this book is based was made possible thanks to the support of the Autónoma University of Madrid (Department of General Psychology, Ph.D. Program on Learning and Instruction, Faculty of Psychology and the University Rectorship), the Spanish Ministry of Education (DGYCIT), the Spanish and the Italian Ministries of Foreign Offices, the British Council and EARLI. The editors wish to thank the students of the Autónoma University who helped them during the meeting. They are also grateful to Rich Mayer and Paul Pintrich for supporting this project in the initial stage. Finally, the editors owe very special thanks to Luciano Fiorotto for his invaluable patience, help and generosity throughout the editing process, even during his holidays.

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INTRODUCTION

MARGARITA LIMÓN* & LUCIA MASON**

* Autónoma Universidad, Madrid, Spain ** University of Padova, Italy

Since the middle of the 1970s research has shown that students have intuitive or naïve ideas about scientific phenomena, which have been labelled “misconceptions” in the literature. Since then, many efforts have focused on changing these ideas in ways that can lead students to a correct understanding of science concepts. Three main findings can be highlighted from current findings. First, radical conceptual change is an effortful, gradual and time demanding outcome. Although instructional interventions are carefully designed to promote it, students’ knowledge revision does not automatically occur. Literature has clearly pointed that often teaching practices are not very successful (e.g. Glynn & Duit, 1995; Mason, 2001; Schnotz, Vosniadou, & Carretero, 1999). Second, it seems that not only purely cognitive aspects are involved in conceptual change processes. For individuals to be able to achieve the deep revision of their prior knowledge that radical conceptual change entails, it seems crucial that they also modify other aspects such as their beliefs about knowledge and knowing, their motivation, affect and achievement goals, and their learning attitudes (e.g. Pintrich, Marx, & Boyle, 1993; Pintrich, 1999). Third, the social and cultural nature of the contexts in which the change of individuals’ conceptions is desired to occur seems to play an essential role. Conceptual understanding and development can be seen as the product of shared social practices within a particular community, in which discourse practices are a cultural tool to construct knowledge (e.g. Kelly & Green, 1998). More recently, the relevance of intentional learning for conceptual change processes has been pointed out (Sinatra & Pintrich, in press). To achieve a radical conceptual change individuals should be intentional, that is, they should be aware of the need to change their conceptions and beliefs, as well as be willing to change and self-regulate their process of knowledge revision (e.g. Limón, in press; Linnenbrink & Pintrich, in press; Pintrich, in press). Moving from these findings, the volume aims at giving an account of the state of the art of both theoretical and practical issues that remain open in present day research on conceptual change. It is divided into four parts and each of them is commented by an invited discussant. The two first parts deal with theoretical perspectives on conceptual change. The last two focus more on implications that can M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, xv-xx. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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be drawn from research and practical aspects to foster knowledge construction and re-construction, even if theoretical problems are also underlying in some chapters. 1. A STATE OF THE ART FOR UNDERSTANDING THEORETICAL PERSPECTIVES ON CONCEPTUAL CHANGE PROCESSES

Part I of this volume introduces four different theoretical views of conceptual change. The nature of individuals’ prior representations and their characteristics as well as the nature of conceptual change itself have been discussed widely. Nevertheless, the discussion is far from closed as the chapters included in this part show. DiSessa points out the limitations of conceptual change research and criticises its current state. He considers that it lacks theoretical accountability concerning the nature of the mental entities involved in the process of conceptual change. The conceptual ecology approach he supports implies hypothesizing that conceptual change involves diverse kinds of knowledge organised and reorganised into complex systems. As an illustration of this approach he presents two very different kinds of mental entities: p-prims and coordination classes. Vosniadou states that researchers in science education and cognitive science disagree on how to characterize naïve physics. She questions the kind of knowledge naïve physics consists of, how it is organised and how it develops. She argues that naïve physics is a complex conceptual system that includes perceptual information, beliefs, presuppositions and mental representations. Children’s knowledge acquisition process starts by organising their sensory experiences, sieved by culture and language, into coherent explanatory frameworks. New information presented through instruction is assimilated to these initial explanatory frameworks creating synthetic models. She presents an empirical study about the development of the meaning of force to support the claim that children organise their physical experiences in narrow but coherent frameworks. Chi also emphasises that even if the nature of misconceptions and conceptual change have been discussed for several decades, the literature only offers a fuzzy picture of what exactly misconceptions are, what constitutes conceptual change, and why it is difficult. She deals with these topics offering her view of these important matters. Ivarsson, Shoultz and Säljö support a sociocultural view of conceptual change as an alternative to the cognitive view supported by the other three chapters of the section. They argue that to deal with conceptual development questions, it is necessary for researchers to clarify their position with respect to the more general question of how to conceive human cognition. Their paper presents a contribution to this age-old debate. They also present their results of a study on how very young children interpret a map. The authors show that using it as a mediational tool, these children can accomplish rather complicated reasoning about the shape of the earth and gravity, demonstrating the flexible and tool-dependent nature of cognition. Finally, Mayer comments on the four chapters of this section. He compares these four views in terms of what changes during conceptual change, who changes, how the change occurs, where the change takes place, the role of prior knowledge,

INTRODUCTION

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and whether there is research evidence to support each one of these views. As a conclusion, he offers a proposal for reconciling alternative views of conceptual change. 2.

MOTIVATIONAL, SOCIAL AND CONTEXTUAL ASPECTS

To widen the cognitive perspective from which mainstream research on conceptual change has been carried out, Part II of the volume deals with the social, contextual and motivational aspects of conceptual change processes. Linnenbrink and Pintrich focus on students’ motivation by examining the direct and mediated effects of achievement goal, affect and cognitive strategy use on students’ understanding in physics. On the basis of findings from two empirical studies, they highlight the importance of students’ purpose of understanding when approaching their schoolwork. Mastery goals appear directly related to the development of current conceptual understandings. In order to shed light on the controversy between the constructivist and sociocultural approaches, Halldén et al. propose an alternative model for conceptual development and change. Their investigation on children’s conceptions of the shape of the earth leads them to look at a child’s emerging conception as a compound model, which includes facts experienced from different sources contextualized in different models. In this chapter contexts are understood as conceptual contexts, that is, conceptual systems. The social and cultural specific contexts in which knowledge construction and re-construction occurs are addressed by Gorodestky and Keiny. By dealing with another conceptual framework alternative to that of traditional research in the field, they explore learning and conceptual change processes as participatory processes. Through excerpts from the ongoing discourse in a team of teachers, the authors show the process, continuity and evolution of learning within this community. The dialogical interaction between the “outer” (the social context) and the “inner” (the individual learner) illustrates the construction of common meanings. Rodrigo, Triana and Simón indicate the importance of considering cognitive variability in a model of conceptual change, that is, people’s understanding at a given age does not correspond to a single knowledge stage. Variety of knowledge states are documented through an empirical study on the development of the concept of family. Both transitional and consolidated states as well as changes in distribution of discordant and concordant states are discussed in the light of gradualist and contextualist views of developmental change. The four chapters of this section are finally commentated by Sinatra who identifies three main themes across them, that is, conceptual change involves more than cognition, appears to be an evolutionary rather than a revolutionary process and what it is discovered about it depends on the theoretical perspectives and research methods. She suggests directions for future research and draws implications for pedagogical practice.

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3. DOMAIN SPECIFICITY AND LEARNING

Part 3 of the volume illustrates and discusses how the particularities of domainspecific learning and teaching may affect the processes of conceptual change. Lehtinen and Merenluoto address some special characteristics of mathematical knowledge that should be considered to understand the processes of conceptual change in this domain. They present a study to examine the difficulties adolescent students experience in achieving the conceptual change that involves enlargement of the concept of number. Their results show that students tend to use the logic of the natural numbers and their everyday intuition, even if they are working on more advanced numbers. Nevertheless, the majority of students also had fragmented pieces of more advanced numbers. Stavy, Tsamir and Tirosh argue that students answer in a similar way some conceptually non-related tasks that differ with regard to either their content area and/or to the reasoning they require, but share some common external features. They have observed this student reaction in both science and mathematical domains. They consider these responses to be instances of a few intuitive rules that lead our responses in many situations, particularly in the domain of science and mathematics. In their chapter they illustrate one of these intuitive rules, “More A-more B”, which is described and discussed. Instructional implications for conceptual change and science teaching are developed. Leach and Lewis deal with the role of students’ epistemological knowledge in the process of conceptual change in science. They support that students’ conceptual knowledge in science has an epistemological dimension. Thus, they argue that models of conceptual change in science should refer to this epistemological dimension. Based on empirical data from their own research they develop two claims: a) a tendency to over-attribute relevance to empirical processes is manifested by many science students when they justify viewpoints on scientific topics or when they have to explain how to solve scientific disputes; and b) students show different epistemological knowledge in different situations. Thus, students’ epistemological knowledge should not be considered in isolation from the context in which that knowledge is used. An agenda for future research on epistemological knowledge and conceptual change in science is outlined. Limón also emphasises the role of epistemological knowledge and beliefs about history as a discipline and how they affect understanding of history. Her chapter questions the extent to which results from research on conceptual change in science education can be applied to the domain of history. Particular attention is paid to second-order concepts (evidence, cause, explanation, empathy, etc.) that seem to play a crucial role in history understanding. The peculiarities of history as a discipline and their implications for history teaching and learning are also reviewed. Finally, some conclusions for conceptual change in history are developed. This section of the volume concludes with the commentary by White. He addresses two issues that appear in the four chapters. The first regards the discussion of what is idiosyncratic of each topic and what principles can apply across a number of them. The second questions if conceptual change requires a different type of

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knowledge that may enable learners to see a subject and the topics within it in a new way. 4.

INSTRUCTIONAL PRACTICES TO PROMOTE CONCEPTUAL CHANGE IN THE CLASSROOM

Part IV of the volume focuses on instructional practices to foster conceptual change in the real and complex learning environment of the classroom. The four chapters deal with implications from different lines of research on conceptual understanding and development. Mason argues about the relationship between personal epistemologies and knowledge revision processes. Issues from research on students’ beliefs in particular domains, i.e. science, maths and history, are introduced to highlight that they may facilitate or impede conceptual change. For each of the three domains an example of an effective instructional intervention, implemented in the learning environment of the classroom, on the refinement of students’ epistemological thinking is also introduced. These examples highlight that the development of naïve beliefs is a crucial condition for knowledge re-construction. Mikkilä-Erdmann examines the role of instructional texts on conceptual change by introducing an empirical study theoretically motivated by research findings on text comprehension and development of conceptions. She compared a traditional text design on photosynthesis with a conceptual text design aimed at producing cognitive conflict in students with varying reading skills, and stimulating their metaconceptual awareness of how to understand this scientific phenomenon. Results highlight that in the complex process of conceptual change, texts play a role more important than we think. Wiser and Am in focus on the use of computer-based conceptual models in learning physics. They refer to a “situated” approach to understanding in that they refer to the developing conceptualisation of things as a relational construct when thinking about students’ sense-making of computer models and internalisation of them as a cognitive tool to construe the physical world. Excerpts from students’ protocols illustrate how computer models, as components of students’ increasing participation in the scientific practice, are the object of student-student and studentteacher interactions and negotiations of meaning. Alonso-Tapia deals with assessment of conceptual understanding and its implications for conceptual change. The main characteristics of tools, procedures, contexts and processes to adequately assess students’ conceptual representations are introduced. Examples taken from his own research on assessment in high school are given to illustrate how alternative conceptions and knowledge gaps can be identified. Moreover, features and benefits of portfolio assessment for assessing conceptual understanding and development are outlined. The need to pay attention not only to particular aspects of teachers’ assessment practices, but to modifying the whole assessment practice is emphasised. The four chapters of this section are finally commentated by Boscolo. He considers them from two perspectives. The first regards the object of change, the second regards the types of interventions that are implemented in the classroom. By

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analysing the distinction between conceptual change and conceptual understanding, the author points out that change emerges as a process and as a disposition. Finally, he critically examines the instructional practices aimed at promoting that process and disposition. As editors of this volume we hope that it contributes substantially to the research on theory and practice of conceptual change processes, thus helping to further current understanding of human learning and development. REFERENCES Kelly, G. J., & Green, J. (1998). The social nature of knowing: Toward a sociocultural perspective on conceptual change and knowledge construction. In B. Guzzetti & C. Hynd (Eds.), Perspectives on conceptual change. Multiple ways to understand knowing and learning in a complex world (pp. 145181). Mahwah, NJ: Lawrence Erlbaum Associates. Glynn, S. M., & Duit, R. (1995). Learning science in the schools. Research reforming practice. Mahwah, NJ: Lawrence Erlbaum Associates. Limón, M. (in press). The role of domain specific knowledge in intentional conceptual change. In G. M. Sinatra & P. R. Pintrich (Eds.), Intentional conceptual change. Mahwah, NJ: Lawrence Erlbaum Associates. Linnenbrink, E. A., & Pintrich, P. R. (in press). The role of motivation in intentional learning. In G. M. Sinatra & P. R. Pintrich (Eds.), Intentional conceptual change. Mahwah, NJ: Lawrence Erlbaum Associates. Mason, L. (Ed.) (2001). Instructional practices for conceptual change in science domain [Special issue]. Learning and Instruction, 11 (4-5). Mason, L. (in press). Personal epistemologies and intentional conceptual change. In G. M. Sinatra & P. R. Pintrich (Eds.), Intentional conceptual change: Mahwah, NJ: Lawrence Erlbaum Associates. Pintrich, P. R. (1999). Motivational beliefs as resources for and constraints on conceptual change. In W. Schnotz, S. Vosniadou, & M. Carretero (Eds.), New perspectives on conceptual change (pp. 33-50). Amsterdam: Pergamon/Elsevier. Pintrich, P. R., Marx, R. W., & Boyle, R. B. (1993). Beyond cold conceptual change: The role of motivational beliefs and classroom contextual factors in the process of conceptual change. Review of Educational Research, 63, 167-199. Sinatra, G. M., & Pintrich, P. R. (Eds.) (in press). Intentional conceptual change. Mahwah, NJ: Lawrence Erlbaum Associates. Vosniadou, S. (1999). Conceptual change research: State of the art and future directions. In W. Schnotz, S. Vosniadou, & M. Carretero (Eds.), New perspectives on conceptual change (pp. 3-13). Amsterdam: Pergamon/Elsevier.

PART I

THEORETICAL PERSPECTIVES

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THE PROCESSES AND CHALLENGES OF CONCEPTUAL CHANGE

MICHELENE T. H. CHI & ROD D. ROSCOE Learning Research and Development Center, University of Pittsburgh, USA

Abstract. Students engaged in learning a large body of related knowledge often possess some incorrect naïve knowledge about the domain. These “misconceptions” must be removed and/or the correct conception must be built in order for students to achieve a deep understanding. This repair process is generally referred to as “conceptual change.” However, although conceptual change has been discussed for several decades within different research contexts, the literature nevertheless presents a somewhat blurry picture of what exactly misconceptions are, what constitutes conceptual change, and why conceptual change is difficult. In this chapter, we suggest that one should think of misconceptions as ontological miscategorizations of concepts. From this perspective, conceptual change can be viewed as a simple shift of a concept across lateral (as opposed to hierarchical) categories. We argue that this process is difficult if students lack awareness of when a shift is necessary and/or lack an alternative category to shift into. These ideas are explored using a detailed example (i.e. diffusion) from a broad class of science concepts (i.e. emergent processes) that are often robustly misunderstood by students.

1. INTRODUCTION

When students engage in the task of learning some large body of related knowledge, such as a specific topic within a science domain (e.g. electricity or the human circulatory system), they are faced with two main obstacles. First, a great deal of information is simply missing from their initial understanding, and this new information must be acquired. However, it is not the case that students enter a learning situation with a blank slate. Instead, students often have some naïve knowledge or prior conceptions about the domain. Naïve knowledge has two properties: it is often incorrect (when compared to formal knowledge) and it often (but not always) impedes the learning of formal knowledge with deep understanding. However, some type of naive knowledge can be readily revised or removed through instruction (for simplicity, instruction in this chapter refers to the presentation of knowledge through written text). We will refer to this type of naive knowledge simply as “preconceptions”. On the other hand, some other type of naive knowledge seems highly resistant to change. These misunderstandings persist strongly even when they are confronted by ingenious forms of instruction. We refer to these robust ones as “misconceptions.” In the following list of prior conceptions, the final four items are thought to be examples of misconceptions: 1) Insects are not a type of animal (Osborne & Wittrock, 1983)

M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 3-27. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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2) The heart is responsible for reoxygenating the blood (Chi, de Leeuw, Chiu, & LaVancher, 1994) 3) The earth is spherical, and people stand on top or inside of it (Vosniadou & Brewer, 1992) 4) Whales are a type of fish 5) A thrown object acquires or contains some internal force 6) An object and the shadow it casts are made of the same kind of substance 7) Electrical current is stored inside the battery 8) Coldness from the ice flows into the water, making the water colder All naive knowledge needs to be repaired in order to promote deep understanding. The challenge is to understand why misconceptions in particular are resistant to change. Thus, although all processes of revising or removing prior conceptions can be generically construed as “conceptual change”, the terms “conceptual change” are often reserved for referring to the processes of repairing misconceptions (Hewson, 1981; Posner, Strike, Hewson, & Gertzog, 1982). For emphasis, sometimes the specific processes of repairing misconceptions have been referred to as “radical” conceptual change (Keil, 1979), “genuine” conceptual change (Gunstone, Champagne & Klopfer, 1981), conceptual change “of the extreme sort” (Carey, 1991, p. 259), or nonconservative conceptual change (Thagard, 1996); whereas the processes of repairing non-robust preconceptions have been described as belief revision (Carey, 1991), mundane (Thagard, 1990), and ordinary (de Leeuw & Chi, in preparation). We will refer to the processes of repairing misconceptions as “conceptual change” and the processes of repairing preconceptions as “conceptual reorganization”. Although conceptual change has been discussed for several decades in the context of developmental research, science education research, and in the philosophy of science, the literature nevertheless presents a somewhat blurry picture of what exactly misconceptions are, what constitutes conceptual change, and why it is difficult. The goal of this chapter is to address these three related questions of process and difficulty in conceptual change. Because we define conceptual change as the processes of removing misconceptions, this definition is circular unless we can first establish what constitutes a misconception. To preview, we base our definition of misconceptions on the assumption that misconceptions are, in fact, miscategorizations of concepts. Thus, our first claim is that misconceptions are concepts categorized into an (“ontologically”) inappropriate category. From such a definition of misconceptions, our second claim follows, that conceptual change is merely the process of reassigning or “shifting” a miscategorized concept from one “ontological” category to another “ontological” category. “Ontological” categories have a lateral relationship to each other. In contrast, reconceptualizations that occur within the same ontology or hierarchy are better referred to as “conceptual reorganization” (Chi, 1992). Our third claim then is that this conceptual shift process itself is not inherently difficult, but is instead challenging mainly when students lack awareness of their misconceptions (i.e., they lack the knowledge that they need to shift) and/or lack the alternative (“ontologically” distinct) categories (missing categories) to which they should reassign their misconceptions. We are not denying that conceptual change can also

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5

be difficult because the concepts involved are complex or “incommensurate” (Carey, 1991); instead, we propose that these issues of awareness and missing categories are an important, new perspective that has not been considered. Thus, these three claims purport to answer the three questions posed above about the nature of misconceptions, the processes of conceptual change, and why it is difficult. These claims are detailed in the remaining part of this paper. Moreover, we will discuss how an ontological category view provides clear and testable definitions of misconceptions and informs unresolved issues in other perspectives. As part of our overall argument, we will provide a detailed analysis of misconceptions of a special class of scientific concepts (e.g. diffusion). 2.

2.1.

PRECONCEPTIONS AT THE “PROPOSITION” AND THE “MENTAL MODEL” LEVELS

The Proposition Level and Removing Incorrect Beliefs

A system of knowledge can be evaluated at the level of single ideas that can be stated as a sentence, or “propositions”. These mentally-represented propositions are beliefs that students assume to be true, such as “Air is not made of matter” (Carey, 1991). If one assumes that beliefs are composed of concepts, then can mistaken beliefs be considered “misconceptions?” When one examines a student’s initial beliefs, and compares this set of propositions to a student’s final beliefs (after reading a text), two classes of beliefs seem to emerge. In one case, beliefs that are incorrect at the outset are replaced by the correct knowledge after instruction. However, in a second case, a student’s initial, inaccurate beliefs remain even after instruction. We might label beliefs of the first sort as “incorrect beliefs,” and those of the second sort as “alternative beliefs.” Are alternative beliefs misconceptions, since they were not removed? It turns out that if we examine the text sentences in detail, and assess whether each individual initial belief was refuted or not by the text sentences, then it became clear that incorrect beliefs were the ones that the text sentences directly or indirectly refuted; whereas alternative beliefs were the ones that the text never addressed. For example, a student may initially believe that all blood vessels have valves. However, after reading the text, which never mentions valves in the context of the arteries but only in the context of veins, then such indirect refutation can revise a student’s initial belief to the correct proposition that veins are the only blood vessels with valves. It is tempting to say that alternative beliefs, since they seem to resist instruction, must be examples of misconceptions. However, our analysis has shown that the difference between incorrect and alternative beliefs relies not on qualitatively different knowledge, but on how they are addressed by the text. Specifically, incorrect beliefs are readily revised because the text tends to contradict them either directly or indirectly, at the individual proposition level. On the other hand, “alternative beliefs”) are not addressed by the text at all, such as the liver restores blood or that veins are like nerves that transmits signals from the brain

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(these alternative beliefs are taken from the protocols of Chi, Siler, Jeong, Yamauchi, & Hausmann, in press). Such results were shown in our study on learning about the human circulatory system (de Leeuw, 1993). In that study, middle school children ( graders) were asked to define 23 terms, diagram the path of blood through the circulatory system, and answer 42 questions, prior to instruction. In such pre-tests, students typically expressed about 15.8 propositions of preconceptions. From these 15.8 cases, only “stable” propositions (those that were repeated at least once, and that were not generated online in response to the content of the 42 questions) were considered. This filtering method reduced the number of preconceptions to 2.8 per student, giving a total of 31 across 12 subjects. In the posttests, 77% of the 31 propositions were correctly revised if the text addressed them (these can be considered the incorrect beliefs). Five of the preconceptions remained. However, these five were not revised because the text never addressed them. We can consider these to be alternative beliefs. The results above lead to a conclusion and a query. Clearly, both “incorrect beliefs” and “alternative beliefs” in this domain are preconceptions in that they can be removed with instruction, and not removed if instruction does not address them. This ease of removal for preconceptions is qualitatively different from misconceptions, which are retained even after much instructional confrontation. For example, if students believed that Electrical current is stored in the battery, then correct understanding cannot be easily achieved by merely confronting students at the proposition level with direct refutation, such as telling them that electrical current is not stored anywhere. It suggests that conceptual change of “false beliefs” require changes at a larger grain size. The query from the results above is why were all the preconceptions removable, once a text refutes them? That is, why were misconceptions not manifested in this domain? The answer alluded to in the preview, will be more obvious and revisited once we detail more clearly what misconceptions are. 2.2.

The Mental Model Level and Repairing Flawed Models

Instead of representing knowledge at a piecemeal level, one can represent knowledge as a set of interrelated propositions, or a “mental model”. What this adds to a discussion of proposition level beliefs is a structure in which the propositions are embedded. Examples of research that represent students’ initial knowledge in terms of mental models are Vosniadou and Brewer’s (1992) studies of young children’s concepts of the shape of the earth, and Chi’s (2000b) work with middle school students’ understanding of the human circulatory system. Like propositions, distinctions can be made about the nature of naïve mental models. One such distinction is made on the basis of coherence. An incoherent, or “fragmented,” mental model can be conceived of as one in which propositions are not interconnected in some systematic way. Such a model cannot be used to give consistent and predictable explanations. Furthermore, because many parts may be unconnected, students are often aware that they lack a complete understanding. Alternatively, mental models can be coherent, meaning that the constituent

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propositions are related in an organized manner. Unlike fragmented models, such representations can be used to generate explanations, make predictions, and answer questions in a consistent and systematic fashion. A coherent model can be correct or flawed. By “flawed” we mean a mental model whose coherent structure is organized around a set of beliefs or a principle that is incorrect. Note that this level of “correctness” is distinct from the correctness of individual propositions. A flawed mental model may share a number of propositions with a correct mental model, but they are interconnected according to an incorrect organizing principle. In addition, though students with fragmented mental models are often aware of their lack of understanding, this is not true for students with flawed, but coherent models. Because these students are able to answer questions adequately and consistently, they may be blind to their lack of deep understanding. Two studies clearly illustrate what we mean by a flawed mental model. Vosniadou and Brewer (1992) have explored young children’s naïve conceptions of the earth and it’s shape. One common misconception they’ve identified is the belief that the earth is shaped like a round, flat pancake. However, children can make sense of their world using this flawed, disk-earth model. For example, the flatness of the earth is compatible with their everyday perceptions, in the sense that the ground appears level. They can use this simplistic model to answer questions and generate explanations that are meaningful to them. Another example is provided by research on middle school students’ naïve conceptions of the circulatory system (Chi, 2000b; Chi et al., 1994). On average, about half of the students think of the human circulatory system as a “single-loop,” in which the blood leaves the heart, travels to all parts of the body, and then returns to the heart (see upper left diagram of Figure 1). This is in contrast to the correct pathway, a “double-loop,” that involves both systemic (heart-to-body) and pulmonary (heart-to-lungs) circulation (see upper right diagram of Figure 1). However, the single-loop model is coherent. We can demonstrate this because it differs from the correct, double-loop model in systematic ways: the source of oxygen, the purpose of blood flow to the lungs, and the number of loops. Specifically, a single loop model is organized by a principle, consisting of the beliefs that the heart (rather than the lungs) is the source of oxygen, that blood goes to the lungs to deliver oxygen (rather than to exchange carbon dioxide and oxygen), and that there is just one loop. Thus, a flawed mental model is one that is organized around an alternative principle, consisting of a set of beliefs shown in the left column of Figure 1, whereas the correct double loop model is organized around another set of beliefs, shown in the right column of Figure 1. With a flawed single loop model, students will give systematic and predicable answers to questions like the following examples (student replies are in parentheses; Chi et al., 1994): 1. Why does blood have to go to the heart? (“to get oxygenated”) 2. Why does blood go to the lungs? (“to deliver oxygen to the lungs”) In data collected, but not reported, by Chi et al. (1994), over half of the students (8 out 14 students in the prompted group) had easily and consistently identifiable mental models that were coherent, but flawed.

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In addition to the factors of coherence and correctness, one can also consider completeness. A complete mental model has a majority of the key propositions. An incomplete model has many missing pieces. Completeness, however, is somewhat orthogonal to either coherence or correctness. Specifically, students may possess a very complete, but flawed mental model, or possess a basically correct model, but with sparse details. For example, a student may have a great deal of knowledge about the human circulatory system, organized according to the incorrect, singleloop principle. In contrast, a student might understand that the system is a doubleloop, but not know how it works or the exact function of every component. This is clearly shown when one looks at the variability in the number of correct propositions that students with a single-loop model hold. In data collected by Jeong (1998), but not reported, we coded students’ prior conceptions at both the proposition and mental model level. Figure 2 shows the distribution of the number of correct propositions that students knew (either at the pre-test or at the post-test). The figure shows that there is a range of correct propositions that students knew, even though they all basically organized their propositions into a single loop model. For example, 5 students expressed between 10 and 15 correct propositions, and 3 students expressed 25-30 correct propositions. This figure shows that although some

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students may have more correct beliefs than others, they all share the same assumptions about the role of the heart and blood flow to the lungs consistent with the flawed understanding of a single loop model. Thus, mental models may not differ in terms of the number of correct propositions, but in how these beliefs cohere.

As Figure 2 shows, a flawed mental model obviously is composed of many correct beliefs as well as incorrect and alternative beliefs. From the analysis presented earlier, we have shown that these preconceptions can be readily removed, at the piecemeal level, if they were addressed; and there does not appear to be any false beliefs or misconceptions for this domain, of the human circulatory system. Therefore, it follows, by definition, that no conceptual change is necessary to achieve the correct mental model. If not conceptual change, then what kind of learning processes can achieve this repair of a flawed mental model? At least two “ordinary” learning processes can be proposed as mechanisms that can remove incorrect beliefs and repair flawed mental models. These two processes, “assimilation” and “revision,” can result in significantly richer and more accurate knowledge about a domain. In the case of learning about the human circulatory system, these mechanisms seem to very adequately explain how students with an initial single-loop model develop the correct double-loop model through instruction in the following way (Chi, 2000). Suppose we assume that learning is the sequential encoding of propositions (sentences). Each new piece of information presented to the student can be considered either compatible with his or her existing knowledge or contradictory. Sentences that are compatible provide information that is consistent with the student’s existing beliefs and consistent with student’s mental

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model. If an incoming proposition is compatible, then learning consists of simply embedding this new information into the existing mental model. This process is called assimilation. Assimilation can occur regardless of whether the student’s mental model is correct or flawed. As long as the statement does not contradict what the student currently believes, it can be understood (or misunderstood) in the context of the existing knowledge structure. For example, consider the text sentence, “Pulmonary circulation is the movement of blood from the heart to the lungs and back to the heart.” A student with a correct, double-loop model would understand this sentence as a description of the pulmonary loop of circulation. However, a student with an incorrect, single-loop model would interpret this sentence to mean “blood travels to the lungs to deliver oxygen, as it does to many organs.” In both cases, the new information is assimilated. However, in the case of the initially flawed mental model, such assimilation would perpetuate its flawness. A similar case occurred in Vosniadou and Brewer’s (1992) data. Children who possessed a flat, disk-earth model (pancake shape) understood and assimilated the statement “the earth is round like a globe” by interpreting it to mean that the flat disk is situated inside of the globe or on top of it. Thus, assimilation alone cannot repair mental models, although it can enrich them. An incoming sentence can also contradict or refute what the student already knows. Suppose that a student originally thought “Systemic circulation is the movement of blood from the heart to the lungs back to the heart” (this is actually pulmonary circulation). The text sentence given above directly contradicts this belief. Upon reading such a contradiction, the student could simply revise his or her incorrect belief, as the results of the de Leeuw (1993) study showed. This process is called revision. Taken together, the accumulation of assimilation and revision processes could lead to a major change in the students’ understanding of a system of knowledge. Chi’s (2000b) analysis detailed how the incremental accumulations of assimilations and revisions of individual propositions allowed a student to achieve the correct, double-loop model from a single-loop model. This repair of the mental model appears to be an example of “accommodation”, a term used in the literature broadly to mean changes in the structure of a mental representation, as opposed to assimilation, in which the mental structure remains unchanged. But such mental model restructuring can evolve from the incremental buildup of ordinary learning processes occurring at the prepositional level, and not from conceptual change processes. Thus, one can achieve a major re-organization by repairing a flawed mental model with ordinary learning processes. No radical conceptual change was necessary since individual beliefs were readily removed and revised. 3.

MISCONCEPTIONS AT THE “DOMAIN THEORY” LEVEL AND THEORY CHANGE

Some researchers prefer to represent initial knowledge at the level of the domain or discipline. These terms usually refer to a large body of knowledge corresponding to

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some field of science, such as biology, psychology (Carey, 1985), or mechanics (McCloskey, 1983). At this level, it seems natural to analogize naïve conceptions to naïve theories and thus to analogize conceptual change to theory change. However, to make this analogy work, one must first demonstrate how students’ naïve knowledge is “theory-like” and what is theory change. 3.1.

Naïve Domain Theories

The first problem of determining whether students’ naive knowledge is theory-like is typically handled in one of two ways. The first method is to demonstrate how naïve conceptions share fundamental assumptions with well-known medieval theories. For example, McCloskey (1983) argued that students’ naïve understanding of mechanical motion and the medieval “impetus theory” both assume that 1) an object set in motion acquires an internal force (impetus) and that this internal force is responsible for the object’s motion, and 2) a moving object’s impetus gradually dissipates (either spontaneously or as the result of external forces) causing it to gradually slow down and come to rest. This is the same approach we used to show that all single-loop models are basically similar because they share the same three basic assumptions (as shown in Figure 1). The second means of showing naïve knowledge to be theory-like is done by capturing regularities in naïve conceptions, and determining any underlying guiding principles or laws (Viennot, 1979). This is also an acceptable way to determine that a set of beliefs is theory-like since it draws upon the nomological sense of a theory, in which laws play a significant role (Hempel, 1966) and explanations are deductively closed. In sum, determining that naive knowledge is theory-like does not pose an insurmountable challenge. 3.2.

Theory Change and Incommensurability

A second more serious problem arises with the naïve theory analogy: How do we define theory change? Some researchers have argued that we can determine the process of theory change by looking at theory shifts in scientific revolutions (Carey, 1985; Posner, et al., 1982). Carey (1985) has done this by appealing to the “incommensurability” of certain concepts in science, and to the processes of differentiation and coalescence. Incommensurability is defined as irresolvable “differences” in the concepts, beliefs (or propositions), and explanations of the theories, as well the phenomena the theories explain. In other words, misconceived concepts may differ from the correct understanding in the sense that they are incommensurable. The problem with such a definition is that it is difficult to define “different” without being circular: Are concepts incommensurate because they participate in incommensurable theories, or are two theories incommensurable because their concepts are incommensurate? The issue boils down into figuring out how we can decide that two concepts or theories are incommensurate. According to Carey (1991), concepts are incommensurate if they can be defined in the context of three processes: “replacement,” “differentiation,” and

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“coalescence.” First, an initial concept can be replaced by an alternative concept. This does not mean, necessarily, that a correct belief replaces an incorrect belief. Rather, the two beliefs are so fundamentally different (i.e. are incommensurable) that acceptance of one belief precludes the existence of the other, and thus overwrites it. Differentiation is another replacement process, but also involves the splitting of the initial concept into two or more new concepts, which may be incommensurate to the initial concept or to each other. These new concepts take the place of the original. Coalescence is the opposite process: two or more original concepts are collapsed into a single concept that replaces the originals. Note that these replacement processes differ from cases of differentiation and coalescence without replacement. That is, a single concept, such as dog, may be differentiated into breeds such as collie or terrier. The concept of dog remains as a superordinate, however. Similarly, a child might originally see collies and terriers as two different types of animals. Later, these two concepts are coalesced into the concept of dog, but the original concepts remain. To validate that differentiation and coalescence with replacement are processes of conceptual change involving incommensurate concepts, several examples of these replacement processes have been drawn from the history of science. In one case, the concept of phlogiston was replaced by the concept of oxygen in later theories of combustion. The interpretation is that theories relying on the concept of phlogiston cannot explain or handle the same phenomena that can be addressed by a theory based on oxygen. Similarly, a favorite example of differentiation is the replacement of the concept degree of heat with the modern concepts of heat and temperature. These new concepts are not subordinates to the original, but replacements (Wiser & Carey, 1983). An example of coalescence can be seen with Galileo’s treatment of the concepts of violent motion and natural motion. He argued that there was no meaningful difference between the two concepts, and collapsed them into a single concept. There are a couple of problems with the notions of incommensurability and replacement as they are described above. First, although one can identify any number of examples of change in the history of science, such historical examples as given above do not clearly specify how two concepts or theories are incommensurable, only whether they are incommensurate because they have been replaced. Such hindsight however, fails to explicate how the concepts are fundamentally different in the first place. Moreover, it is not clear whether replacement processes are conceptual change processes, or whether they are the outcome of reorganization, resulting from processes such as assimilation and revision, much as the way a double loop model replaces a single loop model (Chi, 2000). In sum, without the hindsight of history, how can we tell that two theories are radically different or not? How do we identify conceptual changes that are occurring now, or need to occur (in terms of students’ misconceptions)? For example, in contemporary science, the cause of heart disease has been traditionally attributed to the deposit of plaques. A more recent theory has suggested that it is the depositing of a mineral, iron, that may cause heart disease. It has also been proposed, very recently, that heart disease may be caused by bacterial infection and resulting

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inflammation. How can we determine if these shifts in thinking are radical or not without looking ahead one hundred years? Note that these alternate conceptions are co-existing – although they may eventually replace one another, differentiate, or coalesce at some point, but at the present they are competing theories. With a clearer definition of incommensurability, we could presumably predict which new theory is a radically different one and has the promise of revolutionizing the treatment of heart disease. 3.3.

Misconceptions at the Ontological Category Level and Conceptual Change

Concepts, as defined by cognitive psychologists, are intricately linked with the notion of categories. Simply put, one can represent, understand, and interpret concepts in the context of their category membership. This means that once a concept is assigned to a given category, then that concept inherits all the features of that category. From this perspective, misconceptions can be viewed as instances of miscategorization, not hierarchically, but laterally. More specifically, misconceptions may involve the assignment of a concept to the wrong ontological category. What are hierarchical categories and lateral categories? A concept, such as cobra, can be embedded in a subordinate category of poisonous snakes, which would also include concepts like rattlesnake or adders. Cobra may also be considered a member of the basic level category of snakes. Likewise, it is also a member of the superordinate category of reptiles. All three categories also belong to a more superordinate category called living things. Thus, these categories, cobra, poisonous snakes, snakes, and living things, are hierarchically-related. This type of hierarchically-related categories have been the major focus of research on categorization in cognitive psychology. Misclassification of a concept into a hierarchically-related category would not constitute a misconception. Besides hierarchical relationships, however, one can also consider the lateral relationships among categories. Lateral categories are those that do not participate in any hierarchical relationship to one another. That is, neither category is a “parent,” “grandparent,” etc. to the other. Some lateral categories are “siblings” in the sense that they share a parent category. For example, cobra and rattlesnake are siblings sharing the parent concept of poisonous snakes. Some lateral categories are “cousins” in the sense that they share only a grandparent or higher superordinate category in the hierarchy (but not a parent category). For example, snakes and chairs are lateral categories (one is a natural kind and the other is a man-made artifact) but are only related at a higher level, perhaps at the superordinate category of concrete things. There are also concepts that do not share a category even at the highest levels, such as substances and processes. We say that such concepts exist on different or distinct hierarchies or “trees” (Chi, 1997). We consider lateral categories, especially those that exist on different trees, to be “ontologically distinct.” This distinction can be determined through the use of a predicate test (Keil, 1979; Sommers, 1971). This test consists of a number of sentences constructed so that either a compatible or incompatible statement modifies

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a given concept. Students make judgments about whether these sentences are valid (are plausible or make sense) or are invalid (are impossible or anomalous). For example, a concept belonging to the category of concrete objects such as dog or chair), cannot be modified sensibly by a predicate of the lateral category of processes. In other words, one cannot say that “The dog is an hour long” – students will judge such sentences to be invalid. On the other hand, one could accept a sentence such as “The dog is green” even though that is a very unlikely color for dogs. This is because “green” is an attribute or predicate that concrete objects can possess (color), whereas “an hour long” is a predicate that processes can possess (duration). Consider the opposite example of melting ice. The process of melting has a duration (a few minutes), but could not have a color (i.e. green). To return to the topic of misconceptions and miscategorization, we consider a misconception to be a concept that has been miscategorized into an ontologically distinct category. Imagine that a learner assigned the concept of electricity to the category of substances rather than the lateral category of processes11. For these students, it would make sense to say that electricity is “stored” in a battery, the same way other substances are stored in boxes or cans. These students also understand the current of electricity flowing through a wire as an actual “flow,” analogous to a liquid substance (e.g. water) moving through a pipe under pressure. This is why students would also say that electricity “leaks” out of the battery. Ignoring the fact that this analogy (electricity as water) is a common instructional tool, the point is that these students’ difficulties in understanding electricity at a deep level, their misconceptions, stem from the miscategorization of the concept of electricity. This miscategorization can be determined by the predicates that they use to describe the concept. Thus, using predicates such as “stores” and “leaks” confirm that the students conceive of electricity from the category of substances (Slotta, Chi, & Joram, 1995). In order to gain a formally correct understanding of “electricity”, students must reassign the concept to its correct process category. This is not to say that once this shift is made that students will immediately and deeply understand electricity, merely that a key obstacle will have been removed. But it does allow the concept to inherit the proper categorical features, and provides the correct context (or the appropriate categorical perspective) from which ordinary learning processes can incrementally build a correct understanding. One can immediately appreciate the simplicity and power of the ontological categorization view of misconceptions and conceptual change. This perspective provides a clear definition of what misconceptions are (miscategorization), suggests a simple process for conceptual change (reassignment, or shift), and a rule for what constitutes conceptual change (crossing ontological boundaries). We will take this

1 Misconceptions about electricity are actually much more complex than just a single miscategorization. There are several miscategorizations at work, and even the term “electricity” is broadly misapplied. For simplicity’s sake, we will leave our simplification intact.

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opportunity to look back at the other perspectives and show how this view can resolve certain ambiguities. 4.

4.1.

ADDRESSING UNRESOLVED ISSUES

Old Questions

Recall that the issue was raised with respect to why misconceptions (or false beliefs) were not manifested in the case of the human circulatory system, so that a change from a single-loop model to a double-loop model did not constitute conceptual change. We now see that the reason is that the majority of the concepts underlying the beliefs of the circulatory system (such as the concepts of blood, valves, heart) were the same for both the single loop and the double loop models, therefore no ontological boundaries were crossed. Moreover, even at the mental model level, the two organizing set of beliefs “the circulatory system is a single-loop system” and “the circulatory system is a double-loop system” exist in the same ontology. Thus, because no misconceptions existed, the accommodation or reorganization that occurs can be accounted for by the incremental accumulation of assimilations and revisions, processes that are distinct and different from the process of conceptual change. The domain theory perspective also left us with unanswered questions, even though we agree with the notion of incommensurability taken from examples in the history of sciences. Specifically, we had no way of determining if two concepts were incommensurate, and thus whether any of the replacement processes had resulted from conceptual change or conceptual reorganization. The issue of incommensurability is partially resolved if one considers conceptual differences in terms of ontological categories. Simply put, two concepts may be incommensurable if they exist in separate ontological (lateral) categories (or especially, different ontological trees). Such incommensurability can be determined using the predicate test described above. Concepts or beliefs for which few or no shared predicates can be found can be said to be incommensurate. Concepts with a high degree of overlap are not incommensurate. Unresolved issues of course remain, concerning the degree of overlap necessarily needed in order to consider two concepts (and their respective categories) as no longer ontologically distinct. This definition allows us to address the question of whether the replacement processes in the history of science resulted from conceptual change or conceptual reorganization mechanisms. In the case of replacement, if the new concept is ontologically distinct from the original, then conceptual change has occurred. If the new concept is within the same ontology, then conceptual reorganization has occurred. Similarly for differentiation and coalescence, conceptual change has occurred if the original concepts are ontologically distinct from each other, the new concepts are distinct from each other, or the original concept(s) are distinct from the new. Thus, replacement processes may not be conceptual change processes per se, but may lead to, or result from, conceptual change. Using such a definition does

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allow us to make predictions. For example, if we consider the germ theory of heart disease to be an ontologically distinct perspective (germs being a kind of living thing) from both the plaques and the iron deposit perpective (plaques and iron are non-living things), then presumably the germ theory perspective might give us radically new insights that are not predictable from the plaques and iron deposit perspective. 4.2.

A New Question

One question arises from the discussion of incommensurability and ontological categories: Are all lateral categories incommensurate, or only those that are more “distantly related” or on different ontological trees? For example, artifacts and natural kinds are not hierarchically related to each other, and thus can be considered ontologically distinct. One can also identify a predicate (whether the object can be “built” or “made”) that discriminates between the two. This assumption is consistent with theories about these two concepts in the literature (e.g. Gelman, 1988; Sommers, 1971). However, although these concepts are ontologically distinct, are they incommensurate? One could suggest that incommensurable categories and concepts would share no predicates, and commensurate categories would share many. This doesn’t appear to be true for all cases, however. For example, artifacts and natural kinds can be discriminated by the predicates of “made,” and possibly “discovered,” but not by “duration,” “color”, or “emotion.” How many distinguishing predicates must there be to label two concepts as “incommensurate?” Should there even be a cut-off point, or does incommensurability lie on a continuum? These remaining questions are beyond the scope of this chapter and require much research. For the time being, we can assume that certain categories (and their respective sub-categories) that are useful for thinking about science concepts, appear to be reliably incommensurate: static vs. dynamic, substances vs. processes vs. mental states, time vs. space, linear systems vs. dynamic systems, and so on (see also Chi, 1997). 4.3.

The Process of Conceptual Change

In our discussion of ontological categories, we suggested an uncomplicated mechanism, “reassignment” or “conceptual shifting,” as the main process of conceptual change. Other types of reconceptualization, or shifts within ontological categories, are considered examples of conceptual reorganization. We now elaborate on this reassignment process and begin to discuss why this process is difficult. 4.3.1.

Conceptual Shift

In this chapter, we propose the mechanism of conceptual change to be the process of shifting across ontological categories. This process itself is straightforward, comparable to linking or associating a concept with another category. The same learning mechanism applies to all such shifts, regardless of whether the

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reassignment occurs across relatively similar categories (such as shifting the concept whale from the category of fish to mammals) or categories that are on different ontological trees (such shifting electricity from the substance category to the process category). Thus, this shift itself is a fundamental learning process, comparable to the process of linking or integrating new ideas with old, and can be applied to the learning of all concepts. The proposed process is somewhat analogous to two conceptual change processes proposed by Thagard (1990), called “branch jumping” and “tree switching.” In branch-jumping, one shifts a concept “from one branch of a hierarchical tree to another.” Tree-switching involves “changing the organizing principle” of a class of concepts (Thagard, 1990, see Table 3.1). There terms sound superficially similar to our definition of conceptual change. However, Thagard (1996) primarily used the condition of replacement and/or abandonment as a criterion of conceptual change. For instance, an example of tree switching is one in which the concept of diseases was reconceptualized in terms of its causes to its symptoms. Without implicating the role of ontologies or ontological trees, such reorganization, resulting in the replacement of one organizing principle (causes of diseases) by another organizing principles (symptoms of diseases), may not require conceptual change, much as the replacement of a single loop model by a double loop model, which also requires changing the organizing principle only. Note that the fish-to-mammal shift of whales and the substance-to-process shift of electricity are both considered here to be examples of conceptual change by our definition. Earlier, these two were distinguished because one seems easy, and can be addressed through simple instruction (whales) and one seemed robustly resistant to instruction (electricity). The first case was thought to be a simple preconception, whereas the robust case was given as an example of a misconception. In some sense, this distinction no longer applies because both cases are “misconceived” in the same manner – they are miscategorizations. However, this doesn’t change the fact that one seems harder to repair than the other, which we will address shortly. 4.3.2.

Re-representation, or Perspective Shift

Before we discuss the issue of difficulty, we must make it clear that not all “shift” processes are conceptual change. In other words, not all types of shift involve the reassignment of a concept. One example of such a process is “re-representation.” This term has sometimes been used synonymously with conceptual change or conceptual shift, but according to the definition presented in this chapter, it is a distinctly different mechanism. Suppose we ask students to solve the following two “insight” problems: 1. A man who lived in a small town married twenty different women in that town. All are still living and he never divorced a single one of them. Yet, he broke no laws. How can you explain this? 2. Two strings hang from a ceiling. They are hung far enough apart that a person cannot reach both strings at the same time. The goal is to tie the strings together. Lying on a nearby table are a hammer and a saw.

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In order to solve the first problem, one has to represent “man” not as a bachelor, but as a clergyman. This does not require that the concept of man be reassigned to a new category. Instead, what must be shifted is one’s perspective – one must emphasize or retrieve a subcategory of bachelor. In order to solve the second problem, one must view the hammer not as a “tool,” but as a “heavy tool” (a subordinate category). This heavy weight can be tied to one of the strings to create a pendulum. One simply swings the pendulum, grabs the first string, and then catches the other string on its return – again, a shift in perspective. Thus, re-representation clearly consists of a hierarchical (non-ontological) shift, and thus should be considered reorganization rather than conceptual change. Again, our concept of rerepresentation may be analogous to Thagard’s (1996) notion of “branch jumping”, which he considered to be conceptual change. 4.4.

The Difficulty of Conceptual Change

As we have described above, some naïve conceptions, or misconceptions, seem to be very difficult to revise, while others (preconceptions) respond very readily to instruction. Misconceptions have been proposed to be resistant to repair (i.e. resistant to conceptual change) for a variety of reasons, some of which we have not articulated here but are discussed elsewhere (Chi, 2000a), such as that they involve very hard-to-understand principles and component concepts. In this paper, we have raised additional possibilities, such as that misconceptions are difficult to remove because they are embedded in naive theories, and naïve theories and correct theories are incommensurate, or because shifting across categories is a difficult process. However, we have already stated that the nature of simple misconceptions (e.g. whales) and robust misconceptions is the same (they are miscategorizations), they are repaired through the same simple process (conceptual shift), and that this process is not affected by whether local or distant ontological boundaries are crossed. Thus, it is our claim that the difficulty of conceptual change in many cases does not arise from any of these factors. Instead, we argue that the challenge comes from mainly the fact that students may lack awareness of when they need to shift, and may lack an alternative category to shift into. 4.4.1. Lack of Awareness

In our earlier discussion of mental models, we pointed out that one feature of coherent, flawed models is that students are often unaware that their understanding is incorrect. Because students are able to generate predictable responses to questions and systematic explanations of phenomena, they don’t notice that their model is incorrect. This is in contrast to students with fragmented models, in which students are clued-in to their lack of knowledge by the fact that they cannot answer certain questions or generate consistent explanations. A similar situation applies from the perspective of categorization. That is, students may not be aware of their misconceptions if the miscategorized concept can be interpreted in systematic ways.

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For example, we described before how students may misclassify the concept electricity as a substance rather than a process. Because of this miscategorization, students believe that electricity can be stored in batteries and moves through a wire like water. Although incorrect, this misconception still allows students to function quite well in day-to-day living. For example, students can explain why batteries are needed to operate electronic toys by saying that the battery provides a source of electricity. Similarly, the electricity-as-water analogy can be used to explain why the lights go out if the wire is broken (i.e. the electricity cannot get to the light bulb). Thus, the ability to make sense of everyday events gives students the feeling that their deeper understanding is correct. They are unaware of a need to shift. The issue of awareness is easily addressed, in theory. All one would have to do is tell the student that he or she is wrong, and confront them with information and demonstrations that show the student’s understanding to be flawed. One can even explain the correct principles to the students. However, in practice, this does not always lead to a more accurate, deeper understanding. As described earlier, one may directly refute or contradict a misconception with little or no effect. The problem is that unless students have an alternate category to reassign the concept to, such instruction will not be effective. 4.4.2.

Lack of Alternative Categories

It is this second obstacle that gives rise to much of the “robustness” of misconceptions. Consider two examples of misconceptions, one in which whales are miscategorized as fish, and one in which the process of diffusion is miscategorized as a “causal process” instead of an “emergent process.” The first case is easy to repair because students already have a rich understanding, with many examples, of the category of mammals. Thus, when an instructor or text says that whales are a type of mammal instead of fish, the student can easily shift their concept into this existing category. However, students typically have a great deal of difficulty understanding diffusion. In fact, less than 2% of high school biology students understand it (Marek, Cowan, & Cavallo, 1986). Even when students are taught about the nature and behavior of molecules, concentration gradients, equilibrium, etc., they still describe the process of diffusion in causal terms, which prevents the understanding of diffusion on a deep level. Our claim (regarding this example, which will be explicated in more detail below) is that students lack a category of emergent processes, and thus cannot recategorize diffusion as this type of process. In other words, students cannot repair misconceptions if conceptual shift is not possible. This is what makes certain misconceptions more difficult to repair than others. 5. CONCEPTUAL SHIFT FROM CAUSALITY TO EMERGENCE: A CASE STUDY In order to more clearly demonstrate the reasons why certain misconceptions are difficult, we will provide an in depth analysis of the diffusion example mentioned

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above. Note that diffusion is just one example of a large class of science concepts (e.g. electrical current, heat flow, natural selection) that are particularly troublesome for students at the middle- and high-school grades to learn with deep understanding. These concepts will be referred to as “complex, dynamic processes.” 5.1.

Complex, Dynamic Processes

For these concepts, the observed behavior at the perceptual, or macroscopic, level emerges from the behavior of actors/constituents at the molecular, or microscopic, level. In addition, behavior at the two levels is not isomorphic. By behavior, we refer to the actions and interactions of the actors, and the parameters that affect these actions and interactions. Because the “macro” level behavior emerges from the nonisomorphic “micro” level behavior, we say that these are “emergent processes.” This is contrast to causal processes, in which the macro and micro levels are isomorphic and behavior at the macro level is caused by behavior at the micro level. In general, these emergent process concepts are often misclassified as causal events or processes. This misclassification occurs in part because students lack a category for emergent processes in the first place. This lack also makes the repair of such misconceptions very difficult. 5.2.

Diffusion: Behavior at the Macro (Perceptual) Level

Suppose we pour a dollop of white cream into a cup of dark brown coffee. As the cream “diffuses” throughout the coffee, it presents the appearance of white cream slowly merging or mixing with the brown coffee. Over time, the cream seems to spread out so that the white and brown liquids are indistinguishable. Thus, at this perceptual level, the behavior consists of 1) actors such as the cream and coffee, 2) actions such as the flow-like blending of the two liquids, 3) parameters that affect the action or rate of flow (e.g. concentration of cream, state of the equilibrium, medium or aperture of flow, etc.). Most textbooks are quite capable of describing the nature of such actors, their actions, and the parameters (including formulas) that govern these concepts. How can we characterize behavior at the macro level? Our claim is that the characteristics of behavior at the perceptual level are compatible with the features of a causal event or process. There are five such features: 1. Distinct actions taken by the different actors – the cream seems to be moving in one direction (towards the coffee), while the coffee appears not to be moving in any specific direction 2. Sequential actions – the “flow” of the cream is “from an area of high concentration to low concentration” 3. Dependent actions – the flow pattern (such as initiation, duration, direction) seems to be constrained by factors such as initial concentration differences 4. Termination – the flow seems to cease after equilibrium is reached, when the coffee and cream are blended

PROCESSES AND CHALLENGES OF CONCEPTUAL CHANGE 5.

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Goal-directed actions, or intentionality – its as if the cream molecules need

or want to move into the area of less concentration We posit that these five features (also listed in the left-hand column of Table 1), that one can impose or infer from observation of the macro level, constitute the features of a causal process category. 5.3.

Diffusion: Behavior at the Micro (Molecular) Level

At this level, the behavior consists of 1) the individual objects or actors such as molecules2, 2) the actors’ actions (molecules move in all directions randomly), 3) their interactions (collisions between molecules), and 4) parameters that affect the actions and interactions of molecules (molecular size and mass, which affects speed of motion). Note that the behavior at the micro level is distinct from the behavior at the macro level; they are isomorphic. 5.4.

How the Two Levels are Related

Although it may be difficult for students to untangle the presence of two levels, and the associated behaviors, it is not uncommon for many objects and events to have dual levels with distinct behaviors. For example, students are accustomed to knowing that human skin is made of cells, and that the properties of skin are different from the properties of individual cells. What students don’t understand is how the perceptual, macroscopic level behaviors and the molecular, microscopic level behaviors are connected. In diffusion, the question is: how does the flow-like behavior of the macro level emerge from the collision behavior of individual molecules? In order to understand emergence, students must attend not to the actions (and attributes) of the micro level actors as a class (i.e. how molecules move, their sizes, etc.), but to the collective interactions of all the molecules. This means that they must focus on the sum of all interactions of the individual molecules across time. For example, right after the cream is poured into the coffee, both “cream molecules” and “coffee molecules” are bouncing around and colliding with each other. Some of the cream molecules, by chance, might bounce into empty spaces near coffee molecules. Similarly, coffee molecules might bounce into spaces between the cream molecules. Molecules can also move randomly into spaces between molecules of their same type. Perceptually, because there is much less cream than coffee, it appears that the cream is flowing throughout the coffee. The characteristics of the collective interactions that give rise to the macro level phenomenon are diametrically opposite of those characterizing processes in a causal process category. This suggests that emergent process and causal processes are ontologically distinct. In terms of diffusions, we see: 2

For simplicity’s sake, we will talk about “cream molecules” and “coffee molecules”, although this obviously incorrect. Both coffee and cream are composed ofa number of different substances and molecules, and water is also present.

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Uniform interactions – all actors interact in the same manner (with random motion and collisions). Coffee and cream molecules do not behave in distinct ways. 2. Simultaneous interactions – the actions and interactions are all occurring at the same time, and are not sequential. Both coffee and cream molecules are moving randomly and colliding at the same time. 3. Independent interactions – whether or not two molecules collide is independent of whether others collide. In other words, the interactions occurring at one time point do not depend on prior interactions. If a molecule of cream moves into an area occupied by coffee molecules, a later collision could send the cream molecule back towards other cream molecules or towards other coffee molecules. 4. Continuous interactions – molecular motion and collisions are occurring at all times, and do not stop. When equilibrium is reached, molecules continue to bounce around, although the cream and coffee appear to have stopped mixing. 5. Local and decentralized interactions – the actions of the actors are not directed towards any goal. The coffee and cream molecules don’t have to mix, or achieve a balance of concentrations, they simply move around and collide randomly. These features are presented on the right hand column of Table 1 (see also Chi, 1997). We argue that such characteristics capture the features of an emergent process category. 1.

5.5. Misunderstanding

Our claim is that students miscategorize emergent processes as causal processes. From this perspective, we offer two reasons why understanding diffusion (and other complex, dynamic processes) is so difficult. First, the behavior at the macro level, as we have described, is consistent with a causal explanation of diffusion. The molecules of coffee and cream seem to move in different ways, seem to have a goal or purpose, the process of mixing seems to end with equilibrium, and so on. Thus, when asked to explain diffusion, students’ causal

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explanations are correct at the perceptual level. For example, if students were asked, “What caused the cream to spread in the coffee?” they can respond by saying “The difference in concentration or density of cream and coffee makes it spread.” Because the students can readily answer such questions, they are not aware that their understanding is flawed. From an educator’s point of view, explanations at this level cannot reveal underlying misconceptions. When this same question is asked at the micro level, however, students give the same basic answer, simply substituting the terms “cream molecules” and “coffee molecules” for “cream” and “coffee,” respectively. Thus, they could say, “The cream molecules want to go to the less crowded area of the coffee,” which implies both intentionality and unidirectionality. What these students are doing is treating the micro and macro levels as isomorphic, which is consistent with causal processes. These misconceptions are revealed only when students must give an explanation at the micro level3. Although students may be told that their explanations are incorrect, the main difficulty in repairing these misconceptions lies in the fact that students do not possess an emergent process category. Therefore, they cannot reassign the concept of diffusion to its proper category, and the misconception is maintained because they continue to inherit the features of an inappropriate category. To substantiate this “missing category” claim, we turn to preliminary data collected on another complex, dynamic process, “natural selection”. In Ferrari and Chi (1998), we examined explanations given by college students (Study 1) in response to questions about natural selection in evolution. The explanations in each case were coded not only for correctness, but also (and more importantly) whether they appealed to causal or emergent features, as listed earlier. For example, the following explanation was coded as evidence of the “sequential actions” feature in natural selection: “First, many trees will die, and only a few new trees will adapt to the new climate, and finally, a whole new species may evolve.” The use of terms like “first” and “finally” clearly indicate a view of natural selection as a sequential process, consistent with a causal view. Figure 3 shows that students used many more causal attributes than emergent ones. Specifically, 63% of the identifiable features were causal ones and only 8% were emergent. Thus, these results support the argument that students lack a welldefined category for emergent processes, which prevents the recategorization and repair of such misconceptions.

3

The simplified, correct explanation is that all of the molecules bounce around. At first, the coffee molecules will collide mainly with other coffee molecules, and cream molecules will collide with other cream molecules. At the boundaries between the coffee and the initial dollop of cream, some cream molecules will collide with coffee molecules and vice versa. Over time, such random collisions will result in some cream molecules occupying spaces where coffee molecules were, and vice versa. Thus, the molecules will mix.

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6.

CONCLUSIONS

In this discussion of conceptual change, we have sought to meet two primary goals. Our first goal was to answer the question of what exactly constitutes conceptual change. Does conceptual change include the accumulation of new knowledge and the revision of mental models? Does conceptual change involve shifts in perspective during problem-solving? Is conceptual change analogous to theory change? Our second goal was to explain why some prior conceptions strongly resist repair through instruction. Do these special cases of naïve knowledge involve concepts that are incommensurate with the correct concepts? Is conceptual change just a very difficult process? As part of addressing these questions, we also examined several different views of naive knowledge that exist in the literature and how these speak to the issues of process and difficulty in conceptual change.

PROCESSES AND CHALLENGES OF CONCEPTUAL CHANGE 6.1.

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Miscategorization

We have defined misconceptions as miscategorizations of concepts across ontological categories. In other words, misconceptions are based on the assignment of a given concept, like whales or diffusion, to an incorrect category. This view helped to resolve the circularity problem that arose when misconceptions are defined in terms of “incommensurable” theories. Are theories incommensurate because their participating concepts are incompatible, or are concepts incommensurate because they are embedded in incompatible theories? By defining incommensurability as “ontological distinctiveness,” we were able to circumvent this problem and offer an easy test of incommensurability, the predicate test. One question arose about defining these incommensurable categories. Is there a point at which categories are either “incommensurate” or “commensurate,” or is this a continuous variable? In other words, is incommensurability a matter of degree? We have no way of answering this question at this point in time. However, future work could address this question by systematically testing (through predicate tests) a number of concepts in different ontologies and examining the distribution of predicates that demarcate boundaries. 6.2.

What is Conceptual Change? Why and When Is It Difficult?

In our answer to these central questions, we have argued that conceptual change is the process of shifting concepts across ontological boundaries. This reassignment process is believed to be simple and straightforward, analogous to linking or associating a concept with a different category. Other types of reconceptualization, like perspective shifts, and accommodation, are better described as “conceptual reorganization”. Such reorganization involves hierarchical conceptual shifts or incremental changes, but not ontological shifts. But if conceptual change is a simple process, then why are some naive conceptions, referred to as misconceptions, so difficult to fix? We answer this second question by arguing that when conceptual change is difficult, it is often because students lack awareness of their misunderstanding, or they lack an alternative category to shift concepts into. It is this second obstacle that presents the greatest difficulty to repairing certain misconceptions. For example, there is a class of complex, dynamic processes/concepts (i.e. diffusion, natural selection, heat flow) that few students seem able to understand deeply. We have suggested that these students misclassify these processes as “causal” when they are actually “emergent” processes. Furthermore, students seem to lack this emergent process category, which precludes the repair of this misconception through conceptual change. This raises one final issue. How can we provide students with this emergent process category that they are missing, but need in order to understand so many scientific topics? Would it be sufficient to teach students the five features of emergent processes, and to contrast these with causal processes? Or do students require hands-on demonstrations or simulated environments? This is an open question which will be a focus for much of our future research.

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M. T. H. CHI & R. ROSCOE ACKNOWLEDGMENTS

The authors are grateful for support of this research from the Spencer Foundation. REFERENCES Carey, S. (1991). Knowledge acquisition: Enrichment or conceptual change? In S. Carey & R. Gelman (Eds.), The epigenesis of mind (pp. 257-291). Hillsdale, NJ: Lawrence Erlbaum Associates Carey, S. (1985). Conceptual change in childhood. Cambridge, Mass, MIT Press. Chi, M. T. H. (1992). Conceptual change within and across ontological categories: Examples from learning and discovery in science. In R. Giere (Ed.), Cognitive models of science: Minnesota Studies in the Philosophy of Science, (pp. 129-186). University of Minnesota Press: Minneapolis, MN. Chi, M. T. H. (1997). Creativity: Shifting across ontological categories flexibly. In T.B. Ward, S.M. Smith, R.A. Finke & J . Vaid (Eds.), Creative thought: An investigation of conceptual structures and processes. (pp. 209-234). Washington, DC: American Psychological Association. Chi, M. T. H. (2000a). Cognitive understanding levels. In: Encyclopedia of Psychology, Vol. 2, Kazdin, A.E. (Ed.). Pp 172-175, Oxford University Press. Chi, M. T. H. (2000b). Self-explaining: The dual processes of generating inferences and repairing mental models. In R. Glaser (Ed.), Advances in Instructional Psychology. Mahwah, NJ: Lawrence Erlbaum Associates. Chi, M. T. H., de Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanation improves understanding. Cognitive Science, 18, 439-477. Chi, M. T. H., Siler, S. A., Jeong, H., Yamauchi, T., & Hausmann, R. G. (In press). Learning from human tutoring. Cognitive Science. De Leeuw, N. (1993). Students’ beliefs about the circulatory system: Are misconceptions universal? In Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 389-393). Hillsdale, NJ: Lawrence Erlbaum Associates. De Leeuw, N., & Chi, M. T. H. (In preparation). Self-explanation, comprehension, and conceptual change. Chapter to appear in G.M. Sinatra and P.R. Pintrich (Eds.) Intentional Conceptual Change. Hillsdale, NJ: Lawrence Erlbaum Associates. diSessa (1993). Toward an epistemology of physics. Cognition and Instruction, 10, 101-104. Ferrari, M., & Chi, M. T. H. (1998). The nature of naive explanations of natural selection. International Journal of Science Education, 20, 1231-1256. Gelman, S. A. (1988). The development of induction within natural kind and artifact categories. Cognitive Psychology, 20, 65-95. Gunstone, R.R., Champagne, A. B., & Klopfer, L. E. (1981). Instruction for Understanding: A case study. Australian Science Teachers Journal, 27, 27-32. Hempel, C. (1966). Laws and their role in scientific explanation. Philosophy of Natural Science, Chapter 5, Englewood Cliffs, NJ: Prentice Hall. Hewson, P. W. (1981). A conceptual change approach to learning science. European Journal of Science Education, 3, 383-396. Jeong, H. (1998). Knowledge co-construction during collaborative learning. Unpublished Ph.D. thesis, University of Pittsburgh. Keil, F. (1979). Semantic and conceptual development: An ontological perspective. Cambridge, MA: Harvard University Press. Marek, E. A., Cowan, C. C., & Cavallo, A. M. L. (1986). Students’ misconceptions about diffusion: How can they be eliminated? The American Biology Teacher, 567, 74-77. McCloskey, M. (1983) Naive theories of motion. In D. Gentner & A.L. Stevens (Eds.), Mental Models (pp. 299-324). Hillsdale, NJ: Lawrence Erlbaum Associates. Osborne, R. J. & Wittrock, M. C. (1983). Learning science: A generative process. Science Education, 67, 489-508. Posner, G. J., Strike, K. A., Hewson, P. W., & Gertzog, W. A. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Science Education, 66, 211-27. Slotta, J. D., Chi, M. T. H, & Joram, E. (1995). Assessing students’ misclassifications of physics concepts: An ontological basis for conceptual change. Cognition and Instruction, 13, 373-400. Sommers, F. (1971). Structural ontology. Philosophia, 1, 21-42.

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Thagard, P. (1990). Concepts and conceptual change. Syntheses, 82, 255-274. Thagard, P. (1996). The concept of disease: Structure and change. Communication and Cognition, 29, 445-478. Viennot, L. (1979). Spontaneous reasoning in elementary dynamics. European Journal of Science Education, 1, 205-21. Vosniadou, S., & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24, 535-585. Wiser, M., & Carey, S. (1983). When heat and temperature were one. In D. Gentner & A. Stevens (Eds.), Mental models (pp. 267-297). Hillsdale, NJ: Lawrence Erlbaum Associates.

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WHY “CONCEPTUAL ECOLOGY” IS A GOOD IDEA

ANDREA A. DISESSA University of California, Berkeley, USA

Abstract. This paper motivates the idea of “conceptual ecology” by critiquing the current mainstream of conceptual change research. Most research on conceptual change suffers from too little theoretical accountability concerning the nature of the mental entities involved and too little use of the details of process data to support its theoretical view. Part of the consequences of these limitations is a vast underestimate of the complexity and diversity of conceptual change phenomena. In contrast, a conceptual ecology approach involves hypothesizing that conceptual change involves a large number of diverse kinds of knowledge, organized and re-organized into complex systems. To illustrate a conceptual ecology approach, we explain two very different kinds of mental entities, p-prims and coordination classes. Pprims are small and numerous intuitive elements that are often quite context specific in their activation. Coordination classes, by contrast, are large systems whose very existence entails a high degree of coordination across diverse contexts. We claim that both p-prims and coordination classes are much more explicit and precise in their assumptions than is typically the case, and they both survive substantial empirical test in the form of analysis of process data.

1. INTRODUCTION

My aim in this chapter is to provide a critique of the current state of conceptual change research and a brief account of how I believe better progress may be achieved. In particular, much prior research in conceptual change has taken a vastly oversimplified view of the process. Figure 1 provides a graphical backdrop on which to illustrate these oversimplifications. The figure shows a naïve concept, A, and its trajectory of development into expert concept, B. What could be wrong with such a picture?

M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 29-60. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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A. DISESSA

To begin, we must ask, what are the entities, A and B? The answer most often given is “concepts,” although other types of mental entities are sometimes given, say, ontologies (Chi, this volume), beliefs (Hofer & Pintrich, in press), models (Vosniadou & Brewer, 1992), or theories (McCloskey, 1983; Gopnik & Meltzoff, 1996). (To simplify exposition, for the most part I will use “concepts” as an exemplar type of mental entity, although my arguments are essentially unchanged if other types are substituted or if a few are added to a list of types.) To say A and B are concepts begs the question, what is a concept (or any of these other mental entities)? How do we know a concept when we see one? Might it not be necessary to distinguish different kinds of concepts? In this chapter I will strongly motivate the need for a significant variety of types of mental entities to replace the few listed in the literature. More significantly, I will argue that prior work has typically lacked theoretical accountability; it has, indeed, failed to tell us what concepts are, and how to distinguish them from other actual or possible types of mental entities. Figure 1 shows only two examples of concepts, A and B. Might it not be true, however, that many mental entities contribute to the construction of B? Might it not be true that B is, in fact, a complex system consisting of many interacting parts? My belief is that it is essentially certain that scientific concepts are best considered as complex systems, and prior research has not systematically addressed this possibility seriously. For example, current practice in conceptual change research is far from being able to (and rarely attempts to) match system elements and processes against the details of student reasoning and learning data. The logical extension of Figure 1 has exactly one naïve concept for every expert concept, and it does not make room for the distinct possibility that naïve concepts have rather different properties than expert ones. Empirical data with respect to these possibilities are easy to come by. Beginning students have many ideas that do not come close to matching expert ideas on a one-by-one basis. It well may be that the naïve conceptual ecology has no exemplar whatsoever that approaches the qualities exhibited by expert concepts. With an impoverished view of the nature of concepts, it is no wonder that the long, winding path from naiveté to expertise has little exposed detail in the literature. Instead, one finds a variety of unhelpful, definition-begging and probably unfalsifiable terms, like “partial construction,” “mixed models,” and “confused ideas.” And yet, in the classroom, teachers easily find rich and complex intermediate states with which they have to deal; clinical interviews of students essentially always reveal a textured mix of naiveté and learned knowledge, which, however, has had few, if any, systematic descriptions to date. Figure 2 shows a graphic—obviously simplified—that illustrates the view of conceptual change I advocate in this paper. The naïve state consists of a large number of conceptual elements of varying types. Those elements are modified and combined in complex ways, possibly in levels and into subsystems that, together, constitute the “final” configuration of an expert concept. For reference, I call this a “complex knowledge systems” view of conceptual change—informally, “conceptual ecology.”

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The term conceptual ecology has been used by others. In particular, in their influential work on conceptual change, Strike and Posner (1992) speak of conceptual ecology in a similar spirit.1 More generally, there have been other advocates and allies of the complex knowledge systems view, some implicitly in the details of their analysis of learning complexities, and some more explicitly in the richness of their theoretical framing (e.g., Thagard, 1992). Indeed, in a summary chapter for a section of book on reasoning (Vosniadou & Ortony, 1989), Bill Brewer reports his synthetic conclusion that “in the long run, a proper understanding of the human mind will require that we recognize a large number of very different forms of knowledge and associated psychological processes.” (p. 537) Despite sporadic recognition of the importance of a complex systems view, the mainstream of conceptual change research has persisted with vague and oversimplified assumptions about the entities and processes involved in conceptual change. In addition, of course, I intend my contribution to point out particular ways of pursuing a complex systems view that I expect will be most fruitful. The remainder of this paper elaborates and systemizes the difficulties I see in the contemporary landscape of conceptual change research. Following, I illustrate my approach to improving on the present state. 2. DIFFICULTIES ELABORATED

Broadly, I divide the difficulties in the core of contemporary conceptual change landscape into theoretical and empirical subsets. 1 However, Strike and Posner did not seem to intend the level of detail in articulating and modeling knowledge types and architectures implicated here.

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A. DISESSA Theoretical Considerations

A lot could be said about the lack of cogent theoretical framing for the issue of conceptual change. However, in this chapter, I underscore only one issue: the lack of well-developed technical terms. Dictionary meanings can almost never serve the purposes of science. Instead, whenever science is successful, it refines existing terms or adds supplemental ones that can bear a stronger burden. Everyday words are known to be polysemous, combining multiple senses in useful (if ambiguous) packages. Furthermore, even the various senses of everyday words serve only everyday purposes in everyday ways. “Concept” (or one of its various senses or connotations), in particular, seems clear and useful in common usage. However, in the following section, I argue that it is hopelessly vague, covering multitudes of kinds of mental entities with a common coat. At this point in cognitive studies, we can hope to apply high analytical (as opposed to purely empirical) standards to our technical terms. We could, for example, attempt process models that explain technical terms. Although I won’t press far in this direction here, it is good to realize that the literature on conceptual change has rarely attempted process models, nor has it entertained substitute methods of making technical terms’ meanings precise. Besides “concept,” other common candidates for useful technical terms suffer similar difficulties to varying degrees. We all have a vague sense of what a theory is. Yet, even if the term is sufficiently well-defined within the social conduct of professional science, in transporting the term to individual learning, a host of changes are likely necessary.2 In particular, I believe there is convincing data that many naïve scientific ideas are inarticulate, are not easily expressible in words. This, alone, is a dramatic difference from professional science, where complex, careful and symbolically augmented expression (e.g., using algebra) is almost always evident. It seems indubitable that externalizing ideas is more than for archival purposes in professional science. Externalizing allows extraordinary reflective scrutiny and careful reformulation. In contrast, “naïve theories” are never seen directly in the words of subjects, or we might simply be able to ask students for their theories, the way we do with scientists. “Ontology” has longstanding philosophical roots. To my knowledge, however, no researcher of conceptual change has attempted a process model of ontologies. I don’t need to criticize empirical work that implicates shifting ontologies to point out that such work is weakened unless we know what an ontology is, unless we understand how such mental entities may come to exist in some detail and how they function in reasoning and learning. For ontology, as well as for concept, we want to know how we can surpass images like Figure 1 in detail and cogency. Unless we develop theoretically well-elaborated technical terms, major empirical problems follow. Unless we know what a theory is, how do we distinguish it from a small collection of concepts, or even from a sentence one may utter and toward which one might express some commitment? Tellingly, researchers preferring one 2

With regard to social vs. individual perspectives on theory development, see Harris (1989).

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term of another (concept, theory, belief, ontology) essentially never use data to show students’ reasoning and learning are inconsistent with other theoretical assumptions. diSessa & Sherin (1998) examine the literature of conceptual change. They argue that even the best and most widely-recognized researchers use inexplicit definitions that implicate ill-defined meanings, and they show what difficulties follow in attempting to interpret data in such vague terms. The deep problems of conceptual change remain unscathed when we cling to vague, unelaborated terms. What aspects of “theory” are really critical in theory change, and why, after all, is conceptual change difficult when some kinds of learning proceed effortlessly? In this chapter, I won’t propose general criteria for cogency of technical terms in cognitive studies. However, I will illustrate steps toward more adequate terms with two categories among several I have developed in my own studies of conceptual change. 2.2.

Empirical and Quasi-Empirical Considerations

This section views the current state of conceptual change research through an empirical lens. I will argue that researchers have used very weak empirical strategies that avoid the real complexity of conceptual change. In particular, I make the case that, without much effort, we can strongly motivate, if not prove, that the appropriate default approach to studying conceptual change recognizes diversity in mental entities. Several trends that I take to be paths of improving our study of conceptual change will become evident in this section. The first, already mentioned, concerns types. In particular, I advocate a trend toward multiplicity, a greater number of (more accountable) types of mental entities. A second trend concerns grain size. Here, the trend should be toward a greater number of smaller scale elements. Concomitantly with the second trend, in investigating large-scale accomplishments like “conceptual change” we are necessarily studying systems of interacting elements. A final trend concerns increased care in dealing with invariance, that is, the issue of when two situations evoke the same conceptual elements. With a rich selection of knowledge elements, we are forced into much more specific consideration of context. If a conceptual ecology contains thousands of elements, certainly the issue of when which are activated is highlighted. In fact, we should expect a greater degree of context dependency. Combining trends toward increased contextual dependency, toward multiplicity and toward smaller grain size suggests that an application of a concept is likely to be better viewed as the selected activation of particular concept subcomponents, depending on context. This particular observation will become a core concern when we turn to one of my sample knowledge types, “coordination class.”

34 2.2.1.

A. DISESSA Diversity

This subsection considers three types of diversity in conceptual change that are inadequately handled by current studies. The first is a quasi-empirical view of the diversity of kinds of concepts that exist. I say “quasi-empirical” to indicate that my intention is to draw on good intuitions we all should have about knowledge, rather than to suggest a particular empirical result or program of studies. Consider the following examples of concepts and their diversity along a number of dimensions. “Dog” is a familiar concept. This is a category-like concept; its primary function is to classify entities in the world into members and non-members of some set. We shall see that other kinds of concepts very much background this particular function. Concerning the competence to recognize exemplars and nonexemplars of “dog,” we note that many similar concepts must draw on some similar or identical abilities. Recognizing sheep, cats, raccoons, even people involves similar shape-determining methods; it involves recognizing families of textures (like smooth or hairy), recognizing related categories of things (like eyes, faces, etc.) and considering their systematic variation (bigger, smaller; oblate or round; etc.). Although there is no consensus that category-like concepts work by matching potential exemplars to a prototype, at least this is a plausible mechanism for doing the main work of these kinds of concepts (Rosch, 1994). We know that a fair amount of work goes into learning these concepts since, for example, children take time to get them right. On the other hand, essentially every child masters common categories without a great deal of explicit instruction.3 Now consider the concept “bluare,” which is the artificial category of things that are both blue and square. A long tradition of psychological studies has investigated the properties of such concepts. For adults, the learning trajectory for bluare can be short, perhaps 10 seconds. It is an unproblematic combination of unproblematic other concepts (blue, square, and the logical connector “both”).4 Learning can be accomplished articulately, by explaining the concept, in contrast to the unlikelihood of learning to recognize a new kind of animal, a wombat, for example—or to acquire the ability to classify animals at all—by being given a brief description. Bluare is at an extreme end of learnability. It is less difficult than learning to recognize animals, and far less difficult that acquiring a scientific concept like force. Does it deserve the same appellation, “concept”? If it does, how much does the category tell us about 3

Difficulty in mastering a concept does not necessarily depend on knowledge-structural characteristics of the concept. It might be, for example, that the natural environment is simply impoverished in support for learning it. However, even in that case, difficulties in learning different concepts may certainly be systematic, even if they are in relation to existing or possible learning environments rather than intrinsic to the nature of the concept. 4 The fact that bluare is a simple combination ofalready existing concepts probably explains its ease of learning. Wouldn ’t it seem important to know which already-known elements contribute to learning new scientific concepts? Surely learning most concepts can’t be tabula rasa, and a profile of contributing elements is more than plausible as an important part of understanding a knowledge systems view of a “new” concept. Yet, conceptual change literature, for the most part, treats the issue at the coarsest possible grain size; as in Figure 1, the expert concepts of heat and temperature, or force, etc., grow out of naïve versions thereof.

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learning difficulties or the plausibility of various instructional strategies—such as talking as opposed to examining multiple exemplars?5 Of course, since bluare is an extreme example, few would study its learning as related to scientific concepts. Yet, how do we know there is not a complex continuum of scientific concepts, with importantly different qualitative properties, as illustrated by dog, bluare, and (to come) force? Consider the concept “number,” cardinality. I mean to refer to the operational concept (in somewhat the Piagetian sense), enfolding the operational properties of cardinality, such as invariance on rearranging a set of objects, or invariance in the case of no additions or removals. This is much sparser knowledge territory than animal types. What categories are similar to number and might share perceptual/conceptual strategies, as recognition of dog shares with recognition of raccoon? There simply aren’t any similar categories (until one gets to the rarified air of group and field theory). So, I argue, the learning of the concept number is very likely to be quite different from learning dog. Similarly, there is no plausible prototype for “number.” No exemplar, say 7 as the cardinality of a set of sheep, has the right properties to be a prototype—such as a large number of typical, but neither necessary nor sufficient, properties. All cardinalities have exactly the same operational characteristics. Finally, consider the central concept in most of the examples to follow, the physics concept of force. Quite plausibly (and a significant literature backs this up, e.g., Clement, 1983; diSessa, 1993), kinesthetic experiences of effort and accomplishment are genetic ancestors to this concept. And yet, it is clear from extended learning difficulties that the professional concept exhibits definitive differences compared to any possible naïve version of the concept. This is quite a particular regime of learning: Substantial prior resources exist (perhaps somewhat like bluare), and yet a deep gulf exists between naïve and expert concept. The nature of the gulf is as yet much in debate, which, once again, highlights the need for a refined ability to describe a learning trajectory bit-by-bit in order to understand and catalog such gulfs. With respect to multiplicity, my program of research has attempted to identify many different types of mental entities (diSessa, 1996). For simplicity, however, I will discuss only two particular types that make evident a huge range of kinds of mental entities that may be implicated in a more refined view of conceptual change than we currently have. Fortuitously, the pair of types I discuss are both (a) among the most theoretically developed and also (b) are dramatically different in their properties. So exposition concerning these two types can do double duty in this chapter. I wish to mention briefly two other kinds of diversity not well-respected in the literature on conceptual change. The first was already alluded to in the discussion of diversity in types. That is the diversity of states in the midst of a learning trajectory, including classifying easy and difficult parts of learning a concept and 5

Thomas Kuhn is a good connection here. In the “Structure of Scientific Revolutions ” (Kuhn, 1970) he talks about the complex non-linguistically mediated process of learning scientific concepts in the course of studying exemplars of use of those concepts.

36

A. DISESSA

understanding the reasons for their difficulty (or ease of learning). For example, learning literally the equation is an easy accomplishment in the context of learning the concept of force. That may be obvious, but a theoretical accounting for ease of learning is complementary and may be part and parcel of an accounting for learning difficulties. Later, I will localize and describe the reasons for learning difficulties as part of my discussion of my two exemplar knowledge types. Finally, accounts of conceptual change have all but ignored individual differences. Why do some people learn certain concepts almost effortlessly while others do not? While it might be true that an adequate accounting of naïve conceptual resources available for incorporation into the construction of an expert concept could account for such differences, I believe that meta-conceptual and epistemological issues are at least as prominent. See the discussion of metaconceptual issues in coherence and consistency, later in this chapter and consult diSessa, Elby, & Hammer (in press). All in all, I claim there is a huge diversity in conceptual learning phenomena that is not remotely accounted for in current accounts of conceptual change. Different sorts of concepts are evidently different, one from another, and may need individual accounts of relevant processes of change. Even if concepts are all the same in some deep structural sense, or differ systematically along a few dimensions, reconciling apparent differences with such hypothetical deep commonalty has not been accomplished. In order to deal with apparent empirical diversity in knowledge types, my preferred method is straightforward—to begin developing a larger and more accountable list of types of mental entities.6 It happens that, if one allows certain kinds of mental entities, not only does the number of kinds of entities increase, but the number of exemplars of each kind is likely to dramatically escalate. It may be that dozens or more such elements lie behind the construction of a single professional concept, in which case the class of stories about conceptual change illustrated in Figure 1 is patently hopelessly inadequate. In addition to a diversity of types (multiplicity) and a proliferation in numbers of knowledge elements (grain size) several other trends seem strongly implicated in the above discussion. Reduction in grain size and therefore an increase in the difficulty of even listing all the cognitive elements that go into conceptual change entails a systems approach. If many elements go into the construction of a concept, how are they coordinated and combined to produce “a scientific concept”? Furthermore, if multiple elements are involved, then we must describe much more carefully when they work (contextuality). A greater accountability to contextuality also means we may have a much better chance to describe particular configurations that cause problems or lead to productive new accomplishments along an extended learning trajectory.

6

In principle, other solutions may exist, such as accounting for differences merely in terms of system properties of different configurations of identical elements.

CONCEPTUAL ECOLOGY 2.2.2.

37

Methods

If the arguments in the above section are at all cogent, it is hard to imagine how a core portion of the relatively large literature on conceptual change has managed to ignore the implicated facts. Without entering into too much detail, I suggest that the reason is two-fold. First, as I argued above, the level of theoretical accountability generally is still very low. Hence, we simply have very fuzzy lenses with which to inspect conceptual change. It all seems a mushy soup where what counts as a theoretical perspective can never come to brass tacks in allowing a comparison of its relative effectiveness to that of another view. Vague ideas are extremely hard to hold accountable. Instead, they are mere motivators of experiments and broad interpretive frames for results. Investigators paint data with “word pictures” invoking their favorite terms without ruling out alternative interpretations, and without any strong tests for the cogency and adequacy of the terms they apply. Concomitant to weak theory, empirical studies don’t attend to details. Researchers do not attempt detailed accounts of particular applications of concepts—or descriptions of what has transpired in a segment of learning protocol—for the simple reason that there are no specific, “mechanistic” stories in the offing.7 “Theoretical frames” are too weak to rule anything out, and they don’t have enough detail even to ask good empirical questions. My basic contention is that we have said nothing falsifiable when we say force is a concept, or that impetus ideas constitute a theory (McCloskey, 1983), until we have said much more about what each of these knowledge terms entails. Stunningly little process data is taken into account in conceptual change research. By and large, the paradigm has employed before and after snapshots. Right and wrong answers—or similar behaviors, all distanced from cogent theoretical accounts of the elements and processes of change—are counted. Protocol segments are glossed as suggestive reflections of, for example, an “underlying theory,” without argument that all the elements of a theory are evident, and without competitive argument that other explanatory constructs are less adequate than “theory.” Sentences are taken to represent theories, and words are taken to represent concepts, ignoring the diversity in types of concepts or theories that we should expect. There is a huge ontological gulf between, on the one hand, protocol coding categories and, on the other hand, knowledge element types or system configurations. Yet, our research techniques have yet to clearly distinguish these. To sum up, I advocate a richer empirical accountability, parallel to one for theory. The hallmark of such accountability, I suggest, will be process analyses of concepts (or ontologies, or theories) in use and in change that rule out things that do not happen, predict things that do, and explain detailed properties of what people do in reasoning and learning—especially explaining surprising things we might not have noticed before. While I do not intend to be prescriptive or limiting, my own 7 There are exceptions. See, for example, Schoenfeld, Smith, and Arcavi (1993). Computer modeling of competence, for example, with production systems also constitutes a significant exception. However, conceptual competencies, unlike skill, is a rare target of such modeling efforts.

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empirical efforts have mainly been in terms of clinical interviews. Such interviews allow repeated episodes involving a particular mental entity to be investigated, triangulating on the properties of the entity. They allow nuanced setting of the context to investigate contextuality. They show subjects’ levels of commitment, such as certainty and ambivalence. They also expose paths of reasoning that lead to answers, plainly separating answers from the ideas that generate them. In a clinical interview, we have many opportunities to look at small moves in learning that contribute, overall, to conceptual change. The data sections of this paper will show, by example, some of these properties of clinical interviews and how they can contribute to more refined empirical analysis of concepts and conceptual change. I’ve set out a big agenda for the rest of this chapter. I want to illustrate: 1. What more accountable theoretical terms might look like. 2. What different; exemplars of such terms are plausible and plausibly play an important part in conceptual change. 3. How different from each other knowledge types might be, and how different types can account for different aspects of reasoning and conceptual change. 4. What sort of details of subjects’ behavior can be accounted for with sharpened theoretical terms. For example, what are typical easy and difficult accomplishments along the path to conceptual competence? I don’t intend to prove or demonstrate here, but can only illustrate and suggest. Adequate empirical and theoretical accountability, given the general state of the art, doesn’t fit easily into a half-chapter of a book. There is simply too much theoretical groundwork to do, and too much detail in adequate empirical argument. 3.

3.1.

STEPS TOWARD A SHARPENED THEORETICAL AND EMPIRICAL ACCOUNTABILITY

P-prims

The first knowledge type I discuss has had an extensive history, and it has been rather thoroughly explained in other places. See, for example, diSessa (1983, 1988; 1993; 1996). What stands here is a review. 3.1.1.

The nature of p-prims

P-prims, I claim, constitute the bulk (but not the totality) of intuitive physics, the precursor knowledge that gets reconstructed into schooled competence with Newtonian physics. The name, p-prim stands for “phenomenological primitive.” (The relevant senses of “phenomenological” and “primitive” are explained in diSessa, 1993. However, consider the characteristics described below.) P-prims have the following properties. Small and monolithic: P-prims are small and simple knowledge elements. They are atomic in the sense that they are essentially always evoked as a whole (in contrast to scientific concepts, which I believe can be accounted for only with a systems analysis).

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Many: There are many, many p-prims, in the hundreds or thousands. The full collection of p-prims exhibits some mild degrees of systematicity, but p-prims are loosely coupled. They do not exhibit deductive relations or any other systematicity typically expected of, for example, theories. Work by recognition: A good candidate model for p-prims’ activation and use is “recognition.” One simply sees them in some situations and not in others. Feelings of naturalness; judgments of plausibility: The prototypical function accomplished by p-prims is to provide a sense of obviousness and necessity to events. If you see something pushed, you are not surprised—in fact you expect—that it moves in the direction of the push. An event or explanation feels plausible to the extent that it matches your intuitive p-prims that relate to the circumstance at issue, and it is surprising to the extent that it does not match. Explanatorily primitive: Generally, nothing can be said about why the behaviors prescribed by p-prims happen. There is no “covering theory” or articulate reasoning on tap that explains them. Fluid; data driven; lack of conflict resolution: While p-prims are sometimes strongly cued by a situation, many times they will be much less firm in their activation. In these cases, subjects might have an intuition about what might happen but then lose it as their attention shifts. In some instances, several conflicting p-prims might apply, and there is unlikely to be any way to resolve such conflicts. Problematic connection to language: P-prims are not words or word senses and are not encoded linguistically. Describing p-prims in words is difficult or impossible (for subjects, as opposed to theorists). Origins in “minimal abstractions ”: Generating new p-prims is neither difficult nor particularly rare. They are frequently fairly simple abstractions of familiar event, such as the fact that a pushed object moves parallel to the push. However, p-prims’ properties, especially attachment to particular circumstances, are determined typically by a long process of development. Development by reorganization: P-prims are not extinguished or replaced by learning scientific concepts. Instead, many p-prims find useful places in the complex system that is an effective scientific concept. A p-prim might come to be known as an effective special case of a scientific principle, and it will be used in place of the principle in apt circumstances. However, p-prims will no longer function as explanatorily primitive. Physics explanations need articulate accountability that p-prims can’t provide. The changing function of p-prims in learning and, indeed, the natural evolution of the collection of p-prims, may be described as “shifting priorities,” degrees of attachment to particular contexts of use. These properties of p-prims are not an ad hoc collection. They are mutually dependent and mutually suggestive in many ways. For example, the fact that the elements are small suggests large numbers. Large number are reinforced by the fact that p-rims are relatively easy to generate. A single mechanism of learning (shifting priorities) accounts for naturalistic learning of p-prims and what happens in school. Lack of articulateness goes hand-in-hand with data fluidity. For details on a process

40

A. DISESSA

model of p-prims’s activation and use, which further integrates these characteristics, see diSessa (1993). Here is a list of some mostly important p-prims. All of them will be used in empirical analyses later in the chapter. Some basic p-prims: Ohm’s P-prim: A tri-partite element with an impetus (effort), a resistance, and a result: Effort works through a resistance to achieve a result. Ohm’s p-prim entails the following expectations: More effort begets more result; more resistance begets less result; and so on. Force as a Mover: An abstraction of a push or toss: Things go in the direction you push them. Dying away: Induced motion just dies away, like the sound of a struck bell. Balance and equilibrium: Dynamic balance: Sometimes, efforts or impetuses conflict and (accidentally) cancel out, like two people of equal strength pushing against each other. Overcoming: A situation of conflicting efforts, where one wanes or increases, yields a characteristic switch from the outcome associated with one effort to the outcome associated with the other. For example, a person pushing against another increases his effort and moves the other back. Return to equilibrium: Systems that are “out of balance” tend to return to “equilibrium.”8 For example, a balance scale pushed out of level returns to level. Water levels itself in a pan. Generalized springiness: In “out of balance” systems, the displacement from equilibrium is proportional to the amount of perturbation that is applied. A less important p-prim: Contact conveys motion: An object (typically small or light ones) in contact with another moving object (typically a large or heavy one) just moves with it. For example, a box in a wagon moves with the wagon.

3.1.2.

Process data concerning p-prims

I will illustrate the characteristics and explanatory force of p-prims (and, later, coordination classes) mainly with examples taken from an extensive interviewing corpus involving one freshman college student, whom I call J. Details can be found in diSessa (1996; to be submitted) and diSessa, Elby & Hammer (in press). The following example illustrates several of the characteristic properties of pprims. It shows data fluidity in that J at first feels she sees how a situation will 8

Here and subsequently I use quotation marks on glosses of p-prim based descriptions in order: (a) to suggest how subjects might describe the relevant situations in words and (b) to warn that these descriptions are not proper physics analysis.

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behave (in this case, she seems to evoke generalized springiness), but then she loses track of that intuition (when provoked to consider “why”) and changes her mind. When queried about how she had thought before changing her mind, she has essentially nothing to say except that she lost the sense she once made of the situation (that is, she loses her initial p-prim-based sense of naturalness). Her lack of anything to say illustrates the problematic connections between p-prims and language (inarticulateness). The instigating interview probe was to ask what happens when a small weight is added to a pulley setup in which two large and equal weights are “balanced.” See Figure 3. (The word balance is not used; instead, the idea is provoked by a symmetrical picture.) What J says initially is consistent with generalized springiness. The weight simply perturbs the system by some amount. However, a different intuition soon takes over, one that happens to be correct—the unbalanced system continues to move away from “equilibrium.” Note that, if J had managed to keep a stable view of this situation as illustrating generalized springiness, the prediction is that she would have implicated a more extensive movement for a heavier perturbing weight, and, possibly, a counter-factual “return to equilibrium” if the weight were removed (return to equilibrium p-prim). Had she not evidently lost track of her initial conceptualization, her lack of showing proportionality of excursion from equilibrium with perturbing strength would have contradicted the proposed description of generalized springiness. Thus, matching process data provides many opportunities to contradict theoretical assumptions or prior empirical results (such as the nature of generalized springiness). See the “principle of invariance,” discussed later.

[In protocol transcripts, ellipses denote omissions, and “//” denotes interruptions or abrupt halts, usually followed by a restart. Comments and clarifications appear in italics in brackets.] J: I mean if that’s a tiny, tiny weight, it’ll probably go down, and then it’ll come to rest again. And then the other one’ll go up, and they’ll be hanging, like, there. If that weight is as small as it’s drawn. [Note the suggestion that it might be different (e.g., greater “disequilibration”) if the small weight were larger.] I: So but, so but why would it come to rest? That’s a little funny... why would it stop?

42

A. DISESSA J: It actually// It wouldn’t. It wouldn’t stop. It would keep going slow, slow, slow all the way down. It would not stop. I: So you changed your mind. J: Changed my mind. ... I: Can you say what made you change your mind? J: Cause it didn’t make any sense. I: Cause it didn’t make any sense? J: No. I don’t know why I said that. ... I don’t know. I don’t know if I didn’t think about it or I just sat there thinking in my mind, but I was// I mean, I know that that wouldn’t happen.

Notice that, while not very detailed, this account uses the general properties of pprims to explain (if not predict) many details in this process segment. It uses a previously documented p-prim (generalized springiness) to explain a counter-factual prediction; it explains (momentary) sensemaking; it explains “losing track” as a general phenomenon involving p-prims (data fluidity); it explains inability to articulate.9 Predictions by students that have similar properties to this are incredibly easy to demonstrate. I have personally documented scores of p-prims that are at once plausibly “naturalistic” (learnable with experience in the natural world) and explain surprising non-physics predictions and explanations given by students (e.g., diSessa, 1993). Yet, no other account of conceptual change gives any status at all to “many and little” elements like p-prims. “Large,” intrinsically difficult-to-change entities like concepts, theories, and ontologies provide no explanation whatsoever for commonplace cognitive phenomena. I want to make brief reference to one of the most significant successes of p-prims in accounting for important phenomena in conceptual change. It is described in detail in diSessa (1996), and illustrates how process data can bear on issues of conceptual change. In another session, J was asked to describe what happens when a ball is tossed into the air. Initially, J provided a proper physics explanation, involving only one force, the force of gravity. However, J was then prompted to consider the peak of the toss. The point of this probe was to test the salience to J of dynamic balance and overcoming p-prims. Consistent with data fluidity and in accordance with previously documented p-prims, J began to reformulate her explanation in terms of two competing forces, where one overcame the other. After an extended bout of reasoning in which J tried alternative candidates for the force competing with gravity, J reached a stable explanation of the toss involving at least four p-prims in a natural configuration: J used force as mover, dynamic balance, overcoming, and dying away. One thing that is particularly notable is that the explanation she produced had been documented in the literature and touted as exemplifying a deeply held intuitive theory of motion (McCloskey, 1983). Thus, we see a student’s description emerge on the basis of well-documented intuitive 9

Of course, in a short exposition we cannot rule out explanations such as that the interviewer’s questioning her prediction caused her to hide (rather than lose) her initial idea. Similarly, she might have been able to explain and justify, but just chose not to. None of these alternative explanations are consistent with the broad corpus of data from J, but we cannot enter into details here.

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resources and their properties. J’s description of the toss is a semi-stable—albeit constructed-on-the-fly—configuration of known entities with known properties. If the description constitutes a theory, we have seen in this analysis how that theory can arise, at least in one case. If the description does not implicate a theory, we still see how it came about and probably know more about its properties due to this process data analysis than is contributed by calling it a theory. P-prims show penetration into the details of process data that are exceptional in the conceptual change literature. 3.2.

Coordination Classes

In this section I describe another knowledge type, which has properties almost polar opposite to p-prims. Because this type of mental entity is newer and less researched than p-prims, I make a more extended exposition of its properties. Coordination classes are large, complex systems, rather than atomic elements. Pprims are extremely likely to constitute fragments of coordination classes. Unlike pprims, which couldn’t under the most extreme circumstances be mistaken for a fullblown scientific concept, coordination classes are, in fact, intended to constitute a model of a certain type of scientific concept (and, possibly, some non-scientific concepts as well). Other types of scientific concepts may have quite different properties, and coordination classes themselves have a range of parameters that mean the construction of a coordination class may be different in one case compared to another. For simplicity, parametric differences among coordination classes will be almost completely suppressed in the remainder of the chapter. Unlike p-prims, which play a role in both expert and naïve thought, coordination classes may well not exist (at least with similar parameters of behavior) in naïve thinking. In any case, whether and which naïve coordination classes exist is an open empirical question. 3.2.1.

The function of coordination classes

The functional specification for p-prims is to provide feelings of naturalness in familiar situations, surprise and possibly learning-inducing attention in situations we don’t understand, and expectations that can be instrumental (e.g., we can “increase our effort” in accordance with Ohm’s p-prim if we want “more effect”). In contrast, coordination classes provide a very different functionality. They provide the means for getting a certain class of information from the world. The fundamental assumption behind the idea of coordination classes is that information is not transparently available in the world. Instead, we have to learn how to access different kinds. Indeed, in different circumstances, we may need to use very different means to determine the same kind of information. In general, people must be creative in using any information that may be easily available in a situation, and then inferring the specific information they need from that.

44 3.2.2.

A. DISESSA The structure of coordination classes

While p-prims are nearly atomic, although embedded in a recognition system, coordination classes have a lot of internal structure. A great deal of this structure depends on specifics related to particular coordination classes. However, some large-scale partitioning of its internal parts can be made. In particular, I distinguish the set of methods by which any relevant information is gleaned from the world, which I call readout strategies, from the collection of possible inferences that can be drawn from available information. The latter set of inferences I call the causal net. “ Causal” is to be understood in a very general sense. The causal net encompasses inferences that may seem more mathematical or a priori in addition to some we would instinctively describe as causal. Let me exemplify with one of my favorite hypothetical examples of a (possible) coordination class. This example is taken from Piagetian studies of children’s concepts of time (Piaget, 1969).10 The question is, how do children learn to “see” time interval in the world? “Time interval” is the type of information whose processes of determining (coordination class) we want to explore. Consider the following situation, illustrated in Figure 4. A blue train and a red train leave a station at the same time, A. The blue train is slower than the red train. The red train stops at a time, B, before the blue train stops, at time C. Because the red train travels much faster than the blue train, the blue train doesn’t manage catch up to the red train’s stop position by time it, itself, stops.

There is a lot of variability in what children say in response to such a setup. However, some respond as follows. When asked which train went on for a longer time, they say that the red train did. While this may seem to entail a simple confusion of meaning of “long,” that possibility can be ruled out be rephrasing the question. For example, children may be asked, “If the red train stopped at lunch time, what time did the blue train stop?” Children respond that the blue train stopped before lunch time. 10

I’ve used this example in several places. For example, it appears in diSessa and Sherin (1998).

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On further questioning, it turns out that children are accurately reading relevant information out of the situation. When queried whether the blue train was running when the red train stopped, they (sometimes) answer, accurately, “yes.” Furthermore, they may also acknowledge that the red train was not running when the blue train stopped. In terms of coordination class theory, children have quite adequate readout strategies. To an adult, the information about relative stopping compellingly and automatically suggests a conclusion. If a blue process started at the same time as a red process, and the blue process continued when the red one stopped, adults instantly conclude that the blue process went on for a longer time than the red process. They also know that no information about position (e.g., where the processes ran or stopped) is relevant to deciding time duration. In terms of coordination class theory, adults have a causal net that contains the appropriate inference on the basis of observations about whether one process continued when the other stopped. It is not true that children have no causal net at all. They have a different one. They infer (sensibly enough) that if a moving object gets farther away, it has been running longer. The problem is that they don’t know the applicability conditions for that inference, that it only applies to a single object or to multiple objects moving at the same speed. The causal net is not a homogeneous subsystem. As we shall see, it might contain p-prims (like “farther implies longer duration”), articulate causal assumptions (like force—and only force—causes motion, so that if there is motion, there is a force), and even equations, like We shall illustrate these possibilities shortly. 3.2.3.

The development of coordination classes

The development of a coordination class is an extended and complex affair. The descriptor “coordination” implies that a lot of pieces must be put in place to achieve an effective coordination class. Given what we have said, above, however, we can describe different phases and different kinds of difficulties faced in this construction. In order to read out the particular form of information of interest, one must accumulate both (1) readout strategies and also (2) inferences in the causal net that are sufficient to cover all contexts in which the information is needed. We call this achieving appropriate span. In each context of interest, it may be that particular readout strategies and inferences need to be combined. We call this integration, as in appropriately integrating several pieces of knowledge to serve the needs of particular contexts. Finally, because different readout strategies, different inferences, and different combinations may be used in different circumstances, a properly formed coordination class must be aligned. That is, the same information should be read out, no mater what the context, no matter which readout strategies and which inferences are used. In the data that follow, we will see, in particular, dramatic failures of alignment due to contextuality of pieces of the coordination class.

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Before turning to realistic, empirically investigated coordination classes, a “toy” example of the above-listed accomplishments (span, integration, and alignment) may be helpful. Consider the possibility that reading out “fiveness” (the property of being the alphanumeric character “5”) might be a coordination class. This example, of course, does not contain scientific claims about how people actually see fiveness, and I beg the reader’s indulgence with some perhaps not very plausible grounding hypotheses. The point, however, is in the inferences from the hypotheses, not in the hypotheses themselves. Let us say that your coordination class is already adequate to recognize various 5s (say, in different fonts) in their usual orientation, illustrated in the first element in Figure 5. However, you might come across a shape like the second element in Figure 5, about which you may be uncertain. Can you see fiveness there, or not? It well may be that you need to develop your fiveness coordination class to have a greater span in order to encompass this context.

How might a greater span be accomplished? You might build a new readout strategy to independently see “an arc” (the top graphical component of the second element in Figure 5). Then, you might develop the ability to readout a “right angle,” which describes the bottom part of the element. Finally, you might add an integration to your causal net: “If you see an arc, and, you see a right-angled element, and the arc is connected to the: right-angled element, then you are looking at a five.” These extensions of your initial coordination class now have adequate span to see the fiveness in the second element in Figure 5. The tiny third element Figure 5 illustrates other aspects of this hypothetical coordination class. You initially see (say) a speck because the element is too tiny. But you may already recognize this kind of failure to get appropriate information: You employ another strategy of readout by getting closer to the element, or by fetching a magnifying glass. In this case, these strategies—which extend the causal net to span contexts that involve tiny visual elements—are things you learned in other circumstances. That is, the fiveness coordination class shares readout strategies with “seeing almost anything that might be tiny.” More generally, because coordination classes are complex, their development might enfold other substantial lines of conceptual development. The extrapolation of “seeing tiny things” to real coordination classes might also be very important. Students may frequently be

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uncertain whether they are looking at a force (or an acceleration, or any other technical category). How does one “look closely” to detect whether something is a force or not? This implicates probably a very important class of meta-knowledge. Among other things, it requires an understanding of what is essential to the category “force,” and what is not.

The element in Figure 6 illustrates a failure of alignment. Your coordination class knowledge sees an arc connected to a right angle and concludes that this is a five. However, it is not. It is a mirror-image five. In this circumstance, your coordination class strategies see something other than fiveness, which phenomenon we describe as a failure of alignment (a failure to read out the same information in different circumstances). Alignment can be restored by adding strategies that detect the difference between a true 5 and its mirror image. 3.2.4.

Process data concerning coordination classes

“Coordination class” is intended to be a theoretically well-elaborated candidate for a model of scientific concepts. In particular, we hypothesize that the properties of conceptual development of the physics concept of force are explainable as consequences of its being a coordination class. Force as a “concept” has many properties that suggest it is a good candidate for a coordination class. First, crude data about the difficulty of learning force suggest it may have many pieces and parts—that is, it might well be a system in the range of complexity of a coordination class. Furthermore, force has a huge range of applicability in physics. It seems very likely that students will need to coordinate many readout strategies and causal net inferences to properly see forces and their properties (strength and direction) in different circumstances, such as a ball tossed in the air, a spaceship moving in orbit about the earth, a book sitting on a table (where physicists “see” a force up on the book from the table), and so on. We expect to see typical learning problems in accomplishing appropriate span, integration, and alignment. Before presenting data, it is worth sketching some elements of a physicist’s coordination class for force. First, physicists know one really intuitive way to “see” forces. You can feel them. Physicists expect to be able to feel forces in most circumstances, and to roughly determine magnitude from its feel. This is a particularly interesting aspect of expert coordination: It is informal, and it involves

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sensation (rather than involving “formal” or “rational thought”). Generally, researchers equate learning physics with learning formal aspects of it. But, such a distinction has no obvious place in coordination class theory. Two other methods of coordinating force are important to mention. These are more “formal,” and relate directly to failures to coordinate properly that we will proceed to illustrate. First, physicists know the principle of “action and reaction”: that when a force is applied to any object, the object applying the force always feels on itself an equal force in the opposite direction. This provides a simple inference. Any time there is a force on one object, you know there is another force present, and you can infer its direction and magnitude, “equal and opposite.” Second, the equation allows one to infer strength, magnitude, and perforce, existence of a force in circumstances where you can read out mass (m) and acceleration (a). and “action and reaction” are elements in an expert’s causal net. In the example below, the subject uses a somewhat corrupted special case of that if there is motion (not necessarily acceleration) there is force. Besides the generic challenges of span, integration and alignment associated with achieving a proper coordination class, the notion of p-prim brings a number of expectations and predictions about the development of the concept of force. Most particularly, we know (I claim) that intuitive ideas about physics come mainly in the form of p-prims. Furthermore, p-prims evidently allow inferences that might be part of a causal net. For example, force as a mover implies that the direction of a force can be determined from the direction of motion. The amount of a force is in some measure determinable by Ohm’s p-prim: If the “effort” in question is a force, it must be greater in situations where there is a greater outcome. All in all, p-prims are excellent candidates for early elements in a learner’s causal net. For reasons I will not go into here, it is a good guess that difficulties in learning the proper coordination class “force” reside almost exclusively in the causal net, rather than in readout strategies. P-prims’ theoretical properties lend detail to expectations about learning force. At the broadest level, knowing that intuitive ideas in physics are rich and numerous, we expect a high degree of context sensitivity. Achieving alignment across a wide range of circumstances may be very difficult. More particularly, learners start with a lot of p-prims that are evoked in circumstances that have nothing much to do with learned physics. Thus, there are many opportunities for context dependence that is directly attributable to the context dependence of p-prims. To the extent that we have documented particular p-prims, we can predict or explain behaviors in coordinating force by the use of particular p-prims in circumstances where we know those p-prims are likely to apply. Below, we will, indeed, attribute particular learning difficulties in particular circumstances to the use of particular p-prims. In the following, we again turn to process data from the subject J. In general, we see a very high degree of context sensitivity that undermines a coherent (aligned) coordination class for force. More particularly, we will observe the following: 1. J does not expect to be able to directly feel a force. She does not use that expert coordinating strategy.

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While she is consciously aware that “action and reaction” is a good way to “see” forces (that is, she knows it is a good element of a proper causal net for force), she does not always use it. 3. J exhibits commitment to the general principle that motion implies the existence of a force. However, in a situation where a particular p-prim is salient and explains motion, she abandons that principle to employ the p-prim, denying the existence of force in that context. In the following segment, the interviewer tries to propose a problem to consider. If heavier things experience more gravitational force (which he assumes is obvious), then shouldn’t heavier objects fall faster? 2.

I: ... there are people who say that, well, it sure seems like the heavier one should go faster because it’s being pulled harder. I can feel that it’s being pulled harder. So what would you say to that? J: Well, first I’d say, “how can you tell it’s being pulled harder?” I: ... I guess I’d say, “well, you can feel it in your hand.” You’ve got a heavy thing that’s being pulled hard, you’ve got a light thing that’s // J: Well, um. Gravity’s uniform. So gravity won’t pull any harder on something that’s in the same place as it will on something else. … I: So you’re not feeling the force of gravity when you hold something? J: You’re feeling the weight of the object. I: The weight of the object. So that’s different from the force. J: Right.

J explicitly denies that one can feel gravitational force. Instead, she says you feel “weight.” She coordinates gravitational force here by an abstract principle: “Gravity is the same on all objects.” In this case, no p-prim is implicated in her failure to “see” force properly. Instead, we see that principles can serve as elements in the causal net, as well as p-prims. J evidenced articulate commitment to “action and reaction.” Below, the interviewer picks up on her apparent use of action and reaction to infer that a table is pushing up on a book placed on it from the fact that you know the book pushes down on the table. J implicates “action and reaction” by referring to the force of the table on the book as “equal and opposite.” She elaborates with other examples. I: And you say you know the desk is pushing up because if it weren’t, the book would just come down. J: Right. And it’s the same as like equal and opposite forces. I mean, this chair right now is pushing up on me and the chair is pushing up on you. And the ground is pushing up on your feet. And that’s something that’s hard to think about. [You are tempted to say:] “ No it’s not; I don’t feel it; I’m not moving anywhere.” But it is [pushing up].

A short time later, J explains this is something she learned that would not be evident to “the man in the street.” J: … now the chair is pushing on me as hard as I’m pushing down—130 pounds. This chair’s pushing up on me. I think that’s something that, once you’ve taken physics, that’s totally normal. But if you said it to someone off the street, I think they’d say, “What are you talking about?”

In the following selection, J and the interviewer are discussing pushing a book across a table. The interviewer provides an opportunity for J to use “action and

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reaction” to see another force, that of the book pushing back on the hand, and she follows suit. However, directly following he provides the same opportunity to use “action and reaction” to conclude that, since the table (via friction) is pushing backward on the book, the book must be pushing forward on the table. J declines this opportunity.

I: And now, I’m pushing on this book [Figure 7.]. What about the force that the book is exerting on my finger? J: Umm. It’s the same as the force you’re exerting on the book. I: Alright, what about the force of the book on the table as I’m pushing this thing along? There’s a downward force that the book is exerting on the table. Is there a sideways force? J: [Shakes head no] I: No. So friction is pushing on the book that way [against the motion]. The book is not pushing on the table either way. Alright.

The reason for this failure to use the same principle in almost the same context (a failure of alignment due to context sensitivity in the causal net) is not evident in the available process data here. However, in other parts of the set of interviews, J shows that she thinks friction is simply a different kind of force, and, perhaps, she therefore believes it is not susceptible to the use of “action and reaction.” See the description of “split concepts” in diSessa, Elby, & Hammer (in press). Below, the interviewer tries to make the reaction force of the table salient by invoking another principle. In many contexts J exhibited articulate, reflective and deep commitment to the principle that if there is motion, there is a force. (Again, see diSessa, Elby, & Hammer, in press.) The interviewer puts a paper under the book and shows that it moves when you push the book (hence implicating a force on it). J declines the use of her own principle here. In this case, it seems clear the failure in

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alignment is due to the salience of a particular p-prim, one I cited earlier: contact conveys motion. If contact is creating motion, then there is no need for a force. I: [continuing] But this paper [under the book] moves with the book, so I have to hold it in order to keep it stopped. So, suppose I said that I have to hold it because the book is exerting a force on the paper. J: I think it’s just sliding, and I think it’s just bringing the paper with it. I mean, it’s a really simple situation.… I would just say that it’s [the book is] sliding against the table and bringing the paper with it.

To sum up, we observe in this process data an expectable fragmentation in context dependencies. In two cases, explicit principles that function as causal net inferences are applied in some contexts, but not others. In one case, the reason for this context dependence seems clearly the salience of a particular p-prim in a particular context. Because contact can convey motion, the principle that motion requires a force doesn’t apply to this case. 4. A BRIEF REVIEW

In order to make the connection between my original critique of conceptual change research and what I have displayed concerning “conceptual ecology” more clear, I will undertake a brief review in terms of the program I set out for the chapter, following the critique. 1 .What more accountable theoretical terms might look like. Both p-prims and coordination classes are much more specific than dictionary definitions and typical invocations of, for example, “concepts” or “theories” in conceptual change research. We have discussed the nature of elements, their origins, what happens during development, the function of the knowledge types, typical patterns of use, and the level and kinds of systematicity between elements and across contexts. (More on the latter appears in the next section.) Table 1 reviews some of the main points. Because of the level of specificity, it is not even obvious any exemplars of these knowledge types exist! Empirical investigations are necessary to verify that any hypothetical p-prim or coordination class has the necessary properties. 2. What different exemplars of such terms are plausible and plausibly play an important part in conceptual change. Both p-prims and coordination classes are advanced here as plausible knowledge types that play distinct roles in conceptual change and account for different conceptual change phenomena. P-prims, for example, account for intuitive predictions and judgments of plausibility. Coordination classes provide a specific model of a type of full-blown concept, which entails a lot about the difficult and easy parts of conceptual change.

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3. How different from each other knowledge types might be, and how different types can account for different aspects of reasoning and conceptual change. Following our discussion, summarized in Table 1, p-prims and coordination classes contrast in many ways with each other. Theoretically, there is no way to mistake one for the other. Empirically, of course, any instance of a student’s reasoning may

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require careful scrutiny to determine whether a p-prim or part of a coordination class is involved. More broadly, I fully expect that we will need many other knowledge types to fully explain the transition from naïve student to conceptually-competent physicist. 4. What sort of details of subjects’ behavior can be accounted for with sharpened theoretical terms. For example, what are typical easy and difficult accomplishments along the path to conceptual competence? Starting from the last question, establishing appropriate span and alignment is difficult, and we should expect continued examples of failures of this sort in the trajectory toward competence. Not only did we document failures of these types in a subject’s process data, we even showed how a specific failure of a specific attribute of a mature coordination class (alignment) was due to the invocation of a particular previously-documented p-prim. That p-prim (contact conveys motion) “explained” a situation (a paper moving under a pushed book) and thus aborted the use of an articulate principle (for this subject), that motion requires the existence of a force. P-prims explain many wrong expectations—and many correct ones—that students have about how the world works. They also explain phenomena like data fluidity and the general richness and detail found in intuitive thought. P-prims explain the emergence of particular macro-constructions (e.g., McCloskey’s “impetus theory”) as a confluence of a number of p-prims in a relatively stable configuration for a particular class of contexts. How do p-prims and coordination classes relate to “theories” or “mental models,” and so on? In general this is not a particularly good game to play precisely because of the elements of our earlier critique; most advocates of these terms say precious little about what they actually entail. Nonetheless, I can make some comments that may be at least heuristically useful. P-prims are obviously subconceptual, sub-theoretical, or sub-model-like. They are too small to constitute any of these macro-conceptual structures, and the most plausible developmental path between naïve p-prims and any of these structures is “incorporation as a limited part” of an emergent complex knowledge system. Coordination classes, we have argued, are an appropriate refinement of the idea of “concept.” Theories are likely to be even larger conceptual structures, encompassing several related concepts (coordination classes). For example, force, mass, and acceleration may each constitute coordination classes, and “Newton’s theory” might be abbreviated in a particular relation among these coordination classes, Such a relation provides opportunities for coordination across coordination classes—for example, if you can “see” mass and acceleration, you can also “see” force. Developmentally, therefore, there are likely to be important mutual influences in coordination classes that participate in the same theory. For my own part, I would require “theories” to entail an explicit, articulable component (like ), which requirement I did not introduce into the definition of coordination classes, (although I did not rule it out). I believe language introduces important properties that may not hold in dominantly inarticulate knowledge systems. I expect even less consensus on what a mental model is. To my mind, mental models should (1) involve a strong, well-developed “substrate” knowledge system,

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such as spatial reasoning, (2) allow explicit hypothetical reasoning, and (3) involve only a small, well-defined class of causal inferences (diSessa, 1996). It is possible, for example, that a limited set of p-prims (e.g., perhaps “contact conveys motion”) together with reasoning about spatial configurations (of, for example, gears) could constitute a mental model. However, other principles might define the causality in a mental model, aside from p-prims. Furthermore, the involvement of p-prims wouldn’t necessarily entail the ability to support explicit hypothetical reasoning. In fact, the involvement of p-prims might even make this less likely. I see no obvious generalities about the involvement of mental models in coordination classes, or the reverse, although I also see no principle that would rule those relations out. I know of no even remotely specific process definition of ontology in the literature. However, I believe the idea of coordination class is, in fact, a technically sufficient refinement of the general idea of ontology. This may be a contentious claim. I don’t propose to defend it here, aside from noting that a coordination class may define the ability to know about a particular class of entity in the world—for example, the ability to “see” forces. If it turns out to be sensible to consider coordination classes ontological, most invocations of ontology to explain difficulties in conceptual change pale. The reason is that invocations of ontology merely assume that ontologies are difficult to learn, and also never explain exactly how it is possible to learn one. In contrast, the articulated definition of coordination class shows what is entailed in developing one and provides a list of focal difficulties. In certain cases we can name both the general class and the precise circumstances of conceptual difficulty, such as such when a context-specific p-prim “short-circuits” alignment. 5.

COHERENCE AND CONSISTENCY

Issues of coherence and consistency in reasoning (“systematicity,” speaking inclusively) become salient as one approaches a complex systems view of conceptual change.11 For example, if a concept is, in fact, a complex system, there is likely no point in the learning trajectory where we can unequivocally decide a person “has” the concept. It may always be a matter of degree and context. With large numbers of elements and a heightened accountability concerning contextuality, it is easy to parody a complex systems view as assuming total fragmentation and inconsistency in the conceptual behavior of naïve or novice students. This is far from a sensible view. Rather, conventional assumptions about conceptual change, which I am critiquing in this chapter, are as vague and presumptuous about consistency as they are concerning the mental entities involved in conceptual change. A complex systems view may look necessarily fragmented, but that is only true because it recognizes existing complexity and takes on more accountability for details.

11

The issue of coherence, systematicity, or lack thereof, is an important, unsettled issue in studies of cognition. See, for example, discussion and empirical studies in Rogers, Rutherford, and Bibby (1992).

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5.1. Entailed Elements of Systematicity

Let me begin by sketching elements of consistency that are necessarily entailed by the view of conceptual change described in this chapter. First, although I presume there are a large number of p-prims, the existence of a p-prim actually constitutes, in itself, an important consistency in thinking. A p-prim is precisely a regularity in responding to situations in the world. Without a degree of consistency, identifying particular mental entities, particular p-prims, would make no sense. Indeed, this consistency is an explicit methodological commitment in my own work to identify p-prims. It is embodied in a fundamental idea I call “the principle of invariance.” Roughly, if one has gotten the description of a p-prim correct, the p-prim should be invoked in every situation in which the description applies. Failure in invocation is a failure to describe the p-prim or its contextual specifics adequately. See the methodology section of diSessa (1993). The mere fact that some p-prims are much more important and generally applied than others lends another kind of systematicity to intuitive thought. Sketching an important, widely applicable p-prim catches an important tendency in intuitive thought. Another necessary element of consistency involves coordination classes. If coordination class adequately describes any scientific concept, then, to the extent that anyone learns that concept, they have achieved (a remarkable) consistency and coherence in their knowledge state—surpassing difficulties of span, integration and alignment. Obviously, I can’t sensibly take the position that no one ever learns any scientific concepts. The fact that I list and demonstrate failures to achieve this consistency in several modes (e.g., failures in alignment) merely shows steps along the way to consistency and also the degree of consistency actually achieved when one learns a scientific concept. 5.2.

Allowed Elements of Systematicity

Beyond necessary systematicity, the view of conceptual change presented in this chapter allows other sorts of systematicity. In particular, although space here did not allow it, I have charted in other places several kinds of systematicity in intuitive physics (see diSessa, 1993, for details). First, although elements are not tightly integrated, there are a number of loose relations. I described J’s description of a toss as a (relatively stable) composition of a number of p-prims. In addition, p-prim compositions may generate new p-prims as “phenomenological syllogisms.” If one knows that heavier things move slower and that bigger things tend to be heavier, it is likely one will also expect bigger things to move slower. Along similar lines, I have described a kind of systematicity that appears because of common attributes involved in many p-prims. For example, agency is important in many situations, and conflict is another fundamental attribute involved in many p-prims. Finally, a family of p-prims may engender a common abstraction—a kind of meta-p-prim—which means that a substantial range of situation may be covered, in some degree, by the same (meta) p-prim.

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I mentioned previously in this chapter that coordination classes may or may not exist in naïve, intuitive thought. My guess is that some do. Piagetian object permanence may be part of a coordination class involving reading out information about physical location from the world. This conjecture is elaborated in diSessa & Sherin (1998). If naïve coordination classes exist, then all of the systematicity implied in my description of coordination classes has been achieved in physicsnaïve individuals, with respect to certain ideas. The principal reason to keep the existence of naïve coordination classes hypothetical is that, given the degree of specificity in the concept of coordination class, detailed empirical support would be necessary to establish their existence. I find this far preferable to assuming characteristics of naïve thought in describing its contents as naïve concepts (or theories, etc.), to the extent that one is making any claim at all in making such statements. 5.3.

An Issue of Epistemology

An illusion of fragmentation occurs because we tend to view intuitive ideas normatively (as I have, mainly, here). That is, we measure intuitive ideas against a particular standard, say, the Newtonian concept of force. This essentially guarantees a fragmented view, as we must identify all the pieces and the ways they must be coordinated in order to achieve the Newtonian concept. Scientific concepts, however, differentiate as well as integrate contexts. Galileo made a huge advance in science by concerning himself only with spatial change (motion), in contrast with Aristotle’s physics, which attempted a uniform treatment of all change, including, for example, biological growth and decay. Naïve p-prims of wide scope clearly exist. I’ve argued, for example, that many p-prims apply to both physical and psychological/sociological situations (diSessa, 2000). As such, they clearly extend beyond the boundaries of Newtonian concepts, which are, thus, comparatively fragmented. Making an absolute comparison between the scope of intuitive ideas and scientific ones is very difficult, even disregarding the fact that there are many kinds of ideas on both sides of the transition to scientific expertise. Naïve thinking and expert thinking draw contextual boundaries differently. Hence, we are guaranteed to find, in some instances, naïve ideas are fragmented compared to scientific ones, and, in other instances, scientific ideas are fragmented compared to intuitive ones.12

12

There are difficult analytical issues I am suppressing here. How does one develop a metric to be able to measure objectively the “range of circumstances” in which an idea applies? I believe it is likely that a metric can be established only relatively, that is, noting whether a concept crosses boundaries established with respect to another way of thinking. Once again, we may wind up being able to say only that one way of thinking distinguishes contexts that are treated uniformly in another way of thinking, and viceversa.

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Intention in Systematicity

Other issues concerning consistency and coherence are simply not touched, one way or another, in the account of naïve and expert thinking given here. For example, how much do students strive for coherence? These are meta-conceptual issues—issues of students’ ways of conceiving of their own knowledge, issues of strategies for dealing with it, and so on. I accept the common sense that students (sometimes) strive for consistency. However, I note that this is a highly knowledge intensive activity. Clearly the world is diverse enough that insisting one must think in the same way about all situations is a foolhardy and doomed-to-failure approach. So, one has to make judgments about when it is necessary or plausible to think in the same way. More generally, it is foolish to seek more consistency than the world allows. The physical world, clearly, is quite diverse. If one takes a scientific standard, one needs to learn linear Newtonian mechanics, rotational dynamics, fluid mechanics, electricity and magnetism, optics, possibly quantum mechanics, and so on, in order to understand even everyday phenomena (bouncing balls, wobble in a spinning football, static electricity, a magnifying glass, the strength of different materials). It won’t do to attempt consistency by thinking about all the implied situations in the same way. Deciding when one can and should think in the same way involves subtle judgments. For example, even within Newtonian mechanics, one can describe a toss from the viewpoint of forces, or in terms of energy. The two viewpoints produce different sketches of the same situation. Clearly, one shouldn’t conclude that one is being inconsistent in making these two different kinds of descriptions of the same situation. In some situations the very possibility of striving for consistency is problematic. One may in principle want to be more consistent, but how can one actually make progress? How could one, for example, consider the issue of consistency with respect to p-prims? How could one consider whether dynamic balance should be applied in some circumstances where a different balancing p-prim seems to apply? Without some way of describing the knowledge that is applying—for example, a verbal expression—one can’t even phrase the question of a more integrated view. The correct way of resolving the issue of intentionality in consistency is, I believe, another version of the program described here as applied here to contentlevel knowledge, except applied to meta-conceptualization and epistemology. We need to describe the knowledge that people have about knowledge relevant to consistency and their strategies for dealing with it. Issues of “degree” of search for consistency are very likely at least as complicated as those concerning the relative fragmentation of content-level knowledge.13 13

This precise task is taken on, in a rough and ready form, in diSessa, Elby, and Hammer (in press). We show that the subject whose thinking is displayed here, J, has a very interesting meta-conceptual profile that influences how much fragmentation or consistency she feels is possible. In broad strokes, she feels that the scope of scientific ideas, like is generally smaller than is true. She also simply does not judge that she is being inconsistent if she says there is both one and two forces acting in a situation.

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Finally, there is one more open dimension of possible systematicity that I have simply had no space to touch upon in this chapter. As I mentioned, p-prims and coordination classes are only two exemplars of knowledge types that I feel are necessary to distinguish in thinking about conceptual change. Were we to delve into others, the issue of consistency and coherence becomes yet more complicated (and my position less specified by what has been said in this chapter). 6.

SUMMARY

In this chapter, I have argued that the mainstream in the study of conceptual change is flawed in several respects. Overall, I feel the theoretical accountability of the research community is far from adequate. Instead, researchers use commonsense or dictionary terms, or terms imported from other disciplines, that are much too vague or implicitly defined to allow good progress. Adequate theoretical terms may be developed and validated in many ways, but, first, must come a commitment to clarity and cogency. “Concept,” “belief,” “theory,” and “ontology” have all been used to describe the elements of mind involved in conceptual change. Yet none are elaborated to the point that we know exactly what we are talking about, and to the point that we can even in principle empirically determine whether one or another of these is more adequate than others (or whether they are all necessary) to describe difficulties and accomplishments in conceptual change. Theoretical vagueness and imprecision trickle down and reinforce a tendency to use data impressionistically or merely statistically, without putting strong hypotheses about what is involved in conceptual change to strong tests. I advocate moving from before/after studies, and studies that use only constructs (like coding categories) distanced from cogent theoretical terms, to the use of process data to test and illustrate theoretical commitments about concepts, or other theoretical elements of mind, in use and in change. The greatest casualty of weak theoretical and empirical accountability is a widespread and dramatic over-simplification of the complexity, diversity and nuance in conceptual change data. This complexity is less evident in conceptual change research than in common sense about types of concepts and in expert teachers’ detailed reactions and judgments concerning students’ partial states of development in the process of conceptual change. Clinical data is rich in possibilities for more detailed accountability, if it is used for that purpose. I have argued that, in order to recognize and deal with the diversity and complexity involved in conceptual change, we need to move simultaneously in several directions: With respect to types of knowledge, we need to move toward multiplicity. With respect to “size” and number of elements of mind, we need to move toward smaller grain size and greater numbers. Concomitantly with this move to smaller grain size, we need to deal much more effectively with evident contextual dependence in the way students think. With respect to details in describing both change, and even what constitutes a concept, we need to move toward a systems view that describes scientific concepts as complex, finely configured systems involving named parts and relations.

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To make the case that such progress is possible (and to point out directions I feel will be most fruitful), I have tried to illustrate what more theoretically accountable replacements for “concepts,” or “theories” might look like. I defined and illustrated the idea of p-prims, which are numerous, small, recognition-driven elements that define significant properties of naïve physics knowledge, and which become involved in learning scientific concepts. P-prims exhibit a detailed contextuality and sometimes cause unstable, data-driven conceptualization. I also defined and illustrated coordination classes, which are complex systems that consist of many parts (of types I delineated), in particular ways (that I named and classified). Coordination classes are a proposed model for a particular class of scientific concepts. Finally, I tried to show how an improved theoretical view may be held accountable to details in process data. I showed hypothesized behaviors of p-primdriven cognition, such as data-driven instability. I argued that we can see in process data that intuitive “theories” or other large-scale constructs may actually be composed of p-prims. I also showed classes of learning difficulties predicted by coordination class theory in examples of student thinking. I showed a great deal of context dependence in the ways that students read out and infer information about forces. I showed that p-prims (and other kinds of ideas, like articulate principles) play specific roles in mistakes students make in learning to “see” forces. ACKNOWLEDGMENTS Much of the work reported in this chapter was sponsored at various times by the Spencer Foundation. Its help is gratefully acknowledged. The chapter also benefited from comments by David Kaufman, Joe Wagner, and the editors of this volume.

REFERENCES Clement, J. (1983). A conceptual model discussed by Galileo and used intuitively by physics students. In D. Gentner & A. Stevens (Eds.), Mental models (pp. 325-340). Mahwah, NJ: Lawrence Erlbaum Associates. diSessa, A. A. (1983). Phenomenology and the evolution of intuition. In D. Gentner and A. Stevens (Eds.), Mental models (pp. 15-33). Mahwah, NJ: Lawrence Erlbaum. diSessa, A. A. (1988). Knowledge in pieces. In G. Forman and P. Pufall (Eds.), Constructivism in the computer age (pp. 49-70). Mahwah, NJ: Lawrence Erlbaum Associates. diSessa, A. A. (1993). Toward an epistemology of physics. Cognition and Instruction, 10, 105-225. diSessa, A. A. (1994). Speculations on the foundations of knowledge and intelligence. In D. Tirosh (Ed.), Implicit and explicit knowledge: An educational approach (pp. 1-54). Norwood, NJ: Ablex. diSessa, A. A. (1996). What do “just plain folk” know about physics? In D. R. Olson and N. Torrance (Eds.), The handbook of education and human development: New models of learning, teaching, and schooling (pp. 709-730). Oxford, UK: Blackwell Publishers, Ltd. diSessa, A. A. (2000). Does the mind know the difference between the physical and social worlds? In L. Nucci, G. Saxe, and E. Turiel (Eds.), Culture, development and knowledge. Mahwah, NJ: Lawrence Erlbaum Associates. diSessa, A. A. (to be submitted). An interactional analysis of clinical interviewing. diSessa, Elby, & Hammer (in press). J’s epistemological stance and strategies. In G. Sinatra and P. Pintrich (Eds.), Intentional conceptual change. Mahwah, NJ: Lawrence Erlbaum Associates. diSessa, A. A., & Sherin, B. (1998). What changes in conceptual change? International Journal of Science Education, 20, 1155-1191.

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Gopnik, A., & Meltzoff, A. N., (1996). Words, thoughts, and theories: Learning, development, and conceptual change. Cambridge, MA: MIT Press. Harris, P. L. (1994). Thinking by children and scientists: False analogies and neglected similarities. In L. Hirschfeld & S. Gelman (Eds.), Mapping the mind: Domain specificity in cognition and culture (pp. 294-315). Cambridge, UK; NY: Cambridge University Press. Hofer, B. K., & Pintrich, P. R. (in press). Personal epistemology: The psychology of beliefs about knowledge and knowing. Mahwah, NJ: Lawrence Erlbaum Associates. Kuhn, T. (1970). The structure of scientific revolutions. Second edition. Chicago: University of Chicago Press. McCloskey, M. (1983). Naïve theories of motion. In D. Gentner & A. Stevens (Eds.), Mental models (pp. 299-324). Mahwah, NJ: Lawrence Erlbaum Associates. Piaget, J. (1969). The child’s conception of time. (A. J. Pomerans, Trans.). New York: Ballantine Books. Rogers, Y., Rutherford, A., & Bibby, P. A. (1992). Models in the mind: Theory, perspective and applications. NY: Academic Press. Rosch, E. (1994). Categorization. In V. S. Ramachandran (Ed.), Encyclopedia of human behavior (Vol. 1, pp. 513-523). San Diego: Academic Press. Schoenfeld, A., Smith, J., & Arcavi, A. (1993). Learning: The microgenetic analysis of one student’s understanding of a complex subject matter domain. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 4, pp. 55-175). Mahwah, NJ: Lawrence Erlbaum Associates. Strike, K. A., & Posner, G. J. (1992). A revisionist theory of conceptual change. In R. A. Duschl, & R. J. Hamilton (Eds.), Philosophy of science, cognitive psychology, and educational theory and practice. Albany, NY: SUNY Press. Thagard, P. (1992). Conceptual revolutions. Princeton, NJ: Princeton University Press. Vosniadou, S. & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24, 535-585. Vosniadou, S., & Ortony, A. (1989). Similarity and analogical reasoning. Cambridge, UK; NY: Cambridge University Press.

ON THE NATURE OF NAÏVE PHYSICS

STELLA VOSNIADOU National and Kapodistrian University of Athens, Greece

Abstract The argument will be advanced in this paper that naive physics is neither a collection of unstructured knowledge elements nor a collection of stable misconceptions that need to be replaced, but rather a complex conceptual system that organises children’s perceptual experiences and information they receive from the culture into coherent explanatory frameworks that make it possible for them to function in the physical world. The process of learning science appears to be a slow and gradual one during which aspects of the scientific information are added on to the initial explanatory framework destroying its coherence until (and if) it is restructured in ways to make it consistent with currently accepted scientific views.

1.

INTRODUCTION

Researchers in science education and cognitive science seem to agree that naive physics exerts a great deal of influence on the way new information is understood and science concepts are acquired, but disagree on how to characterize the exact nature of naïve physics. What kinds of knowledge elements naive physics consists of, how is it organized, and how does it develop? This disagreement has important implications for the teaching of science. Are there persistent misconceptions that represent relatively stable and internally consistent beliefs that interfere with the teaching of science, or is it the case that naïve physics consists of a multiplicity of knowledge pieces that are mainly unstructured and unsystematic? And, is the process of knowledge acquisition in science a process that increases the systematicity of initially fragmented pieces of knowledge or a process of replacing stable and resistant misconceptions with currently accepted scientific theories? In this paper we will try to outline a different theoretical framework within which this debate can be reframed. We will argue that children start the knowledge acquisition process by organizing the multiplicity of their sensory experiences under the influence of everyday culture and language into narrow but coherent explanatory frameworks that are different from the currently accepted science. Naïve physics thus does not consist of a collection of unstructured knowledge elements or of stable misconceptions but constitutes a complex system that includes perceptual information, beliefs, presuppositions, and mental representations. This knowledge M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 61-76. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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system represents children’s attempts to organize their perceptual experiences and information they receive from the culture into coherent explanatory frameworks. The process of learning science appears to be a slow and gradual one during which elements of the scientific theory become assimilated to the initial explanatory framework destroying its coherence and creating synthetic models. This is the case because currently accepted scientific explanations and concepts have evolved over thousands of years of scientific discovery to become rather elaborate, counterintuitive theories that differ in their structure and in the phenomena they explain from initial explanations of the physical world based on everyday experience. In the pages that follow we will describe the misconceptions and knowledge in pieces positions in greater detail. We will continue by discussing the theoretical framework we have developed. An empirical study investigating the development of the meaning of the term force 1 will be presented to provide an example of conceptual change as we see it. We will argue that the results of this study add further evidence to those earlier conducted in our lab (Vosniadou, 1994; Vosniadou and Brewer, 1992, 1994) in showing that from an early age children organize their physical experiences in narrow but coherent explanatory frameworks. During development, we observe neither a sudden change from an impetus misconception to Newtonian physics nor the gradual development of more coherent and systematic networks of knowledge. Rather, information received through instruction seems to become assimilated to the initial explanatory framework creating synthetic or internally inconsistent models.

2.

THE “MISCONCEPTIONS” VERSUS “KNOWLEDGE IN PIECES” POSITIONS IN SCIENCE EDUCATION

The proposal that the learning of science involves the replacement of persistent misconceptions has its roots in the work of science educators like Novak (1977), Driver and Easley (1978), Viennot (1979) and McCloskey (1983a, 1983b). They were among the first to pay attention to the fact that students bring to the science learning task alternative frameworks, preconceptions, or misconceptions that are robust and difficult to extinguish through teaching. Misconceptions are defined as student conceptions that produce systematic patterns of error. Misconceptions can be the result of instruction or they may originate prior to instruction. Posner, Strike, Hewson and Gertzog (1982) drew an analogy between Piaget’s concepts of assimilation and accommodation and the concepts of “normal science” and “scientific revolution” offered by philosophers of science such as Kuhn (1970) and derived from this analogy an instructional theory to promote “accommodation” in students’ learning of science. The work of Posner et al. (1982) became the leading paradigm that guided research and practice in science education for many years.

1 This study is based on a dissertation submitted by Christos Ioannides and is reported in detail in C. Ioannides and S. Vosniadou, Exploring the Changing Meanings of Force, Cognitive Science Quarterly (in press).

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Smith, diSessa, & Rochelle (1993) have criticized the misconceptions position on the grounds that it presents a narrow view of learning that focuses only on the mistaken qualities of students’ prior knowledge and ignores their productive ideas that can become the basis for achieving a more sophisticated mathematical or scientific understanding. Smith et al (1993) argue that misconceptions should be reconceived as faulty extensions of productive knowledge, that misconceptions are not always resistant to change, and that instruction that “confronts misconceptions with a view to replacing them is misguided and unlikely to succeed” (p. 153). Other research has shown that it is very difficult to identify internally consistent misconceptions in mechanics and kinematics in high school or college students who had little exposure to formal physics (e.g. Ranney, 1994) diSessa (1988; 1993) has put forward a different proposal for conceptualizing the development of physical knowledge. He argues that the knowledge system of novices consists of an unstructured collection of many simple elements known as phenomenological primitives (p-prims for short) that originate from superficial interpretations of physical reality. P-prims appear to be organized in a conceptual network and to be activated through a mechanism of recognition that depends on the connections that p-prims have to the other elements of the system. According to this position, the process of learning science is one of collecting and systematizing the pieces of knowledge into larger wholes. This happens as p-prims change their function from relatively isolated, self-explanatory entities to become pieces of a larger system of complex knowledge structures such as physics laws. In the knowledge system of the expert, p-prims “can no longer be self-explanatory, but must refer to much more complex knowledge structures, physics laws, etc. for justification (diSessa, 1993, p. 114). We appreciate the efforts of diSessa (1993) and Smith et al (1993) to provide an account of the knowledge acquisition process that captures the continuity one expects with development and has the possibility of locating knowledge elements in novices’ prior knowledge that can be used to build more complex knowledge systems. We also agree that we need to move from single units of knowledge to systems of knowledge that consist of complex substructures that may change gradually indifferent ways. Finally, we agree with Smith et al’s (1993) urge to researchers to “move beyond the identification of misconceptions” towards research that focuses on the evolution of expert understandings and particularly on “detailed descriptions of the evolution of knowledge systems over much longer durations than has been typical of recent detailed studies (p. 154). In the last few years we have been involved in a program of research that attempts to provide detailed descriptions of the development of knowledge in specific subject-matter areas mainly of the physical sciences, such as astronomy (Vosniadou and Brewer, 1992; 1994; Vosniadou 1994; 1998), mechanics (Ioannides and Vosniadou, in press; Megalakaki, Ioannides, & Vosniadou, & Tiberghien, 1997), geophysics (Ioannidou & Vosniadou, in press) chemistry (Kouka, Vosniadou & Tsaparlis, in press), and biology (Kyrkos & Vosniadou, 1997). The above-mentioned studies are all cross-sectional developmental studies investigating the knowledge acquisition process in subjects ranging from 5 to 20 years of age. We have also used the results of our research to develop curricula and

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instruction that has been tried in schools in Greece (see Vosniadou et al., in press). The results of these studies show that young children answer questions about force, matter, heat, the day/night cycle, etc. in a relatively consistent way revealing the existence of narrow but coherent explanatory frameworks. These explanatory frameworks are usually different in their structure, in the phenomena they explain, and in their individual concepts from the scientific theories to which children are exposed through instruction. The position we have been developing is similar in many respects to the views developed by Carey (1985), according to which even very young children form “theories” that embody causal notions, allow distinct types of explanations and predictions, reflect basic ontological commitments, and are subject to modification and radical revision. In our work (Vosniadou, 1994; 2000), we have used the term “framework theory” to refer to the conceptual system that young children form to interpret their observations about the physical world, as well as their interpretations of the information provided by the culture. The term “theory” is used relatively freely to denote an explanatory system with some coherence. Unlike Gopnik (1996) it is assumed that this system differs in many respects from a scientific theory. It lacks the systematicity of a scientific theory as well as other characteristics of scientific theories such as their abstractness, and social/institutional nature. It is also assumed that children differ from scientists in important ways, for example in the strategies they use to evaluate evidence (e.g., Kuhn, Amsel, & O’Loughlin, 1988), or in that they lack metaconceptual awareness of their naive theories, and therefore do not seek to verify or falsify them. While this kind of developmental research has so far concentrated on very young children, the research we have pursued investigates older children and young adults as well, in an effort to find out what happens after they are exposed to systematic science instruction in school settings. Our results show that in the process of learning science, children add or delete beliefs and presuppositions to their explanatory frameworks destroying their coherence, while at the same time distorting the scientific concepts to which they are exposed. More specifically, we assume that in physics children’s initial explanatory framework (their “framework theory”) consists of certain basic ontological and epistemological presuppositions about the nature of physical objects and the way they function in the physical world. Some of the ontological presuppositions are that physical objects are solid and stable, that space is organized in terms of the directions of up and down and that unsupported objects fall in a downward direction. Children also seem hold certain epistemological presuppositions, such as that rest is the natural state of inanimate objects and motion needs to be explained, and that entities such as force, heat and weight are properties of physical objects. Children’s continuing observations and the information they receive from the culture are interpreted under the constraints of presuppositions such as the above to create specific explanations of phenomena. For example, as shown in Figure 1, there can be various specific explanations of the day/night cycle such as that the sun goes behind the mountains, or that the sun goes down to the other side of the earth. These specific explanations are embedded within the above-mentioned explanatory framework because the earth is considered to be a physical object (as opposed to an

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astronomical object), and thus to be constrained by all the presuppositions that apply to physical objects in general. In other words, children assume that on the earth space is organized in terms of the directions of up and down and gravity works in an up/down direction. These presuppositions can stand in the way of children’s understanding of the spherical shape of the earth and of the earth’s axis rotation, which in turn are necessary for understanding the scientific explanation of the day/night cycle. It could be argued here that our attempts to explain conceptual change are similar to the explanations proposed by Chi and her colleagues (Chi, 1992; Reinner et al., 2000). Chi argues that misconceptions arise when a person associates the wrong ontology with a scientific concept, such as force or heat. She notes that many concepts in physics are wrongly associated with a substance ontology when in fact they belong to a process (or acausal) ontology. Chi seems to believe that conceptual change is a radical process that happens in a short period of time. There are, however, important differences between our position and the one put forward by Chi and her colleagues. Unlike Chi, Vosniadou (1994) argues that conceptual change does not happen suddenly but is a gradual and time consuming process. This is the case because we are dealing with a complex knowledge system that consists of a network of beliefs or presuppositions that take a long time to change. We agree with Chi and her colleagues that conceptual confusions often arise in science learning from the assignment of scientifically incorrect ontological presuppositions to concepts such as force, heat, the earth, etc. However, ontological change is only one of the many kinds of changes that need to take place in the process of changing theories. Furthermore, we believe that Chi's theoretical framework does not provide an adequate account of the nature of ontological categories and their development. There is no theory about where ontological categories come from, how they develop, how new ontological categories are formed and why, etc. In our theoretical framework we try to account for how children slowly construct the explanatory framework within which their observations about the physical world are interpreted (see also Vosniadou, 1994; 1998). Information from infancy studies substantiates our claims that children start from very young to organize their perceptual experiences in conceptual structures, such as the concept of the physical object (e.g., Spelke, 1991). Ontological and epistemological presuppositions are attached to these conceptual structures. Perceptual information, as well as beliefs, and mental representations also constrain the knowledge acquisition process. Our position is not inconsistent with the view that something like diSessa’s pprims constitute an element of the knowledge system of novices and experts. We believe that p-prims can be interpreted to refer to the multiplicity of perceptual and sensory experiences that are obtained through our observations of physical objects and our interactions with them. In the conceptual system we propose, diSessa’s pprims would take the place of the perceptual information obtained through observation. These perceptual experiences provide the basis for forming beliefs, presuppositions, and mental models. The proposal that the conceptual system consists of different kinds of knowledge elements (such as beliefs, presuppositions and mental models) is also consistent with diSessa’s proposal that we need to focus

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not on single conceptions but on rich knowledge systems that are composed of many constituent elements. The main difference between the present proposal and that of diSessa is in our views of development. It appears that diSessa believes that p-prims are basically unstructured or loosely organized in the conceptual system of the novice. It is through instruction and exposure to the scientific theory that p-prims lose their selfexplanatory status and become organized in larger theoretical structures such as physical laws. According to diSessa this change in the function of p-prims is a major change from “intuitive to expert physics”.

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In our view, to the extend that knowledge elements such as p-prims could be postulated to operate in our conceptual system, they become organized in knowledge structures much earlier on than diSessa believes. If this is so, the process of learning science is not one of simply organizing the unstructured p-prims into physics laws but rather one during which they become re-organised into a scientific theory. This is a slow, gradual process, precisely because we are dealing with many knowledge elements. One could argue that our position is really not very different from the traditional misconceptions position criticised by Smith et al (1993). But this is not the case. Our position meets all the criticisms of Smith et al (1993). First, we are not describing unitary, faulty conceptions but a knowledge system consisting of many different elements organized in complex ways. Second, we make a distinction between initial explanations prior to instruction and those that result after instruction and which we call synthetic models. Synthetic models are not stable but dynamic and constantly changing as children’s developing knowledge systems evolve. Finally, our theoretical position is a constructivist one. It can explain how new information is built on existing knowledge structures and provides a comprehensive framework within which meaningful and detailed predictions can be made about the knowledge acquisition process. In the pages that follow we will report the results of a study that investigated the development of the meaning of the term force. 3.

THE DEVELOPMENT OF THE MEANING OF FORCE

If the arguments made earlier are correct, then the development of the meaning of force2 should start with a small number of relatively coherent interpretations of force revealing aspects of the explanatory framework within which the meaning of force is embedded. In the process of learning science these initial meanings should change as aspects of the scientific theory are assimilated into the framework theory creating synthetic meanings (or misconceptions). This prediction is very different from what the knowledge in pieces hypothesis would predict. If naive physics is fragmented then we should see increasing systematicity and coherence in the development of the meanings of force after instruction. Before continuing, it should be mentioned here that the study was conducted in the Greek language and that in Greek there is only one word – dynamis – that is used as an equivalent for the two English words force and strength.

2

We refer to the “meaning of force” rather than the “concept of force” because the present study investigated students’ interpretations of the term force. There are different psychological theories regarding the meaning of words (semantic feature or network theories, image theories, etc). We have adopted the position that the meaning of a term such as force can be best thought of as a “theory” consisting of an interconnected set of beliefs and presuppositions. The Meaning of the term force may be only part of the concept of force.

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ON THE NATURE OF NAÏVE PHYSICS

The participants of this study were all Greek students ranging in age from 4 to 16 years. In individual interviews they were asked to answer verbally a 27 items questionnaire developed after extensive pilot work. The questionnaire is shown in

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Table 1. Simple questions inquired about the existence of forces on simple objects in various kinetic states (stationary or moving). The comparison questions asked children to compare forces applied in situations that differed in some critical respect (i.e., in the size of objects being compared, the size of the people pushing the objects, etc.). Questions about force were phrased either using the scientific form “Is there a force exerted on the x? Why?” (group I) or the colloquial form “Is there a force on the x? Why?” (group II)3. Analysis of the data revealed no statistically significant differences between these two groups and therefore the data were collapsed into one set. All results mentioned in this paper are made on the basis of the combined data from both group I and group II. Based on previous work in this area, it was hypothesized that force would be interpreted as a property of physical objects and that it may be related to an object’s weight and size (Piaget, 1972). Much of recent science education research has shown that the currently accepted Newtonian framework for force is very difficult to be acquired and that there is a persistent misconception according to which force is related to the movement of inanimate objects (e.g., Nersessian & Resnick, 1989, Osborne & Freyberg, 1985, Clement, 1996, Ministrel, 1982). Based on this prior work, it was hypothesized that the students in the present study would also find it difficult to understand the currently accepted scientific interpretation of force. More specifically was hypothesized that force would be related to movement, and that various other synthetic meanings of force (or combinations of meanings) may be created. Vosniadou and Brewer (1992, 1994) have argued that when children are exposed to science instruction, they assimilate aspects of this instruction that are inconsistent with prior knowledge to their existing mental representations, forming synthetic meanings. It was therefore expected that as children would start receiving systematic instruction on the Newtonian theory, they would construct synthetic meanings of force, although we were not exactly clear about the exact form these meanings would take. Children’s responses to the questions were scored twice: first for the questions comprising each of the five sets of questions (question set level, QSL) and second for all the questions combined (overall level, OL). At the first level, students’ responses to each set of questions were scored as a group, on the basis of a scoring key containing a set of categories for each set of questions. Following the scoring at the set of questions level, we tried to see if we could find evidence in the data for the consistent use of a small number of explanatory structures or meanings of force by the individual subjects in our sample. The scoring at this, overall level, was done on the basis of a second scoring key which outlined the pattern of expected responses for each meaning. Agreement between two independent judges who used the scoring key to score all the responses was high (between 90% and 95%). All disagreements were resolved after discussion. 3

The kindergarten children were asked the questions in the colloquial form only, because they did not understand the scientific form. All the other children were divided in two groups, one group received the simple question, in the scientific form and the other in the colloquial.

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The results of the second scoring revealed that the majority of the students were systematic and internally consistent in responding to our questions. It was possible to explain the responses given by 88.6% of the students by assuming that they were consistent in using one out of a small number of meanings of force. These meanings of force appear in Table 2. The observed meanings can be grouped in two categories: Those that appear to be based on everyday experience and show no influences from the scientific theory, and those that have been influenced by the scientific theory. Following Vosniadou and Brewer (1992, 1994) we will call the first group of meanings “initial” and the later “synthetic”. There were no meanings of force in the present sample that showed a complete understanding of the scientific concept of force. There seemed to be two initial meanings of force: internal force and acquired force. As was mentioned earlier the majority of the kindergarten children (46.7%) used the internal force meaning according to which force is exerted either on all objects because they have weight, or only on “heavy or big objects”4. There was also an additional interpretation according to which there is more force exerted on heavier objects. In all these interpretations, force is conceptualised as an internal property of physical objects and is considered to be affected only by their weight and/or size. We hypothesize that children interpret observations such as that big/heavy people/objects can cause damage on other people/objects, or can resist the push/pull of other objects, and relate these observations to the presence of force. It appears that the meaning of force for these children is closer to what is expressed by the word strength. As shown in Table 2, between the ages of 8 to 12, the internal force meaning is replaced by the acquired force meaning. In the acquired force meaning the criterion for deciding whether a force has been exerted or not, is movement. The students talk about objects being pushed or pulled by agents but they do not assign a force to them unless they move. The acquired force meaning, which is the most stable interpretation of force in the students in our sample, is similar to the “internal motor” idea of force reported by Piaget (1972), to the “force of mass” reported by Viennot (1979), and to the “impetus” notion reported by McCloskey (1983), Clement (1982), and diSessa (1988). The finding that the great majority of the younger children used one of two well defined initial meanings of force (or one of two combinations of them as will be discussed later), in a logically consistent way, supports the view that they are guided by an explanatory framework.

4

This is a qualitative not a quantitative understanding of “heavy” or “big”. Since in this study only inanimate objects were used, than we could safely say that this change of meaning applies in the case of inanimate objects. We do not know what happens in *the case of animate objects. 5

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The presence of the combined meanings internal force affected by movement and internal and acquired force, provide a great deal of information regarding the process of conceptual change, and more specifically, regarding the emergence of the acquired force meaning from the original internal force theory. It appears that children become sensitive to movement and the relationship between movement and force early on6, but have difficulty explaining this relationship. In the context of the internal force meaning, the natural interpretation of the movement of an inanimate object is to consider it as “weakness”, i.e., as failure of this object to resist to the push/pull of other objects, and thus to lack of force, or less force. This is exactly the interpretation of movement present in the meaning internal force affected by movement. From the point of view of the acquired force meaning, however, the movement of an inanimate object is, of course, an indication that a force is being exerted. So, from this point of view, the acquired force can be conceptualized as an additional force that is combined with the internal force to produce greater force. This is the interpretation of movement present in the synthetic meaning internal and acquired force. This interpretation of force was a very popular one not only with kindergarten children but also with and grade children as well. However, there is an internal inconsistency that characterizes the synthetic internal and acquired force meaning. If we think of an object that has been set in motion by an agent as having an acquired force, such an object cannot be thought of as having an internal force also, because if it did, the agent should not have been able to move it (following the logic of the argument given by the children placed in the internal orce meaning). It is maybe the realization of the internal inconsistency implicit in this synthetic attempt that this synthetic meaning is eventually abandoned in favor of the acquired force meaning. It is not uncommon in the developmental literature to have cases where conceptual change occurs from the need to solve internal inconsistencies (e.g., Vygotsky, 1962; Karmiloff-Smith, & Inhelder, 1974). In the acquired force meaning, force has been differentiated from weight, at least in the case of inanimate objects. So, inanimate objects may have weight as an internal property, but force is an acquired property related to the push/pull of a (usually animate) agent, when that push/pull causes the inanimate object to move. Again, cases of differentiation of two concepts from a parent concept have been reported by Piaget (1972) and Smith, Carey & Wiser (1985), while similar phenomena have also been observed in the history of science (Kuhn, 1977). It is also very interesting to observe that most of the children placed in the mixed category did so because they were caught between the internal and acquiredforce meanings and were unsure about how to interpret movement. Ten of the twelve children placed in the mixed category sometimes interpreted movement in the context of the internal force meaning - as an indication of “less” internal force - and sometimes in the context of the acquired force meaning - as an indication for the application of an external force (see Table 14 that presents all cases of inconsistency obtained). 6 About half of the kindergarten children were placed in one of these two synthetic meanings (see Table 2).

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While the first four meanings of force do not show an influence of the Newtonian theory presented through instruction, the remaining three do show such an influence. As in the case of astronomy studies conducted earlier (Vosniadou & Brewer, 1992; 1994) these synthetic meanings result from the assimilation of scientific information into the existing explanatory framework, which in the present case is the acquired force meaning. The students who used the acquired force and force of push/pull meaning interpreted force as an acquired property of moving inanimate objects but added to it the force of push/pull (in the case where an animate agent was shown to exert a push/pull force). These students show some progress towards the scientifically accepted meaning, to the extend that they interpret the push/pull action of an animate agent as force exerted, (regardless of whether the push/pull results in the movement of the affected object or not). This meaning is synthetic because the force of push/pull is added to the existing acquired force meaning. Moreover, the push/pull force does not appear to be conceptualized in ways consistent with the scientific theory (force as interaction between two objects), but in ways that show a confusion between force, effort, and internal strength or energy7. Finally, another synthetic meaning is the gravitational and other forces meaning. The gravity meaning of force starts to appear first in the case of falling objects (Question 22) and thrown objects (Question 27 - with acquired force) and then generalizes to stationary objects as well. In the majority of the responses in our sample, gravity was mentioned as a force that operates both in the case of moving and of stationary objects, except in the case of push/pull. It appears that in the later case children focus on the push/pull action and forget about gravity. In summary, it appears that children start with a meaning offorce which is not differentiated from weight (force as an internal property of big/heavy objects). This meaning is spontaneously replaced by a different meaning according to which force is the acquired property of objects that move (acquired force meaning). The acquired force meaning is well in place in the conceptual system of the 11-12 year old child ( grader) and is not substantially changed through instruction until the age of 15 ( grade). Under the influence of instruction, children add the force of push/pull and the force of gravity to the already existing acquired force meaning creating various synthetic meanings. 4.

CONCLUSIONS

The results of the present study add further support to the arguments made by Vosniadou (1994) and Vosniadou and Brewer (1992, 1994) that children construct a narrow but coherent explanatory framework that guides the process of acquiring knowledge about the physical world from early on. The great majority of the younger children in this study, were consistent in their interpretations of the situations where they thought force was exerted. Overall, a small number of meanings of force were obtained. All these meanings of force were constrained by 7

See Megalakaki, Ioannides, Vosniadou, and Tiberghien (1997).

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the underlying presupposition that force is a property (inherent or acquired) of physical objects. This is similar in many respects to the finding by Reiner, Slotta, Chi and Resnick (in press) that naive conceptions of force are tied to the notion that force is a property of material substances (see previous discussion about the differences between the two positions, however). The results of the present study add to the existing literature showing that there is considerable conceptual change happening in childhood (in biology-Carey, 1985; Hatano & Inagaki, 1987; Keil, 1989; Springer & Keil, 1989; in the nature of matter Smith, Carey & Wiser, 1985; in heat and temperature- Wiser, 1987; in astronomyVosniadou & Brewer, 1992; 1994). Unlike our previous studies in astronomy, where the observed changes in the concept of the earth and in explanations of the day/night cycle were the product of instruction, the findings of the present study show that considerable change can happen prior to the beginnings of systematic instruction. More specifically, the change from the internal force to the acquired force meaning of force can be conceptualised as spontaneous conceptual change. The meaning of acquired force is a different explanatory framework for interpreting the situations where force has been exerted, than that of internal force. It is a different explanation, addressed to different phenomena (e.g., the motion of inanimate objects), and where the individual concepts have been radically modified (differentiation between force and weight). Nevertheless, this conceptual change still happens in the context of an explanatory framework where force continues to be categorized as a property of physical objects. The effects of instruction, while considerable, do not succeed in producing radical changes in the established acquired force meaning. The results of the present study show that the meanings of gravitational force and force of push/pull are added on to the existing explanatory framework, destroying its coherence and distorting the scientific concept. This finding is consistent with the argument that the knowledge acquisition process starts with the formation of a relatively coherent, but narrow explanatory framework which, however, fails to be replaced by another coherent explanatory framework after instruction. Instruction in Newtonian mechanics is assimilated into the dominant acquired force meaning, creating synthetic meanings or internally in consisted (mixed) interpretations of force. REFERENCES Carey, S., & Spelke, E. (1994). Domain specific knowledge and conceptual change. In L.A. Hirschfeld and S.A. Gelman (Eds.) Mapping the mind (pp. 160-200). New York: Cambridge University Press. Chi, M.T.H. (1992). Conceptual change within and across ontological categories: Examples from learning and discovery in science. In R. Giere (Ed.) Cognitive Models of Science: Minnesota Studies in the Philosophy of Science. (pp. 129-160). Minneapolis, MN: University of Minnesota Press. Clement, J. (1982). Students’ preconceptions in introductory mechanics. American Journal of Physics, 50, 66-71. Clement, J. (July, 1986). Misconceptions in mechanics and an attempt to remediate them: The use of analogies and anchoring intuitions. Paper presented at the conference “The Psychology of Physics Problem Solving: Theory and Practice”, Bank Street College. diSessa, A.A. (1988). Knowledge in pieces. In G. Forman & P.B. Pufall (Eds.), Constructivism in the computer age (pp. 49-70). Hillsdale. NJ: Lawrence Erlbaum Associates. diSessa, A. (1993). Toward an epistemology of physics. Cognition and Instruction, 10, 105-225.

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Gopnik, A. (1996). The scientist as a child. Philosophy of Science, 63, 485-514. Hatano, G., & Inagaki, K.(1987). Everyday biology and school biology: How do they interact? The Quarterly Newsletter of the Laboratory of Comparative Human Cognition, 9, 120-128. Ioannides, C., & Vosniadou, S. (in press). Exploring the changing meanings of force: From coherence to fragmentation, Cognitive Science Quarterly. Ioannidou, I., & Vosniadou, S. (in press). The development of knowledge about the composition and layering of the earth’s interior. Nea Paideia (in Greek). Karmiloff-Smith, A., & Inhelder, B. (1974). If you want to go ahead get a theory. Cognition, 3, 195-212. Keil, F. (1989). Concepts, kinds, and cognitive development. Cambridge: MIT Press. Kuhn, D., Amsel, E., and O' Longhlin, M., (1988). The development of scientific thinking skills. London: Academic Press. Kyrkos, C., & Vosniadou, S., (1997) Mental Models of Pant Nutrition. Poster presented at the Seventh European Conference for Research on Learning and Instruction, Athens, Greece Lesley, A.M. (1994). ToMM, ToBY, and Agency: Core architecture and domain specificity. In L.A. Hirschefeld, & S.A. Gelman (Eds.), Mapping the mind. Cambridge University Press. McCloskey, M. (1983): Naive theories of motion. In D. Gentner & A.L. Stevens (Eds.), Mental models. Hillsdale, NJ: Lawrence Erlbaum Associates. Megalakaki, O., loannides, C., Vosniadou, S., & Tiberghien, A. (August, 1997). Differentiating force from energy: Children’s understanding of the concepts of energy and force. Seventh European Conference for Research on Learning and Instruction, Athens, Greece. Ministrell, J. (1982). Explaining the “at rest” condition of an object. The Physics Teacher, January, 10-14. Nersessian, N. J., & Resnick, L.B. (1989). Comparing historical and intuitive explanations of motion: Does “naive physics” have a structure? Proceedings of the Annual Conference of the Cognitive Science Society (pp. 412-417). Hillsdale, NJ: Lawrence Erlbaum Associates Osborne, R. & Freyberg, P. (1985). Learning in science: The implications of childrens’ science. London: Heineman. Ranney, M (1994). Relative consistency of subjects’ “Theories” in domains such as naive physics: Common research difficulties illustrated by Cooke and Breedin. Memory and Cognition, 22, 494502. Reif, F., & Allen, S. (1989). Interpreting and teaching scientific concepts: A study of acceleration. Cognition and Instruction, pp. Reiner, M., Slotta, J.D., Chi, M.T.H., and Resnick, L.B. (2000) Naive physics reasoning: A commitment to substance-based conceptions. Cognition and Instruction,18,1-34. Springer, K., & Keil, F.C. (1989). On the development of biologically specific beliefs: The case of inheritance. Child Development, 60, 637-648. Smith, J.P., diSessa, A.A., & Rochelle, J. (1993). Misconceptions Reconceived: A Constructivist analysis of knowledge in transition, The Journal of Learning Sciences, 3, 115-183 Viennot, L. (1979). Spontaneous reasoning in elementary dynamics. European Journal of Science Education, 1, 205-225. Vosniadou, S. (1994). Capturing and modeling the process of conceptual change. Learning and Instruction, 4, 45-69. Vosniadou, S., & Brewer, W. F. (1992): Mental models of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24, 535-585. Vosniadou, S., & Brewer, W. F. (1994): Mental models of the day/night cycle. Cognitive Science, 18, 123-183. Vosniadou, S., Ioannides, C., Dimitrakopoulou, A., & Papademitriou, E. (in press). Designing Learning Environments to Promote Conceptual Change in Science. Learning and Instruction Vygotsky, L. (1962). Thought and language. The MIT Press. Wiser, M. (1987). The differentiation of heat and temperature: History of science and novice-expert shift. In S. Strauss (Ed.), Ontogeny, phylogeny, and historical development. Norwood, NJ: Ablex.

MAP READING VERSUS MIND READING

Revisiting children’s understanding of the shape of the earth

JONAS IVARSSON*, JAN SCHOULTZ ** & ROGER SÄLJÖ* *Göteborg University, Sweden **Linköping University, Sweden

Abstract. Any study pursuing questions of conceptual development has to position itself with respect to the more general questions of how to conceive human cognition. At one level this study thus presents a contribution to this age-old debate about the nature of human thinking and learning. At another level – the empirical – it provides a discussion of the difficulties that children face when reasoning about the shape of the earth and gravity. The study reported is part of a project that explores issues of how people use physical artefacts, embodying conceptual distinctions of considerable complexity, when thinking and reasoning. The results suggest that even very young children are familiar with sophisticated knowledge about how to interpret a map. Furthermore, using it as a mediational tool, they can accomplish rather complicated reasoning about the shape of the earth and gravity. This is a demonstration of the flexible and tool-dependent nature of cognition. It is, however, inconsistent with a more formal stage theory or a theory in which children’s reasoning is characterised by means of distinctively different conceptions. It is also at odds with a dualist perspective on human cognition in which the embeddedness of physical tools in human reasoning is not taken seriously.

1.

INTRODUCTION

For centuries, the question of how to conceive human cognition was an issue that mainly concerned philosophers. During the and century, however, new disciplines emerged, and researchers within areas such as psychology, anthropology, linguistics, neuroscience, artificial intelligence and educational science joined this lively debate. Although its roots go further back, the one perspective that has been dominant in recent decades, or at least up until recently, is the one represented by cognitive psychology. The traditional focus of cognitive psychology is to posit cognition as a fundamentally individual process. The assumption is that human mental functions are located in individuals and can be modelled accordingly as mental entities such as memory systems, thought processes, and cognitive structures. The empirical approach that resonates with this conception usually explores allegedly basic cognitive and perceptual processes (thinking, memory, problemsolving, perception, etc.) by attempting to unpack the basic mechanisms of mental processes and/or the conceptions of the world that people hold when reasoning. The focus is on cognitive systems and thought processes that – as the metaphor goes – M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 77-99. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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underlie reasoning at the level at which it is visible externally in linguistic and physical activities. A major challenge to this tradition comes from a sociocultural and discursive perspective inspired by Vygotskian and Wittgensteinian views of human cognition and communication (Wertsch, 1991, 1998; Vygotsky, 1986). The sociocultural tradition places human cognition in a historical and situated perspective. Cognition is conceived as a problem of how people use tools – physical as well as conceptual/discursive. This is as much an interactive process as an individual one; in fact, it is very much in the middle as joint and mediated action. And even when reasoning on their own, people do not do this in social isolation - human action is always situated. An important assumption is that such cultural tools form an integrated part of cognitive processes. There is no sense, following such perspectives, in assuming that there is a level of thinking that is “pure” and that underlies reasoning in human practices. We cannot separate thought processes, say in the context of doing geometry or playing chess, from the conceptual tools that are applicable to such activities. Thinking is the use of tools. Or, as Wittgenstein so suggestively put it in the context of the use of language; “When I think in language, there aren’t ‘meanings’ going through my mind in addition to the verbal expressions: the language is itself the vehicle of thought” (Wittgenstein, 1953, § 329). Although it would be tempting to create syntheses between traditions, our preference is to keep them apart. They build on conflicting assumptions regarding the nature of human cognition and action that have a long history in western philosophy, and the difference between them is of a paradigmatic nature that cannot be. easily resolved by appealing to empirical data. However, on some issues the critical differences between these traditions should be explored. The particular area that we will be considering in this context is that of learning and conceptual reasoning. In these areas, the views of these traditions differ very clearly, and these differences have apparent implications for how one conceives human learning and conceptual knowledge and also for establishing what is difficult in such activities. 2.

STUDYING HUMAN COGNITION

A critical point of departure in any research on human cognition, and one which deserves to be taken seriously, is that the object of inquiry is somewhat elusive. As scholars we are forced to consider that the observations we are attending to in our analyses are symptomatic and have, as it were, an indirect relationship to what we are interested in. Cognitive phenomena can be described at many different levels, for instance, in terms of neural signals and reactions, blood flow in the brain and all the way up to how people reason and interact in complicated everyday situations. The relationships between these levels are complex, to say the least. Since the object of inquiry is contested and ambiguous, one has to consider how various paradigms construe their studies, design experiments and relate theory to observation. Rather than arguing about thinking and learning in general, one should scrutinise precisely how the empirical studies are carried out in various paradigms in

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order to establish in what sense the observations can be seen as valid indicators of human thought processes and reasoning. When looking at the area that we shall be exploring – children’s understanding of the shape of the earth and certain concepts from elementary astronomy (such as gravitation) – these differences between theoretical traditions are obvious. In the following, we shall give a brief introduction to research in this area from a cognitive psychology and sociocultural perspective, respectively. We do not pretend to cover all the research. Rather, in order to address our main question about how children understand the shape of the earth and some related matters, we will give a brief summary of relevant studies with the ambition of illustrating the clear differences in how children’s competences and learning trajectories are portrayed. But before embarking on this presentation, we shall say a few words on the notion of conceptual change. 2.1.

Conceptual Change in a Sociocultural Perspective

Central to a sociocultural tradition is the idea of mediation and tool-mediated action (Wertsch, 1991). Language, and its conceptual resources, is the most important tool, and it is also unique to the human species – it is the “tool of tools”. Concepts and categories thus mediate the world for us in real world activities, and they are, in fact, basic to our perception, reasoning, remembering, and any kind of cognitive activity. Seeing an object as “a square” or “a circle” relies on, and reproduces, a certain, socioculturally generated, set of categories for describing and thinking about objects. However, concepts are not just mental entities that reside inside our heads, they are part of human social practices. People use concepts to do things in a world of physical and intellectual actions; discourse is an important aspect of practical action. The judge uses the concepts of the legal system such as “intent”, “fraud”, and “assault” when passing a sentence on a suspect. The construction engineer uses the conceptual tools of mathematics, mechanics and other specialised scientific areas when designing a new engine. Thus, and this is one of Vygotsky’s (1986) fundamental insights, concepts (or as he referred to them: psychological or intellectual tools) are used by people when thinking (i.e. intramentally) as well as when communicating with each other (i.e. intermentally); thinking in this perspective is conceived as a kind of silent and private dialogue where people use the conceptual resources of their society for reasoning. In this sense, our thinking is sociohistorically produced as we have already alluded to. So, how does one conceive conceptual development in such a perspective? When regarding concepts as tools (and not just abstract, internal representations of the world), a critical feature of conceptual development is how people come into contact with various kinds of tools that exist in a society. Concepts are elements of discourses that are used in various practices in society. Everyday reasoning relies on conceptual tools as much as does any other kind of activity. But an important arena for the communication of more specialised kinds of conceptual tools is schooling. It is here that the individual encounters scientific (or, more generally, institutional) forms of reasoning that may not be familiar or widely used outside institutional settings. When learning physics, for instance, we have to familiarise ourselves with

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new modes of reasoning that build on concepts such as force, velocity, momentum, acceleration and so on that are defined in particular manners. And learning to use these in an insightful manner (which is not the same as being able to define them in a formal sense) can be a long and complicated learning process. But what, then, is the nature of this process? This is a critical question from a psychological and communicative point of view. Vygotsky (1986) originally suggested that learning and conceptual development could be seen as a process of internalisation by individuals of conceptual tools. However, this is a problematic position, since this formulation somehow recreates a boundary between thinking and communication that Vygotsky was eager to do away with. The point of much of his argumentation is that conceptual tools are used in both these types of human actions, and it therefore seems more fruitful to avoid reintroducing the Cartesian split between “the outside” (communication and physical action) and “the inside” (thinking). Alternative modes of formulating the processes of conceptual development have been suggested by, for instance, Rogoff (1990) and Wertsch (1998). The traditional preference has been to view learning and conceptual development in terms of appropriation of mediational means. Appropriation, as used here, implies that the individual gradually familiarises herself with a set of conceptual tools and begins to realise how they are used. For instance, Saxe (1991), who studied Brazilian children acting as candy sellers, observed how the young children with a low or no formal education performed complex calculations that involved the awareness not only of proportional relationships between goods and price, but also included consideration of the problems imposed on the activities of selling and buying by hyper-inflation. Appropriation thus implies that the individual is able to reason and act in situations by means of a certain conceptual tool. This does not imply that the tool is appropriated in all its details. This is probably rarely the case. Even if one understands and is able to use the concepts of force or energy when solving physics problems, there are many aspects and potential uses that may take years of further study to appropriate. In a similar vein, the candy-sellers in Saxe’s study had not appropriated the concept of inflation in the same sense as an academically trained economist. Yet, in some settings they were able to take this highly complex phenomenon into account in quite a sophisticated manner. In this sense, appropriation implies an increasing familiarity with how a tool can be used for different purposes. Recently, Wertsch (1998) has suggested that it might be useful to make a distinction between appropriation and mastery, a suggestion which is interesting in this context. The latter concept is developed in the context of observations made by the Estonian psychologist Peeter Tulviste (e.g., 1994), who studied the learning of history in Estonia under Soviet rule. In these studies it was shown that the students in school and at universities learned the officially sanctioned explanations and accounts of history and historical development in the SovietMarxist tradition without appropriating the conceptual tools or the worldviews these accounts implied. Sometimes the students even mastered these accounts to perfection, but they never used them in any other settings as conceptual tools. So, mastery of a particular kind of tool may be seen as something different from

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appropriating a tool in order to actively use it. This is a fascinating perspective on human cognition, but we shall not go deeper into this matter here. There is another layer to this argument about the tool-dependent nature of thinking, which is essential to the research reported here and has to do with conceptual knowledge. In a sociocultural perspective, the intimate relationship between concepts (i.e. intellectual tools) and physical tools (i.e. artefacts) is emphasised (Bliss & Säljö, 1999; Säljö, 1998). Thus, calculators, calendars, computers, instruments for measuring entities such as distance, volume, pressure, etc. are seen as physical embodiments of human conceptual constructions such as number systems, units of measurement and so on. This implies that when reasoning with artefacts, the tool serves as an aid to thinking in the sense that it represents the world in relevant conceptual categories. This is an important aspect of the role that artefacts play as support and prosthetic devices for thinking, which we will come back to below (see also Wyndham & Säljö, 1998). But before going into this, let us review some of the work done on the particular issue of children’s understanding of some elementary astronomical and/or geographical concepts. 3.

STUDIES OF CHILDREN’S UNDERSTANDING OF THE SHAPE OF THE EARTH AND GRAVITATION: A COGNITIVIST PERSPECTIVE

The interest in studying children’s learning and understanding these matters goes back quite some time. In the cognitivist, and Piagetian, tradition a series of empirical studies have examined the nature of the conceptual problems that children have in this area, and the conceptual change that takes place as they develop (Mali & Howe, 1979; Nussbaum, 1979; Nussbaum & Novak, 1976; Sneider & Pulos, 1983; Vosniadou, 1994; Vosniadou & Brewer, 1992, 1994). A major theme of this line of research has been the illustration of the apparent difficulties children have in understanding that the earth is a sphere. These difficulties were clearly outlined in the pioneering studies by Nussbaum and colleagues during the 1970s. Their findings have later been refined and elaborated but are still, by and large, confirmed by more recent studies. Since these early observations, considerable effort has been put into describing in detail the different constructs children hold (see below), and the transitions in conceptual understanding that take place during ontogenesis. Vosniadou and Brewer (1992), two of the recent leading specialists in this area, suggest that the reason for the problems children have is that information about the shape of the earth contradicts the child’s basic ontological presuppositions. That is, the scientifically appropriate model is contradictory to the beliefs held by the children, beliefs based on years of convincing everyday experiences. According to Vosniadou (1994) these experiences form the foundation of our knowledge base. A revision of this base is not easily achieved, and, when this happens, it will have profound implications for subsequent knowledge structures.

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Mental Models

In the cognitivist paradigm, the analyses of conceptual change are closely linked to the assumptions of the existence of mental models. Following Vosniadou (1994), mental models are intermediate phenomena that exist between the overt (verbal or written) responses given by children in empirical studies, and something that she refers to as underlying theoretical constructions or, to use her language, framework theories. Although the specific, individual, mental model may vary in its relations to the underlying structure, it is believed that the generic aspects of a mental model can provide information about these underlying so-called framework theories. Mental models are dynamic and generative representations which can be manipulated mentally to provide casual explanations of physical phenomena and make predictions about the state of affairs in the physical world. It is assumed that most mental models are created on the spot to deal with the demands on specific problem-solving situations. Nevertheless, it is possible that some mental models, or parts of them, which have proven useful in the past, are stored as separate structures and retrieved from long-term memory when needed. (Vosniadou, 1994, p. 48.)

Having taken a brief look at the conceptual foundations, we shall now, following our previous argumentation, take a closer look at some of the elements of what has actually been studied in this line of research. 3.2.

Mental Models and Children’s Reasoning

The methodology used in these studies varies, as do the modes of analysing data. One prominent method for generating data on children’s mental models/framework theories, though, is the structured interview in the Piagetian tradition of the méthode-clinique (Piaget, 1929). The nature of the responses generated has also varied. In some cases, children have responded verbally, in other cases they have been asked to draw a picture or even to construct physical models using clay or other resources. At any rate, the basic assumptions are that the questions have a potential to unravel the mental models students have. The general results obtained within this tradition of research on children’s understanding of the earth can be summarised by means of the study reported by Vosniadou and Brewer in 1992. Here the “mental models of the earth” that children use are depicted as illustrated in Figure 1. At one end we find various kinds of flat entities that are described and/or drawn by children. These are followed by so-called

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combined models (where the earth may take on different shapes) to hollow spheres, and, finally, we end up with versions that are close to the scientifically correct one. According to this cognitivist perspective, all children seem to follow the same line of development. The demands placed on them – the cognitive conflict – to integrate the culturally accepted view of the earth as a sphere with their everyday experience force children to go through a number of steps in which they hold different conceptions of the earth. What is not entirely clear is where these models come from, an obscurity that seems to be a general problem for this tradition. In fact, as it has been argued, “cognitivism remains perennially unable to resolve such thorny problems as the origin of ideas or concepts” (Gergen, 1985, p. 270). In this case, it seems as if the models are constructed anew by each child on the basis of personal experience and essentially without cultural support. The ontological presuppositions (i.e. the framework theories) are constraints that the children simply have and that they have to struggle with. The procedure of inferring a level of mental models on the basis of observed responses is not uncommon within the cognitivist perspective. In fact, Gardner (1987) describes this mode of working as one of the major accomplishments of cognitive science. Nevertheless, we believe there is good reason to be cautious. This practice of introducing such an intermediate level in explanations implies a shift from specific observable events to generalisations and abstractions on a totally different level, a jump between logical types (Bateson, 1972, 1979). Also, such a strategy introduces not only theoretical and epistemological problems but also ontological ones; what is the ontological status and psychological reality of mental models? Having pointed this out, we would like to emphasise that we do not deny that the children in the studies commented on above are reasoning in terms of, for example, a disc shaped or hollow sphere earth. But we are far less convinced that there is anything to be gained by saying that children have mental models of these kinds. We believe that a distinction can be drawn between having mental models and reasoning in terms of them. The latter assumption avoids making ontological assumptions and makes a clear distinction between the researcher’s perspective and analytical tools on the one hand, and mental models that children allegedly have on the other. 3.3.

Situating Children’s Reasoning in the Interview Setting

A point that needs to be emphasised here is the fact that the children in the cited studies do not reason in a vacuum. In many studies (Mali & Howe, 1979; Nussbaum, 1979; Nussbaum & Novak, 1976; Sneider & Pulos, 1983; Vosniadou, 1994; Vosniadou & Brewer, 1992) participants have been asked to express themselves using physical objects, pictures or drawings (see Figure 2).

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The status of such physical artefacts and drawings is not taken up in any of these studies. The drawings, for instance, are only regarded as expressions of underlying conceptions, and never as resources in themselves that contribute to and codetermine the process of reasoning. Very few of these studies present their data in a manner that makes it possible to discern how these drawings are produced and what role they play in children’s reasoning. However, one point that is worth exploring is if children can be assumed to always be clear about the relationship between the drawing and what it is supposed to model (the earth as an astronomical object). It does not seem far-fetched to suspect that the relation between the (physical) model and its referent is lost from time to time in these interviews. An observation from Vosniadou (1994) illustrates this. Here, we find the girl Kristi being asked to draw the “real shape of the Earth.” Kristi draws a circle and is then asked to reason about what happens if one walks in a straight line for many days. Kristi (first grade) E: What is the shape of the Earth? Child: Round E: Can you make a drawing which shows the real shape of the Earth? C: (Child draws a circle.) E: If you walked and walked for many days in a straight line, where would you end up? C: You would end up in a different town. E: Well, what if you kept on walking and walking? C: In a bunch of different towns, states, and then, if you where here and you kept on walking here (child points with her finger to the “edge” of the circle which she had drawn to depict the Earth) you walk right out of the Earth. E: You’d walk right out of the Earth? C: Yes, because you just go that way and you reach the edge and you gotta be kinda careful. E: Could you fall off the edge of the Earth? C: Yes, if you were playing on the edge of it. E: Where would you fall? C: You’d fall on this edge if you were playing here. And you fall down on other planets.

(From Vosniadou, 1994, p. 51.)

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In this example, Kristi makes active use of the drawing as a resource for her reasoning as can be seen. She repeatedly points to it to make explicit and support her arguments. However, what is interesting here from the point of view of her cognitive performance is that this drawing of the earth is nothing but a thin line; it de facto contains something that in some sense is the “edge of the earth.” If we assume that Kristi for the moment is talking about her drawing, and temporarily disregards the fact that it is a model of something else, it seems quite logical to assume that one can fall off the edge. Also, the approach of the interviewer in this excerpt is anything but neutral and passive (which is how interviewers in research generally are described as). Rather, s/he can be read as signalling that s/he is not satisfied with the response given by the child in line six (“You would end up in a different town”). By insisting on this topic of what would happen if “you kept on walking and walking” in her next contribution, the child might be seen as being provoked into saying something different rather than merely repeating the same response. In our view it is essential not to go abstract at too early a stage. Children’s reasoning in situations of this kind are better studied as situated practices where the dynamics of the context, the dynamics of the interviewing, and the tools available, are decisive for what children say or do. 4.

STUDIES OF CHILDREN’S UNDERSTANDING OF THE SHAPE OF THE EARTH AND GRAVITATION: A SOCIOCULTURAL PERSPECTIVE

Physical tools originate in collective cultural practices, and human cognition is socialised through participation in activities where tools are used for particular purposes. A very important dimension in sociocultural development is the increasing sophistication of tools that occurs over time. Powerful intellectual distinctions and resources are built into tools that are used for a wide range of purposes when performing activities such as calculating, navigating, communicating, reading, analysing substances at microlevels, playing games and so on. The attitude towards thinking that characterises this perspective thus emphasises the intimate links between cognition and the use of tools in situated practices. There is no such thing as “pure” cognition that can be accessed per se as we have already pointed out. Even in interview situations, such as the ones commented on above, the terminology used, the manner in which questions are formulated as well as the drawings and artefacts used, mediate people’s reasoning. To reason with a physical object as a model is one thing, to reason without such resources represents another situation with very different cognitive demands. This view of cognition as the use of tools was the background of the study on children’s conceptions of the shape of the earth and gravitation carried out by Schoultz, Säljö and Wyndhamn (in press). The main idea behind this study was to analyse how children reason about elementary astronomical concepts when doing this in the context of an artefact, a globe. The interviews were conducted in a Piagetian fashion and to a large extent modelled on the studies in the cognitive tradition summarised above. The children (aged 6 to 11 in grades 1 to 5) were first asked to identify and name the object in front of them (which all children did

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without any problem). All children also realised that the globe was a model of the earth. The results show that when using the globe as a resource for reasoning, the children were surprisingly knowledgeable and sophisticated. Even amongst the youngest, there were several who argued in terms of a concept of gravity (sometimes without using the term) as an explanation of why things fall to the ground. None of the children considered it possible to fall off the earth. Even when put under considerable pressure by the interviewer, who pointed at countries such as Argentina and Australia visibly located on the downside of the globe, and explicitly asking if people would not fall off, did any of the participating children agree to the possibility that people “down under” might fall off the earth. None of the children suggested that the earth might be flat, hollow or take on any of the shapes that have been found in previous research (see Figure 1). The authors conclude that the differences in outcome testify to the mediated nature of reasoning. The globe was obviously a familiar artefact for the children. When reasoning with this tool as a resource, the children were in a completely different situation as compared to when being interviewed or when making drawings on their own. For instance, they could read the names of the countries on the globe, and they knew from other sources (media and friends) that people live in Australia and other countries that appear to be on the downside of the earth. This information was enough for them to realise that people do not fall off the globe irrespective of whether they could explain why this does not happen. The globe in this sense is doing concrete discursive/cognitive work by supporting certain kinds of reasoning and by positioning the children differently in comparison to a situation without such a tool. It served as an orienting device that gave the children something concrete to refer to when reflecting on the questions. It also served as an aid to memory by operating as an inference-rich tool that reminded them of other sources of information. Carrying this line of reasoning further, one conclusion is that if one considers the unit of analysis to be children operating with mediational means (Wertsch, 1998) in the form of intellectual and physical artefacts, the image of children’s knowledge that is produced in empirical research will be very different. In the study by Schoultz, Säljö and Wyndhamn (in press) above, basically all the conceptual problems that have been pointed to in the cognitively grounded research seem to disappear when the globe is available. Cognitive development cannot be exclusively, or even predominantly, conceived as changes in mental models or cognitive structures. Rather, it seems better captured in terms of the increasing mastery of mediational means that might be intellectual or physical, or, as in the case with the globe, that are simultaneously both. Artefacts thus re-present in material form certain conceptual distinctions, and this is precisely why the globe served as such a powerful tool for thinking for the children. An interesting question in this perspective, then, is to what extent the children’s considerable sophistication when reasoning with a globe present can be seen as limited to the use of this particular tool only. The three-dimensional nature of a globe makes it a rather powerful model of the earth. What will happen to their reasoning if they encounter these issues of the shape of the earth and gravity in the context of another mediational means, the map? This is the question that will be

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pursued in the present study. But before presenting our analysis of how the children reasoned with the aid of a map as an intellectual tool, it is helpful within a sociocultural perspective to consider somewhat the sociogenesis of this particular tool and the conventions built into it. 4.1. The Sociogenesis of Maps

Every artefact has a history. In the case of maps this sociogenesis is quite complicated, and it is related to the development of concepts, insights and improvements in representational technologies. The interesting point from a sociocultural perspective is the extent to which these concepts and distinctions are perceived by the present-day user, and how they are appropriated when using the tool. In the history of the Western World we know that the earth was recognized as being spherical at about the time of Aristotle (384-322 B.C.) (although this did not become the accepted view until much later in history). The evidence for this conclusion varied. From an empirical point of view, it was evident that ships seemed to “come over” the horizon when sailing away or towards the observer. From the point of view of ideas and cultural beliefs, there was an assumption that the sphere was the most perfect form. Early calculations of the size of the earth were carried out by both Eratosthenes (ca. 276-195 B.C.) and Posidonius (ca. 130-50 B.C.). Although the methods used were correct, the assumptions and the precision of the observations were not. These errors, however, tended to compensate each other. Since the calculations were based on a unit called stadia, we cannot be entirely sure of the exactness of the estimations. It seems, though, as if they overestimated the size by only 12 to 15% (Robinson, Sale, & Morrison, 1978). The early history of the representational tool that we know as maps seems somewhat disputed. Some (see Harvey, 1980) claim that the topographical map developed quite late in our cultural history, while others (see Fremlin & Robinson, 1999) maintain that the topographical map was conceived already in prehistory. Irrespective of these differing views, one can find occasional references to maps in the classical Greek literature. This, according to Robinson, Sale and Morrison (1978), makes it possible to infer that mapping was not an uncommon practice at this time. On the other hand, none of these maps appears to have survived. The writings of Claudius Ptolemy (ca. 90-160 A.D.), however, did survive. In his production there was one book, simply called Geography, which covered what was known about the earth at the time. Among other things, the Geography included a treatise on cartography in which Ptolemy described how maps should be made. He commented on the problems of presenting the spherical surface of the earth on a flat sheet, and he clearly recognised the inevitability of the deformation that must follow in such a process (Robinson, Sale, & Morrison, 1978). Although refined and developed throughout the centuries, many of the techniques used in the construction of maps of the earth seem to have been recognised rather early. Maps of today carry with them many conventions. Some of these have changed through the course of time, others have stayed more or less the same for long

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periods. In medieval times, most maps of the known world – mappa mundae – were drawn with Jerusalem at the centre and paradise at the top. Paradise was believed to be found beyond the farthest area known, the Orient. It is from this practice that we have derived the expression “to orient” a map. Today we orient our maps towards the north instead of the east, but the practice as such is the same. Another example is given by the geographical coordinate system, which is the procedure of dividing the sphere into latitude and longitude. This system was introduced some 2200 years ago and has not been changed since (Robinson, Sale, & Morrison, 1978). 4.2.

Method

The present study, thus, is a continuation of the interest in how children reason when using culturally meaningful mediational means. The map (see Figure 3) we have used thus gives a two-dimensional image of the earth. The map is taken from a type of atlas frequently used in schools.

4.2.1.

Participants and Analysis

The empirical data were collected through interviews in schools. Eighteen children, aged 7 to 9, participated. In accordance with the study by Schoultz, Säljö and Wyndhamn (in press), the interviews were conducted in a Piagetian fashion and lasted between 10 and 20 minutes. The central questions were approached by talking about different countries, colours on the map etc. The interaction between the interviewer (JS) and the child was audio recorded and later transcribed in full. The analysis is based on the transcripts.

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Results

In this first part, we will show how the interviewer and the children reach a common understanding of the artefact and the purpose of the encounter. This is a coordinating activity that precedes the discussion of the main topic of the interview – the questions about shape and gravity. The precise manner in which the map functions as a prosthetic device for reasoning will be discussed in the second part. 4.3.1.

Coordinating the Activity: Identifying the Artefact and Contextualising the Issues

Being introduced to the atlas, the children thus face a complex artefact with a long history. The artefact is well known to all of them, which per se is a sign of their position in a sociocultural sense. But in spite of the familiarity of the artefact, it is not clear to the children how it is going to be discussed in the interview setting, especially at the start of the encounter. There are many options. The artefact in front of them could be temporarily discussed as a book of a certain type, that is, one could focus form rather than content. It could also be discussed as a map with different colours, names and states, etc. A third option would be to talk about the artefact as a model of the earth. Although one might refer to these three approaches as “levels of abstraction”, they are better conceived as different forms of situated talk relying on different interpretations of what is of interest. These three alternatives are all reasonable manners of discussing in a school setting, and there is initial uncertainty when the interviewer asks the question “What is this?” with reference to the artefact. The problem for the child is to identify what is the expected type of discourse. Excerpt 1. David

1 2 3 4 5

I: David: I: David: I:

Excerpt 2. Anton

25

I:

26 27 28 29

Anton: I: Anton: I:

grade

Do you know what this is? A book And what is this supposed to be? A globe A globe, do you recognise any countries? grade

But now Anton I’m going to ask you some questions. Then, of course, you know what this is? A map What does it represent? The whole earth The whole earth. Do you recognise any places or countries or something you ... you can read if you want to

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Excerpt 3. Anna

1 2 3 4

I: Anna: I: Anna:

grade

What is this? It’s the earth Why is it drawn like this? [Points at the corners of the map] It’s round

We emphasise this problem of the choice of discourse in order to illustrate that the multitude of manners in which it is possible to carry out a discussion is a concrete problem for the child. The difficulty with the questions asked does not reside solely in what the object in front of the children is in a factual sense or the conceptual issues that are involved in interpreting a map. The problem for the child is also to identify what the questions are all about, and how one is to contribute to the conversation. This is thus primarily a communicative problem and not a conceptual one. This is illustrated in Excerpt 4, where the uncertainty expressed clearly refers to the interview-situation. Excerpt 4. Paul

3 4 5 6 7 8 9 10

I: Paul:

I: Paul I: Paul I: Paul:

grade

Do you know what this is? Nope This? A globe... noo Is it that? Yes If we assume that this is a globe, why is it drawn round like this? The globe is round

When being asked if he knows what is in front of him, Paul responds with an initial “Nope.” This cannot be taken as evidence of the fact that he does not know what the artefact is. Rather, it seems likely that he is uncertain as to what is a relevant way of talking in this situation. After the following utterance by the interviewer, he argues that it is “a globe.” We have to be aware of the fact that an interview is a communicative and interactive project. Without appropriate guidance from the adult, who is the dominant party in this interaction, the child will often respond in a vague and non-committal manner (which is also a common strategy in other conversational settings when people are uncertain what the purpose of an utterance is). It is an interesting problem if the ability to identify an artefact as a “globe” or as the “earth” is itself indicative of having a particular mental model. There is, of course, always the option of making such an assumption by introducing an object of inquiry at this intermediate level. But the critical question is what is gained by such an explanation. To refer to these modes of talk as indicators of “conceptions” or “mental models”, and to locate them in the head of the individual, will not help us understand why people choose one or the other. If we instead focus on the actual interaction, the choice of explanation should be made on the basis of what can be observed. We believe that the manner in which the topic is discussed is not a discrete act but a process that unfolds, a process that is

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both possible to study and to understand. Dialogical as it is, in the sense of building on the contributions of both parties, the interaction can be conceived as a mode of talking and thinking that is not only temporally distributed, but also distributed among the participants. This makes the method of looking for conceptions ‘behind’ answers even more problematic. If not even answers can be fully attributed to individuals, how could we possibly consider them primarily as mental constructs and give them priority as explanatory concepts? Excerpt 5. Carl

5

I:

6 7 8 9 10 11 12 13

Carl: I: Carl: I: Carl: I: Carl: I:

14 15

Carl: I:

16 17

Carl: I:

grade

It’s difficult to know. Well I have a question for you. What is this? The earth Does the earth look like this? Yes, perhaps Perhaps, it does. What does the earth look like in reality? Round Round like a ball Mm But if you’re going to make it like a map you have to do it like this right Mm And then you have to make some bends like this. Why does it look flattened? Why does one draw it like an egg do you think? You can look at the whole around No, that’s right you can’t see the backside otherwise. You can imagine taking the ball and cutting it open

Excerpt 5 illustrates what can be seen as a distributed answer. We believe that it is more appropriate to say that the answer to the question posed in line 5 is to be found between lines 6 and 17 rather than in line 6 alone. The question initiates a dialogue, and the genuine answer sought for is not merely what kind of label one would put on the object, but rather how one should conceive of this object and its properties/functions. In this passage, it is clear how the interviewer is an active coconstructor of meaning, and that he sometimes elaborates the children’s contributions considerably. In some traditions, this would probably be regarded as an improper procedure for an interview, a confounding variable as it were. From our dialogical perspective on communication, however, we regard this as a natural and realistic attitude to interaction, perhaps even necessary in order to maintain a joint focus. The ideal of the passive partner in interview research probably hampers the progression of the interview in many cases. Furthermore, participation in certain discursive practices presupposes that one focuses on some aspects. When talking about a map, the thickness of the paper is seldom relevant. Varying artefacts and discourses also presuppose familiarity with certain concepts or pieces of information. On a political map, for instance, colours signify something different than topographical cues. This kind of awareness of the

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specific rules that should serve as premises when reading maps is an important feature of a person’s ability in our material. It is most striking how conscious the children seem to be of the artefact as being a form of representation. Bearing in mind the young age of the participants this is not something that should be taken for granted, rather it is something that should be looked into more carefully. It is important to consider how the artefact supports thinking. For the interviewer and the children to end up with a shared understanding of the object under scrutiny, however, some time needs to be invested. Excerpt 6 provides a prototypical example of what this process looks like. Excerpt 6. Tim

3 4 5 6 7 8 9 10 11 12 13

I: Tim: I: Tim: I: Tim I: Tim: I: Tim: I:

14

Tim:

grade

I would like to ask you about this. What is this? A map, the globe Why does it look like this? [Elliptical] Because it’s round Does the earth look like this? Yees So it does But it’s more round And then? It’s more even, not long like this No, why do you think you draw it like that and not rounder? Why can’t you do that? Because you can’t draw the backside

In Excerpt 6, the interviewer and the child come to the conclusion that they are dealing with a map of the earth projected on a flat piece of paper. We can follow the discussion on the transforming processes involved in producing this kind of projections. When dealing with an object like this, the participants can make active use of its physical properties, something that is done in line 12. Here, Tim refers to the stretched look of the map and calls the interviewer’s attention to the fact that this is a by-product of the process of mapmaking. By using an observable property like this, he shows awareness of some of the conventions of map-making, and he is also very clear about the distinction between the model and what the earth looks like as a physical object. Although the interpretations of the questions may differ between the interviewer and the children, as we will discuss below, the referent of the map as a model of the earth remains a reasonably shared focus throughout the discussion. However, we should like to emphasise that this coordination of perspectives is an achievement (Rommetveit, 1988, 1992), and not something that can be taken for granted. The children can be made to share this perspective, but it has to be established as the one intended for this particular discussion. However, this can be efficiently done without the interviewer adding further pieces of information or explanations.

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93

Cognition and Reasoning: Utilizing the Artefact as a Cognitive Prosthesis

As we have shown, the interviewer, in co-operation with the interviewees, initially establishes the artefact as being a map of the earth and that this is what is of interest in the following discussion. This is followed by a discussion of what the different colours on the map signify. When this is over, the interviewer follows his agenda and turns to the main problem of the interview, namely if one can fall off the earth (which, in a sense, is the question about gravity, framed in a particular way borrowed from previous research). The question is paraphrased as whether humans can inhabit the whole earth (or, in a later step, if they can live “down there”). Although all the children answer the initial query with a unanimous “no”, the answers do not mean what they at first would seem to mean. The question presumes that one talks about the earth as an astronomical body, where gravity is the principle explaining why objects fall to the ground and why there is no up and down on the earth. Scrutinising the children’s responses, however, we find that they bring in new topics such as political and geographical conditions. This is a shift in conversational focus that illustrates the polysemic nature of the questions. A typical example is given by Excerpt 7. Excerpt 7. Eric

43 44 45 46 47 48 49 50

I: Eric: I: Eric: I: Eric: I: Eric:

grade

Can people live down here, then? Nope Why not? Because it’s so far down Why isn’t that possible, then? Mm perhaps you get an inflammation of the ear Why would they get an inflammation of the ear down here, then? Perhaps it’s cold

What this and the following excerpts illustrate is a conversational problem that Lemke (1990) refers to as a matter of “thematic continuity” in interaction. The interviewer takes the astronomical framing of the issue for granted (the interview is organised so as to be about the earth as a celestial body and about gravity), while the children choose other categorisations. In Excerpt 7 above, Eric refers to unfavourable climatic conditions and the risks of catching ear infections as a reason for why one cannot live “down there.” In the following excerpt, the boy Jakob in a more general sense refers to the fact that there are places where it is too hot or too cold to live. Excerpt 8. Jakob

37 38

I: Jakob:

grade

Mm, can people live all over the earth? What do you think? Nope

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39 40 41 42

I: Jakob: I: Jakob:

Where can people not live? Where it’s cold Anywhere else? Where it’s hot

From Excerpts 7 and 8 one could argue that the children never understood the meaning intended by the question. And in a sense we agree, they did not overtly consider the option that one cannot live on the down side of the earth. There is a clear difference in how the interviewer and the interviewees read these questions. But, it is also quite possible that the children consider the option that one could fall of the earth as absurd. They therefore construe, on the spot, a response to why one cannot live everywhere that might serve as a reasonable suggestion. The line of reasoning found above could be seen as an issue of the problems the children have with identifying the precise nature of the topic of discussion and how to proceed with the dialogue. This problem of thematic continuity, thus, is not located in the conceptual knowledge of the child. It seems better conceived as a problem that has to do with the fact that the agenda is partially hidden from the child, while it is clear to the interviewer. The problem of thematic continuity should therefore preferably be studied from both an interviewer and child perspective, respectively. The children are not given a sufficiently clear indication that they should stick to the astronomical framing. Being engaged in a conversation obliges the participants to follow a number of more or less tacit interactional rules. Mastering these rules is an important element of the process of becoming a competent member of our society. For example, failing to provide a response when being asked a question is a sharp violation of these rules. Another important rule is to regard our conversational partners as being intelligible and coherent. In an interview-situation these guiding principles tend to be of utmost importance for the interviewee, sometimes followed ad absurdum. What we find, then, in this material is the children proving to be qualified language users. When the interviewer hints that there exists a problem, the interviewees read him as being intelligible. The only way they can do this, supposing that they do not hold it possible that one can fall off the earth, is to change the topic or extend it in a reasonable direction and this is precisely what the children seem to be doing in the excerpts we have used. A further point, which supports our line of reasoning, is that when the question about gravity is explicitly expressed, not a single child accepts the claim that it is possible to fall off the earth. On the contrary, most children show a remarkable ability to participate in a discussion on this difficult topic and to make meaningful contributions. Excerpt 9 illustrates how educated a conversation a pupil in the first grade can accomplish if only given a bit of support in the interaction. Excerpt 9. John

124 I: 125 John:

grade

Of course one can live in South Africa, one can live in South America. Don’t you fall off the earth down here then? No

MAP READING VERSUS MIND READING 126 I: 127 John: 128 I:

129 John: 130 I: 132 John: 132 I: 133 John: 134 I: 135 John:

95

You don’t If you come like this outside you don’t fall off if you walk outside the earth But if you walk far down here in the south, then? Don’t you think it’s strange that you can live down here? What if they just slip and fall off the earth? No, they won’t do that Why won’t they do that then? They think they’re walking in their way. They’re more used to walking like that or something Oh, I see But actually you walk … it feels as if you walk straight ahead and then you walk around the earth if you go too far So you can’t fall off the earth? No, it’s almost as big as anything

Given all the research within the cognitivist perspective illustrating the apparent difficulties children have with understanding the shape of the earth and gravity, one would not expect to find any satisfactory explanations of why it is impossible to “fall off” the earth. But notice in line 133 how seven-year old John in a very exact way resolves the supposed conflict between the information about the shape of the earth and his “basic ontological presuppositions” (Vosniadou, 1994, p. 49). He is clearly able to distinguish between what happens on a psychological or personal level and what happens on a physical level: one can walk “straight ahead” and still walk “around” the earth. This is quite an amazing insight for a seven-year old. Having arrived at this point, we will conclude this part by commenting on one general feature of the empirical material. Our impression is that in order to maintain the dialogue the participants have to reach temporarily shared contextualisations (Rommetveit, 1992). The children, operating under the specific conditions provided here, have to coordinate their way of conceptualising the activity with the one represented by the dominant party in the interaction. Posing a question is maybe not enough to put the child in a communicative situation where the contextualisations of what is talked about are sufficiently shared. Perhaps this problem of coordination is a more important feature of learning contexts than is generally recognized; it is by being supported in the complex task of adopting and sharing specific perspectives that one learns to talk and think under the guidance of a more experienced partner. 5.

CONCLUSION

The results of this study in many respects confirm the general observations made in the previous work where the globe was present in the interview situation. The conceptions about the earth as a flat object, as hollow, etc., do not appear in this material either, in spite of the fact that this study involves the use of a twodimensional artefact. The claim that children hold such mental models (or framework theories) seems questionable and appears primarily as a product of the

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methods used. When children are interviewed without any support in the form of a meaningful artefact, they obviously express views that disappear completely when there is a map present. In a similar vein, none of the participants in this study accept the view that one can fall off the earth. Not even when being explicitly asked, in quite a provocative manner, what happens if one is “down under” on the map do they suggest that this would be possible. This is a strong indication of the familiarity on the part of the child with the map as a cultural artefact and of the efficiency with which it serves as a prosthetic device for reasoning. What is it, then, that so clearly differentiates this study from the studies made within the cognitivist perspective? Methodological differences regarding what are legitimate inferences of what children mean by what they say aside, two major factors stand out. The first element is the use of a physical artefact with a long history. The map is a powerful device that carries a number of conceptual distinctions with it, many of which may be totally unknown to the children. With a more competent conversational partner to help them, though, this map functions as an effective resource for reasoning. The map helps create what Latour calls “a meeting ground, a common place” (1986, p. 8). Due to its “optical consistency” in Latour’s sense the two-dimensional surface of the map will provide the same “windowpane” for any observer who is familiar with this particular piece of technology. The map affords viewpoints and information. In this study, it is clear that both children and interviewer make active use of this optical invariance as a resource for their reasoning (see Excerpts 3, 4, 5, 6 & 9). They go back and forth between thinking, talking and consulting the artefact. The use of a physical artefact alone, however, is not a sufficient condition, as is illustrated by the multitude of objects used by, for example, Sneider and Pulos (1983) (see Figure 2) in their study. The children also have to know what they are supposed to talk about. The second factor, differentiating this study from many others, is therefore associated with the way the artefact, and the whole interview situation, is framed (Goffman, 1974) in a communicative sense. How one is supposed to talk about an object is not self-evident, which is illustrated in Excerpts 1 to 3. It is necessary that the interviewer and the interviewees reach some sort of common understanding of the artefact and, in this case, its relation to its referent. Given the uncertainty initially expressed by most children regarding the status of the artefact and the point of the interview-situation as such, we believe that the map can be seen as a “boundary object” (Star & Griesemer, 1989). The concept of “boundary objects”, as developed by Star and Griesemer, is an attempt to describe how objects may help create mutual comprehensions across intersecting social worlds. This is an analytic concept of those scientific objects which both inhabit several intersecting social worlds and satisfy the informational requirements of each of them. Boundary objects are objects which are both plastic enough to adapt to local needs and the constraints of the several parties employing them, yet robust enough to maintain a common identity across time. They are weakly structured in common use, and become strongly structured in individual-site use. (Star & Griesemer, 1989, p. 393.)

Although boundary objects have different meanings in different social worlds their structure is common enough to more than one world, to make them recognizable. In their description, Star and Griesemer portray four different types of boundary

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objects. Of these, the ideal type is the one most in agreement with our map. The ideal type of boundary objects, such as a diagram or an atlas, is abstracted from all domains and may remain rather vague. Due to this vagueness it can be adapted to a local site and function as a means for communication. This adaptation of the map to the local context is exactly the process we have observed (see Excerpt 6), and we regard such adaptation as necessary for the communication to function properly. Following Star and Griesemer, “boundary objects act as anchors or bridges, however temporary” (1989, p. 414) between contexts and persons, and this, we believe, is the reason why the interviews in this study have a rather stable character, why the relation between the map and the earth can be sustained in spite of the low age of the participating children. As has already been pointed out above, the main theme of this study is the assumption that there is no baseline for cognition. Although we admit that there are phenomena that can be labelled mental processes, we cannot accept the claim that these are possible to study independently of cultural tools. There is nothing to be gained by positing such a level of inquiry as the one implied by a notion of pure cognition underpinning our thinking. Our mental functioning is irrevocably intertwined with a vast array of cultural tools. When we, for example, do mental calculations, no visible or otherwise apprehensible borders can be found between the human as an “information processor” (Ashcraft, 1994), and the multiplication table as a cultural artefact. This is the reason why we prefer to change metaphors and, instead, talk about cognition as the use of tools. Although it has been common practice in the educational area to test the abilities of pupils, stripped of most of their ordinary tools, we do not feel the need to import this thinking into scientific inquiries. On the contrary. There is no sense in saying that functioning without support in the form of physical artefacts is the more natural or basic state of human cognition, or that such an approach provides a more correct measure of an individual’s competence. From our perspective, an important part of cognitive development is the gradual appropriation and/or mastery of mediational means. Early in this process, when the mediational means are unfamiliar and still poorly under control, one is more open to influence and more in need of communicative support. Under such conditions, the unit of analysis (children operating with mediational means) is in a sense less stable or less coordinated. This is why studies, using somewhat different methods, can come up with results that vary. Provided with various forms of artefacts and varying levels of support, children of the same age span will present responses within a very large spectrum. This is not particularly surprising. Consequently, we do not propose that the children in this study have presented their “normal” functioning or that this is necessarily how they reason in their everyday lives. We would, rather, like to point out the flexible nature of human cognition and the potentialities that exist in this area; how understanding and reasoning are not so easily confined within the boundaries of a single individual, but how mental activities instead, metaphorically speaking, interact with artefacts and other people. The distinction between cognition of individuals, communication between individuals and tools must be regarded as blurred. What we have shown is that given favourable conditions even young children can accomplish rather

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complicated forms of reasoning and make distinctions between what they see in front of them and what applies in a physical world and when looking at the earth as an astronomical object. In some fascinating sense, the distinctions made by these children would have been impossible for the most advanced scholars a few hundred years ago to make: This is a strong indication of the intimate links between culture and human reasoning, and, ultimately, between culture and human development. ACKNOWLEDGEMENTS The work reported here has been financed by the Swedish Council for Research in the Humanities and Social Sciences through a grant to the project Information technologies as prosthetic devices for cognition and communication. A sociocultural analysis of computer-mediated learning in science instruction.

REFERENCES Ashcraft, M. H. (1994). Human memory and cognition (2nd ed.). New York: Harper Collins. Bateson, G. (1979). Mind and nature: A necessary unity. London: Wildwood. Bateson, G. (1972). Steps to an ecology of mind. New York: Ballantine Books. Bliss, J., & R. Säljö, R. (1999). The human-technological dialectic. In J. Bliss, R. Säljö, & P. Light (Eds.), Learning sites. Social and technological resources for learning (pp. 1-11). Amsterdam: Pergamon/Elsevier. Fremlin, G., & Robinson, A. H. (1999). Maps as mediated seeing. Cartographica, 31. Gardner, H. (1987). The mind’s new science. A history of the cognitive revolution. New York: Basic Books. Gergen, K. J. (1985). The social constructionist movement in modern psychology. American Psychologist 40, 266-75. Goffman, E. (1974). Frame analysis. New York: Harper and Row. Harvey, P. D. A. (1980). The history of topographical maps. London: Thames and Hudson. Latour, B. (1986). Visualization and Cognition. Thinking with Eyes and Hands. Knowledge and Society. Studies in the sociology of culture past and present, 6, 1-40. Lemke, J. L. (1990). Talking science. Language, learning, and values, language and educational Processes. Norwood, NJ: Ablex. Mali, G. B., & Howe, A. (1979). Development of earth and gravity concepts among Nepali children. Science Education 63, 685-691. Nussbaum, J. (1979). Children’s conceptions of the earth as a cosmic body: A cross age study. Science Education, 63, 83-93. Nussbaum, J., & Novak, J. D. (1976). An assessment of children’s concepts of the earth utilizing structured Interviews. Science Education, 60, 535-550. Piaget, J. (1929). The child’s conception of the world. London: Paladin. Robinson, A., Sale, R., & Morrison, J. (1990). Elements of cartography. New York: John Wiley & Sons. Rogoff, B. (1990). Apprenticeship in thinking. Cognitive development in social context. New York: Oxford University Press. Rommetveit, R. (1988). Literacy and the myth of literal meaning. In R. Säljö (Ed.), The written world (pp. 13-40). New York: Springer. Rommetveit, R. (1992). Outlines of a dialogically based social-cognitive approach to human cognition and Communication. In A. Heen-Wold (Ed.), The dialogical alternative. Towards a theory of language and mind (pp. 19-44). Oslo, Norway: Scandinavian University Press. Saxe, G. (1991). Culture and cognitive development: Studies in mathematical understanding. Hillsdale, NJ: Lawrence Erlbaum Associates. Schoultz, J., Säljö, R.,. & Wyndhamn, J. (in press). Heavenly talk discourse, artifacts, and children’s understanding of elementary astronomy. Human Development. Sneider, C., & Pulos, S. (1983). Children’s cosmographies: Understanding the earth’s shape and gravity. Science Education, 67, 205-221.

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Star, S. L., & Griesemer, J. R. (1989). Institutional ecology, “translations” and boundary objects: Amateurs and professionals in Berkeley’s museum of vertebrate zoology, 1907-39. Social Studies of Science 19, 387-420. Säljö, R. (1998). Thinking with and through artifacts: The role of psychological tools and physical artifacts in human learning and cognition. In D. Faulkner, K. Littleton, & M. Woodhead (Eds.), Learning relationships in the classroom (pp. 54-66). London: Routledge. Tulviste, P. (1994). History taught at school versus history discovered at home: The case of Estonia. European Journal of Psychology of Education 9, 121-126. Wittgenstein, L. (1953). Philosophical investigations. Oxford: Blackwell. Vosniadou, S. (1994). Capturing and modeling the process of conceptual change. Learning and Instruction 4, 45-69. Vosniadou, S., & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24, 535-585. Vosniadou, S., & Brewer, W. F. (1994). Mental models of the day/night cycle. Cognitive Science, 18, 123-183. Vygotsky, L. S. (1986). Thought and language (A. Kozulin Ed.). Cambridge, M: MIT Press. Wertsch, J. V. (1998). Mind as action. New York: Oxford University Press. Wertsch, J. V. (1991). Voices of the mind. A sociocultural approach to mediated action. London: Harvester Wheatsheaf. Wyndham, J., & Säljö, R. (1999). Quantifying time as a discursive practice: Arithmetics, calendars, fingers and group discussions as structuring resources. In J. Bliss, R. Säljö, & P. Light (Eds.), Learning sites. Social and technological resources for learning (pp. 80-96). Amsterdam: Pergamon/Elsevier.

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UNDERSTANDING CONCEPTUAL CHANGE: A COMMENTARY RICHARD E. MAYER University of California, Santa Barbara, USA

Abstract In this essay, I compare and contrast four views of conceptual change--Vosniadou’s synthetic meaning view, Chi and Roscoe’s misconception repair view, diSessa’s knowledge-in-pieces view, and Ivarsson, Schoultz, and Säljö’s sociocultural view. In particular, I compare these four views in terms of what changes during conceptual change, who changes, how the change occurs, where the change takes place, the role of prior knowledge, and whether their is research evidence. As a conclusion, I offer a proposal for reconciling alternative views of conceptual change.

1. INTRODUCTION

How does a learner come to understand how force and motion work, how the human respiratory system works, or how gravity keeps objects on the earth? In each case, the learner undergoes a process of conceptual change in which he or she builds a coherent mental representation capable of explaining the target phenomenon. Conceptual change is the mechanism underlying meaningful learning. Conceptual change occurs when a learner moves from not understanding how something works to understanding it. For decades scholars have recognized that conceptual change is at the heart of meaningful learning. Over the years, conceptual change has been represented as a process of achieving structural insight, accommodative learning, understanding of relations, deep learning, or--more recently--mental model building (Mayer, 2000). Conceptual change has long been recognized as a fundamental aspect of science learning, and as a key process in learning in other domains. If scholars could understand how conceptual change works they would make important contributions both to learning theory and to educational practice. Throughout the first half of the 20th century researchers sought to build general theories of learning that could account for all forms of learning, but by mid-century it became clear that such efforts had failed (Mayer, 2001). Instead, today scholars focus on domain-specific theories of learning, such as trying to understand how people learn how something works or how to carry out a given procedure. Gone are the days when grand theories of learning dominated psychology and education, replaced today with more focused

M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 101-111. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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and modest theories of learning. The search for a research-based theory of conceptual change represents a major component in this focused strategy. My assignment in this piece is to compare and contrast four views of conceptual change: Vosniadou’s (this volume) synthetic meaning view, Chi and Roscoe’s (this volume) misconception repair view, diSessa’s (this volume) knowledge-in-pieces view, and Ivarsson, Schoultz, and Säljö’s (this volume) sociocultural view. In each of four respective sections, I analyze the views in terms of what changes during conceptual change, who changes, how the change occurs, where the change takes place, the role of prior knowledge, and whether their is research evidence. Finally, in the last section, I attempt to synthesize a vision of conceptual change based on the ideas in these four views. 2. VOSNIADOU’S SYNTHETIC MEANING VIEW OF CONCEPTUAL CHANGE: CHANGE AS SYNTHESIS

What changes? In Vosniadou’s theory, the learner seeks to builds a coherent explanatory framework (or mental model) of how some system works. In short, what changes is the learner's mental model. Who changes? In Vosniadou’s theory, learners are synthesizers who attempt to reconcile inconsistent models of how something works. The learner is a model builder who creates conflict by acquiring inconsistent new knowledge but who seeks to build internally consistent models. How does change occur? Learners build a mental model by integrating new material from science instruction with their existing explanatory frameworks: “Information received through instruction seems to become assimilated to the initial explanatory framework creating synthetic or internally inconsistent models.” Conceptual change begins with the learner’s existing explanatory framework, that is, a naive theory of how something works based on personal experience: “Children construct a narrow but coherent explanatory framework that guides the process of acquiring knowledge about the physical world from early on.” The next step in conceptual change occurs when learners are exposed to science instruction that is inconsistent with their existing mental representations; as they assimilate this new knowledge with existing mental representations they form synthetic meanings that lack coherence and stability. The final step is to resolve the internal inconsistencies, so “conceptual change occurs from the need to solve internal inconsistencies.” This process of resolving internal inconsistencies in the learner’s knowledge is a gradual one which can result in a progression of mental models. Rather than involving sudden replacement of misconceptions, conceptual change involves assimilating new scientific knowledge to existing explanatory frameworks, thereby creating internal inconsistencies that must be gradually reconciled. Rather than involving the process of organizing isolated knowledge fragments, conceptual change is a process of assimilating knowledge to existing structures, which must then be reorganized. Where does change occur? Vosniadou presents a cognitive account of conceptual change in which the changes occur within the learner’s mind.

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What is role of prior knowledge in conceptual change? In Vosniadou’s view of conceptual change, prior knowledge is both an obstacle for change--because it must be revised--and a vehicle for change--because new conflicting knowledge is assimilated to it. Is there research evidence? In an exemplary study, kindergarteners, 4th graders, 6th graders, and 9th graders were asked in an interview to answer a series of questions about force. For example, in one question they were shown a drawing of a stone standing on the ground and asked, “Is there a force exerted on the stone? Why?” For most of the students, it was possible to classify their answers as consistent with one out of a small number of mental models of force. The most common model for kindergarteners was internal force, the idea that objects have internal force based on their weight or size. The internal force model is an example of an initial explanatory framework based on personal experience. The most common model for 4th graders was internal and acquired force, the idea that objects have internal force based on their weight or size, but there is also an acquired force within moving objects only. There is an internal inconsistency in the synthetic meaning of combining internal force and acquired force. The most common model for 6th graders was acquired force, the idea that there is an acquired force within moving objects only. The reliance on acquired force, which is another explanatory framework, can be seen as an attempt to resolve the inconsistency inherent in the internal and acquired force model. The most common model for 9th graders was gravitational and other forces, the idea that forces in objects come from gravity, from being pushed or pulled, and from moving. Students appear to be assimilating Newtonian concepts within their existing framework based on acquired force. By adding the force of gravity and the force of push/pull to the force of movement, learners create various synthetic meanings that eventually need to be resolved. 3.

CHI AND ROSCOE’S MISCONCEPTION REPAIR VIEW OF CONCEPTUAL CHANGE: CHANGE AS REPLACEMENT

What changes? In Chi and Roscoe’s view, the learner seeks to construct an accurate mental model of how something works. When mental models initially are based on incorrect conceptions (as in naive knowledge), these conceptions must be replaced: “All naive knowledge needs to be repaired in order to promote deep understanding.” Thus, what changes is the learner's mental model and the conceptions from which it is built. In particular, a misconception is defined as a miscategorized concept, so what changes is the placement of a concept from an incorrect category to a correct category. The resulting mental model changes from being flawed to being correct. Who changes? Learners are fixers who repair erroneous conceptions in their mental models. Learners engage in the repair process by recognizing misconceptions (i.e., miscategorized concepts) and creating or finding new categories into which the miscategorized concepts can be placed. How does change occur? Conceptual change occurs when a learner identifies a faulty conception in his or her mental model, and repairs it. Learners begin with naive knowledge--or existing conceptions--that are often incorrect. Naive knowledge

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can consistent of preconceptions, which easily can be revised or removed through instruction, and misconceptions, which are misunderstandings that persist even when confronted with focused instruction. In short, “cognitive change is the process of removing misconceptions.” The mechanism by which misconceptions are repaired involves recategorizating a concept from an incorrect category to a correct category: “Misconceptions are, in fact, miscategorizations of concepts” so “conceptual change is merely a process of reassigning or shifting a miscategorized concept from one … category to another.” To accomplish conceptual change, learners must become aware that they have miscategorized a concept and must invent or find an appropriate category to which it can be reassigned. Conceptual change means to change from a flawed (or incomplete) mental model to a correct mental model through assimilation (i.e., adding new pieces of knowledge) and revision (i.e., correcting pieces of knowledge). This is an incremental process--of changing many small pieces of knowledge--rather than a process of sudden accommodation. Where does change occur? Conceptual change is a cognitive process that occurs within the learner’s mind. What is the role of prior knowledge in conceptual change? Prior knowledge-when it contains misconceptions--is an obstacle to conceptual change: “Naive knowledge ...often (but not always) impedes the learning of formal knowledge with deep understanding.” Is there research evidence? First, Chi and Roscoe describe previous research on 8th graders' preconceptions about how the human circulatory system works (Chi, 2000). Based on in-depth interviews, a collection of incorrect conceptions was identified (such as “all blood vessels have valves”). Then, students read a text about the human circulatory system and were interviewed again as a post-test. Many of the preconceptions that were addressed in the text were correctly revised on the post-test (such as “veins are the only vessels to have valves”), but those not addressed in the text were not correctly revised on the post-test. This research shows that some incorrect conceptions can be changed easily through instruction--namely, preconceptions. The authors also describe a more recent study in which students read a text about the human circulatory system and explain to themselves what various sentences mean. Interviews with students show that the self-explanation process fosters incremental revisions of individual propositions about how the human circulatory system works, enabling students to change from a single loop model (in which only the heart is involved in pumping oxygen to the body) to a double-loop model (in which the lungs and heart are involved). This research shows that what appears to be a major conceptual change (from a single-loop to double-loop model) can be created by repairing individual pieces of knowledge about the circulatory system.

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4. DISESSA’S KNOWLEDGE-IN-PIECES VIEW OF CONCEPTUAL CHANGE: CHANGE AS ORGANIZING What changes? In diSessa’s view--expressed in his chapter and elsewhere (diSessa, 2001)--the learner organizes many fragments of naive knowledge into a structured mental representation of complex system. Learning involves the construction of what diSessa calls a complex knowledge system (or conceptual ecology) consisting of a large number of different kinds of conceptual elements that are modified and combined in complex ways such as levels and subsystems. What changes, then, is the way that knowledge is organized--from fragmented to structured. Who changes? Learners are knowledge organizers who strive to build connections among the diverse elements in their knowledge base. How does change occur? The process of conceptual change relies on mentally reorganizing one's knowledge: “Conceptual change involves a large number of diverse kinds of knowledge organized and re-organized into complex systems.” Learners begin with intuitive knowledge called p-prims (for phenomenological primitives)--small, simple, plentiful, natural-feeling pieces of knowledge used to help understand one's experience. For example, in intuitive physics, a p-prim is the idea that “induced motion just dies away”, that is, an object in motion requires a force acting on it to stay in motion. However, in the course of conceptual change, pprims are integrated into more complex explanatory systems. P-prims no longer function as isolated monolithic explanations but rather become part of a larger system. DiSessa notes that “many p-prims find useful places in the complex system” and might “come to be known as an effective special case of a scientific principle.” Thus, the mechanism underlying conceptual change is not a simple process of deletion or replacement of p-prims, as in contrasting views of conceptual change, but rather a complex process of integration and reorganization. Where does change occur? Conceptual change is a cognitive process that occurs in the learner’s mind. What is the role of prior knowledge in conceptual change? Prior knowledge-such as p-prims--form the basis for conceptual change. Prior knowledge enables conceptual change because conceptual change involves organizing existing pieces of knowledge. Is there research evidence? The supporting empirical evidence for diSessa’s argument comes from selected segments of the protocol of a structured clinical interview about physics problems with one child called J. However, diSessa correctly warns that “I don’t intend to prove or demonstrate here.” 5. IVARSSON, SCHOULTZ, AND SÄLJÖ’S SOCIOCULTURAL VIEW OF CONCEPTUAL CHANGE: CHANGE AS TOOL APPROPRIATION What changes? In conceptual change, learners appropriate intellectual tools (i.e., agreed-upon concepts such as the concept of gravity) and physical tools (i.e., agreed-upon representations such as maps and globes). The authors claim that cognition is the use of tools, so conceptual change involves the development of tool-

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using practices. Thus, what changes is the way that tools are used by learners in various contexts: “An important part of cognitive development is the gradual appropriation and/or mastery of mediational means.” Who changes? Learners are tool users in social context: “Mental functioning is irrevocably intertwined with a vast array of cultural tools” so it is not possible to study mental processes independently of cultural tools. Accordingly, conceptual change does not occur within individual minds. Rather the change occurs as an interaction between the learner, tools, and other people. How does change occur? Conceptual change through the learner's participation in using intellectual tools (e.g., concepts) and physical tools (e.g., artefacts) within relevant social activities, or what Ivarsson, Schoultz, and Säljö call collective cultural practices. The authors state that “human cognition is socialized through participation in activities where tools are used for particular purposes” so there are “intimate links between cognition and the use of tools in situated practices.” For example, in using a globe or a map to answer questions about whether it is possible to fall off the earth, a learner is using a physical tool--the globe or map--to reason. Conceptual change occurs through interacting with other people in situations requiring the use of intellectual and/or physical tools. Where does change occur? Ivarsson, Schoultz, and Säljö challenge the “assumption that human mental functions are located in individuals.” Taking a sociocultural perspective, human cognition takes place in a sociocultural context as an interactive process rather than a purely cognitive one. What is the role of prior knowledge in conceptual change? In Ivarsson, Schoultz, and Säljö’s view, prior knowledge is neither an obstacle nor a prerequisite for conceptual change. The learner begins without using appropriate tools and must learn to become a more effective tool user. Is there research evidence? The major empirical evidence comes from structured interviews with children who are asked geographic questions such as whether it is possible for people to fall off the earth. When the children are allowed to use a world map (as a mediational tool) they display sophisticated reasoning about the nature of the earth. Such evidence supports the idea that human cognition is tooldependent so that different kinds of reasoning occur when children have access to different kinds of tools. It therefore does not make sense to describe conceptual change as a progression of mental models, because students’ mental models are influenced by the mediational tools they have available in any particular situation (such as maps). 6. RECONCILING COMPETING VIEWS OF CONCEPTUAL CHANGE

In this section, I attempt to reconcile the four competing views of conceptual change represented in these four chapters. For purposes of conciseness, I refer to the four chapters by their first or sole author’s name--Vosniadou, Chi, diSessa, and Ivarsson, respectively. The four views are summarized in Table 1. Which version of constructivism best characterizes conceptual change? My attempt at synthesis begins with a thorny problem: Three of the four chapters

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(Vosniadou, Chi, and diSessa) grow out of a cognitive tradition of viewing conceptual change as a process of knowledge building whereas one of the chapters (Ivarsson) comes from a sociocultural tradition which the authors claim cannot be reconciled with the others: “Although it would be tempting to create syntheses between traditions, our preference would be to keep them apart.” In spite of Ivarsson’s us-versus-them view, I believe my efforts at synthesis are still warranted. Ivarsson lays out the major thesis that cognition always occurs in social and cultural (or historical) context because cognition requires the use of appropriate cultural tools: “We cannot separate thought processes, say in the context of doing geometry or playing chess, from the conceptual tools that are applicable to such activities.” “Cultural tools form an integrated part of cognitive processes. “ “There is no sense…in assuming that there is a level of thinking that is pure.” “Thinking is the use of tools.” I fail to see how this thesis is inconsistent with the cognitive view that conceptual change involves knowledge construction. I agree that it is impossible to think in general; rather thinking is always about something ranging from how to solve a geometry problem to how to find the meaning of a text, that is, cognition always occurs in context. If knowledge is framed as a cultural tool, then the goal of research on conceptual change remains to determine how knowledge changes in learners. Following Vygotsky’s theory, Ivarrson states that “learning and conceptual development could be seen as a process of internalisation by individuals of conceptual tools.” This characterization of the conceptual change process appears to be consistent with a cognitive psychological perspective in which learning results in a change in the learner’s knowledge. In short, I see room for reconciliation between Ivarsson’s points and the cognitive psychology tradition. Not all of Ivarsson’s points appear easy to reconcile with the other views, especially the assertion that “concepts are not just mental entities that reside inside our heads, they are part of human social practices.” However, read in the most optimistic way, this statement allows for cognitive representations--and hence the cognitive tradition--because it suggests one aspect of concepts is that they are mental entities that reside inside our heads. Further, the idea that concepts exist as part of social practices--that is, that knowledge must be used within certain situations--also does not seem to contradict the idea that people possess and use knowledge. Finally, the emphasis on language--particularly speech--as the major cognitive tool seems to exclude other forms mental representation such as visual imagery: “Thinking in this perspective is conceived as a kind of silent and private dialogue.” However, even Ivarsson’s examples using maps and globes show that representational systems used to support human cognitive activity can include visual imagery. Again, the use of representational tools to build knowledge is highly consistent with the cognitive tradition. The most troubling aspect of Ivarsson’s piece is the refusal to consider ways of synthesizing the cognitive and sociocultural approaches because of “conflicting assumptions about the nature of human cognition…that cannot be easily resolved by appealing to empirical data.” What is wrong with insisting that “my ism is better than your ism”? In analyzing the various forms of constructivism, it is worthwhile to

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distinguish among cognitive constructivism, social constructivism, and radical constructivism (Mayer, 1997). In cognitive constructivism, the learners build knowledge in their minds. In social constructivism, this knowledge building process is guided by social interaction and takes place in a social context. In radical constructivism, there are no such things as knowledge representations in learner’s minds; rather, knowledge exists only within a social context. Both cognitive constructivism and social constructivism are mutually compatible and allow for scientific testing; radical constructivism is not compatible with the others and does not appear to support a rigorous scientific approach. Instead, radical constructivism depends on a relativistic view in which all theories are equally valid, and in which scientific testing is obsolete. If Ivarsson’s approach is cast as social constructivism, then synthesis with the other approaches is possible; however, if Ivarsson’s approach is cast as radical constructivism, it is irreconcilable but it also relinquishes any claims of being scientific. My opinion is that a doctrine-based approach to the study of conceptual change is not likely to be productive. My assessment is supported by the 100-year history of failure of doctrine-based approaches to human learning (Mayer, 2001). During the last century scholars attempted to build grand theories of learning by arguing about which brand of behaviorism was best, comparable to today's arguments about which version of constructivism is best. In summary, my point is simple: The search for the perfect ism is not a fruitful path for our science. A doctrine-based approach to our science has been tried and it has failed. I urge scholars to take an issue-based approach in which we agree to try to understand how conceptual change works rather than to determine which ism is right. What is conceptual change? The chapters I have reviewed offer thoughtful and insightful analyses of the mechanisms underlying conceptual change. I characterize the four competing views of conceptual change as synthesis, replacement, organizing, and tool appropriation. In each theory, conceptual change is a cognitive process in which the learner seeks to construct knowledge that is coherent and useful. In some, it is also a social process in which the learner comes to use the agreed-upon cognitive tools of one's culture. What changes? In each of the theories, the learner’s knowledge is the locus of conceptual change. The result is a mental representation that is organized and functional. In some, it is also a socially agreed-upon representation. Who changes? In each of the theories, the learner is an active sense maker-conceived of as synthesizer, fixer, organizer, or tool user. The sense making process includes detecting and correcting inconsistencies in one’s knowledge--as highlighted by Chi--as well as building coherent structures--as highlighted by Vosniadou and by diSessa. How does change occur? In all of the theories, conceptual change is a gradual process of knowledge building. Specifying the mechanism underlying conceptual remains as the central challenge of research on conceptual change. Can all conceptual change be explained as replacing incorrect conceptions that form a larger mental model

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(as suggested by Chi), as organizing one's prior experiences (as suggested by diSessa), as reorganizing one’s old and new knowledge (as suggested by Vosniadou), or as becoming increasingly proficient in using cognitive tools (as suggested by Ivarsson)? In order to answer this question, the theories must be specified in more detail so that they can be subjected to rigorous scientific testing. Where does change occur? Three of the four theories share a common goal of determining the mechanism by which conceptual change occurs in learners-Vosniadou’s synthetic meaning, Chi’s misconception repair, and diSessa’s knowledge in pieces theories. In these three theories, conceptual change occurs in the learner's mind. Ivarsson’s sociocultural theory emphasizes the idea that the change may be influenced by and is dependent upon the social and situational context. However, in my reconciliation, the human mind remains as the venue for change. What is the role of prior knowledge in conceptual change? Prior knowledge is both an enabler of conceptual change--providing the building blocks out of which new knowledge structures are built--and an obstacle to conceptual change--when existing knowledge is incorrect but entrenched. DiSessa stresses the first aspect of prior knowledge and to varying extents Vosniadou and Chi stress the second aspect, but both aspects can be seen all theories. Is there research evidence? Most of the research evidence comes from structured interviews in which students are asked to explain various scientific phenomenon--such as whether a resting object has a force exerted on it, how the human circulatory system works, whether heavier objects fall faster, and whether it is possible for a person to fall off the earth. In some cases, comparisons are made between children at various age levels (e.,g., Vosniadou) and in others the comparisons are made with children at various points in their learning about a topic (e.g., Chi). In my opinion, the field benefits from both cross-sectional and longitudinal studies. In some cases, the results are presented in quantitative form such as the percentage of students with each type of conception (e.g., Vosniadou and Chi) and in others the results are presented in qualitative, form as a segment of a transcript (e.g., diSessa and Ivarsson). In my opinion, the field benefits from both quantitative, and qualitative data. Quantitative data are useful for theory testing but may fail to capture the richness of authentic learning. For example, Vosniadou provides important statistics showing developmental changes in the kinds of conceptual models that children use for understanding force and motion; however, the data do not clarify exactly how the change occurs from one level of understanding to the next. In contrast, qualitative data can be useful in providing detail but may be less useful in theory testing. For example, diSessa shows how qualitative data provides a rich texture in which to better appreciate the complexity of conceptual change within individual learners; however, selected portions of transcript from a single learner are unlikely to meet the criteria for rigorous scientific testing of a theory of conceptual change. In my opinion, the best course of action is to include a variety of research methods that converge on the explication of conceptual change.

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From my vantage point, the biggest challenge facing conceptual-change researchers is to specify testable theories and find empirical data to test them. Chi and Vosniadou provide exemplary research programs in which they offer detailed testable hypotheses concerning the nature of conceptual change supported by impressive amounts of both qualitative and quantitative data. Now, what is needed is to continue to specify detailed theories about the mechanisms of conceptual change and to create rigorous methodologies capable of generating high-quality data to test them. In short, the two most challenging ingredients for research on conceptual change are mechanisms and methodologies--that is, mechanisms embodied in detailed theories and methodologies that generate relevant data for testing the theories. Finally, the ultimate challenge is to use our understanding of conceptual change to improve science education. The educational implications of research on conceptual change make clear that presentation of information should not be the only goal of teaching science. Students may need guidance in their efforts to make sense of their experiences in science. Determining the nature of that guidance is the driving force for research on conceptual change. Therefore, intervention studies offer an important component in any program of research on conceptual change. REFERENCES Chi, M. T. H. (2000). Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In R. Glaser (Ed.), Advances in instructional psychology (vol. 5, pp. 161-238). Mahwah, NJ: Lawrence Erlbaum Associates. diSessa, A. A. (2000). Changing minds. Cambridge, MA: MIT Press. Mayer, R. E. (2000). Conceptual change. In A. E. Kazdin (Ed.), Encyclopedia of psychology (Vol. 2, pp. 253255). Washington, DC: American Psychological Association. Mayer, R. E. (1997). Searching for the perfect ism: An unproductive activity for educational research. Issues in Education, 3, 225-228. Mayer, R. E. (2001). Changing conceptions of learning: A century of progress in the scientific study of education. In L. Corno (Ed.), Education across a century: The centennial volume--One hundredth yearbook of the National Society for the study of Education (pp. 34-75). Chicago: National Society for the Study of Education. Vosniadou S., & Brewer, W. F. (1992). Mental meanings of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24, 535-585.

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PART II

MOTIVATIONAL, SOCIAL AND CONTEXTUAL ASPECTS

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THE ROLE OF MOTIVATIONAL BELIEFS IN CONCEPTUAL CHANGE

ELIZABETH A. LINNENBRINK & PAUL R. PINTRICH

University of Michigan, Ann Arbor, USA

Abstract. The authors discuss the importance of considering students’ motivation when investigating conceptual change. They begin by presenting a general model of the direct and indirect relations of achievement goals to conceptual change. Next, two empirical studies examining college students’ changing understandings of projectile motion are presented. Study 1 investigated the direct and mediated effects of achievement goals, affect, and cognitive strategy use on students’ change in physics understanding (N=105). Results indicated that adopting mastery goals resulted in higher levels of conceptual change, especially for those students with low prior knowledge. Performance goals were unrelated to conceptual change. Neither affect nor cognitive strategy use mediated the relation of mastery goals to change in physics understanding. Study 2 (N=l 10) was designed to replicate Study 1 and further examine potential mediators of achievement goals to conceptual change. As in Study 1, mastery goals were positively related to a change in physics understanding; however, this did not vary based on prior knowledge. Furthermore, elaborative strategy use and negative affect partially mediated the relation between mastery goals and change in physics understanding.

1. INTRODUCTION Research on the development and change in students’ conceptual understandings has focused almost exclusively on cognitive processes (Pintrich, Marx, & Boyle, 1993). However, given the levels of engagement and in-depth cognitive processing required for conceptual change processes to occur, it is also essential to consider students’ motivational processes so that we may gain a clearer understanding of when and why students’ conceptual understandings emerge and change. In this paper, we focus on students’ achievement goals and the role they play in changing students’ understanding of scientific phenomena. We begin by briefly discussing the development of conceptual understanding. Next, we discuss achievement goal theory and why it is important to consider in the development of conceptual understanding. Finally, we present data from two recent studies and discuss how the results help to inform our knowledge about the role of students’ motivation in the development of conceptual understanding. Conceptual change research has developed from two rather diverse fields of inquiry: science education and developmental psychology (Vosniadou, 1999). Each of these fields of research makes various assumptions about how knowledge develops and changes as a result of instruction. Our research here is based on M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 115-135. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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theories stemming from developmental psychology, especially framework theories (e.g., Vosniadou & Brewer, 1992). That is, we assume that prior knowledge and misconceptions can be thought of as theories or integrated schemas. Conceptual change does not readily occur as these underlying frameworks help to shape the way that new information is viewed. That is, since the prior theories are rather developed, it is often easier for students to try to fit new information into their prior frameworks then to develop new frameworks. The key to conceptual change, then, is to encourage students to question existing frameworks and develop new theories or substantially refine older theories to better meet the existing evidence. Thus, for conceptual change to occur, students must perceive that their prior conceptions do not fit with the new information they are learning. Once they have acknowledged this discrepancy, they must work to resolve it through either assimilation, incorporating the new knowledge in with the old knowledge, or through accommodation, replacing or reorganizing old concepts with new concepts. This type of reconceptualization requires high levels of engagement in the material and the use of adaptive cognitive strategies. The importance of engagement and adaptive strategy use suggests that students’ motivation to learn may play a role in determining whether or not students alter their conceptual understandings. Indeed, Pintrich et al. (1993) suggest that it is essential to consider “hot” cognitions such as motivation when studying conceptual change. In their discussion of the importance of motivation for conceptual change, Pintrich and his colleagues suggest that a variety of motivational theories may be of relevance to understanding the conceptual change process including achievement goal theory, expectancy-value theory, and self-efficacy theory. For the purposes of this paper, we focus on achievement goal theory as one way for understanding how motivation relates to the development of conceptual understanding. Briefly, achievement goal theory is a theoretical approach to understanding why and how students engage in particular academic activities (Ames, 1992). Two primary goals, mastery and performance goals, are the focus of much of the research using achievement goal theory. Mastery goals represent a focus on learning and understanding. That is, students who adopt mastery goals indicate that they do their schoolwork so that they can really learn and understand the ideas presented in the curriculum. Typically, these students are not afraid to make mistakes and view challenging tasks as an opportunity to learn. Mastery goals are generally associated with adaptive outcomes such as the use of complex cognitive strategies, positive affect, and persistence (e.g., Pintrich, 2000a). In contrast, performance goals represent a focus on demonstrating one’s ability, often in relation to others. A basic premise behind a performance goal orientation is that one is trying to demonstrate the quality of one’s ability and self-worth. Students with this goal focus more on these aspects of the self rather than the task to be learned (Maehr & Kaplan, 2000). Students who endorse performance goals report that they do their schoolwork in order to show that they are better than their classmates or to demonstrate to others that they are smart. Challenging tasks are viewed as a threat to the self, so many students with performance goals are less likely to engage in challenging activities. Normative models of goal theory suggest that performance goals are associated with negative outcomes such as reduced use of

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adaptive cognitive strategies and self-regulation as well as increases in negative affect (e.g. Ames, 1992). More recently, researchers have suggested that performance goals can be adaptive in certain situations such as college classrooms where normative grading is emphasized (Harackiewicz, Barron, & Elliot, 1998). This revised goal theory model suggests that students with performance goals may use more adaptive strategies such as increased self-regulation (Pintrich, 2000a,b). Achievement goals seem especially relevant to consider when investigating conceptual change processes because achievement goal theory suggests that students with mastery and performance goals should react differently to academic situations requiring conceptual change. Students with performance goals should be less likely to alter their understanding of a phenomenon since this would require that they first acknowledge that their prior beliefs are incorrect. That is, when confronted with a situation in which pre-existing beliefs or ideas are challenged, performance oriented students should be less likely to consider new ideas because they first need to admit that they were incorrect in the past which may threaten their ideas about being better or smarter than others. In contrast, mastery oriented students would likely see new information as a way to meet their goal of learning and further their understanding of the topic; they may therefore be more open to changing their ideas about the phenomenon, thus facilitating the conceptual change process. In addition to this potential direct relation between achievement goals and conceptual change, it also seems likely that achievement goals relate to conceptual change via affective and cognitive mediators (see Figure 1). Research relating achievement goals to affect, engagement, and cognitive strategy use suggests that mastery and performance goals are differentially related to these outcomes. Moreover, it seems probable that differences in the types of strategies used and affect experienced are important to the conceptual change process.

Research on achievement goals and affect suggests that mastery goals are generally related to increased positive affect and decreased negative affect while performance goals are unrelated to positive affect and related, at least in some cases, to increased

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negative affect (Linnenbrink, Ryan, & Pintrich, 1999; Roeser, Midgley, & Urdan, 1996; Skaalvik, 1997). The affect students experience while completing an activity may be important for their conceptual change in that it may influence how “open” they are to new concepts. That is, students who feel happy or are in a good mood may be less likely to view new information or information which contradicts their prior ideas as threatening. These students may be more open to new ideas. In contrast, students who are feeling anxious, sad, or unhappy may view new or contradictory information as a threat and would therefore be less likely to fully consider the information presented or may simply dismiss the information because it is contrary to what they already believe. In addition to the way students may view information based on affect, students’ affect may also influence the way they process information. For instance, Bless (2000) suggests that people in positive moods use general knowledge structures such as scripts and schemas to process information. However, when they perceive that the new information does not fit with their existing schemas, they are more likely to attend to the new information. This could be applied to conceptual change such that students in positive moods are able to detect discrepancies between new information and existing conceptions thus making a change in existing schemas more likely. In contrast, those in a negative mood are likely to attend to the details of the situation (Bless, 2000). Thus, students in negative moods may process the information in the situation, but they would be less likely to link the new information with prior knowledge; therefore, conceptual change would be unlikely to occur. Research on the relation of achievement goals with cognitive engagement suggests that mastery goals are related to increased levels of cognitive engagement while performance goals are generally associated with decreased levels of cognitive engagement (Pintrich, 2000a; Pintrich & Schrauben, 1992). Given the intentional nature of the conceptual change process, it seems plausible that increased engagement in an activity designed to promote conceptual change would result in increased conceptual change. Finally, mastery goals are associated with a variety of cognitive strategies that seem adaptive to conceptual change processes. The increased use of metacognitive self-regulatory strategies as well as deeper processing strategies such as elaboration associated with mastery goals would likely facilitate a change in conceptual understanding. In contrast, performance goals are not consistently associated with adaptive strategy use so it is unclear how performance goals might relate to conceptual change via strategy use. Although theoretically it seems plausible that achievement goals play an important role in the conceptual change process, few studies have examined this process. One exception is a qualitative study conducted by Lee and Anderson (1993). These researchers studied 12 students in two sixth grade classrooms during a series of science lessons. They interviewed students before the lessons to assess their motivation, attitudes, and understanding of the science concepts. They then observed the students during the lessons and interviewed them after the students completed the lessons. Students who reported a focus on understanding as their primary goal orientation (mastery goals) showed the greatest gains in conceptual understanding. These students were actively engaged in the learning activities and had an improved

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understanding of the concepts after the lesson. In contrast, students who reported espousing performance goals as their primary goal did not improve their conceptual understanding after the lesson. These students either did not engage in the activity or were disruptive. Overall, this study suggests that mastery goals relate to higher levels of engagement and conceptual change. In contrast, performance goals relate to lower levels of cognitive engagement and conceptual change. Although Lee and Anderson (1993) examined patterns in behavior associated with achievement goals based on their observations and interviews, they were not able to determine if differences in engagement and strategy use mediated the relation of goals to the development of conceptual understanding. In the present studies, we thought it necessary to further examine the relation of achievement goals to conceptual understanding using a methodology that would allow us to explore the mediational role of strategy use and affect. More specifically in the present studies, we attempted to induce a mastery or performance goal orientation and then studied the effects of this goal orientation on the change in students’ understanding of Newtonian physics. It is important to note that although we are studying conceptual change, we examined change in understanding over a relatively short period of time based on reading a refutational text. That is, we assessed change in understanding based on the differences in students’ understanding at the beginning of the experimental session and at the end of the experimental session (after reading a text designed to challenge students’ “naïve” understandings of Newtonian physics and teach accepted notions of projectile motion). This experimental session took place in less than one hour; therefore, we were not able to examine long-term changes in physics understanding. Nevertheless, there is evidence to indicate that refutational text is a viable means to change students’ understanding and that these changes in understanding are long lasting (Guzzetti, Snyder, & Glass, 1992). We hypothesize that mastery goals will result in increased levels of conceptual understanding while performance goals will be either unrelated to conceptual understanding (based on a revised goal theory model) or will be negatively related to conceptual understanding (based on a normative goal theory model). Since mastery goals help the student to focus on the material itself and students should be more inclined to disregard prior beliefs in order to reach their goal of understanding, a mastery goal orientation should facilitate a change in physics understanding. In contrast, performance goals should be unrelated or negatively related to conceptual change. Although there are some potential benefits to performance goals in terms of engagement in an activity and strategy use, it is unlikely that performance goals would result in increased conceptual change because students’ sense of self may be challenged by the new information. Thus, students with performance goals should be more likely to dismiss new information and retain their prior beliefs. In addition to these direct effects, we hypothesize that both affect and cognitive strategy use will partially mediate the effects of mastery goals on physics understanding. The increase in positive affect and decrease in negative affect associated with mastery goals should facilitate conceptual change. Further, the increased use of metacognitive self-regulatory strategies as well as elaborative

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strategies associated with a mastery goal orientation should enhance the development of conceptual understanding. 2.

STUDY 1

The first study represents an initial attempt to examine the relation between achievement goals and the learning of Newtonian physics. Students were asked to adopt a mastery or performance goal so that we could examine the effects of these goals on their change in physics understanding after reading a text passage. 2.1. Method 2.1.1.

Participants

Participants were 105 undergraduate introductory psychology students from a large research university in the Midwestern United States. The majority of participants were Caucasian; 44% were male and 56% were female. 2.1.2.

Procedure

This study used a between-subjects design where participants were randomly assigned to either a mastery or performance goal condition. All participants were tested individually in sessions lasting approximately 30 minutes. First, participants completed a pre-test measure of their physics understanding. Following the pre-test, students were induced into a mastery or performance goal condition (see Appendix A for goal induction). Next, students were asked to read a passage about Newtonian physics. Participants then completed a working memory test as a buffer task in order to erase any effects of rehearsal on the post-test measure of physics understanding. A post-test measure of physics understanding followed the buffer task. Finally, participants were asked to respond to a series of self-report questions querying them about their thoughts and feelings while working on the reading and completing the post-test. 2.1.3.

Materials

Physics materials. The text materials and comprehension measures were drawn from Qian and Alvermann (1995). The topic of the text concerned ideas about basic concepts in physics, in particular, Newton's theory of motion, impetus models, and gravity (e.g., If a ball rolls off a table, what is the trajectory of its fall? If an object is dropped from a plane what is its trajectory?). Students were told that they could read the text as long as they desired and that they could take notes or mark on the passage as they read. The amount of time they read the text was recorded. Both the pre- and post-test measures of comprehension were used to assess students’ understanding of Newtonian physics. The pre-test comprehension measure

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consisted of ten true/false questions and one multiple-choice question (possible scores 0 – 11). The post-test comprehension measure consisted of 24 multiplechoice items (possible scores 0 – 24). Self-report questions. At the end of the study, participants completed questions assessing their goal orientation, affect, and cognitive strategy use. Scales were created based on exploratory factor analysis. All items were rated on a 5-point Likert scaling (1 = Not at all true, 5 = Very true). All items began with “While I was reading the physics passage and answering the questions...” to instruct students to focus on their thoughts and feelings while they were working on the physics passage and post-test. To measure their goal orientations, participants were asked to respond to ten questions about their mastery goals and performance goals. Both scales were adapted from the Patterns of Adaptive Learning Survey (Midgley, Maehr, Hicks, Roeser, Urdan, Anderman, & Kaplan, 1996). The mastery goal scale had a reliability of .84 and the performance scale had a reliability of .88 (see Appendix B for a list of items). We also measured participants’ affect by asking them to complete items about their positive and negative feelings. The positive affect scale consisted of five items (alpha = .85) and was adapted from the Patterns of Adaptive Learning Survey (Midgley et al., 1996). This scale measured positive mood with items such as “I was in a good mood” and “I enjoyed it”. Negative affect was measured with a five-item scale (alpha = .78) adapted from Pintrich (2000a). Sample items included “I felt frustrated” and “I was anxious” (see Appendix B for a complete list of items). In this case, negative affect refers to feeling frustrated, anxious, and annoyed. Finally, we assessed students’ cognitive strategies and thoughts with three scales (see Appendix B). Metacognitive strategy use assessed students’ self-regulatory strategies with three items (reliability = .70). Items were adapted from the motivated strategies for learning questionnaire (MSLQ, Pintrich, Smith, Garcia, & McKeachie, 1993). Students’ use of elaborative strategies measured the degree to which they related what they were reading to what they already knew. This scale contained two items and had a reliability of .94. Finally, we created a scale to measure students’ task-irrelevant thoughts. This scale had a reliability of .84 and included items such as “I thought about things other than the task” and “I had difficulty keeping my mind on things”. 3. 3.1.

RESULTS

Results of Goal Induction

To assess the efficacy of the goal induction, we conducted two independent t-tests examining differences in self-reported goals by goal condition. There were no significant differences in self-reported mastery goals by condition In contrast, self-reported performance goals differed significantly by

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condition with students in the performance condition reporting higher performance goals than those in the mastery condition It is important to note that although those in the performance condition reported higher performance goals than those in the mastery condition, students in the performance condition reported higher levels of mastery goals than performance goals The finding that students in the performance condition espoused higher mastery than performance goals and the lack of differences in self-reported mastery goals based on condition suggested that the goal induction was not successful in inducing mastery and performance goals in the respective groups. To further assure ourselves that the goal condition did not have an effect on participants’ approach to the physics reading or post-test, we also conducted independent t-tests on the various self-report measures. There were no significant differences in positive affect, task-irrelevant thoughts, metacognitive strategy use, or elaborative strategy use. There was, however, a significant difference in negative affect with those in the performance condition reporting higher negative affect than those in the mastery condition Finally, we ran an analysis of covariance (ANCOVA) with the pre-test comprehension measure as the covariate and the post-test comprehension measure as the dependent variable to ensure that there were no differences in the change in physics understanding based on condition; we found no significant effect of condition. Given that the students in the performance condition were still adopting higher mastery goals than performance goals and there were no differences in mastery goals by condition, we decided that it was more appropriate to use self-reported post-test goals from the questionnaire in all subsequent analyses rather than the original experimental grouping variable. Because the goal condition was somewhat successful (in terms of altering performance goals) and did have an effect on negative affect, we tested to see if there were any interactions of goal condition x self-reported goals. Including these interaction terms did not result in a significant change in variance explained for physics understanding. Therefore, the goal condition x self-reported goals interaction terms were dropped from subsequent analyses. 3.2.

Correlational Analyses

Tables 1 and 2 display the means, standard deviations, and bi-variate correlations among variables. As expected self-reported mastery goals correlated positively with adaptive outcomes such as metacognitive strategy use, elaborative strategy use, and positive affect and negatively with negative outcomes such as negative affect (see Table 2). In line with a revised goal theory model, self-reported performance goals were positively correlated with adaptive outcomes including positive affect and metacognitive strategy use. Furthermore, performance goals were unrelated to negative outcomes such as negative affect and task-irrelevant thoughts suggesting that performance goals can be adaptive in some cases and do not seem to be

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maladaptive in other cases, contrary to what was initially suggested by the normative model of achievement goal theory.

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To examine the relation between achievement goals and the amount of learning that occurred, we conducted a simultaneous multiple regression with post-test physics knowledge as the dependent measure and pre-test knowledge, self-reported mastery and performance goals, and the goal by pre-test knowledge interactions as predictors. The goal by pre-test knowledge interaction terms were included to determine whether the goals had different effects for students who had a great deal of knowledge and understanding of physics prior to the study and those who did not. The results of the regression analysis showed that pre-test knowledge, self-reported mastery goals, and the pre-test knowledge x self-reported mastery goal interaction term were all significant predictors of a change in physics understanding (see Table 3). Self-reported performance goals were unrelated to a change in physics understanding. In addition, we also tested to see if there were differences in conceptual understanding based on the relative levels of both mastery and performance goals. To test this, we included a self-reported mastery goal X performance goal interaction term in the regression model. This interaction term was not significant suggesting that it is not necessary to consider multiple goals when predicting the development of conceptual understanding.

Figure 2 depicts the significant pre-test knowledge x self-reported mastery goal interaction. Those students with low levels of prior knowledge seemed to be benefiting the most from adopting mastery goals. That is, for the participants low in prior knowledge, mastery goals seemed to relate to increased learning from the physics reading. In contrast, mastery goals were unrelated to changes in physics understanding for those high in prior knowledge. In addition to the direct relation of achievement goals to the change in physics understanding, we were also interested in why mastery goals related to a change in prior understanding. One reason that students with mastery goals might be learning more is that they spent more time reading the text. To test this possibility, we examined the bi-variate correlations between mastery goals, time spent reading, and post-test physics knowledge. Neither the correlation between mastery goals and time spent reading nor the correlation between post-test physics knowledge and time spent reading were significant suggesting that the amount of time students spent

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reading the passage did not explain why students with mastery goals seemed to learn more from reading the passage.

Cognitive strategies and affect might also mediate the relation between mastery goals and post-test score (see Figure 1). To test this possibility, we again examined the bi-variate correlations to see which variables were related to self-reported mastery goals. Positive and negative affect, elaborative strategy use and metacognitive strategy use were all significantly related to mastery goals (see Table 2). Further, positive and negative affect as well as elaborative strategy use were significantly related to post-test physics knowledge suggesting that these three variables may mediate the relation of mastery goals to post-test physics knowledge. To formally test for mediation, a series of regression analyses were conducted (Baron & Kenny, 1986). First, we regressed post-test physics knowledge on mastery goals, mastery x prior knowledge, prior knowledge, and positive affect. We then ran two more identical regression analyses substituting negative affect and then elaborative strategy use for positive affect. Although mastery goals, mastery x prior knowledge, and prior knowledge were all significant predictors of post-test physics understanding as in our prior analyses, none of the proposed mediators related significantly to post-test physics knowledge suggesting that these variables do not mediate the relation of mastery goals to the gain in physics understanding.

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DISCUSSION

These results suggest that it is important to consider students’ motivation, more specifically their achievement goals, when attempting to understand what aids in the learning of scientific concepts such as Newtonian physics. More specifically, mastery goals, or a focus on learning and understanding, promoted students’ understanding of Newtonian physics. This seemed especially important for students who initially had low levels of knowledge. In contrast, performance goals did not appear to relate to a change in physics understanding. That is, focusing on demonstrating one’s ability in comparison to others neither promoted nor was it detrimental to learning Newtonian physics. The lack of significant differences in the amount of time mastery oriented students spent reading the passage suggests that mastery oriented students are engaging in the reading differently, not just spending more time on the task. The bivariate correlations suggest that differences in students’ affect (mastery students reported more positive and less negative affect) and their strategy use (mastery students reported more adaptive strategy use) may help to explain why mastery goals were adaptive. However, these variables did not mediate the relation between goals and understanding. In Study 2, we further investigate possible variables to test this mediation. Furthermore, because our goal induction was not successful, we were only able to examine the correlational relations among the variables. In order to examine the effect of achievement goals on the development of understanding, a successful goal induction is necessary; therefore, we revised the goal induction procedures for Study 2. 5.

STUDY 2

Study 2 was designed to replicate the findings of Study 1, investigate possible mediators of the relation between mastery goals and the gain in physics understanding, and address the issue of the failed goal manipulation. More specifically, to address the issue of the mediators, some of the measures were refined to better assess affect and strategy use. Additionally, the goal manipulation and experimental setting were altered to enhance the goal manipulation. 5.1. 5.1.1.

Method Participants

110 undergraduate psychology students participated in the study for course credit. Half of the participants were male and half were female. Participants were primarily Caucasian.

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Procedure

The procedure was essentially the same as Study 1 with four changes. First, since we found no differences in the length of time it took students to read the passage based on mastery and performance goals in the first study, the amount of time was not recorded in the second study. Second, rather than using a working memory test as an intervening task, participants were asked to complete a word scramble lasting approximately three minutes. This change was made to reduce the time required for the experimental session. Third, participants were tested in groups of 8 to 28 students rather than individually. Students were tested in groups in order to facilitate the data collection process and enhance the performance goal induction. Since students in the performance goal condition were told to focus on doing better than the other participants, we thought that testing students in groups (with other participants present) would make this goal induction more realistic and plausible. Finally, the goal induction itself was altered to enhance the saliency of the induction. In Study 1, participants were asked to read a short paragraph telling them to focus on mastery or performance goals. In Study 2, participants were first asked to read a story about a student who focused on mastering academic activities or on outperforming others in school. Next, they were asked to recall a time when they acted in this way. Finally, students were asked to read a paragraph telling them to focus on mastery or performance goals, similar to the one used in Study 1. 5.1.3.

Materials

The materials assessing physics understanding (pre and post-test comprehension measures) and the physics passage were identical to the ones used in Study 1. The self-report scales assessing students’ goals, affect, and cognitive strategy use were identical to the ones used in Study 1 with the following exceptions: positive and negative affect and metacognitive self-regulation. To measure positive and negative affect, we used the shortened version of the positive and negative affect scale (PANAS) (Watson, Clark, & Tellegen, 1988). Each scale consisted of 10 items. The positive affect scale had a reliability of .90 while the reliability of the negative affect scale was .70. We also added three additional items to the scale assessing metacognitive strategy use resulting in a reliability coefficient of .77 (see Appendix B for revised scale). 6. 6.1.

RESULTS

Results of Goal Induction

To assess the effectiveness of the goal induction, we ran independent t-tests on selfreported mastery and performance goals. In this second study, the between group means were significantly different with the mastery induction group reporting higher mastery goals than the performance induction group Similarly, students in the performance

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induction group reported higher performance goals than those in the mastery induction group However, an examination of the within-group means for the performance induction group still showed them to have higher levels of mastery goals than performance goals To further test the effectiveness of the goal induction, we conducted an ANCOVA on the post-test measure of physics understanding with goal condition (mastery, performance) as the predictor variable and pre-test physics understanding as a covariate. The results revealed that there was no effect of the goal condition on the change in physics understanding Further, independent t-tests revealed that there were no significant differences in any of the mediator variables (affect and cognitive strategy use) based on the goal conditions. Given that the students in the performance condition were still adopting higher mastery goals than performance goals and there were no effects of the goal condition on any of the dependent variables, we used self-reported post-test goals from the questionnaire in all subsequent analyses rather than the original experimental grouping variable. Because the goal condition was somewhat successful, we tested to see if there were any significant interactions of goal condition x self-reported goals when examining the change in physics understanding. These analyses did not reveal any significant interactions; therefore, the goal condition x self-reported goals interaction terms were dropped from all subsequent analyses. 6.2.

Correlational analyses

Means, standard deviations, and bi-variate correlations among variables are depicted in Tables 1 and 2. As expected self-reported mastery goals related positively to adaptive outcomes such as post-test score, strategy use, and affect. In line with a revised goal theory model, self-reported performance goals related positively to positive affect, metacognitive strategy use, and elaborative strategy use. As in Study 1, performance goals were unrelated to negative outcomes including negative affect and task-irrelevant thoughts. To examine how achievement goals related to a change in physics understanding and to replicate the findings from Study 1, we first conducted a simultaneous multiple regression analysis with pre-test physics knowledge, self-reported goals, and the pre-test physics knowledge x self-reported goals interaction terms as predictors and post-test physics knowledge as the dependent variable. As in Study 1, both pre-test physics knowledge and self-reported mastery goals were positive, significant predictors of post-test physics knowledge (see Table 3). The interaction of pre-test knowledge x mastery goals, however, was not significant. In sum, we replicated the main effect findings from Study 1 but not the interaction. In addition, we tested to see if the relative levels of mastery and performance goals should be considered simultaneously in order to predict the development of conceptual understanding. To test this possibility, we included a self-reported

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mastery x performance goal interaction term in the regression model. As in Study 1, this interaction term was not a significant predictor of post-test physics knowledge. We were also interested in examining the affective and cognitive strategy variables to determine if any of these variables mediated the relation of mastery goals to the change in physics understanding. The significant bi-variate correlations between mastery goals and the potential mediators suggest that metacognitive strategy use, elaborative strategy use, task-irrelevant thoughts, positive affect, and negative affect were all potential mediators (see Table 2). However, only elaborative strategy use, negative affect, and task-irrelevant thoughts had significant bi-variate correlations with post-test physics knowledge (see Table 2). Therefore, we chose to examine these three variables as possible mediators of the mastery goal effect. Because of the relatively high correlations among these three mediators, we tested for mediation separately before constructing a full model. Therefore, we regressed post-test physics knowledge on pre-test knowledge, mastery goals, and each of the three potential mediators in three separate regression equations. We then regressed each of the mediator variables on pre-test knowledge and mastery goals. Based on these regressions, all three variables (elaborative strategy use, negative affect, and task-irrelevant thoughts) were all potential mediators of the relation.

However, when all three were included in one model, only negative affect and task-irrelevant thoughts were significant predictors of the change in physics understanding. Due to the multicollinearity among these three variables, however, we thought it more important to consider a model with one or two mediators. As we were most interested in how affect and strategy use related to a change in physics understanding based on students’ goal adoption, we decided

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to test a model with both elaborative strategy use and negative affect as mediators. The results from this model suggested that both negative affect and elaborative strategy use partially mediated the relation of mastery goals to change in physics understanding (see Figure 3). Although not shown in Figure 3, pre-test comprehension was in the model predicting post-test comprehension, so the dependent measure was post-test gain in comprehension. For mediation to occur, the relation of mastery goals to post-test change must decrease when the mediator variables were included in the model (Baron & Kenny, 1986). When the mediator variables were not included in the analyses, the beta coefficient for the relation between mastery goal adoption and change in physics understanding was 0.38. However, when both negative affect and elaborative strategy use were included in the model, this relation was decreased to 0.22. It was also necessary that the mediators related to both the predictor variable (mastery goals) and the dependent variable (post-test change in physics understanding). As shown in Figure 3, this criterion for mediation was also met. Thus, it seems that mastery goals may be related to physics understanding, in part, because they were positively related to the use of elaborative strategies which enhanced the change in physics understanding and because they were negatively related to negative affect which was detrimental to students’ change in physics understanding. 6.3.

Discussion

In summary, Study 2 was successful in addressing some of the concerns raised by Study 1. A clearer understanding of why mastery goals are important to consider when examining students’ change in physics understanding based on the reading of a text was revealed. That is, mastery goals were related to the use of more elaborative strategies and were related to decreased negative affect, both of which were adaptive for a change in physics understanding. We were not, however, able to address the issues of the failed goal manipulation and this will need to be the focus of future work in this area. Finally, although we replicated the main effect of mastery goals on the change in physics understanding, we did not replicate the effect of the prior knowledge x mastery goal interaction. Future research should more closely examine the possibility that mastery goals may be more adaptive for those with lower levels of prior knowledge. 7. GENERAL DISCUSSION

Taken together, these two studies highlight the importance of considering not only students’ strategy use but also their motivation when attempting to understand why conceptual understanding emerges for some students but not others. The results of both studies suggest that students who focus on learning and approach their schoolwork for the purpose of understanding the material are more likely than students who do not take this approach to develop a more refined understanding of physics. These results are consistent with Lee and Anderson’s (1993) findings that a

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mastery goal orientation facilitated the development of students’ conceptual understanding. Interestingly, although performance goals were positively related to adaptive strategy use, the adoption of performance goals was unrelated to the conceptual change process. Thus, although our findings that students who adopt performance goals tend to use more metacognitive and elaborative strategies support a revised goal theory model (Pintrich, 2000 a, b), the use of these strategies did not enhance their conceptual understanding of physics. This suggests that students with performance goals may be regulating and trying to elaborate on the material; however, their focus on demonstrating their ability may not allow them to perceive the full ramifications of what they are learning. That is, since their focus is on being correct and showing others they are smart, they may not attend to the details of the text in a way that allows them to revise their current understandings. Instead, they may read at a more superficial level or may fail to see how the new information contradicts their prior beliefs in an effort to avoid acknowledging that their prior understandings were not correct. This may hinder the conceptual change process for performance oriented students thereby cancelling out the benefits of adaptive strategy use. In addition to the direct relation of mastery goals to the development of conceptual understanding, we also found that mastery goals were indirectly related via affective and cognitive mediators. More specifically, Study 2 suggested that students espousing mastery goals also tended to report reduced negative affect; this reduction in negative affect seems beneficial for the development of conceptual understanding. One possible explanation for the benefits of reduced negative affect is that a reduction in negative feelings such as anxiety allows students to focus more attention on the material to be learned. Study 2 also suggests that mastery oriented students are more likely to use elaborative strategies and that this is beneficial for the conceptual change process. Contrary to what was expected, the increase in metacognitive self-regulation associated with mastery goals did not enhance the development of conceptual understanding. This may be because students need to do more than monitor their understanding. Monitoring their understanding may be necessary for conceptual understanding to emerge, but this may not be sufficient, especially for those students low in prior knowledge. That is, a student may report that he reread sections he did not understand or asked himself questions to understand the reading; however, an awareness that one does not understand is not always sufficient for the development of understanding. There may need to be increased instruction or additional information for a student with especially low levels of prior knowledge to enhance his understanding. This suggests that that some types of strategy use (elaborating and linking current information to prior knowledge) are beneficial for the development of conceptual understanding while other types of strategies (selfregulation) are not sufficient for conceptual change to occur. While this study provides an exciting new direction for both researchers studying conceptual change and teachers trying to promote conceptual understanding in their classrooms, there are a number of issues raised by this current research that need to be addressed in future studies. First, it is unclear whether mastery goals may be

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more adaptive for those with particularly low levels of prior knowledge. In the first study, we found that students with low levels of prior knowledge who reported adopting mastery goals were likely to increase their conceptual understanding of physics while the level of mastery goals for those high in prior knowledge did not predict an increase in physics understanding. However, we did not replicate this finding in the second study. Although it seems plausible that mastery goals would be especially beneficial for those low in prior knowledge because mastery goals may help students circumvent low feelings of efficacy for learning physics and could draw students’ attention away from their low prior performance in physics, future research is needed to clarify whether this finding is reliable across a number of studies. Second, because of the problems with the manipulation of achievement goals in both studies, we were not able to examine causal relations between achievement goals and the development of conceptual understanding. Future research should attempt to further revise these goal manipulations in order to examine the causal effects of achievement goals on the development of conceptual understanding. Nevertheless, our results do provide preliminary evidence that achievement goals are important to consider in the conceptual change process. Third, future research should examine the role of achievement goals in the development of conceptual understanding over a longer time period. Because our study used a short-term measure of conceptual understanding, it is difficult to determine if any long-term changes in students’ thinking about physics occurred. Studies following students over a longer period of time (at least over the course of a several week unit in a classroom) would be able to better determine the importance of achievement goals in the conceptual change process. In summary, these studies suggest that educators interested in promoting conceptual development in classrooms need to consider students’ motivation in addition to the types of activities used and strategies employed to promote scientific understanding. More specifically, our results suggest that educators should encourage a focus on learning and understanding in order to facilitate conceptual change. Furthermore, researchers interested in conceptual change should pay more attention to both motivational and affective components of students’ learning in order to gain a more complete understanding of the various processes which relate to the development of students’ conceptual understanding. REFERENCES Ames, C. (1992). Classrooms: Goals, structures, and student motivation. Journal of Educational Psychology, 84, 261-271. Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182. Bless, H. (2000). The interplay of affect and cognition: The mediating role of general knowledge structures. In J. P. Forgas (Ed.), Feeling and thinking: The role of affect in social cognition (pp. 201222). Paris: Cambridge University Press. Guzzetti, B. J., Snyder, T. E., & Glass, G. V. (1992). Promoting conceptual change in science: Can texts be used effectively? Journal of Reading, 35, 642-649.

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Harackiewicz, J. M., Barron, K. E., & Elliot, A. J. (1998). Rethinking achievement goals: When are they adaptive for college students and why? Educational Psychologist, 33, 1-21. Lee, O., & Anderson, C. W. (1993). Task engagement and conceptual change in middle school science classrooms. American Educational Research Journal, 30, 585-610. Linnenbrink, E. A., Ryan, A. M., & Pintrich, P. R. (1999). The role of goals and affect in working memory functioning. Learning and Individual Differences, 11, 213-230. Maehr, M. L., & Kaplan, A. (2000, April). It might be all about self: Self-consciousness as an organizing scheme for integrating understandings from self-determination theory and achievement goal theory. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans, LA. Midgley, C., Maehr, M. L., Hicks, L., Urdan, T., Roeser, R. W., Anderman, E., & Kaplan, A. (1996). Patterns of Adaptive Learning Survey (PALS) manual. Ann Arbor, MI: University of Michigan. Pintrich, P. R. (2000a). Multiple goals, multiple pathways: The role of goal orientation in learning and achievement. Journal of Educational Psychology, 92, 544-555. Pintrich, P. R. (2000b). The role of goal orientation in self-regulated learning. In M. Boekaerts, P.R. Pintrich, & M. Zeidner, (Eds.), Handbook of self-regulation (pp. 451-502). San Diego, CA: Academic Press. Pintrich, P. R., Marx, R. W., Boyle, R. B. (1993). Beyond cold conceptual change: The role of motivational beliefs and classroom contextual factors in the process of conceptual change. Review of Educational Research, 63, 167-199. Pintrich, P., & Schrauben, B. (1992). Students' motivational beliefs and their cognitive engagement in the classroom academic tasks. In D. Schunk & J. Meece (Eds.), Student perceptions in the classroom (pp. 149-183). Hillsdale, NJ: Lawrence Erlbaum Associates. Pintrich, P. R., Smith, D., Garcia, T., & McKeachie, W. (1993). Predictive validity and reliability of the Motivated Strategies for Learning Questionnaire (MSLQ). Educational and Psychological Measurement, 53, 801-813. Qian, G., & Alvermann, D. (1995). Role of epistemological beliefs and learned helplessness in secondary school students’ learning science concepts from text. Journal of Educational Psychology, 87, 282292. Roeser, R., Midgley, C., & Urdan, T. (1996). Perceptions of the school psychological environment and early adolescents' psychological and behavioral functioning in school: The mediating role of goals and belonging. Journal of Educational Psychology, 88, 408-422. Skaalvik, E. (1997). Self-enhancing and self-defeating ego orientation: Relations with task avoidance orientation, achievement, self-perceptions, and anxiety. Journal of Educational Psychology, 89, 7181. Watson, D., Clark, L., & Tellegen, A. (1988). Development and validation of brief measures of positive and negative affect: The PANAS scales. Journal of Personality and Social Psychology, 54, 10631070. Vosniadou, S. (1999). Conceptual change research: State of the art and future directions. In W. Schnotz, S. Vosniadou, & M. Carretero (Eds.), New perspectives on conceptual change (pp. 3-13). Amsterdam: Elsevier Science. Vosniadou, S., & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24, 535-585.

APPENDIX A Goal Induction Instructions Mastery I will be giving you a reading about physics. After you've done the reading, I will give you a set of questions to see how much you've learned. Please read the passage carefully so that you really learn and understand the ideas in it. While you are reading the passage, you may go back and review the passage so that you can really try to understand it; once you've started

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answering questions that follow the passage, you may not return to the passage. I will be looking to see how much you improve, so you should try to do your best. Performance I will be giving you a reading about physics. After you’ve done the reading, I will give you a set of questions to see how you compare to other college students. Please read the passage carefully so that you can answer the questions better than anybody else. While you are reading the passage, you may go back and review the passage; once you’ve started answering questions that follow the passage, you may not return to the passage. I will be ranking you based on your performance, so you should study this passage as though you are trying to beat all of the other students.

APPENDIX B Self-Report Measures for Study 1 Mastery Goal Orientation I focused on understanding the ideas I thought about learning physics. I focused on improving my understanding of physics. I focused on learning the material, not just memorizing it. I tried to master the material. Performance Goal Orientation I focused on doing better than the other participants. I thought about doing my best so that I could be ranked higher than the other participants. I tried hard so that I could beat out all of the other participants. I thought about what my score was going to be. I thought about my performance relative to others. Positive Affect I was in a good mood. I felt happy. I was content. I felt good about myself. I enjoyed it. Negative Affect I felt frustrated. I was annoyed. I felt dumb. I was anxious. I was in a bad mood. Task-Irrelevant Thoughts I thought about things other than the reading.

THE ROLE OF MOTIVATIONAL BELIEFS IN CONCEPTUAL CHANGE I had a hard time concentrating. I had a hard time working on the task at hand. I often lost track of what I was thinking. I had difficulty keeping my mind on things. Elaborative Strategy Use I tried to relate the ideas in the reading to what I already knew about physics. I tried to relate the material to what I already knew. Metacognitive Strategy Use I asked myself questions to help focus my reading. I skimmed the reading to see how it was organized before I began reading. I asked myself questions to make sure that I understood the material. Revised Scales for Study 2 Metacognitive Strategy Use I asked myself questions to help focus my reading. I went back and tried to figure out things that I was confused about. I skimmed the reading to see how it was organized before I began reading. I asked myself questions to make sure that I understood the material. I tried to determine which concepts I did not understand well. I went through the reading to try to find the most important ideas.

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SITUATING THE QUESTION OF CONCEPTUAL CHANGE

OLA HALLDÉN, GUNILLA PETERSSON, MAX SCHEJA, KARIN EHRLÉN, LIZA HAGLUND, KAROLINA ÖSTERLIND & AGNETA STENLUND

Stockholm University, Sweden

Abstract. The contemporary debate regarding the question of conceptual change relates to the learning paradox in Plato’s dialogue Menon, where Menon asks how it is possible to engage in a search for knowledge of something entirely new. How is it possible to change from a commonsense view of a phenomenon into a scientific one that also sometimes goes quite contrary to the commonsense view? Sociocultural analysis dispatch the question by talking of situated cognition and by that ignoring individual cognitions. Constructivist approaches describes cognitive development as an evolution from simple naïve models of a phenomenon to more complex and powerful models, often by implying that the simple models are abandoned in favour of the new ones. Here, another model for conceptual development and conceptual change will be advanced. It is proposed that conceptual development and conceptual change is constituted by a process of a continuous assimilation of new information into an all-embracing model and, simultaneously, a differentiation within this compounded model resulting eventually in different new models. This description that stick to the Piagetian way of describing cognitive development, will be illustrated by means of empirical data from a study of children’s conceptions of the shape of the earth.

1. INTRODUCTION

To have undergone a process of conceptual change is often to have learned something entirely new, to be able to look at a phenomenon in an entirely new way. For example, to have grasped the Newtonian concept of force is to have understood that what is required is an explanation of the change of the velocity or direction of an object in motion rather than an explanation of why the object moves. Plato formulated the problem of whether it is possible to learn something entirely new as a paradox. In his dialogue Meno, Meno discusses with Socrates whether it is possible to engage in an investigation of virtue and the nature of virtue. It is Meno who questions the possibility of coming to know something entirely new, but it is Socrates who puts the paradox into words: a man can inquire neither into what he already knows nor into what he does not know. If he knows, he need not inquire for he already knows. And if he does not know, he cannot inquire because he does not know what to ask about. Furthermore, how would he know whether he has found an answer?

M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 137-148. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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Plato’s, or Socrates,’ solution to the paradox was that all knowledge is recollection; we already know what we are trying to learn and learning is merely a recollection of what we already know. Socrates «proves» this thesis by putting certain questions to a slave, whereby the slave is eventually able to state that if the diagonal of a square forms the side of another square, the area of the second square is equal to the first square doubled. Likewise, from an empiricist or behaviouristic perspective there is no paradox. If knowledge is a mirror of reality, as it is perceived, then new knowledge is simply the mirroring of a new reality, as it is perceived. This way of looking at the acquisition of complex knowledge was effectively refuted by Chomsky (1959) in his criticism of Skinner’s Verbal behaviour (Skinner, 1957). According to Chomsky, pure experience cannot account for the learning of such complex phenomena as a person’s native language. The behavouristic standpoint is questionable also from the perspective of what Lakatos (1980) calls the “theory-impregnation” of observations. More promising, then, is the solution proposed by Piaget and stated, among other places, in his concluding chapter in The Origin of Intelligence in the Child: the growing child’s knowledge is formed by the interaction between pre-existing cognitive structures and experience (Piaget, 1935). However, famous is the debate between, among others, Jean Piaget and Noam Chomsky published by PiattelliPalmarini (1980). The paradox still exists but has perhaps been better expressed by Carl Bereiter: “How can a structure generate another structure more complex than itself?” (1985, p. 204). How, then, is it possible to change from a commonsense to a scientific view of a phenomenon, particularly when the scientific view can be quite contrary to the commonsense one? In the contemporary debate, sociocultural analysis makes short work of both Bereiter’s question and the paradox by restricting itself to situated cognitions, thereby ignoring individual cognitions altogether. The constructivist approach, on the other hand, describes cognitive development as an evolution from simple, naïve models of a phenomenon to more complex and powerful models, often by implying that the simple models are abandoned in favour of the new ones. However, this approach does not solve the problem of how is it possible for the learner to create these new more complex models? Here, we will advance another model for conceptual development and conceptual change. We will say that conceptual development and conceptual change are constituted by a process of continuous assimilation of new information into an all-embracing model and, simultaneously, by a process of differentiation within this compounded model that eventually results in different new models. This description remains true to the Piagetian way of describing cognitive development. We will introduce our model by using empirical data from a study of children’s conceptions of the shape of the earth. But first, a comment on the vagueness of the terms “concept” and “conception” as used in the literature. Richard White once suggested that concept has to do with classification; we understand the meaning of a concept when we know which things can properly be classified as belonging to that concept. This, in turn, has to do with the ability to differentiate between different contexts. Conception, on the other hand, has to do with “all the knowledge that the person has and associates with the

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concept’s name” (White, 1994, p.118). According to White, then, a conception is constituted by a system of concepts. Learning a new way of classifying, in White’s frame of reference, involves conceptual change, whereas reconsidering a conception – that is, a system of concepts – involves conceptional change. White’s distinction between the different meanings of concept and conception is important, but we refrain from adopting his linguistic usage here for the reason that the recognition of different contexts is probably important in White’s idea of conceptional change as well. Moreover, there is an intimate relationship between different ways of classification and the changing of a conceptual system. This, it is hoped, will be apparent from what follows. Thus, when we refer in this context to conceptual change, we mean the changing of a conceptual system. 2.

THE CUSTOMARY METAPHOR

In the literature on the problem of conceptual change, different metaphors are used to describe the process of change. The most common one refers to the transition from mental state A to mental state B (A B), where “A” denotes one conception and “B” another. Thus, the process of conceptual change goes from a less distinct way to apprehend a phenomenon to a more distinct way to apprehend that phenomenon (see e.g. Driver & Easley, 1978). Although there is a variety of descriptions of the transition from state A to state B (see e.g. Strike & Posner, 1982, 1992; also, see Gilbert & Watts, 1983, for an overview), the relation between state A and state B has been explored very little in the literature, if we disregard the fact that they are different and that the underlying assumption in most of the literature on conceptual change is that conception B is a better and more potent one than conception A. Here we intend to explore another metaphor of conceptual change, where the transition goes from the conception A to other conceptions such as Al and A2.

By this, we mean that it is more fruitful to look at conceptual change as a differentiation within one and the same conception than to view it as the replacement of one concept with another; that is, the establishment of a totally new way of conceptualising the world. The metaphor introduced here indicates that a process of assimilation of new information in an already existing conceptualisation parallels a process of differentiation within this conceptualisation and eventually leads to two, or more, new ways of conceptualising the world. These new conceptualisations can thus be looked upon as being embedded within the earlier conception. In order to explore this metaphor, we will draw on some examples from an ongoing study about children’s conceptions of the shape of the earth.

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3. CHILDREN’S CONCEPTIONS OF THE SHAPE OF THE EARTH

In The child’s conception of the world, Piaget (1929) presented data on children’s ideas about the earth and about the moon. Well known is the observation that the child believes that the moon follows us when we, for example, travel by car on a moonlit night. Ever since Piaget presented his findings, there have been many studies on children’s beliefs about the earth and about astronomical phenomena (e.g. Nussbaum, 1979). An influential program in this area of research was recently carried out by Stella Vosniadou and her colleagues. In their investigation of pupils’ understanding of concepts relating to the shape of the earth, Vosniadou and Brewer (1992) argued that children between six and twelve years old maintain distinct, though quite divergent, mental models of the earth. Also, they noted that the younger children in the study often expressed beliefs indicating a notion of the shape of the earth as a flat disc, whereas the older children’s accounts testified to notions of the earth as either “dual”, a hollow sphere, a flattened sphere or a regular sphere. These findings were questioned in a recent study by Schoultz, Säljö and Wyndhamn (1997) of Swedish children who were in the same age interval as the children in the Vosniadou and Brewer study. In the Schoultz et al. study, however, all the children said that the earth was round. The researchers explained the differences in the findings from a sociocultural point of view; that is, children’s answers to such questions as what is the shape of the earth have to do with how the questions are asked. In other words, in what kinds of interaction are the children being invited to take part? This controversy led us to initiate a pilot study where we interviewed children about how they envision the shape of the earth. Our approach in this study was to frame the interview as weakly as possible to enable the children to present a range of views. We tried as far as possible to shift control over the interaction away from the interviewer and into the hands of the interviewee. One of the ways in which we arranged a weak framing was to force the children to choose between different “communicative tools”, to borrow a concept from the sociocultural perspective. Of course, freeing the situation from imposed communicative constraints or affordances is only possible to a certain extent. Obviously, there was a difference in age between the counterparts in the interview. Furthermore, just the fact that someone asks someone else to answer questions or to talk about something and the second person agrees to do so makes a difference in the balance of power between them. Thus, according to the sociocultural perspective, it is impossible to free a situation from the kinds of factors that regulate an interaction. Just to engage in an interaction is to influence what happens. But by inviting children to talk about the earth in different ways and by providing them with a variety of communicative tools, we tried to prepare for a situation that would allow us to understand what kinds of contexts, or communicative practices, the children themselves introduced. 4.

THE PILOT STUDY

Three types of interviews were carried out. In the first type, the children were shown illustrations of the earth and asked to choose which one, in their view, best depicted

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the shape of the earth. These illustrations were the same that Vosniadou (1994) presented as a result of their interview study of children’s conceptions of the earth (Figure 1). Each illustration was transferred onto a separate sheet of paper.

In the second type of interview, the children were asked what would happen if they walked straight ahead in one direction. On a table in front of them was a variety of objects that they could use to illustrate what they were saying. There were balloons of various shapes, paper and crayons, a real pancake, a ball and a piece of

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clay. In the third type of interview, the children were asked to draw a picture of the earth while the interviewer asked questions about what each child was drawing. Our aim was to achieve a variation in descriptions of the shape of the earth. To increase the probability of this occurring, we interviewed children who were between six and eight years, that is, at the same age as the youngest children in the studies by Vosniadou and Brewer and Schoultz, Säljö and Wyndhamn. In the first part of our study, where the children were asked to choose between different pictures of the earth, seven children were interviewed. In the second part of the study, where the children were asked what would happen if one walked straight ahead, five groups of three children each were interviewed. In the third and last part, where the children were asked to draw a picture, ten children were interviewed. 5. RESULTS Four of the children in the first part of the study chose a picture of the earth as a sphere and three children chose a picture of the earth as a hollow sphere. When asked to draw the house where he lives, one of the children, Philip, drew a house on level ground inside the sphere. However, when asked to draw the sun, the moon and a few stars, he drew them outside the sphere (Figure 2).

One way to interpret the hollow sphere model of the earth is as a hemispheric model; that is, we live under a globe. The roots of such a model can be found in traditional mythological thinking. In the Finnish poem Kalevala, for example, there is a blacksmith named Ilmarinen who “hammered out the vault of heaven such as no blow of the hammer was to be seen”. But in our case the child Philip did not seem to have had a hemispheric model of the earth in mind. Rather, he seemed to have combined two models in one picture – one being the flat earth we live on and the

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other the spherical earth as a celestial body. Thus, we have to look at his picture in the same way that we look at a painting by Picasso where an object can be viewed from several angles at the same time; we can see a person in profile and en face simultaneously. Looking at the picture Linus chose and completed, it would seem that he, too, was working with two different models simultaneously (Figure 3).

Linus also chose the hollow sphere model, but when asked what is the shape of the earth, he replied that it is spherical like a ball. Thus, when making a pictorial model of the earth, Linus drew a compounded one, but when talking about the earth, he referred to the earth as a sphere. This way of combining different models of the earth can also be found in the interviews where the children were asked what would happen if they walked straight ahead in one direction. As already mentioned, they had at their disposal paper and pencils, clay, balloons of different shapes and a pancake which they could use to illustrate their explanations. A common characteristic of the children interviewed in this part of the study was that they used more than one object to illustrate their way of reasoning. In one group, the children used of all the objects. It appeared that they understood their task to be to illustrate what would be the case if they used either several or all of the objects. What we have said so far refers only to how the children seemed to have understood the assignment. But there is also reason to believe that their way of understanding the task also has something to do with how they think about models of the earth. One boy, Luke, who talks here about a spherical earth, used the pancake to illustrate what would happen if someone walked straight ahead. Luke: First you walk, then you take another step and then another, because the earth is turning around, so you are rotating. I: How do you mean? Can you show me? How is the earth turning? Can you show me with this? /the pancake/ Luke: If you walk like this, straight ahead, you come to the end-way-out (slutgång). Then you go downward, but you don’t notice it because the earth is turning. When it’s night-time we’re upwards and they... no, we’re upside-down, like.

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Luke: If you walk around like this (shows with two fingers how one walks on the surface and then on the underside)... but this is only a pancake… and then you do like this (he picks up a balloon).

Thus, Luke seems to be quite aware that he is working with models of the earth and that these models have their limitations. The shape of the earth can be illustrated to a certain extent with a flat pancake, but if you want to talk about certain characteristics of the earth, you need a spherical model. This would seem to parallel the way physicists use the Newtonian model in classical dynamics and the quantum model for explanations on the atomistic level. Nina, a girl in another group, is not so clear about how to relate different models of the earth to each other. First, she says that she thinks she knows the answer to the question of where we would end up if we walked straight ahead in one direction: “I think I know where we end up. Shall I say?”. When the other children in the group reply in the affirmative, she says: “Denmark”. The children eventually come to an agreement that you come to other countries, and when you have walked through them all, you come to a “star barrier” (stjärnstopp). This expression is part of the children’s jargon and denotes a definite stop of some kind. You cannot go any further. “You have to stop”, says Nina and shrugs her shoulders. To illustrate their way of reasoning, Nina chooses the pancake as an illustration. The interviewer then asks the children to say something about the shape of the earth and suggests that they use the clay to illustrate their reasoning. Now the children roll the clay into a ball and talk about the earth as a sphere, saying that it is possible to go around the earth; “You can keep going around it”, says Nina. The interviewer asks if it is possible to live anywhere on the globe and when the children answer “Yes”, she asks why people do not fall off the globe. Nina replies, “They don’t because the globe is turning around like this (shows a circular movement in the air). And you live inside the globe”. The interviewer tries different ways to find out what “living inside the globe” means. She asks where the people live and Nina replies “In houses, of course. Inside the globe”. A bit later in the conversation, the children divide the ball in half and Nina shows how to walk around the earth on the inside of one of the halves. The interviewer objects that a moment ago they had said that one walks on the surface of the globe. To this Nina replies, “Yes, but that’s only because then we couldn’t cut through the ball”. Thus, it seems that Nina uses two different models of the earth, and when trying to combine the two she invents a new model. First, she talks about a flat earth, illustrated by the pancake. Then, when asked to talk about the shape of the earth and prompted to use the clay to illustrate her way of reasoning, she talks about the earth as a sphere. But when trying to combine these two models, she invents the model of the earth as a hollow sphere. In the interviews in which the children were asked to draw a picture of the earth, Burt, six years old, asked: “Which earth?”. Then, when asked to draw as many different ‘earths’ as he liked, he made a drawing of a vegetable plot, another of the earth “all around” which was flat, and lastly a picture of the earth as an astronomical body much like a sphere. Thus, to use the terminology of the sociocultural perspective, Burt was inquiring about in what kind of discursive practice he was

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being asked to engage. But, another way to describe what has happened here is to say that he was able to differentiate between different conceptions of the earth. Not all of the children had the ability to do so. Some of them seem to have tried to combine all three conceptions of the earth within one model. The children actualised other conceptions of the earth as well. One child seems to have equated the concept “planet” and “the planet earth” with the concept “nation” (Figure 4).

I(interviewer): On this (earth that you have drawn) there are all the things you talked about. What was it; the land of sweets, the tropical forests ...? C(hild): Yes. I: And Spain. C: Perhaps not just on this earth. Perhaps on the next one up here. I: Is this also an earth? C: Yes, all of these small ones are earths.

When travelling from Sweden to Spain you leave one “earth” and enter another. In the drawing this is illustrated by an aeroplane leaving the “earth” Sweden (‘joden’). (In the middle of the drawing we find the sun and the “M” on the left hand side stands for the moon). 6. DISCUSSION One of our aims in undertaking this study was to throw light on the controversy between a constructivist and a sociocultural approach. It is, of course, impossible to say anything conclusive about the sociocultural approach. If you postulate as an ontological fact that concepts exist only in communicative settings and then only as conceptualisations, there is no way to prove the opposite. In like manner, if you

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assert that it is methodologically impossible to directly observe what conceptions people embrace, nothing can be said against that either. With regard to the ontological presupposition, only the plausibility and the fruitfulness of the approach can be questioned; and, with regard to the methodological claim, it is only possible to argue that we have evidence by which we infer the conceptions held by individuals and that these inferred entities help us to arrive at a better understanding of what is occurring in the verbal interaction. We believe that these preliminary results from our pilot study already provide a basis for questioning the fruitfulness of the ontological postulate and for arguing that it is possible to infer mental entities such as conceptions. When the children in our study were presented with different kinds of communicative tools, they chose tools indicating different conceptions of the shape of the earth. This could have been a matter of chance, but it seems more fruitful to look at these different choices as reflecting different conceptualisations children form about the earth. This is also the reasonable conclusion to draw from the reply “Which earth?” given by one of the children who were asked to draw the earth. But the results from our preliminary study also give us some evidence to question the idea, sometimes fostered in constructivist approaches, that the conception of specific phenomena develops according to qualitatively different stages. Rather, it seems reasonable to look at the child’s emerging conception of, for example, the earth as a compounded conception, or perhaps better as a compounded model, embracing facts experienced from different sources contextualized in different models. So far, the acquisition of knowledge looks like a process dominated by generalizing assimilation, in the Piagetian sense of the term (Flavell, 1963; Piaget, 1935). This was illustrated in the cases of Philip and Nina above who tried to fit into one model both the experiences of the earth on which we live, where the sun rises and the sky forms a vault above, and information about the earth as an astronomical body that successively turns different sides towards the sun and is orbited by the moon. If, then, we wish to speculate on the development of this compounded model, we would have to look at this development as a differentiation within the compounded model. That is to say, conceptual change is brought about when the child, or any learner, becomes able to differentiate between contexts and to relate new information or new problems to adequate contexts (see Halldén, 1999). This was exemplified by Luke, who exchanged the pancake for a balloon in order to explain what happens if you walk in one direction and never stop. If we are talking about the earth we see around us and about walking on that particular bit of ground, then a pancake is a very useful model. But if we extend our walk far enough, in this case so far that it almost never ends, then the pancake or map is no longer a good representation of the earth; instead, a globe, or, as in the case of Luke, a balloon, is much more suitable. This differentiation between contexts seems to be a gradual process. In the first instance it appears as a vague and uncertain use of different contextualizations, as was indicated by Linus above who, in order to illustrate the earth, chose the hollow sphere model but talked about the earth as a globe. This sort of contextual diffusion may result eventually in a contextual awareness (Wistedt, 1993), as in the case of

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Burt above who asked which earth he was supposed to draw; that is, he was capable of choosing deliberately from among different contextualizations. When talking about contexts here, we mean first and foremost conceptual contexts; that is, conceptual systems. In order to account for the differentiation between different conceptual systems, it is probably also necessary to differentiate between different levels within such systems, such as the theoretical, conceptual and empirical levels (Caravita & Halldén, 1994); or the levels of theory, model and experimental field of reference (Tiberghien, 1994); or between a framework and a specific theory (Vosniadou, 1994). One of us has argued elsewhere that the learner’s discovery and delimitation of an alternative conceptual system is contingent upon a simultaneous processing taking place at these different levels within an already existing system of knowledge (Halldén, 1997). In the successful learning of something entirely new, the learner’s meditations at the theoretical level and temporary interpretations at the field-of-reference level have to match. Then, when these meditations and interpretations constitute a new Gestalt, a new context for interpretation is germinated. This makes possible a more decentered view, enabling the learner to make deliberate choices between different contexts for situating a problem or a description. Such a process can be compared to the simultaneous processes of assimilation and accommodation within the Piagetian theory of intellectual development. Here, we have talked about how children incorporate new information and interpret new problems in an already existing model, and, in addition, we have tried to show how this model expands in order to make it possible to incorporate information contextualized in other models as well. So far, this can be considered as an illustration of the Piagetian process of generalizing assimilation. This process brings about a compounded conception within which differentiations are made. These differentiations are generated by the simultaneous processing of concepts at different levels within this compounded conception, eventually resulting in new conceptualisations. Thus, this could be seen as an exemplification, and perhaps also as an explication, of the double-sided Piagetian process of assimilation and accommodation, both within the individual and between the individual and the outside world. REFERENCES Bereiter, C. (1985). Toward a solution of the learning paradox. Review of Educational Research, 55, 201226. Caravita, S., & Halldén, O. (1994). Re-framing the problem of conceptual change. Learning and Instruction, 4, 89-112. Chomsky, N. (1959). Review of B. F. Skinner’s Verbal Behaviour. Language, 35, 26-58. Driver, R., & Easley, J. (1978). Pupils and paradigms: A review of literature related to concept development in adolescent science students. Studies in Science Education, 5, 61-84. Flavell, J. H. (1963). The developmental psychology of Jean Piaget. New York: VNR. Gilbert, J. K., & Watts, M. (1983). Concepts, misconceptions and alternative conceptions: Changing perspectives in science education. Studies in Science Education, 10, 61-98. Halldén, O. (1997). Conceptual change and the learning of history. In J. F. Voss (Ed.). Explanation and understanding in learning history [Special Issue]. International Journal of Educational Research, 27, 201-210.

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Halldén, O. (1999). Conceptual change and contextualization. In W. Schnotz, M. Carretero, & S. Vosniadou (Eds.), New perspectives on conceptual change (pp. 53-65). Amsterdam: Pergamon/Elsevier. Lakatos, I. (1980). Falsification and the methodology of scientific research programmes. In I. Lakatos & Musgrave (Eds.), Criticism and the growth of knowledge (pp. 91-196). Cambridge: Cambridge University Press. Nussbaum, J. (1979). Children’s conceptions of the earth as a cosmic body: A cross age study. Science Education, 63, 83-93. Piaget, J. (1929/1973). The child’s conception of the world. London: Paladin. Piaget, J. (1935/1970). The origin of intelligence in the child. London: RKP. Piattelli-Palmarini, M. (red.). (1980). Language and learning: The debate between Jean Piaget and Noam Chomsky. London: Routledge & Kegan Paul. Schoultz, J., Säljö, R., & Wyndhamn, J. (1997, August). Heavenly talk. A discursive approach to conceptual knowledge and conceptual change in children’s understanding of elementary astronomy. Paper presented at the 7th European Conference for Research on Learning and Instruction, Athens, Greece. Skinner, B. F. (1957). Verbal behaviour. New York: Appleton-Century-Crofts. Strike, K. A., & Posner, G. J. (1982). Conceptual change and science teaching. European Journal of Science Education, 4, 231 -240. Strike, K. A., & Posner, G. J. (1992). A revisionist theory of conceptual change. In R. A. Duschl & R. J. Hamilton (Eds.), Philosophy of science, cognitive psychology, and educational theory and practice (pp. 147-176). New York: State University of New York Press. Tiberghien, A. (1994). Modeling as a basis for analyzing teaching-learning situations. Learning and Instruction, 4, 71-88. Vosniadou, S. (1994). Capturing and modeling the process of conceptual change. Learning and Instruction, 4, 45-70. Vosniadou, S., & Brewer, W.F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24, 535-585. White, R. T. (1994). Commentary. Conceptual and conceptional change. Learning and Instruction, 4, 117-121. Wistedt, I. (1993). Elevers svårigheter att formulera matematiska problem [Students’ difficulties in construing mathematical problems]. Nordisk Matematikdidaktik.

PARTICIPATIVE LEARNING AND CONCEPTUAL CHANGE

MALKA GORODETSKY & SHOSHANA KEINY Ben Gurion University, Beer Sheva, Israel

Abstract. Conceptual Change is a research tradition that relates to the learning of scientific concepts and theories that are anchored in the conception of learning as the acquisition of knowledge. This chapter attempts to illuminate another side of learning that of learning as a participatory process. The latter adheres to the learning process of a team of learners and illuminates the interactions that shape and drive the evolving dialogue and the process of knowledge construction. A conceptual framework for analysis of the process is offered. It is based on the analysis provided by Meyer and Woodruff (1997) that suggest three mechanisms involved in the process of consensus building; Mutual knowledge; Convergence; and Coherency, and on that suggested by Park (1999) that is using the concepts of representational, relational and reflective knowledge. On the basis of these a process related vocabulary is suggested, i.e. Interpretive learning, Relational learning, and Reflective learning. This model is being applied to the analysis of the learning process of a community of learners, consisting of high-school teachers that jointly strive to develop a pedagogy that will better suit their needs. To expose the differences between the analysis of learning within the two conceptual frameworks, that of conceptual change and that of participatory learning, the process of the team of teachers is analyzed through both prisms.

1. INTRODUCTION

Conceptual Change is a research tradition that relates to the learning of scientific concepts and theories that were endorsed by the scientific community. This tradition is anchored in the conception of learning as the acquisition of knowledge, specifically bodies of knowledge about Matter rather than Processes (Chi 1994). The major objective of this tradition is to map students’ or adults’ alternative conceptions that hinder their ability to understand phenomena within a framework of "correct" concepts, and to offer possible remedies i.e. didactical advice. Our purpose in this chapter is to illuminate another side of learning - the side of the learning process. This adheres to the participative nature of learning, to the interactions that shape the evolving dialogue that drives and fuels the process of learning and knowledge construction of a team of learners. These conceptions of learning, that of acquisition and that of viewing learning as participation in processes of knowing (Sfard, 1998), can be viewed as highlighting M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 149-163. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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two different facets of the complex phenomena of learning. Naturally each facet is not independent of the other, however, attempts to highlight one of them, discloses that each approach is based on different underlying assumptions, points of interest, and different “outcomes”. By differentiating between these points of view, our understanding is sharpened and more critical decisions based on educational preferences, can be made. 2.

CONCEPTUAL CHANGE

Conceptual change is an offspring of cognitive psychology that is based on a rationalistic approach that acknowledges the existence of true knowledge that is to be attained. It uses concepts of assimilation and accommodation to understand changes in conceptual states and the mechanism of a conceptual conflict to trigger dis-equilibrium that finally can lead to conceptual change. Within this understanding, the drive towards conceptual change is usually external. Outsiders to the learning community decide about the set of concepts that the student is expected to master in order to be qualified as a literate person. The learning process, as well as the attained goals, focus on the individual. Interactions with peers may promote or facilitate the processes of individual learning, however they are not mandatory and the acquired knowledge does not vary in different learning contexts. There is always only one legitimate conception and students’ learning is valued with reference to this. In conceptual change de-contextualized signs play a major role as the goal is to attain concepts that are detached from specific contexts and supposedly have a universal meaning. The complexity of conceptual change has recently been acknowledged. In addition to the cognitive processes that were considered as the major intervening factor in this process, students’ motivational constructs about themselves and their roles within the classroom, as mediators in the process of conceptual change were recognized (Pintrich, Marx, & Boyle, 1993). Moreover, it seems that enough information has been accumulated by now, indicating that the learner can have concurrently an arsenal of different conceptions of which he is choosing the appropriate one to be applied in a given situation. Mortimer (1995) referred to it as a conceptual profile rather than a defined conceptual state. These recognitions brought Tao and Gunstone (1999) to undermine the usefulness of the research on conceptual change. They suggest that “a more productive approach is to focus on the nature and process of conceptual change” (Tao & Gunstone, 1999, p. 859). Diverting attention to the nature of the process is in coherence with a more general trend that finds its way also to research in the sciences (Barak & Gorodetsky, 1999). This approach is quite young and has not yet developed a language that will be proficient to describe the ongoing, continuous nature of a process. Furthermore, there is no clarification as to what is meant by “process” as compared to the traditional analysis in terms of conceptual change. We ourselves have experienced the difficulties that are associated with the change from conceiving learning in terms of “matter” towards that of “processes”. In this hard endeavor, we have been aided by research literature from two different

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streams. One stream views process as the summation of many discrete snap shots at various junctures that together provide the delineation of student’ conceptual development process. This approach is actually based on the same epistemological conceptual framework as that of conceptual change. Though a more sensitive resolution scale is applied, attention is paid to discrete states that reflect the student’s understanding in conjunction with the context. Tao and Gunstone (1999) use this approach in their analysis of the process of conceptual change indicating the strong dependence of conception on the specific contexts. Another approach towards “process” claims that its nature can not be captured in terms that fit discrete states, nor can a language that concentrates on individual understandings describe the interactions within a community of learners. Rather, a completely different epistemological framework is needed; one that will provide linguistic tools for the analysis and understanding of the complex interactions - the discourse, that leads to common understandings of a team of learners. Thus we have to attend to theories that address not the individual but the discourse that is generated and sustained in a community, i.e. we should look for participative theories. 3.

THE PARTICIPATIVE APPROACH

Participative theories of learning (e.g. Vygotsky, social constructivism) that view learning as a process that involves a community of learners in an ongoing discourse, seem to be more suitable for grasping “processes”. The participatory approach focuses on the dialogical interaction between “the outer” (the social context) and “the inner” (the individual learner) interacting to construct meaning (Marton & Booth, 1997, p. 11). The established partnership among the members of the community is geared towards constructing common meaning. The situatedness in the social - cultural specific context is leading to the emergence of meaning knowledge, that is appropriate to “here and now”. The nature of the discourse that is the major “tool” in this process cannot be predetermined (Gadamar, 1990). Rather, it emerges in the process of conversing and unfolds the reciprocal interactions among the involved persons. The group members open themselves to others and at the same time open the possibility of affecting their understanding of the world (Freire, 1971). This idea that the group’s discourse leads to collective new understandings has been described as “structural coupling” or “co-emergence” (Davis & Sumara, 1997). Knowledge, within this approach, is understood in terms of what emerges from the continuous discourse and reciprocally fuels the process of learning to go on. 3.1. Different Kinds of Learning and Knowledge

As mentioned, attention to the nature and ways of analysis of processes seems to have become more abundant. The view of learning “as a process of becoming a member of a certain community… entails, above all, the ability to communicate in the language of this community and act according to its particular norms” (Sfard, 1998, p. 6). We wish to suggest that this approach could provide a supplementary learning approach that highlights a different facet of learning. Though not stated

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explicitly as a possible alternative approach to that of conceptual change, we believe that it actually provides a participatory alternative. This approach focuses on the “outer" rather than the “the inner”, meaning on the common dialogue of the interactive team. The research by Crawford, Kelly and Brown (2000) supports this direction. They describe the inquiry opportunities that Lori, as a motivated teacher, was sensitive enough to detect and enact as part of the classroom activities. They stress the importance of attending towards science as science-in-the-making in a social context, i.e. to the processes by which new knowledge is constructed, rather than concentrating on the substantive content of the ready made science. They address the nature of students' constructed knowledge not in terms of scientific concepts they gained, but in terms of the scientific processes they came to appreciate. Some of these are: what colleagues have to say is important and worth listening, weighing the contributions of others is a viable scientific practice, reason and evidence are part of argumentation, or appreciating the nature of the process of reaching consensus. A similar approach is also expressed by Meyer and Woodruff (1997) who are calling to abandon learning that is based on the delivery of facts in favor of the process of inquiry. Their alternative learning environment is defined as consensually driven explanations. They suggest that the process of consensus building within group discussions is the appropriate learning context for generating, refining and connecting ideas and can provide an alternative for teaching that is based on delivering facts. They consider their approach as a compromise, between the two dichotomous approaches towards teaching; namely, emphasis on students’ cognitive engagement without paying attention to the “correctness” (as compared to canonical knowledge) of the constructed knowledge, versus focusing on the acquisition of the “correct” concepts. Their understanding of “consensus” is in the sense implied by C.S. Peirce meaning “convergence of informed opinion in a community of inquirers” (Smith, 1965, p. 108). Thus the analysis that focuses on the group's convergent ideas reflects the collective knowledge of the team. They have identified three possible mechanisms that are involved in the consensus building process. 1) Mutual knowledge. This refers to the process by which the group is creating its mutual required knowledge, i.e. establishing common grounds for predictions and initial explanations. The participants are aided by the use of analogies to clarify and expound meaning. 2) Convergence. Convergence occurs when the established mutual knowledge is short in understanding an unexpected effect and knowledge must be restructured towards more complex causal reasoning. The restructuring convergence, is aided by a more critical analysis of the phenomena through questioning and possible answers. 3) Coherency. This is the step of moving towards a coherent “theory” rather than attempting to understand phenomena with “mini-theories”. It happens after cycles of convergence. The mechanisms describe the nature of the processes by which students succeeded to move from situation-specific explanations to a more coherent and general explanation of the behavior of light (not necessarily congruent with that of the scientific community).

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Meyer and Woodruff (1997) describe the process in terms of the involved mechanisms. However, the mutual, convergent or consensually attained explanations (theories) can actually be regarded as different kinds of knowledge that emerge along the learning process of a community. Such an approach would highlight the nature of the knowledge that emerges from the dialogue. Indeed, within the research literature on participatory action research this approach towards the analysis of a process a community is engaged in, in terms of the nature of knowledge that is built up, is actually applied (Park, 1999). Within the action research approach that deals with processes a community undertakes to embetter its actions taking into account their abilities and needs, representational objective knowledge is often inappropriate and irrelevant. These communities expand the understanding of knowledge to include knowledge that stems from the community and serves its specific needs. Park (1999) distinguishes between three major categories of knowledge: representational, relational and reflective. Representational knowledge can be either functional or interpretive. Representational - functional knowledge refers to abstract scientific knowledge that is associated with the acquisitional dimension of learning or of conceptual change. The other three are related to the participatory dimension. 1) Representational - interpretive knowledge is the understanding that is attained in a collaborative dialogue that rests on the inter-subjective meanings of the participants. Interpretive knowledge promotes the undergoing discourse and thus is more appropriate for describing participative processes. 2) Relational Knowledge relates to the understandings that unite the knower and the known. It encompasses the process and the product of the interactions within the collaborative learning team. Characteristic values associated with this kind of knowledge are “sharing, caring, togetherness, commitment and trust” (Park 1999, p. 148). These are essential features for establishing an egalitarian common discourse within a community. 3) Reflective Knowledge relates to “critical and communicative rationality in which reflection plays a key role” (Park 1999, p. 148). It is associated with the understanding of the social - political realm, and a moral commitment that drives towards engagement and change. It is expressed in Freires (1970) concept “conscientization” which is a hybrid of “consciousness” and “conscience”. 3.2.

Learning, Knowledge and Processes

Park comes from the realm of action research, i.e. from a tradition that relates to the collaborative dialogue as leading towards action - towards taking some initiative to embetter the present. Thus it is only natural that he is speaking in terms of what emerges i.e. in terms of knowledge. As we wish to focus on the process we prefer to use verbs rather than nouns namely, Interpretive learning, Relational learning, and Reflective learning. These are three perspectives for understanding the nature of the collaborative dialogue within a community that shares a common goal and the commitment towards achieving it.

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Park (1999) suggests that the values that sustain advancement and change in representational knowledge (scientific revolutions in Kuhnian terms) such as fruitfulness, accuracy, consistency, simplicity and scope, should also be applicable to the analysis of participative learning processes. In addition he suggests specific values that motivate the emergence of knowledge that is associated with the participatory nature of learning. As already mentioned he offers the values of caring, sincerity and trust for the development of relational knowledge, and autonomy and responsibility, for reflective knowledge. We wish to add the values of sharing for relational learning and the values of tolerance towards pluralism of ideas and world views as well as tolerance to ambiguity to Reflective learning. The mechanisms that were suggested by Meyer & Woodruff (1997) as being involved in the consensus building processes are complementary to the participative learning processes suggested here. If we understand the concept of “consensus building” not in terms of achieving a coherent generalized theory but in terms of achieving a coherent process (or coherent emerging knowledge) then the above described three mechanisms can be applied to each of the suggested learning processes (or emerging knowledge). Thus in the perspective suggested by us we wish to consider these mechanisms as promoting each of the natures of learning, e.g. interpretive learning, relational learning, and reflective learning (see Table 1).

In this sense each of the mechanisms or all of them can be instrumental in each process of learning. Our attempt in integrating knowledge, mechanisms and learning (knowing) provides us with an approach that could yield deeper understanding of collective learning processes. Understanding is used here in the sense of becoming participants in a community of learners that are involved in practicing a specific domain rather than seeking externally endorsed resolutions (Hiebert et al., 1996; Cobb et al., 1999).

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In the following part of the chapter, we apply this approach to analyze the discourse of a community of teachers attempting to develop a pedagogy that will better suit their needs. Though most of the research on conceptual change was done on children’s understanding of scientific concepts, attempts to understand teachers' classroom behavior as associated with their conceptual change regarding professional concepts, e.g. assessment, have been done (e.g. Gorodetsky et al., 1997; Keiny, 1994). The discourse is analyzed within the two conceptual frameworks under discussion, i.e. the participative approach and the conceptual change approach. We chose this direction as we believe that it will highlight the differences between the two approaches. 4.

THE STORY

Our case study involves a group of eight teachers from the “Zafit” regional highschool, that together with an out of school researcher (one of the authors) formed a “navigating team”. The group included the principal and the deputy principal and 5 head-teachers representing grades 7th-11th. Their aim as a team was to develop a different pedagogy for the entire school. The collaboration of the researcher with the school was established a few years earlier through a STES project (Keiny, 1994). The pedagogy that underlied the STES project aimed to develop students' autonomous learning through the inquiry of authentic social - environmental problems. This was an alternative way of learning to the more common teaching that focuses on prescribed curricula. In 1998 a new Principal was appointed who decided to extend this student-centered inquiry towards a pedagogy that will encompass the entire school. This actually meant that the school was faced with the need to construct a new core-curriculum for all grades. The navigating team’s first step was to decide on focal inquiry themes for each grade, e.g. “roots” for the 7th grade, “my settlement” for the 8th grade, and “ones right to dignity and respect” for the 9th grade, etc. These themes were to serve as an organizing umbrella for the individuals or small teams of inquiry. It was postulated that students' learning skills as well as research methodologies will develop along the grades, thus preparing the students for their final assignment project, to be submitted as part of school matriculation. The navigating team met regularly during the school year. The meetings were audio-taped, transcribed and distributed to the participants. The transcripts served as basis for the process of reflection in the group, as well as a database for analysis by the researcher. We will attempt to analyze these transcripts from the two different points of view; that of “participatory learning” and that of “conceptual change”. The excerpts are not necessarily dealing with the same issue. Rather, they provide examples of dialogues that the group was involved in and that we found as productive in illustrating the different ways of analysis. Though in a way they reflect development along both facets of analysis, this is not intended. Each excerpt is analyzed through the two approaches.

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M. GORODETSKY & S. KEINY Excerpt 1 (15.9.1998)

This excerpt, taken from the navigating group meeting dwells on the 7th grade theme, i.e. “roots”: Uri: The roots study misses the point, it does not fit our idea of an inquiry project. Jonathan (the Principal): The idea is that each student does an inquiry study of his own family… Uri: Roots I see as a strong personal experience, I would like them to stay there, instead of turning it into inquiry... sit with their mother over a cup of coffee and listen to her stories. Shosh: Three questions are at the basis of our discussion: ‘what is an inquiry’ ‘what is the role of the teacher’ and ‘what is the role of this team’. Uri: I have worked with kids on individual research studies. I gave them a sheet of instructions, explaining item by item, took them to the library and followed up the whole process. Shosh: The question is what do we mean when we say an inquiry study. This is one model of an inquiry study, could it be extended? Jonathan: This is a turning point in our work, we aim to construct new thinking strategies, to liberate ourselves in many respects from our old conventional thinking... I admit that your question is most intriguing: what do we mean by an inquiry study.... Shosh: Our role is to “unfreeze” our thinking, question our previous work and see how we can improve it. Neomi: I am less interested in the subject, I see my main goal to train my students to ask questions. Sharona: We, the teachers already underwent change, I do not teach the way I did before, I believe that as teachers we are now a sole part of the learning process.

The dialogue is oriented towards establishing common understandings. The participants are attentive to each other and relate to the questions and interpretations being raised in the dialogue. Their comments are not voiced as separate monologues, but rather merge into the flow of a narrative. Through the support of this relational learning intersubjective common understandings are established. The researcher is instrumental in pinpointing the issues that are in disagreement, rather than providing new knowledge. By doing so a continuos process towards mutual and convergent learning is sustained. As convergence of meaning on a certain level seems to be attained, the dialogue opens again in the direction of personal preferences with respect to learning. The latter are expressed as intuitive “guts feelings” preferences (I see.., I believe…) that potentially can lead towards relational learning. An analysis from the conceptual change (acquisitional) point of view focuses rather on the conceptions of the individuals in the group and how these are

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changing. Uri’s conception of inquiry is in terms of an objective rational enterprise that excludes the legitimization of emotions in the process. He cherishes emotions as authentic experiences, but not as data in an inquiry project. Uri’s conception is in disagreement with the conception of inquiry as a naturalistic endeavor. The facilitator attempts to question this conception by suggesting that there are other possible understandings of inquiry. Jonathan catches up and is intrigued by the possibility that more than one way of conceiving inquiry is possible. Neomi and Sharona seem to be familiar with both conceptions and go on beyond the discussion of the nature of inquiry towards expressing a preference for the conception of inquiry as a process of learning. 4.2.

Excerpt 2 (27.10.98).

This excerpt comes from the second group meeting. The discussion focuses on the 8th grade theme - "My settlement". It is pertinent to add here that Tzafit as a regional school has a wide catchment area, covering some 17 different settlements, of various types. Shosh: What do we find in this theme (“my settlement”) that justifies it as a main topic of inquiry? Anat: I see it as a way to come to know the other settlements, to abridge between students of different places, we could organize mutual visits. Irit: The same way they investigated their families, they now investigate their environment. We should also extend the sources of information, teach them how to access different sources of data. Amalia: I see “my settlement” as a continuity of the family. In constructing a model for the whole school, we naturally widen the circle... Our student population is so versatile, socially, ethnically, and culturally. This is an opportunity to deal with pluralism, and it leads to the next theme: respect and dignity. Jonathan: I find it rather a sensitive issue, many kids say they want to leave their settlement. My aim is to educate them as world citizens rather than as Kibbutz (a communal settlement) citizens. Methodologically, I would like to give more emphasis to research skills, for example, observations, teamwork. Shosh: Our role is becoming clearer. As a team we experience conversation, dialogues, which should help us understand how to initiate a dialogue or teamwork. In terms of contents, I believe we have touched important ideological issues embedded in our reality, which indicate it's worthiness as a theme.

In terms of participatory learning, the meeting continues the previous discussion. Caring as well as responsibility for the students are expressed within a broader educational dilemma that adheres to the aims of the educational system. It relates to the educators’ commitment; is it to prepare the young to cope with life in a multicultural society, i.e. to socialize them to pluralism, or to promote loyalty to the past and present place of living. Is the commitment of the educational system towards preparing the students for the future or enculturing them to the past - present

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reality? This discussion reflects interpretive, relational as well as reflective learning. It questions the autonomy and responsibility of the learner as well as that of the teacher. Jonathan (the principal) feels uncomfortable in this sphere of discussions that addresses values, expressing his preference for dealing with supposedly neutral “research skills”. Along the discussion, questions are raised for which no answers are provided. Is this a manifestation for tolerance and respect towards a multicultural understanding of the aims of the educational system, that was developed? The researcher is diverting the dialogue to another hidden issue, a didactical one. Is learning by making the experienced tacit knowledge explicit, a useful model for understanding team work? The latter issue that addresses learning as what emerges from the team's activities, versus the import of information and strategies from the outside, became central in the following meetings. From the conceptual change (acquisitional) point of view, the excerpt extends the participants’ understanding of inquiry. Moving to a wider context, from family to the entire settlement demands coping with new aspects. While dealing with the “family” the associated attributes of inquiry were multi-ethnicity, moving to the inquiry of the settlement is associated with multi-cultural, multi-social and multiideologies which characterize the present Israeli society. Moreover, inquiry in these directions demands different methodologies of inquiry, e.g. social research. 4.3.

Excerpt 3 (17.11.1998)

The issue of teamwork continues to occupy the group discussions on its third meeting. Shosh: Are we clear about what we mean by teamwork? Uri: First we have to construct criteria. The group then generates questions, and decides together on one inquiry question. Roles are then negotiated, and the process is mapped. The same criteria could also serve as criteria of evaluation. Judith: If we work here as a team, we illustrate what we mean by teamwork. Shosh: Could we extract criteria from this group meeting, for example? Uri: I feel great about the way we listen to each other, sharing each others’ problems... Irit: To me the most important issue is being connected to the real needs of the school.

The team attempts to reach convergence and coherency in their understandings of the nature of team work. Sharing and caring for each others needs are expressed as part of the team work. Relational learning provides an appropriate egalitarian setting for their own team learning. In terms of conceptual change (acquisitional) learning, the discussion reflects two different approaches for learning which are “from theory to practice” and “from practice to theory”. Uri represents the first conception suggesting that the starting point is constructing criteria, then generating questions etc. The other approach to learning “team working” is expressed by Judith who claims that to really understand

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team work, one should experience it and then through reflection and formalization build the model.

4.4.

Excerpt 4. (1.12.1998) Elisheva: How does a teacher cope with a classroom of 35 kids, and conducts individual or team inquiry studies? Uri: I want to share with you my experience in my classroom, grade 7, where I teach both history and “roots”. I shall start with history. I opened the lesson by saying, “I don’t feel like teaching you, you teach me.” What a commotion aroused. They started talking about forming teams. I asked them, “how do you divide into teams?” they threw ideas: criteria, according to the different settlements, what is the size of a team, 2,3,4? One girl decided she preferred to work alone. Teams were formed and they sat together, negotiating how to design their work. One team wrote down: “What do we want to know from this particular chapter?” “How, in what way, are we going to present it in the classroom?” This was a new experience for me, and that is how I approached my second task, “roots”. I told them that I do not feel like teaching the way I did in the past, then drew a circle on the board, and wrote “roots” in the middle. “What do we do now?” I asked. “Add my name to the circle” responded one boy. “Why?” I asked, “Because the study begins with me.” I handed out pages, everyone added their names to the circle. “What now?” “We extend the family”. This raised a discussion, who is included and who is not. One boy commented. “I have a problem, my grandpa was killed in Kurdistan, and my grandma cannot talk about it”. A girl joined, “I have a similar problem, I lost my brother when I was 5 years old, but when I wrote a poem about him, my father was deeply heart”. Many more joined the conversation, throwing suggestions, raising more problems... Neomi: What did it do to you? Uri: From an inquiry study activity it turned into a value education lesson.

From the participatory learning dimension, Uri’s monologue within the dialogue reveals his and his students' relational learning. He practically “jumps into deep water” and initiates a move towards a new classroom culture, based on an equal relationship between teacher and students. He opens by a plea for help from the classroom disclosing sincerely his feelings of dissatisfaction with his role as a teacher. He describes the relational learning that developed through sharing and caring that characterized the interacting community of teacher and students. Responsibility for collaborative learning was taken up by the classroom as an entirety. We believe, though there is no evidence in the excerpt, that Uri emerged with reflective learning about the different nature of the pedagogy that was enacted in his classroom learning. From the conceptual change (acquisitional) point of view it is clear that Uri in his actions in the classroom exhibits a conceptual change in his understanding of inquiry. His discomfort with “non-scientific” inquiry (excerpt 1) has disappeared. Moreover he managed to translate his new conception into classroom activities, or vice versa; the classroom activities were instrumental in promoting his abstraction towards a new conception. Conceptually, Uri has extended his understanding of inquiry beyond that of a scientific rational method, to include values. However he is

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labeling the lesson not as inquiry, but as a lesson on values. Is this a reflection of the coexistence of certain compartmentalizations in his mind? Despite this, his change seems to be genuine and comprehensive as indicated from an excerpt taken from later in the meeting. Judith: Uri, how do you intend to evaluate such work? Uri: I have a story for you about evaluation. In yet another classroom, while sitting in the library, I threw an idea: “What would you say if I asked you to construct your own test?” They accepted it enthusiastically. One group composed a test, another, decided on criteria of evaluation. Later they assessed themselves, and surprisingly, the gap between my and their scores was small. I would like to add another criterion for evaluation of the “roots” project. I know that the inquiry question is important, but no less is the learning experience the students underwent, both in the classroom and in their families. Irit: Because they feel it is theirs… Amalia: They used to re-produce their older brother’s or sister’s inquiry study, and here, I was really fascinated how through the classroom discussions they were given full legitimization to write on what interests them. Elisheva: The question is not whether you assess or they do, but what are the criteria of assessment.

The dialogue seems to rest on a common understanding of the nature of the new pedagogy (paradigm) the school wants to establish. Judith poses a question that sounds as a pragmatic and trivial one regarding the nature of assessment. However this question actually tackles one of the strongholds of the teaching profession. It seems that the common (mutual) understanding of the new pedagogy enabled the attendance to and questioning of issues that were taken for granted; “but what about assessment”? Uri is sharing with the team his past experience in involving his students in constructing their own test, as well as in assessing themselves. He recognizes that though he has given his students autonomy within a domain that is purely dominated by teachers, he actually missed to assess the process of learning that is so important in their different pedagogy. Uri is conscious of the different needs and aims of the new pedagogy and feels responsibility to go along this line. Uri is sensing reflective learning in integrating his and his students needs in a combined conscientization process. From the conceptual change (acquisitional) point of view, it is clear that Uri’s understanding of the nature of inquiry has broadened. Yet, he tends to adhere to the concept of “inquiry” as a didactical tool for learning predefined content. He shares with his students the responsibility for learning as well as for assessment, but the criteria for assessment remain more or less similar. He recognizes that the evaluation of the process of learning is central to inquiry and wishes to add it to the list of criteria. Yet, the decision as to the criteria for evaluation rest with him.

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DISCUSSION

Our attempt in this chapter was to develop a vocabulary that will better suit learning as a participative process rather than as a “conceptual change”. The analysis concentrated on “problematizing” (Hiebert, 1996) rather than on problem solving, i.e. acquiring the 'correct' conception. Problematizing brought to the surface alternative views and discussions leading to the development of mutual new understanding rather than eliminating pre-determined “uncorrect” conceptions. This process of dialoging nourished the emergence of learning within the community of teachers. We were able to illustrate the emergence of interpretive learning, relational learning and reflective learning that were enabled by the team’s “real talk”. This is a conversation that is typified by talking, listening, questioning, arguing and speculating. A dialogue that sprouts within a community that the participants feel safe to voice their half baked ideas without fear of being ridiculed. They feel free to criticize each others’ work, and at the same time accept criticism (Belenky, 1986). We chose not to be precise about the nature of what emerges, using simultaneously terms of knowledge, mechanisms and learning. We believe these are different labels to describe the same emerging phenomena, and that the choice of a particular label is more dependent on the analyst, i.e. his purposes and preferences. Thus, the action research tradition would prefer to address the outcome - the knowledge that is appropriate to improve the present situation of the community. The cognitivist would emphasize the cognitive processes that are involved in the process and would prefer the use of cognitive mechanisms. Ourselves who wish to emphasize the process, the continuity and evolution, prefer to speak in terms of learning. We believe that it is a clear case where the “means” and the “ends” are interwoven in a non-separable manner. Accordingly three concepts have been coined: Interpretive learning, Relational learning and Reflective learning. We believe that some elaboration is needed regarding the latter concept. Reflection is a widely used concept that usually addresses the meta-cognitive processes a learner is activating to monitor or understand his process of learning. It is accepted as an intrapersonal mental process of individuals though outsiders can be a trigger that initiates or promotes reflection (e.g. Korthagen, 1995). Actually what we attend here while addressing the participative communal reflection is referred in the literature as reflexivity, i.e. the interpersonal process. Rothman (1997) defines reflexivity as embracing the relationships between the self, the others and the specific context. Reflexivity is linked to the concept of authorship or actually collective authorship (Zimmerman, 1999) and thus is central to discussions on higher order change. Reflexivity questions issues of responsibility by asking who is responsible for the learning process and the undertaken actions. Reflexivity thus becomes conscientization and as such can be addressed as the mechanism, the outcome or as sustaining collaborative processes of development and change. We have started from a point of dissatisfaction with the conceptual change approach in attempting to understand learning, specifically concepts. We hope that while writing this chapter, we ourselves have experienced reflexive learning that shaped this manuscript. We have experienced “tolerance to ambiguity” and actually

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feel a strong urge to share our unresolved ambiguities with the readers. We are content with the participative approach we have suggested as an alternative view of analyzing learning. However we were left in the state of ambiguity as to the epistemological nature of these alternatives to describe learning. Different understandings are possible and we invite the readers to participate in this process of reflexive learning. A possible suggestion is to view the two approaches, that of participative learning and that of conceptual change, as attempts to highlight different facets of the same phenomena. We believe that the learner that is immersed in the dialogue is a holistic identity. Those immersed in the process sense a unified experience that intertwines the different kinds of knowledge and the different processes into a unified experience. It is only from the “outside” (literally or metaphorically) that learning can be interpreted in different ways. Another possibility is that the two alternative approaches are an extension of the understanding of the concept “conceptual change”. These aspects, of acquisition and participation, are dialectically connected in a cyclic (not linear) intertwined process of learning. Thus they can’t be separated. Yet a third alternative is that the alternative approaches are actually intrinsic to the conception of learning within the framework of activity theory. The choice to get involved in a specific socio-cultural activity is dependent on the learners’ interpretation of the situation. By doing so the learners are contextualizing themselves in a specific context that influences that which emerges from the interactions of those engaged in constructing meaning (Van Oers, 1998). We will leave the discussions on the alternative epistemological understandings to the readers and hope that this will bring them to reflective (reflexive) learning. REFERENCES Barak, J., & Gorodetsky, M. (1990). As “process” as it can get: Students’ understanding of biological processes. International Journal of Science Education, 21, 1281-1292. Belenky, M. F., Clinchy, B. M., Goldberger, N. R., & Tarule, J. M. (1986). Women's ways of knowing: The development of self, voice, and mind. New York: Basic Books. Chi, M. T. H., Slotta, J. D., & Leeuw, N. D (1994). From things to processes: A theory for conceptual change for learning science concepts. Learning and Instruction, 4, 27-43. Cobb, P., & Bowers, J. (1999). Cognitive and situated learning perspectives in theory and practice. Educational Researcher, 28, 4-15. Crawford, T., Kelly, G. J., & Brown, C. (2000). Ways of knowing beyond facts and laws of science: An ethnographic investigation of student engagement in scientific practices. Journal of Research in Science Teaching, 37, 237-258. Davis, B., & Sumara, D. J. (1997). Cognition, complexity, and teacher education. Harvard Educational Review, 67, 105-124. Freire, P. (1991). Pedagogy of the oppressed. New York: Seabury Press. Gadamer, H.G. (1990). Truth and method. New York: Continuum. Gorodetsky, M., Keiny, S., & Hoz, R. (1997). Conceptions, practice & change. Educational Action Research, 5, 423-433. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Oliver, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of Mathematics. Educational Researcher, 25, 12-21.

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Keiny, S. (1994). Teachers professional development as a process of conceptual change. In I. Carlgren, G. Handal, & S. Vaag (Eds.). Teachers minds and actions. Research on teachers' thinking and practice (pp. 232-246). London: Falmer Press. Korthagen, F. A. J., & Wubbels, T. (1995). Characteristics of reflective practitioners: towards an operationalization of the concept of reflection. Teachers and Teaching. Theory and Practice, 1, 5172. Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah, NJ: Lawrence Erlbaum Associates. Meyer, K., & Woodruff, E. (1997). Consensually driven explanation in science teaching. Science Education, 81, 173-92. Mortimer, E. F. (1995). Conceptual change or conceptual profile change? Science & Education, 4, 267285. Park, P. (1999). People, knowledge, and change in participatory research. Management Learning, 30, 141-157. Pintrich, P. R.. Marx, R. W., & Boyle, R. A. (1993) Beyond cold conceptual change: The role of motivational beliefs and classroom contextual factors in the process of change. Review of Educational Research, 63, 167-199. Rothman, J. (1997). Resolving identity-based conflict: In nations, organizations and communities. San Francisco: Jossey-Bass Publishers. Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27, 4-13. Smith, J. (1965). Community and reality. In R. Bernstein (Ed.), Critical essays on Charles Sanders Peirce. New Haven, CT: Yale University Press. Tao, P. K., & Gunstone, R. F. (1999). The process of conceptual change in force and motion during computer-supported physics instruction. Journal of Research in Science Teaching, 36, 859-882. Van Oers, B. (1998). From context to contextualizing. Learning and Instruction, 8, 473-488. Zimmerman, D. P. (1999). The role of Reflexivity in the orders of change: the unraveling of the theories about second-order change. Doctoral dissertation submitted to the Fielding Institute.

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COGNITIVE VARIABILITY IN THE DEVELOPMENT OF THE CONCEPT OF FAMILY: A CONTEXTUALIST OR A GRADUALIST VIEW?

MARÍA JOSÉ RODRIGO, BEATRIZ TRIANA & MARÍA ISABEL SIMÓN University of La Laguna, Tenerife, Spain

Abstract. The purpose of this chapter is to demonstrate the existence of cognitive variability in the development of the concept of family and to highlight its relevance to a model of conceptual change. Cognitive variability is indicated by the existence of a variety of knowledge states displayed across tasks. It is argued that stable and transitional knowledge states can be captured through the observation of discordances or mismatches between responses given by an individual on two tasks tapping knowledge at implicit or explicit formats. Instructional implications of detecting transitional knowledge in educational settings are also examined. Finally, an empirical illustration of this approach within the development of the concept of family among children, preadolescents and young adults is presented. In this study, the distribution of knowledge states according to the age groups and to the nature of the relation property involved in the concept was explored. Discordances and concordances between responses given on the recognition and definition tasks were registered to reveal transitional and stable knowledge states. The implication of the results for a gradualist or a contextualist view of cognitive variability is discussed.

1. INTRODUCTION

Recent accounts of conceptual change have challenged the view that school learning requires the replacement of prior ideas with scientific theories (e.g., Caravita & Halldén, 1994; Spada, 1994). Instead, it is proposed that different kinds of representations can co-exist and can be used in different ways according to the context (e.g., task demands, communicative settings). This model of conceptual change requires to know how people deal in their minds with multiple representations of the same phenomenon (Spada, 1994). Moreover, it requires a view of cognitive development that emphasizes the study of age differences with respect to the variety of cognitions displayed across tasks or situations. Such a view may admit that there is not a single knowledge state exhibited at a given age that is totally replaced by other at later ages. Cognitive variability across contexts is the rule and not the exception in child development. The main purpose of this chapter is to contribute to the understanding of cognitive variability in the development of the concept of family and to highlight its relevance to a model of conceptual change.

M. Limón & L. Mason (Eds.), Reconsidering Conceptual change. Issues in Theory and Practice, 165-185. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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1.1. Cognitive Variability and Developmental Change

Situational or task variability of a child’s responses is a developmental phenomenon observed by many researchers that reveals the existence of many types and degrees of partial knowledge in his/her mind. Piaget (1971), for example, found differences in timing between the successful application of a given skill in one type of task and its successful application in another type of task (“horizontal decalages”). Chomsky´s (1965) “competence/performance” distinction has been also invoked to explain the pervasive fact that task variables may interfere in a child’s performance while the competence implied may exist in his/her repertoire of capabilities. In both cases, it seems that response variability is a troublesome fact to deal with in many developmental theories. A sociocultural point of view of child development (e.g., Vygotsky, 1978; Rogoff, 1990; Valsiner, 1997; Wertsch, 1998), however, may expect variability in performance across situation and social contexts as a normal finding. For instance, Rogoff (1998) and Göncü (1999) stressed participation in sociocultural context as a mechanism of growth. According to this approach, a child at any given point reveals many types and degrees of partial knowledge. These are supported by the contributions of more experienced partners in the course of joint activity, guiding cognitive development along particular paths. Our view of cognitive variability tries to conciliate some ideas from a sociocultural view with those of a cognitive developmental view (e.g., Billett, 1996). Cognitive developmental psychologists are concerned with the description of cognitive changes across ages with little commitment to the study of the situational or task factors linked to these. Cognitive performance at a given age is viewed as a result of a child’s internal competence that can be revealed under any task circumstances or situational factors. The radical sociocultural view, in turn, denies the existence of internal representations in the mind and proposes replacing these with discourse processes taking place among people in specific situations (Säljö, 1994). Therefore, they are interested in tapping transient and collective products built in during the individual´s participation in social or cultural activities. But the study of the evolving relationship between contextual factors and the individual´s developmental level is a field of research largely neglected in the contextualist view (Van Oers, 1998). Bridging the gap is a view of cognitive development that is sensitive to task variations. Such a view emphasizes the study of age differences with respect to the variety of cognitions displayed across tasks. There is no doubt that the tasks children are confronted with are embedded in social activities or practices pertaining to different learning communities. This means that participation in these communities involves for the individual child not just increasing knowledge of content but also incorporation of values and cultural meanings attached to the tasks and to the learning process itself. However, it is also true that the tasks children are confronted with may also differ in terms of the cognitive demands required to solve them. Thus, children’s engagement in the resolution of different tasks provides a good opportunity to reveal different forms of individual approaches or ways of thinking.

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Siegler (1996, 2000) offers a view of cognitive development focused on the study of gradual changes in children’s use of strategies. The overlapping waves theory is based on the main assumption that children typically use a variety of strategies and ways of thinking, rather than just a single one, to solve a given problem. For instance, in studies of arithmetic, serial recall, spelling, and other tasks, most children used at least three strategies as was revealed by closely following children’s performance across sessions with microgenetic methods. During a learning process the diverse strategies and ways of thinking coexist over prolonged periods of time, not just during brief transition periods. Although there is an increasing reliance on the more advanced strategies, most children used the same set of strategies across sessions or showed some improvement in effective performance. Thus, cognitive variability is a ubiquitous fact present not only between ages but more interestingly within individual children at a given age in two presentations of the same task and even within a single trial. 1.2. Cognitive Variability and Conceptual Change

The existence of cognitive variability across ages and tasks is relevant for a model of conceptual change. According to this view, the process of knowledge acquisition should be described as gradual changes or states of “in-between understanding” (Schwitzgebel, 1999). There is not a single moment at which a child comes to understand something once and for all. Likewise, there is not a single knowledge state achieved at certain age no matter the task or situation used. A given child may exhibit a variety of knowledge states across tasks or situations. This picture of knowledge change is also coherent with the mental model view according to which people create dynamic representations on the spot to deal with the demands of specific tasks or situations (e.g., Vosniadou, 1994). Variability may not only indicate the existence of different ways of thinking in the individual child but the existence of knowledge represented in different formats. Thus, the same knowledge content may be represented either in implicit or explicit formats. Explicit knowledge is generally interpreted as consciously accessible knowledge, while implicit knowledge usually means knowledge that is represented in the mind but of which he/she is not aware. Karmiloff-Smith (1992) suggested the transition of different knowledge states according to the level of awareness and availability to verbal reports. In the first level E1, the representations are open to analysis and are manipulable but are not available to conscious access and verbal report. At level E2, the representations are consciously accessible but may not be available to verbal report. Finally at a level E3, the representations are available in a code that permits verbal report. Thus, children may have an implicit understanding of a larger set of representations than they can fully articulate in speech (Karmiloff-Smith, 1992; Halford, 1993; Mandler, 1998). Once children are able to redescribe their implicit knowledge into explicit formats they become aware of their own beliefs. Consequently, our models of conceptual change should pay attention to the development of cognitive variability and metaconceptual awareness (Vosniadou,

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1994). On the one hand, instructional efforts should not try to reduce the variety of knowledge states displayed by the child in order to adjust to a single view. It should take into account that a variety of knowledge states are represented in the child’s mind in order to deal with task or situation requirements. On the other hand, instructional programs should encourage children to provide verbal explanations of a phenomenon, that is, to redescribe their implicit representations into explicit ones. In this way they can realize that their beliefs are just interpretations of the phenomena and not unquestionable true facts. 2.

TRANSITIONAL KNOWLEDGE AS IMPLICIT-EXPLICIT REPRESENTATIONS

The process of knowledge acquisition proceeds through transitional and stable phases. In several studies, transitional knowledge was indicated by the observation of discordance among different response modalities given by an individual on a task. On the contrary, concordance among responses was a signal of a stable phase in the process of knowledge building. Three indicators of transitional knowledge have been reported in the literature. First, the discordance between looking and verbal behavior in a false belief task (Clements & Perner, 1994). Second, the verbal imprecision of children’s explanations such as false starts and self-repairs, deletions in the production of sentences, long pauses and metacognitive comments in a gear movement task (Graham & Perry, 1993; Perry & Lewis, 1999). Children were asked to indicate which direction the gear with a symbol on it would move if the gear with the handle moved in the given direction. Finally, the gesture-speech discordance in conservation and mathematical equivalence problems (e.g., Goldin-Meadow, Alibali & Church, 1993; Garber, Alibali, & Goldin-Meadow, 1998). In all these studies children’s knowledge indicated either by looking behavior, gestures and by verbalizations was compared in the same task. Whenever discordance among response modalities was found it was considered as an index of transitional knowledge. This transitional knowledge was available in implicit or explicit formats but not both. For instance, in the gesture-speech discordance the use of gesture can allow the learner to explore implicit knowledge inaccessible in a verbal format. Stable knowledge was available in both formats Recognition techniques, multiple-choice tasks and confidence ratings can also tap implicit knowledge. For instance, in the field of conceptual development we can compare children’s performance on a recognition task and on a verbal definition task. The former task requires identifying the features that a particular exemplar possesses, whereas the latter requires reporting the general rule underlying the concept (Roberts, 1998). A recognition task tapped implicit knowledge in the sense that one can easily report the features of a particular exemplar but not the general rule underlying the concept. Therefore, implicit knowledge is implicit not because is unreportable under any task condition, but because its verbalization is restricted. In the above example, discordances found between a recognition task and a definition task may indicate either the presence of knowledge represented in implicit

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formats not available to explicit ones, or viceversa. There are many examples of the first type of discordance, that is, the existence of a large set of representations that remain implicit until they can be “redescribed” into explicit forms as Karmiloff-Smith (1992) proposed. There has been less empirical evidence and theoretical support for the second type of discordance, that is, the existence of explicit representations without the corresponding implicit forms. That type of discordance, however, may be observed in school learning when students are presented with explicit information regarding a given notion, without implicit counterparts. For instance, Vosniadou (1994) suggested that certain kinds of questions have a greater potential for providing information about the students’ underlying explanatory framework than others provide. Generative questions (“Does the Earth have an end or edge?”) confront children with phenomena about which they have not received any explicit instruction yet. Factual questions (“What is the shape of the Earth?”) can be answered by repeating information heard in class. Consequently, it is relatively frequent, for instance, to observe children replying that the Earth is round to the factual question, whereas in answer to the generative question they reason in a way consistent with an implicit model of the Earth as a suspended disc. 3. INSTRUCTIONAL IMPLICATIONS OF IMPLICIT-EXPLICIT KNOWLEDGE

According to Tirosh (1994), implicit knowledge and explicit knowledge are terms constantly used in the psychological and educational research literature along with their synonyms (tacit, intuitive, inaccessible knowledge and reflective, accessible, articulate knowledge). Yet, areas such as the contribution to the thinking and learning process of a change in the state of knowledge from implicit to explicit and viceversa, the sources of these two types of knowledge and the types of intervention strategies that promote them are still underdeveloped. In this section we will reflect upon the usefulness of the implicit-explicit distinction for education. First, the existence of implicit knowledge not available in explicit formats is useful in detecting receptivity to instruction. It has been hypothesized that children may have implicit knowledge at a stage where explicit knowledge is minimal, if present at all. Implicit understanding of false beliefs, as indicated by looking measures, may serve as a marker for the onset of the zone of proximal development (Clements & Perner, 1994). Verbal imprecision in the explanations given on the gear movement task was found to predict improved performance after a training stage (Perry & Lewis, 1999). The implicit understanding of equivalence problems indicated by the child’s spontaneous gestures index the zone of proximal development, providing a mechanism by which adults can calibrate their input to that child’s level of understanding (Goldin-Meadow, Alibali, & Church, 1993; Goldin-Meadow, 2000). Thus, in all these studies the presence of transitional knowledge is linked to receptivity to instruction. Secondly, the presence of discordant states between implicit and explicit knowledge is useful to detect different stages in the formation of a concept, from the

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abstraction of situational regularities to the induction of an explanation based on existing pieces of explicit knowledge (Gopnik, 1993). The abstraction of situational regularities is an early stage of concept formation that is indicated by a predominance of implicit understanding (Roberts, 1998). At this stage, knowledge comes from the observation that certain events tend to go together and form a typical sequence. It is a process of pattern formation and recognition for which connectionist modelization seems particularly appropriate. In contrast, the explanation stage of a concept formation is indicated by a predominance of explicit understanding. Children are able to go beyond associative expectations and create a mental scenario in which, if the conditions were different than the one observed, an explanation based on explicit knowledge is used to guide the response. Finally, discordances between implicit and explicit knowledge are good indicators of the existence of implicit or explicit learning. Reber (1989) defined implicit learning as a knowledge-acquisition process that occurs in the absence of conscious, reflective strategies to learn the particular stimulus regularity (e.g., an associative procedure). Implicit learning is unselective, it involves the storage of all associations between stimulus variables and it is not capacity limited. In contrast, the term explicit learning is used to refer to the conscious knowledge-acquisition process that occurs when people invoke active strategies to discover the rules or principles that underlie the task (e.g., hypothesis-testing or metacognitive procedures). Explicit learning utilizes only those variables selectively maintained in a limited-capacity working memory. It has also been argued that implicit learning predates the evolution of explicit learning (Reber, 1993). Compared to explicit processes, implicit processes should also be stable across the age span (Maybery & O´Brien-Malone, 1998; Vinter & Perruchet, 2000). Whenever a concordance between implicit and explicit knowledge is found, this indicates the presence of a stable state in the process of knowledge building. We propose that discordances indicate transitional periods marked by the operation of implicit or explicit learning processes. The onset of implicit learning is marked by one type of discordance characterized by the existence of implicit representations without the corresponding explicit forms. For example, when a child recognizes and identifies an exemplar of a category but she or he does not verbalize it when asked to define the prototype (only-recognition knowledge). In turn, the onset of explicit learning is marked by another type of discordance characterized by the existence of explicit representations without the implicit counterparts. That is, when a child describes a prototype containing a given feature that she or he does not recognize or identify as an exemplar of the category (only-definition knowledge). In our view, discordances involving only-definition knowledge may be conceived as a natural consequence of having been exposed to external sources of information via verbalization, a case that frequently occurs in school settings. For instance, children may be exposed to a cultural prototype or to a scientific notion not available in their repertoire of implicit knowledge. A radical constructivist view would challenge the effectiveness of explicit learning given the lack of background knowledge in the children’s minds. But this position is too restrictive. What usually makes explicit learning ineffective in school settings may be the lack of adequate teaching methods. Whereas implicit learning operates under conditions usually met

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in classrooms, explicit learning may require systematic teaching efforts. Implicit learning may simply require the students´ unintentional exposition to a set of exemplars or cases to feed the operation of associative processes underlying the acquisition of implicit knowledge. In turn, explicit learning may require students to be intentionally engaged in metacognitive, hypothesis-testing procedures, or to be exposed to explicit knowledge conveyed in social dicourses. Therefore, instructional efforts should be more intensive in promoting explicit learning than implicit learning. 4. COGNITIVE VARIABILITY IN THE DEVELOPMENT OF THE CONCEPT OF FAMILY

In this section, we describe a study aimed at capturing cognitive variability in the development of the concept of family. This is a very useful area for demonstrating cognitive variability for three reasons. First, developmental trends can be traced within a wide range of ages allowing for the observation of dramatic changes in the implicit and explicit formats. This gives the opportunity to detect discordant as well as stable states in between. Secondly, cognitive variability is not constrained by the existence of a narrow set of “right ways” to solve the task. There are many ways to combine family dimensions and most of them are suitable within the range of modern societies characterized by a great diversity of family forms. Thirdly, the family concept is an example of natural-like social categories (Hirschfeld, 1994). These relational categories such as family, gender, age or race fall in between biological and psychological understanding. For instance, the concept of family may involve the understanding of Kinship relationships (e.g., family membership, blood links) as well as certain types of Interpersonal bonds (e.g., affective ties, caring). However, this concept may also involve the understanding of societal functioning (e.g., co-residence, legal bonds). It is an interesting question to explore whether cognitive variability may differ according to the nature of the relational property involved in the concept. The main aim of the study was to develop a within-subject procedure to detect discordances and concordances between individual´s responses on two tasks. Interestingly, in other studies the use of two tasks in a within-subject design has been conceived as a way to tap into intensional or extensional aspects of a concept (Newman, Roberts, & Syré, 1993). It has also been used to provide a test of internal consistency of the use of a single, underlying mental model (Vosniadou, 1994). In our case, the within-subject procedure is conceived as a way to detect cognitive variability by comparing the individual’s responses on a task that presumably promote implicit processing, with those obtained on a task that promote explicit processing. In this way we can explore the distribution of discordances and concordances between responses according to age groups (children, preadolescent and young adults) and to the nature of the relational property involved in the concept (Kinship, Interpersonal or Societal bonds).

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The recognition task was intended to tap into implicit knowledge. The task involved: (1) a presentation of an exemplar to induce the criteria of grouping; (2) an identification through self-report of the criteria of the exemplar just presented. Participants can respond to this task even if their knowledge reflects a simple abstraction of situational regularities that produce associative expectation according to the stored exemplars of family (families live together, kiss frequently, take care of children, etc.). It is implicit knowledge in the sense that verbalization is restricted to the identification of the features that particular exemplars possess (Roberts, 1998). Therefore, we expected that even preschoolers would be able to report knowledge on this task, as would preadolescents and young adults. In turn, a definition task was intended to tap into explicit knowledge. This task involved the description of the prototype of family without the induction of an exemplar. To respond to this task one would have to generate a hypothesis about the nature of the relational property or properties that distinguish a family group such as co-residence, affect, legal bonds, etc. and test this mental model "in the head" (Roberts, 1998). It is explicit knowledge in the sense that it should easily support a verbal report of the underlying conceptual rule. Therefore, we expected that preadolescents and young adults would be more able to report knowledge in this task than preschoolers would. To illustrate the different picture obtained from a within-subject comparison procedure with that from a standard comparison procedure, we first examined changes with age in the pattern of dimensions reported in the recognition task and in the definition task. The complexity of the concept allows for exploration of whether the combination of Kinship, Interpersonal and Societal dimensions changed across age groups. Then, the results obtained with the within-subject procedure aimed at capturing cognitive variability in the responses given by an individual on the two tasks will be presented. 4.1.

Sample

The sample consisted of 454 participants classified into three groups ranging in age from 4 to 23 years. Thus, group 1 included 140 participants ( years; 4- to 6-years old). Group 2 included 154 participants ( 10- to 12 years old). Group 3 included 160 participants ( 18- to 23 years old). The sample was equally distributed by gender, parents’ educational and professional level (low, medium and high) and family structure (biparental and monoparental families). The sample was taken from a wider sample of five age groups and a large study aimed at exploring other aspects of the family concept such as gender roles and family functions (Simón, 2000). At each age we registered the participants’ responses given on a recognition task of family-like patterns and responses given on open-ended family definitions. The order of presentation was reversed for half of the sample, but no differences were found.

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Tasks and Procedure

Participants in the recognition task of family groupings were asked the following question: Is this group of people a family? Participants were presented with instances of human groupings in a verbal format involving nine dimensions (see Table 1). Instances of family included either single presentations of each dimension (e.g., Co-residence: “They live together”) or paired presentations of two dimensions in negative and positive form: e.g., +Co-residence -Affective: “They live together and they do not love each other”. Preschoolers were also presented with a drawing depicting the dimension involved in the exemplar of family (e.g., a couple just married, in their wedding clothes to illustrate “legal bonds”).

Each dimension was presented in two items, single and paired. In the present study, however, only recognition judgments given in items with single presentations were included to make sure that the dimension was unequivocally identified (a total of nine items). An immediate self-report of the dimension involved in the instance was also registered. Only recognition judgments followed by correct identifications of the dimension presented were computed in this analysis to make sure that they were not random recognitions. The scores ranged from 0 to 9 for each family dimension. Participants in the family definition task had a semi-structured interview that included several questions about family functioning and family roles along with the target one: What is a family? What would you say to help a person from another planet to figure out what a family is? Open verbalizations were registered and were later coded by two judges as to whether they contained reports on the family dimensions (see Table 1). Inter-rater reliability was very high (96%). The scores ranged from 0 (absence) to 1 (presence) for each family dimension. 1 In the recognition task, Family membership and Family descendency were presented together in the same instance, and Social unit was not presented. Nevertheless those dimensions were spontaneously reported by participants.

174 4.3.

M. J. RODRIGO, B. TRIANA & M. I. SIMON Developmental Patterns of the Dimensions of Family in the Recognition and the Definition Task

In this section, we described the hypothesis, results and discussion of the study aimed at capturing changes with age in the pattern of dimensions reported in each task separately. It is expected that this pattern would differ according to the task given. Particularly, few changes with age would be observed in the pattern of dimensions obtained in the recognition task than in the definition task. The reason is that the recognition task is less demanding than the definition task. According to Neimark (1990), the early stages of concept acquisition are exemplar based and only with progressive encounters and advances in knowledge are organizing principles induced. Thus, we expected than even preschoolers would be able to identify exemplars of different levels of complexity. With respect to the definition task, many studies have found that the concept evolves from simple to complex versions (Gilby & Pederson, 1982; Newman, et al., 1993; Triana & Simón, 1994; Wedemeyer, Bickhard, & Cooper, 1989). Simple versions of the family definition included observable dimensions such as Family membership, Co-residence or Affective links. Complex versions included less directly observable dimensions such as Biological, Support or Legal ties. Thus, we could expect a clear pattern of changes in the complexity of the dimensions reported in the definition task. In the recognition task, changes with age in the number of items identified as referring to each family dimension were examined (see Table 2). One-way ANOVAs were applied to test whether mean number of items differed on each dimension as a function of participants’ age. Tukey test of significance were set at p < .05 (*) for between group differences.

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The results showed that Family descendency Caring and Helping were less identified as dimensions of family across ages. Blood links Affective and Social unit were progressively more identified as dimensions of family. Family membership and Legal bonds remained stable across ages. Co-residence Support and Sharing showed a “V” pattern of changes. The results indicated, as expected, that participants’ responses were distributed across the three types of dimensions and the pattern of changes did not show a clear developmental progression from the simple dimensions to the complex ones. In fact, the youngest group identified almost all dimensions except three of them. Preadolescents and young adults tend to concentrate their positive recognitions to less dimensions indicating that certain organizing principles of the family concept are being formed (Neimark, 1990). In the definition task, changes with age in the percentage of participants who mentioned each dimension were examined (see Table 3). Chi-square analyses (p < .001) were applied to test whether frequency of participants who mentioned each dimension differed across ages. Except for Caring, the results showed age differences in all dimensions: Family membership Blood links Affective Sharing Helping Support Co-residence and Social unit

Preschoolers tend to verbalize descriptors related to Family memberships, Caring and Co-residence, so their concept was based on the simplest forms of Kinship, Interpersonal and Societal relationships. With age, the descriptors involved the complex forms of each type of dimension. Preadolescents verbalized descriptors 2

Percentages did not add up to 100% because participants can mention more than one dimension.

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related to Family members and Blood links, Affective links, Caring, Sharing, Helping and Support, as well as Co-residence. Finally, young adults added a descriptor of family as a Social unit to the list reported by the preadolescent group. Therefore, the developmental pattern showed a progression from the use of the simple forms of each type of dimensions to the use of the complex ones, as expected (Newman et al., 1993). As expected, developmental changes in the pattern of family dimensions observed differed according to the task given. The demands involved in each task may be responsible for the differences, given that the same individuals have solved both tasks. It seems that the recognition task is less demanding that the definition tasks, but we can not tell from the results how each individual has dealt with the task requirements in both tasks. In the next section we will address this issue. 4.4.

Developmental Patterns of Cognitive Variability across the Recognition Task and the Definition Task

In this section, two within-subject comparison analyses are described to capture two aspects of cognitive variability in the development of the family concept. The first comparison was performed to examine changes with age in the number of dimensions reported on the recognition and the definition task. The second comparison was aimed at capturing the pattern of discordances and concordances within individuals in the responses given on the recognition and the definition tasks. In both cases, the data set was constructed taking into account participants’ responses to both tasks. 4.4.1.

Developmental Changes in the Number of Family Dimensions

Within-subject variability in the number of responses given on two tasks is an interesting aspect of the data not frequently reported in developmental studies (Siegler, 1996). From the results in Table 2 and Table 3 it is difficult to tell whether participants have recognized or mentioned most of the dimensions (little variability) or participants have reported few dimensions but different ones with respect to those mentioned by other participants (much variability). Variability in the number of family dimensions considered may change with age. As Siegler (1996) suggested, younger individuals’ thinking is generally more variable in terms of the number of strategies used than that of older ones. Analyses were performed to compare the number of dimensions (0-9 score) mentioned by the participants in each task across ages (see Table 4). One-way ANOVAs were applied to test whether number of dimensions mentioned in each task differed as a function of participants’ age. Tukey tests of significance were set at p < .05 (*) for between group differences. Results indicated that the number of dimensions reported on the recognition task decreased from preschoolers to preadolescents but slightly increased in young adults Number of dimensions reported on the definition task significantly increased from preschoolers to preadolescents

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A Pearson correlation was also performed for each age group relating the number of dimensions reported on the recognition and the definition task for each participant. Only the correlation obtained in adults was significant In the recognition task, preschoolers’ thinking appeared as the most variable in terms of the number of exemplars accepted as family groups (around seven as a mean). These exemplars corresponded either to simple or complex forms of Kinship, Interpersonal and Societal relationships. Therefore, young individuals’ thinking involved a great variety of examples of family dimensions in their earlier forms of knowledge, as expected (Siegler, 1996).

The picture of preschoolers’ thinking is very different from the results of the definition tasks. There is a poor prototype of a family concept with one descriptor as a mean. This prototype was based on the simplest forms of each type of dimensions: Family memberships, Caring and Co-residence. Thus, cognitive variability was drastically restricted when preschoolers had to generate a prototype of family. In the recognition task, preadolescents and young adults restricted the selection of exemplars to a mean of five or six. As in the preschoolers’ group, the exemplars accepted corresponded to simple or complex versions of the three types of dimensions. The selection of dimensions would indicate the operation of abstractive processes that facilitate the construction of a prototype (Neimark, 1990). In the definition task, preadolescents and young adults revealed a rich prototype of the concept with two or three descriptors as a mean. Descriptors involved the complex forms of Kinship, Interpersonal and Societal relationships (e.g., Blood links, Affective bonds, and Co-residence or Social unit). Only in the older group was the number of dimensions reported in the recognition task related to the number of dimensions reported in the definition task, indicating a close correspondence between the two sets of responses. In the next analyses we will directly address this issue. 4.4.2.

Developmental Changes in the Pattern of Discordant and Concordant States

The second within-subject analysis was aimed at exploring the distribution of discordant and concordant states according to age groups (children, preadolescent and young adults) and to the nature of the relational property involved in the concept (Kinship, Interpersonal or Societal bonds). It is proposed that discordance between responses given by the same individual across the two tasks is a good indicator of

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the existence of transitional knowledge learned through implicit or explicit learning processes (Reber, 1989), whereas concordance indicate the existence of stable knowledge. Discordance may be classified into two types. The first type is Only-recognition knowledge indicating the existence of transitional states characterized by the predominance of implicit knowledge and probably under the operation of implicit learning processes. The second type is Only-definition knowledge indicating the existence of transitional states characterized by the predominance of explicit knowledge and probably under the operation of explicit learning processes. Instead, concordance or Full knowledge is characterized by the existence of a stable phase in which knowledge is available in both formats and no learning process is at work. We may expect developmental changes in the relative distribution of discordant and concordant states. As a whole, we would expect that the discordance characterized by only-recognition knowledge would diminish with age and concordance would increase with age. That is, implicit knowledge would be more available to explicit report leading to stable states with age (Karmiloff-Smith, 1992). We do not have clear expectations for the discordance involving only-definition knowledge but this presumably would increase in older participants more open to external sources of information. Three dependent measures were developed to capture discordance and concordance. The two measures of discordance consisted: a) Only-recognition knowledge: number of dimensions recognized but not mentioned in the definition (herein implicit discordance); b) Only-definition knowledge: number of dimensions not recognized but mentioned in the interview (herein explicit discordance). The measure of concordance was Full knowledge: number of dimensions both recognized and mentioned in the two tasks. A fourth dependent variable Absent knowledge was a control category involving the number of dimensions never recognized and never mentioned in any task (see Table 5). Scores ranged from 0-9 dimensions in all categories of responses. For these analyses, a dimension was considered as recognized only if it was identified in the item that included this dimension. A dimension was considered as mentioned if it was reported in the definition. In this way, the likelihood of reporting the dimension was the same in both tasks.

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One-way ANOVAs were applied for each dependent measure as a function of participants’ age. Tukey tests of significance were set at p < .05 (*) for between group differences. Only-recognition knowledge showed significant decrements and only-definition knowledge showed significant increments among the three age groups Significant increments were found on full knowledge and absent knowledge between preschoolers and preadolescents, and between preschoolers and adults, but not between preadolescents and adults. The results indicated that transitional states characterized by a predominance of implicit knowledge were less frequent with age. As we expected, implicit knowledge was more available to explicit report with age (Karmiloff-Smith, 1992). Transitional states characterized by a predominance of explicit knowledge without implicit counterparts were more frequent with age, especially from preadolescence to young adulthood. As expected, stable states characterized by the presence of knowledge in both formats were more frequent with age. Finally, knowledge absent in both formats also increased. However, the last result was not easy to interpret. It may indicate an early state of knowledge in which knowledge is still absent in both tasks (e.g., in preschoolers). But it may indicate a later state of knowledge in which some dimensions are consistently rejected (e.g., in preadolescent and young adults). It is also interesting to examine changes with age in the percentage of participants in each knowledge state for Kinship, Interpersonal or Societal Bonds. It could be the case that certain basic family dimensions such as Kinship and Societal bonds may remain more implicit whereas Interpersonal dimensions may become more explicit across ages, due to the influence of social discourses about the family. Changes with age in the percentage of participants in each knowledge state and for each dimension were examined (see Table 6 and Table 7). Chi-square analyses (p < .001) were applied for each knowledge state to test whether frequency of participants differed on each dimension as a function of participants’ age.

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The percentage of participants with only-recognition knowledge showed significant decrements across ages in all dimensions. However, this trend was less pronounced for dimensions of family involving Kinship relationships as Family descendency and Blood links and for dimensions involving Societal relationships as Legal bonds but not Co-residence and more pronounced on dimensions of family involving Interpersonal relationships as Affective links Caring Sharing Helping and Support The percentage of participants with only-definition knowledge showed significant increments across ages in the following dimensions: Blood links Affective links Caring Sharing Helping Support and Co-residence In general, the trend was more pronounced in Interpersonal relationships and Societal relationships as Co-residence.

The percentage of participants with full-knowledge showed significant decrements across ages in Caring and significant increments in Blood links Affective links Helping and Co-residence Finally, the percentage of participants with Absent-knowledge increased across ages in dimensions as Family descendency Affective links Caring Sharing Helping Co-residence and Legal bonds and decrements in Blood links To sum up, most preschoolers seemed to be engaged in implicit learning processes. Implicit discordance was characteristic of most Kinship, Interpersonal and Societal dimensions, probably indicating that preschoolers were intensively collecting exemplars on those dimensions and producing associative links among them. It is quite intriguing for a domain specificity argument how young children are able to combine Kinship, Interpersonal and Societal knowledge in their earliest form of implicit understanding in the concept of family. However, family is a relational

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concept applied to a collectivity of individuals who show some observed patterns of behavior (Hirschfeld, 1994). Thus, children, like adults, rely on certain patterns of enduring and habitual associations involving people with physical resemblance, sharing activities in the same space and showing a variety of interpersonal relationships. Probably, living in a family provides a unique case of a compound experience in which young children are exposed to information from different domains that is easily integrated in meaningful ways. The picture of knowledge states displayed by the older groups was more complex. The distribution of discordant and concordant states among preadolescents and young adults seemed to indicate the operation of both implicit and explicit learning processes (the latter was particularly clear in the adult group). Implicit discordance on Blood links and Legal bonds were especially salient, indicating that both dimensions were under the focus of implicit learning processes. In contrast, explicit discordance on Affective bonds, Support, Sharing and Co-residence indicated that those dimensions were mainly under the focus of explicit learning processes. By preadolescence the pattern of consolidated knowledge was evident and did not substantially change beyond this point. Blood link, Affective bonds, Caring, Helping and Co-residence were consolidated knowledge available in both formats. 5.

CONCLUSIONS

In this chapter cognitive variability was addressed as an important developmental phenomenon to be explored in the process of knowledge building in the concept of family. This was illustrated by the existence of transitional states with implicit and explicit discordances. Consolidated states occurred when knowledge was available in both formats. Changes in the distribution of discordant and concordant states were observed across ages and dimensions. First, the results will be discussed in the light of gradualist and contextualist views of developmental change. Then, the relevance of our results for a model of conceptual change will be considered. Overall, the results speak in favor of a gradualist view in the process of conceptual development. The dimensions of family coexisted over prolonged periods of time as new ones did not abruptly replace older ones. However, there were changes with age in the implicit or explicit format of the dimensions. First, the number of dimensions entertained on the implicit side decreased and the number of dimensions increased on the explicit side. But only in the adult years there was a significant correspondence between the number of dimensions available in both formats. Probably, the progressive symmetry between the pool of implicit and explicit dimensions plays an important role in the process of knowledge building. Secondly, discordances between responses diminished as knowledge available in implicit formats is progressively available to explicit formats (Karmiloff-Smith, 1992). Concordant states increased across ages but did not reach the maximum scores in adult years, indicating that transitional knowledge was still substantial at that age.

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Third, discordances and concordances also differed according to the nature of the relational property involved in the concept of family. We suggest that changes in capacity constraints may influence participants’ selection of dimensions in terms of their complexity. For instance, it is said that by preadolescence there is a clear increase in processing capacity permitting the semantic representation of complex concepts (Siegler, 1996; Halford & McCredden, 1998; Rodrigo, Castañeda, & Camacho, 1999). This would explain why complex dimensions were more likely to be conveyed in explicit formats than simple dimensions in the older groups. But we may also consider cultural changes in the concept of family as a possible contextual factor accounting for the results. For instance, traditional dimensions of family based on Kinship or Legal relationships are challenged in modern societies by a social discourse emphasizing other family groups based on a variety of interpersonal links and residential forms (Melton & Wilcox, 1989; Simón, Triana, & González, 1998). This would explain the result that the latter were more frequently conveyed in explicit formats than the former. To what extent are the above results compatible with a sociocultural view? In principle, the crucial question to be asked from a sociocultural view is how children and others learn to think in particular ways through being induced into social practices and ways, of using language (e.g., Säljö, 1994). Children may reveal many types and degrees of partial knowledge according to the discursive practice that they have been engage in. In our case, participants were induced to participate in two discursive practices in which a wide range of “right” answers was considered. In the first task, participants got involved in an everyday communicative tradition that consisted in identifying instances of family. In the second task, participants got involved in the scientific communicative tradition requiring explicit definitions of family. Thus, from a sociocultural view it seems reasonable to expect discordances between responses given on the tasks, but no specific prediction is made for age differences. However, our results showed that participants’ age modulates the likelihood of finding discordances. Preschoolers had an implicit representation of the family concept but they were not be able to produce a definition based on this representation. Progressively, preadolescents and young adults’ level of understanding was less discordant across the two tasks. Therefore, a sociocultural view should explain why the two communicative practices produce different results according to the participant’s age. But the study of the evolving relationship between types of communicative practices and the individual´s developmental level is a field of research largely neglected (Van Oers, 1998). We now turn to the issue of the relevance of our results to a model of conceptual change. We are aware that the design used was cross-sectional and no intentional learning process was involved. Nevertheless, based on some evidence coming from the within-subject patterns we may come to some tentative conclusions concerning the presence of implicit and explicit learning processes in the course of conceptual development. On theoretical basis, we have assumed that implicit and explicit discordances indicate the existence of implicit and explicit learning processes, respectively. Our results suggest that different types of learning were presumably involved in the process of concept formation.

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First, implicit learning processes seemed to operate across ages, whereas explicit learning was restricted to preadolescence and adult years. This is compatible with the claim that implicit learning predates the evolution of explicit learning (Reber, 1993), and that it is stable across the age span (Maybery & O’Brien-Malone, 1998; Vinter & Perruchet, 2000). Secondly, the relative balance between implicit and explicit processes changed with age. The ubiquitous presence of implicit processes in preschoolers was followed by an increased balanced between both processes in preadolescents and young adults. More research is needed to know whether both learning processes interact at these ages to produce consolidated states or worked independently. According to Siegler (1996, 2000) the acquisition of new understanding may involve a mixture of associative and metacognitive processes. In at least some cases, new strategies are constructed on an unconscious level before people are aware of doing anything different than they had done previously. But in other cases, discovery is a metacognitive process resulting from the application of a new strategy based on a conscious rule. We agree with Vosniadou (1994) that cognitive variability is not the only aspect to consider in theorizing about conceptual change. However, cognitive variability illustrates how people´s understanding at a given age does not correspond to a single knowledge state. By using different tasks a variety of knowledge states emerged. In addition, it shows the way people deal at different ages with the variety of cognitions displayed across tasks. In this sense, the analysis of changes linked to task variations would give a picture of the gradual process of conceptual change and how is promoted by implicit and explicit learning processes. 6. ACKNOWLEDGEMENTS

The research reported in this chapter was supported by CICYT Grant PS96-1037 from the Spanish Ministry of Education and Culture to the first author and by DGI Grant PI97-038 from the Canary Islands Regional Government to the second author. REFERENCES Billett, S. (1996). Situated learning: Bridging sociocultural and cognitive theorizing. Learning and Instruction, 6, 263-280. Caravita, S., & Halldén, O. (1994). Re-framing the problem of conceptual change. Learning and Instruction, 4, 89-111. Chomsky, N. (1965). Aspects of the theory of syntax. Cambridge, MA: MIT Press. Clements, W., & Perner, J. (1994). Implicit understanding of belief. Cognitive development, 9, 377-397. Dienes, Z., & Berry, D. (1997). Implicit learning: Below the subjective threshold. Psychonomic Bulletin and Review, 4, 3-23. Garber, P., Alibali, M. W., & Goldin-Meadow, S. (1998). Knowledge conveyed in gesture is not tied to the hands. Child Development, 69, 75-84. Gilby, R. L., & Pederson, D. R. (1982). The development of the child's concept of the family. Canadian Journal of Behavioral Science, 14, 111-121. Goldin-Meadow, S. (2000). Beyond words: The importance of gesture to researchers and learners. Child Development, 71, 231-239. Goldin-Meadow, S., Alibali, M. W., & Church, R. B. (1993). Transitions in concept acquisition: Using the hand to read the mind. Psychological Review, 100, 279-297.

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MOTIVATIONAL, SOCIAL, AND CONTEXTUAL ASPECTS OF CONCEPTUAL CHANGE: A COMMENTARY

GALE M. SINATRA University of Nevada, Las Vegas, USA

Abstract. Three themes are identified in Part II: 1) conceptual change is a complex interplay of learners’ knowledge and motivations, and the environmental and social context, 2) conceptual change is evolutionary not revolutionary, and 3) our theoretical perspectives and research methods shape our understanding of the change process. Directions for future research on motivational, social and contextual aspects of conceptual change are suggested, as well as implications of this area of research for conceptual change pedagogy.

1.

INTRODUCTION

The view of conceptual change that emerged during the 1980s focused on individual students’ knowledge representations and restructuring (see for example, Posner, Strike, Hewson, & Gertzog, 1982; Vosniadou & Brewer, 1987). Researchers documented the nature and structure of students’ existing conceptions and how these conceptions served as scaffolds and barriers to learning. Despite the significant contribution of this literature to our understanding of conceptual change, several caveats must be acknowledged. First, this view depicted the change process as largely cognitive and did not address critical motivational influences on knowledge reconstruction. Second, the situational context within which students applied their knowledge was largely unexamined. Third, change was portrayed as sudden conceptual replacement, or revolutionary change, a view that has been called into question (Siegler, 1996). The four papers in Part II seek to illuminate these aspects of conceptual change that were not addressed in early cognitive perspectives. In this commentary, I will identify three themes raised by the articles: 1) conceptual change is a complex interplay of learners’ knowledge and motivations, and the environmental and social context, 2) conceptual change is evolutionary not revolutionary, and 3) theoretical perspectives and research methods shape our understanding of conceptual change. I also suggest directions for future research aimed toward a broader perspective on knowledge reconstruction. Finally, I discuss the implications of motivational, social and contextual conceptual change research for educational practice.

M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 187-197. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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THEMES

2.1. Conceptual Change Involves More than Cognition

There is no doubt that cognition is at the heart of conceptual change. This premise established, it must be acknowledged that cognitive processes do not occur in a vacuum. Rather, cognitive processes are evoked by the learner and/or by the context in which learning occurs. In other words, cognition can be internally or externally initiated (Reynolds, 2000). Internal initiation of the processes involved in conceptual change learning can be sparked by such catalysts as intentions (see Sinatra & Pintrich, in press), motivations, (see Pintrich, 1999), the executive control of attention allocation (Reynolds, 2000), affect (Linnenbrink & Pintrich, this volume), or metacognition (Paris & Winograd, 1990). External initiation of knowledge reconstruction can be brought about by impetuses such as the social context (see Dole & Sinatra, 1998; Gorodetsky & Keiny, this volume), the structure of activities in which students engage (Rodrigo, Triana, & Simón, this volume), instructional materials, texts, and objects designed to promote change (Guzzetti & Hynd, 1998), and the situational demands of the learning context (Halldén, et al., this volume). Pintrich, Marx, and Boyle (1993) in their influential article, Beyond Cold Conceptual Change, inspired researchers of the 1990s to examine internally and externally initiated aspects of conceptual change beyond those involved in “cold cognition.” As part of a decade long research program exploring “hot cognition”, Linnenbrink and Pintrich (this volume) considered students’ motivations, specifically--achievement goals, and their role in changing students’ conceptions. Goals can be either internally or externally initiated. Goals that are internally initiated are under the learner’s intentional control. Goals that are induced experimentally or by teachers are externally-initiated. However, students may choose to regulate externally-initiated goals and thus, bring them under their intentional control at some point. Goals, therefore, play an important role in conceptual change, because they either are under or can be brought under a learner’s conscious control. Linnenbrink and Pintrich (this volume) demonstrated that students with mastery goals (the goal to learn), showed increased use of elaborative strategies and decreased presence of negative affect. Both of these outcomes increased the likelihood of conceptual change. Although the exact mechanisms by which these effects operate are not yet understood, goals may lead to attention allocation and strategy regulation in the processing of information about the new conception. Minimizing negative affect may eliminate a distraction from these efforts. These combined effects likely allow for the high engagement necessary for learners to change their conceptions (Dole & Sinatra, 1998). The cognitive processes involved in conceptual change learning can also be externally initiated by social and contextual situations. In such instances, the initial impetus for the conceptual change process comes from external events, situations, stimuli or social interactions. Gorodetsky and Keiny (this volume) examined the external initiation of conceptual change though social interaction. They described

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the conceptual change process as participation in the social construction of individual knowledge or “the dialogical interaction between the “the outer” (the social context) and “the inner” (the individual learner) interacting to construct meaning” (p. 3). Through case study analysis, they traced the construction of a curricula by a small group of educators. By examining the group dynamics and analyzing the group’s discourse practices, they revealed how the ideas of individual group members developed and gradually evolved in response to the social exchange. They explained how the members of the social group served as a “trigger” (p. 11) to promote individual reflection and the increased awareness of one’s conceptual knowledge. How do members of a group trigger individual knowledge restructuring? As noted, group discussion can create the preconditions necessary for change: awareness of and reflection on one’s initial conception. Moreover, group members demand that individuals justify and explain their ideas by posing challenging questions. Gorodetsky and Keiny (this volume) explained how one teacher involved in the curriculum project, Uri, responded to a series of difficult queries raised by his group. Uri explained his position using an example from his teaching. His explanations of the events in his classroom led Uri to conclude that his inquiry lesson had “turned into a value education lesson” (p. 10). Although we can not be certain, we suspect that it is this realization that ultimately led him to broaden his views of inquiry activities1. What Gorodetsky and Keiny (this volume) observed in this group interaction may have been an instance of the “self-explanation effect” (Chi, de Leeuw, Chiu, & LaVancher, 1994) Chi and her colleagues as well as Chan, Burtis, and Bereiter (1997) have demonstrated convincingly that generating explanations can be a powerful mechanism to promote conceptual change-presumably because it helps learners realize the flaws in their initiate conceptions. In additions to social group members, the context itself can serve as an external impetus for conceptual change. Rodrigo et al. (this volume) demonstrated how contextual factors such as the task demands and the setting can influence what knowledge learners bring to the fore and use to think, reason, and learn. For example, these researchers demonstrated that certain tasks tap implicit knowledge, and others evoke explicit knowledge. Thus, the tasks we ask students to accomplish can serve to elicit certain types of knowledge and perhaps even particular ways of thinking that make change more or less likely to occur. Rodrigo et al. (this volume) pointed out that too often teaching promotes implicit learning. Implicit learning may facilitate knowledge acquisition but is not likely to promote knowledge restructuring. By definition, we can reflect easily only on our explicit knowledge. Rodrigo et al. demonstrate that through the careful design of instructional tasks, contexts can be created which activate relevant explicit knowledge. Then, explicit learning can be fostered by instruction which would “require students to be intentionally engaged in metacognitive, hypothesis-testing procedures” (Rodrigo et al., this volume, p. 7). These are precisely the conditions necessary for conceptual change learning to occur. 1

This suggests that although social interaction may be an impetus, whether or not change occurs depends, ultimately, on the individual’s consideration of the information.

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Halldén et al (this volume) also explored the contextualized nature of knowledge. They described evidence suggesting that children hold multiple conceptions about a single idea (such as both a pancake and a spherical model of the shape of the earth). These “compounded models” (p. 11) are developed from experiences in different situations and contexts. The conceptual change process then, is described as one of differentiating between contexts and adeptly applying the appropriate conceptual knowledge. The context plays a major role in eliciting conceptual differentiation. The students Halldén et al. described seemed to be developing what Searle called “mind-to-world fit” (Searle, 1998). Searle explained that there are different ways in which states of the mind can relate to states found in the world. Conceptual change may occur to satisfy the conditions of improved mindto-world fit. That is, if our thoughts do not represent the way the world really is, as suggested by our experiences in different contexts, then we may reorganize our conceptions to fit the reality of our world. For instance, the pancake model of the earth has poor mind-to-world fit when one wishes to illustrate why we never fall off the edge. Therefore, one might adopt the spherical model to explain this phenomenon. If the spherical model demonstrates improved mind-to-world fit, it may become the model of choice for explaining the earth’s shape. 2.2.

Conceptual Change is Evolutionary Rather than Revolutionary

The view of conceptual change as sudden conceptual replacement was challenged by Siegler (1996) and Smith, di Sessa, and Roschelle (1993). They described the change process as evolutionary rather than revolutionary. According to this gradualist perspective, knowledge is slowly transformed from one state to another over time. Conceptual change occurs, according to this view, by transforming and refining existing conceptions into more and more adapted forms of knowledge. Knowledge can exist in various states of transition for some time. Therefore, variability of conceptual knowledge is the rule rather than the exception (Rodrigo et al. this volume) in conceptual development. Once fully formed, the new conception does not replace the old, rather the two may continue to exist indefinitely. Siegler (1996) describes the incremental changes in children’s conceptual development as similar to the manner in which a biological organism evolves. That is, children’s thinking continuously becomes more adapted to its context. Siegler explains that children hold multiple conceptions about a single phenomena, rather than a unitary conception. Change occurs as children adaptively select among these various ideas to better fit the demands of their environment. In an evolutionary sense, a particular conception prevails when it proves to be more successful over time. Halldén et al. (this volume) described empirical evidence supporting Siegler’s view. They demonstrated that a spherical notion of the earth does not replace a child’s flat earth concept. Rather, children not only hold both views simultaneously, they can use the two models to solve different problems based on the task and situational demands. This is consistent with the argument made by Smith et al. (1993) that conceptual replacement is “neither plausible nor always desirable” (p.

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153). They argued that existing knowledge not only forms a basis for the development of new conceptions, but prior knowledge may remain an integral part of the new conception. The gradualist perspective suggests that as children apply their knowledge in contextually appropriate ways one concept proves to be the more useful. The original conception does not necessarily meet the fate of the dinosaurs, however. Rather, as long as the concept remains useful in some context, the idea may continue to hold a limited niche in the child’s conceptual ecology. The notion that the mind may store two alternative conceptions of the same phenomena begs the question of how these representations might be stored in memory. Perhaps individuals hold two mental models or two schemas of the same concepts which may be connected, loosely connected, or even compartmentalized. The evidence is not yet clear how two alternative concepts could be represented but there is evidence to suggest that it is possible. Driver, Asoko, Leach, Motimer, and Scott (1994) point out that scientists routinely use lay concepts such as “let’s watch the sun set” when they know perfectly well the correct scientific explanation. There are many instances of individuals holding two contradictory explanations of the same phenomena at the same time (diSessa & Sherin, 1998). Other evidence suggests that seemingly “lost” memories often are recovered years later when activated by a particular scent, sound, or other contextual event. Instances such as these suggest that original conceptions may not be lost, but rather, their activation strength is lowered. Perhaps multiple conceptions exist at different activation strengths depending on their utility. The gradualists’ view would suggest that, over time, activation weights adjust such that the more useful concept enjoys a higher level of activation, while the activation of the other conception weakens with disuse. Rodrigo et al. (this volume) describe how children represent knowledge in Various ways which can be used differentially according to context demands. Such cognitive variability typifies the gradual and evolving nature of transitional knowledge or states of “in-between understanding” (p. 3). Transitional knowledge states are revealed by the presence of discordances between implicit and explicit knowledge of the same concept, suggesting that children often know more implicitly than they can verbalize or reflect upon explicitly. Over time, knowledge becomes more explicit bringing these two representational forms into concordance, suggesting that the conceptual ecology has reached a steady state. Such conceptual evolution is gradual with stable states not evidenced in Rodrigo et al.’s data until adolescence or even adulthood. Transitional states also continue to appear well into adulthood suggesting that gradual conceptual development may be a lifespan phenomenon. In sum, several of the articles in Part II lend support to the view of conceptual change as evolutionary rather than revolutionary. The gradualist position suggests that multiple conceptions of the same phenomena may exist simultaneously and such transitional knowledge may be used differentially according to context. Thus, the evolutionary view of knowledge development highlights a formative role of context in the acquisition and restructuring of conceptual knowledge.

192 2.3.

G. M. SINATRA Our View of Conceptual Change is shaped by our Theoretical Perspectives and Research Methods

What we discover about the process of conceptual change depends on where we look. As noted, conceptual change researchers in the 1980s using a cognitiveinformation processing framework, saw conceptual change as a cold, cognitive process of fitting information into existing knowledge structures. Science educators who studied paradigmatic change in the history of science, saw individual conceptual change as recapitulating the process of scientific discovery produced by the scientific community. Now, sociocultural theorists see change not as an individual process but as the joint construction of knowledge through social or cultural activities. Each of these perspectives has contributed to our understanding of the conceptual change process by highlighting factors such as change in knowledge structures, dissatisfaction with existing explanations, and the social construction of knowledge. At the same time, we run the risk of neglecting critical aspects of conceptual change when we use only one theoretical spotlight. Conceptual change, like any aspect of the human condition is a complex phenomenon. It has a decidedly cognitive component. But, cognition takes place within the broader individual and social context. An individual’s psychology is itself a complex context. Individuals have more than thoughts, they have beliefs, intentions, motivations and emotions which color their interactions with the world. Individual cognition is further embedded in an environmental and social context which impacts and shapes its development. The articles in Part II highlight how the theories we hold, the questions we frame, and the research methods we use to explore those questions shape our views of conceptual change. By examining the process of individual knowledge construction within a team, Gorodetsky and Keiny (this volume) where able to document shifts in both individual and group knowledge. As we watched the group of educators wrestle with what it means to involve their students in inquiry study activities, we also saw Uri change his understanding of inquiry beyond the scientific method to include the examination of values. Had Gorodetsky and Keiny looked at only individual or group change, they would have seen evidence supporting cognitive or social knowledge reconstruction. But, by looking at change through “both prisms” (p. l) they illuminated the reciprocal influence of one on the other. The influence of our methods of research on our understanding of children’s conceptual ability is illustrated by Rodrigo et al. (this volume). They demonstrated that the type of knowledge representation we observe depends on the type of task we present to students. By using multiple methods of assessing students’ knowledge, Rodrigo et al. were able to show a developmental shift in the relationship between implicit and explicit knowledge. Had they assumed there was only one important type of knowledge relevant to conceptual change learning, they would have missed this intriguing aspect of conceptual development. Similarly, Halldén et al. (this volume) asked students myriad questions about the shape of the earth and gave students objects of various shapes to use in demonstrating their understandings. They illustrated that the types of questions

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researchers asked as well as the objects they provided to their research participants influenced what children where able to express about their conceptions. Their choice of methodology allowed the observation of multiple conceptions which may otherwise have gone undetected. Their research illustrates that the methods used to explore knowledge influence researchers’ interpretations of the development of conceptual knowledge. Linnenbrink and Pintrich (this volume) continue a research tradition of examining both cognitive and motivational aspects of conceptual change. Pintrich et al. (1993) lead us away from a strict emphasis on the cognitive processes towards explorations of the role of motivation in knowledge restructuring (Pintrich, et al., 1993). But, by continuing to include cognitive process measures (such as strategy use) along with motivational measures (such as achievement goals), Linnenbrink and Pintrich (this volume) enrich our understanding of the discernible influence of both constructs in shaping conceptions. However, this line of research’s strongest contribution comes from looking under the light shed by both cognitive and motivational frameworks. In doing so, Pintrich and his colleagues have illuminated the interconnected role of cognitive and motivational factors in knowledge restructuring. 3.

3.1.

DIRECTIONS FOR FUTURE RESEARCH

Examine Relation Among Constructs Involved in Conceptual Change

Researchers must continue to address motivational, social, and contextual aspects of conceptual change. Indeed, we have known for some time that “cold conceptual change” is a limited perspective on the change process. Despite our progress in recognizing the importance of these influences, we are a long way from understanding exactly how they affect conceptual change. What are the mechanisms through which internal initiation of conceptual change occurs? By what means do externally-initiated catalysts exert their influence on individual knowledge reconstruction? Conceptual change researchers need to pursue both internal (cognitive and motivational) and external (social and contextual) aspects of conceptual change with particular attention on how these influences interact. Most important, we must explore the mechanisms involved within these complex interactions. Just how do internally initiated motivations such as goals exert their influence on performance? Is it through the strategic allocation of attention or through self-regulatory processes, or both? By what mechanisms do social interaction spur change? Is it through fostering reflection? Recent interest in the role students play in initiating and regulating the change process has burgeoned. This view, called “intentional conceptual change”, examines the role of affective, motivational, and dispositional constructs such as epistemological beliefs, goal formation, belief identification, and willingness to question one’s beliefs on learners’ conceptual formation and restructuring (Sinatra &

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Pintrich, in press). Sinatra (2000) has argued that affective and dispositional constructs can be brought to bear intentionally on the process of learning. That is, the learner can play a significant role in choosing whether and how to consider alternative points of view. As an illustration, researchers studying learning in the potentially emotional domain of human evolution have begun to tease out the manner in which affective and intentional constructs impact student learning in biological evolution (see Sinatra, Southerland, McConaughy, & Demastes, in submission). As Gorodetsky and Keiny (this volume) demonstrated, the impetus for individual conceptual change can come from an external event. Externally-initiated events contributing to conceptual change have been extensively examined in the form of instructional interventions designed to promote change (see Guzetti & Hynd, 1998). More recently, the social and cultural context as a mechanism of change has been highlighted (Saxe, 1999). It is clear that we can ill afford to ignore contextual and social influences on change. Yet, much work needs to be done to understand how external events can and do exert their influence. Documenting shifts in individual knowledge representations as a result of experiences within a social or cultural context is one, but only one, important part of the story. More significant advances in our knowledge of conceptual change will come from documenting the mechanisms by which external and internal events interacts to create change in conceptual knowledge. 3.2.

Investigate the Process of Change not Just the Outcome

Too often, due to the methods and procedures we rely on as educational researchers, we examine the outcome of the change process by measuring students’ knowledge after some form of conceptual change pedagogy. However, if change is truly evolutionary, more studies must be done to examine the process of change as it is occurring, not simply the outcome. Of course longitudinal studies are tremendously informative about developmental change, but qualitative shorter-term studies examining students during the learning process are also valuable for painting a picture of the change process. Significant advances in our understanding of basic processes in cognition came through methodology designed to examine those processes in action. On-line measures, such as response times and think aloud protocols, allowed researchers to examine the relation between basic processes such as activation of information in working memory and text comprehension (Kintsch, 2000). Conceptual change researchers need to apply more of the research techniques from basic cognitive process research to look more closely at knowledge restructuring as it occurs “online.” This approach will allow researchers to more precisely determine the relation between externally- and internal-initiated causes of conceptual change. Can conceptual change be documented in short time spans? How long does change have to last to be considered “strong conceptual change” (Dole & Sinatra, 1998)? What methods are most suitable to capturing the process of change as it is occuring? Perhaps we need more mirogenetic investigations of knowledge

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restructuring to capture the process (Carey 1991). One point is clear, capturing the process as well as the outcome of change should be a goal for conceptual change research. 3.3.

Use Multiple Methods and Approaches to Study of Conceptual Change

Clearly we need to use multiple methods for determining students’ conceptual knowledge and change as it occurs in conceptual understanding. The studies in Part II revealed that task demands and environmental and social context shape what students reveal about their conceptual knowledge. On-line measures might provide insight into the basic processes involved in knowledge restructuring, but using such measures alone would not reveal effects due to external events. Therefore, researchers need to explore the change process through triangulation of multiple theoretical approaches and multiple methods. In doing so, they will fill in the gaps in our knowledge of conceptual restructuring. 4. EDUCATIONAL IMPLICATIONS

4.1.

Conceptual Change Involves More than Changing Students’ Conceptions

Educators need to be aware that for students to change their knowledge, change also may be required in their motivations, beliefs, or affective stance toward learning (Linnenbrink & Pintrich, this volume). If conceptual change demands that students intentionally compare their conceptions to scientific ones, this may require relatively non-absolutist epistemological beliefs, and an open-minded personal disposition or stance toward alternative points of view (Sinatra et al., in submission). The conditions required for conceptual change necessitate a classroom climate that promotes reflection, values questioning, and helps student knowledge become explicit and open to evaluation. Science educators have proposed Nature of Science (NOS) instruction as one way to create such a climate (see for example, National Academy of Sciences, 1998; Southerland, 2000). NOS instruction advocates teaching about the methodological principles of scientific knowledge and the tentative nature of scientific understanding. NOS instruction portrays science as a powerful but limited human enterprise and helps students understand which questions science can ask and answer, and which it can not. NOS instruction has the potential to promote the deep processing (Chinn & Brewer, 1993) or high engagement (Dole & Sinatra, 1998) required for conceptual change. Such instruction would utilize activities such as conducting inquiries, writing personal reflections, and justifying one’s reasoning, with the goal of developing a greater understanding of both personal epistemology and how scientific knowledge is constructed. Allowing students the opportunity to juxtapose their beliefs against those ideas presented by their teacher, can engage the cognitive as well as the motivational, contextual, and social aspects of the conceptual change process.

196 4.2.

G. M. SINATRA Change Takes Time

If change is evolutionary, teachers can not expect conceptual change in their students over the course of one biology or physics lesson. Educators need to be aware that conceptual development emerges or evolves over time. Like concept attainment, conceptual change is not an all or none phenomenon. Children learning new concepts overgeneralize, miscategorize, and misapply concepts as they are learning. Concepts are refined as students hone in on their defining features and characteristics. Likewise, conceptual change requires multiple experiences with the new conception, opportunities to reflect, and time for students to modify their understandings. As students’ knowledge evolves, alternative conceptions exist simultaneously allowing students to apply their knowledge differentially according to the context (Halldén et al., this volume) Therefore, educators should not assume that children “just don’t get it” when they apply a naive conception after conceptual change instruction designed to promote knowledge restructuring. A concept is not likely to change without repeated experiences with the new idea over the course of substantial instructional time (weeks or months). More than one experience is probably necessary for a child to reliably use a new conception in its proper context. 4.3.

Give Students Opportunities for Social Interaction

The Gorodetsky and Keiny (this volume) study highlights the opportunity social interaction affords for creating the conditions necessary for conceptual change learning. Cooperative and peer learning has been shown to be powerful for concept acquisition (Slavin, 1999) and it may be even more effective in promoting conceptual change. Conceptual change can not occur if students reject alternative views or information that is anomalous to their perspective (Chinn & Brewer, 1993). Students may be more likely to listen to peers who hold different views than their own. They may find their peers’ views more compelling than those of their teachers. Social interaction may provide a motivation to consider alternative points of view (Dole & Sinatra, 1998) which can stimulate reconsideration of one’s own perspective. 4.4. Use Multiple Forms of Assessment to Determine Student Understandings

Given the results of the Rodrigo et al. study, it is clear that what we know about students’ conceptions depends in part on how we assess their knowledge. Students use their knowledge differentially in response to particular task demands. What students reveal about their conceptual understanding depends not only on what we ask of them, but also on what tools we provide them to reason and explain their thinking (Halldén, et al., this volume). These findings suggests that assessment of students’ conceptions at one point in time with one form of assessment may be insufficient to evaluate conceptual change. Teachers may need to provide students with more than one opportunity to show what they know. Further, they may need to utilize more than one method of

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assessment to allow students to reveal appropriate application of the new conception. REFERENCES Carey, S. (1991). Knowledge acquisition: Enrichment or conceptual change? In S. Carey, & R. Gelman (Eds.), The epigenesis of mind: Essays on biology and cognition, (pp. 257-291). Hillsdale, NJ: Erlbaum. Chi, M. T. H., de Leeuw, N., Chiu, M. H., & LaVancher, C. (1994), Eliciting self-explanations improves understanding, Cognitive Science, 18, 439-477. Chinn, C., & Brewer, W. (1993). The role of anomalous data in knowledge acquisition: A theoretical framework and implications for science instruction. Review of Educational Research, 63, 1-49. Chan, C., Burtis, J., & Bereiter, C. (1997). Knowledge building as a mediator of conflict in conceptual change. Cognition and Instruction, 15, 1-40. Dole, J. A. & Sinatra, G. M. (1998). Reconceptualizing change in the cognitive construction of knowledge. Educational Psychologist, 33 (2/3), 109-128. Driver, R., Asoko, H., Leach, J., Mortimer, E., & Scott, P. (1994). Constructing scientific knowledge in the classroom, Educational Researcher, 23, 5-12. diSessa, A. A., & Sherin, B. (1998). What changes in conceptual change? International Journal of Science Education, 20, 1155-1191. Guzzetti, B., & Hynd, C. (1998). Theoretical perspectives on conceptual change. Hillsdale, NJ: Erlbaum. Kintsch, W. (1998). Comprehension: A paradigm for cognition. London: Cambridge University Press. National Academy of Sciences. (1998). Teaching about evolution and the nature of science. Washington, DC: National Academy Press. Paris, S. G., & Winograd, P. (1990). How metacognition can promote academic learning and instruction. In B. F. Jones & L. Idol (Eds.), Dimension of thinking and cognitive instruction (pp. 15-51). Hillsdale, NJ: Lawrence Erlbaum Associates. Pintrich, P. R (1999). Motivational beliefs as resources for and constraints on conceptual change. In W. Schnotz, S. Vosniadou, & M. Carretero (Eds.). New perspectives on conceptual change (33-50). Amsterdam: Pergamon/Elsevier Science. Pintrich, P. R., Marx, R. W., & Boyle, R. A. (1993). Beyond cold conceptual change: The role of motivational beliefs and classroom contextual factors in the process of conceptual change. Review of Educational Research, 63, 167-199. Posner, G., Strike, K., Hewson, P., & Gertzog, W. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Science Education, 66, 211-227. Reynolds, R. E. (2000). Attentional resource emancipation: Towards understanding the interaction of word identification and comprehension processes in reading. Scientific Studies of Reading. Saxe, G. B. (1999). Sources of concepts: A cultural-developmental perspective. In E. K. Scholnick, K. Nelson, S. A. Gelman, & P. H. Miller (Eds.), Conceptual development: Piaget’s legacy (p. 253-267). Mahwah, New Jersey: Lawrence Erlbaum Associates. Searle, J. R. (1998). Mind, language and society: Philosophy in the real world. New York: Basic Books. Siegler, R. S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press. Sinatra, G. M., & Pintrich, P. R. (in press). The role of intentions in conceptual change learning. In G. M. Sinatra & P. R. Pintrich (Eds.) Intentional conceptual change. Mahwah, NJ: Lawrence Erlbaum Associates. Sinatra, G. M., Southerland, S. A., McConaughy, F., & Demastes, J. (in submission). The role of intentions and beliefs in students understanding and acceptance of biological evolution. Slavin, R. E. (1999). Comprehensive approaches to cooperative learning. Theory into Practice, 38, 74-79. Southerland, S. A. (2000). Epistemic universalism and the shortcomings of curricular multicultural science education. Science & Education, 9, 289-307. Smith, J. P, diSessa, A. A., & Roschelle, J. (1993). Misconceptions reconceived: A constructivist analysis of knowledge in transition. The Journal of the Learning Sciences, 3, 115-163. Vosniadou, S., & Brewer, W. F. (1987). Theories of knowledge restructuring in development. Review of Educational Research, 57, 51-67.

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PART III

DOMAIN SPECIFICITY AND LEARNING

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THE ROLE OF STUDENTS’ EPISTEMOLOGICAL KNOWLEDGE IN THE PROCESS OF CONCEPTUAL CHANGE IN SCIENCE

JOHN LEACH & JENNY LEWIS University of Leeds, UK

Abstract. This chapter addresses the role of students’ epistemological knowledge in the process of conceptual change in science. The chapter begins by making a case that students’ conceptual knowledge in science has an epistemological dimension, and that models of conceptual change in science should therefore make reference to this epistemological dimension. The following claims are then developed: (1) many science students tend to over-attribute significance to empirical processes in suggesting how scientific disputes might be resolved, and in justifying viewpoints on scientific issues; and (2) students draw upon different epistemological knowledge in different situations, and for this reason it makes no sense to refer to students’ epistemological knowledge in isolation from the situations in which that knowledge is used. Each claim is supported with data from recent studies, involving the authors, of students’ epistemological knowledge in science. The chapter concludes with suggestions about potentially fruitful directions for future research on epistemological knowledge and conceptual change in science.

1.

WHY LOOK AT STUDENTS’ EPISTEMOLOGICAL KNOWLEDGE IN RESEARCH ON CONCEPTUAL CHANGE IN SCIENCE?

The overwhelming focus of research on conceptual change in science to date has been upon learners’ domain-specific knowledge structures. In this chapter, we make a case for broadening this focus to incorporate students’ epistemological knowledge. There are fundamental reasons for broadening the focus of research in this way, relating to the nature of science itself and how it is portrayed in the curriculum. In order to provide a nation with a good pool of well-qualified students who will train as scientists and technologists, thereby contributing to the national economy (Ziman, 1980), the curriculum for students in compulsory secondary education1 tends to be structured around conceptual content which is judged as forming an appropriate basis for future pre-professional study in science. As well as training future science specialists, however, the science curriculum is also charged with the responsibility of contributing to the general education of young people, whether or not they intend to go on with their studies in science. In effect, the school science curriculum is given the aim of underpinning the scientific literacy of all future citizens. There is a 1 It is recognised that there are considerable national variations in the organisation and content of education for school students. In line with UK practice, the phrase “secondary education” is used to refer to education for students in the broad age range 11-18.

M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 201-216. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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growing literature on the nature of scientific literacy and the role of school science in supporting it, and a number of problematic issues are emerging. In the first instance, there is little specification or agreement about what a scientifically literate person is able to do, that a scientifically illiterate person is not. A number of writers (e.g. Layton, Jenkins, Macgill, & Davey, 1993; Driver, Leach, Millar, & Scott, 1996) have drawn upon Shen (1975) in identifying different ways in which groups of people might draw upon scientific knowledge for specific purposes. Using scientific knowledge for utilitarian purposes involves individuals in drawing upon scientific knowledge that is useful to them in a practical way. This might involve, for example, using knowledge about the germ theory of disease to prevent contamination during the preparation of food. It has also been argued that individuals need a degree of scientific knowledge in order to deal with science and technology as they are encountered in modern society. In modern societies, decisions have to be taken about matters with a science dimension, such as how energy should be generated and used, how refuse should be disposed of, how the safety of food should be maximised and so on. Using scientific knowledge for these kinds of democratic purposes involves individuals in drawing upon knowledge to understand and participate in such debates. In addition, cultural scientific literacy involves individuals in understanding science as a cultural achievement of society, along with art, music and literature. The extent to which school science curricula can promote scientific literacy is the subject of debate (e.g. Jenkins, 1999; Shamos, 1995), though there is some agreement that a curriculum for scientific literacy will include content about the practice of science, as well as the laws and theories of science. Indeed, several science curricula from around the world include some content about the history, epistemology and sociology of science, with the aim of promoting scientific literacy. In addition, there is ample evidence that students develop ideas about the nature of science as a practice, and the nature of scientific knowledge itself, as a result of following typical science curricula. However, these messages may not be communicated explicitly, and might well be in sharp contrast to the understandings of teachers (e.g. Brickhouse, Dagher, Shipman, & Letts, 2000; Brickhouse, 1990; Hodson, 1993; Ryder & Leach, 1999). If theories of conceptual change in science are to engage with the content that science students are taught in the curriculum, it is therefore necessary for them to address changes in students’ concepts of the nature of science itself. From now on, we will use the term epistemological knowledge as a convenient shorthand for the knowledge about science as a practice, and the nature and status of scientific knowledge, that individuals use in various situations. Many science curricula focus exclusively on the laws, theories and concepts of science, and do not make specific reference to the history, epistemology or sociology of science. In these cases, it is tempting to assume that theories of conceptual change in science learning do not need to make reference to students’ epistemological knowledge. However, we would argue that conceptual knowledge in science has an epistemological dimension. Part of learning the laws, theories and concepts of science is learning to recognise how specific items of scientific knowledge are used to generate predictions and explanations, and inform action, in specific situations. We find it useful to draw a distinction between learning the laws,

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theories and concepts of science (traditionally described as “learning scientific concepts”), and learning how that knowledge is used in actual situations (which involves epistemological knowledge about the nature of scientific concepts, the boundary conditions that govern the application of concepts in particular situations, and so on). For example, it is possible to learn a meaning for several thermodynamic concepts, and to have a view of how these concepts relate to each other, without being able to use those concepts to explain how an Italian coffee pot works. Such a distinction has been elaborated in both the philosophy of science and in studies of learning. In the book Objective Knowledge: an evolutionary approach the philosopher Karl Popper refers to three worlds. The first of these worlds is the material world of actual objects and events. The second world is the ‘mental world’ of knowledge held by individuals. The third world contains formal, symbolic entities (including much of the scientific content taught in school science). The entities that populate each world are ontologically different, so that entities such as force (which belong in the third world) are different in kind from the events in the first world (pushes, pulls) that they describe. Furthermore, an individual’s understanding of the meaning of force (belonging in the second world) may or may not correspond with formal definitions of force in the third world. Several perspectives on science learning highlight ontological differences between the entities from which scientific explanations are constructed, and objects and events in the material world (e.g. Tiberghien, 1996; Driver, Asoko, Leach, Mortimer, & Scott, 1994; Driver et al., 1996; Bereiter, 1994; Leach & Scott, 1999). In particular, these studies suggest that many science learners do not appreciate epistemic features of the formal scientific knowledge of the third world. This line of scholarship has important implications for researchers in conceptual change in science. It becomes necessary to recognise epistemological differences between students’ personal knowledge (second world) and the scientific ideas themselves (third world), to understand how these differences influence students’ explanations of objects and events in the first world, and to appreciate how students’ personal knowledge changes as a result of instruction. In this chapter, we present two claims about the significance of students’ epistemological knowledge in processes of learning and conceptual change in science. The chapter concludes with a discussion of the significance of these claims for research in science education, and the practice of science teaching. 2. CLAIMS ABOUT THE ROLE OF STUDENTS’ EPISTEMOLOGICAL KNOWLEDGE IN THE PROCESS OF CONCEPTUAL CHANGE IN SCIENCE

Two claims about the role of students’ epistemological knowledge in the process of conceptual change in science are presented in this section. The first of these relates to the significance of epistemological knowledge in accounts of students’ understanding of scientific content, whereas the second relates to the nature and status of students’ epistemological knowledge.

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2.1. Many science students tend to over-attribute significance to empirical processes in suggesting how scientific disputes might be resolved, and in justifying viewpoints on scientific issues Although the media carries a limited number of stories which present science in an unconditionally positive and celebratory way, the majority of situations involving science that reach a wide public are more equivocal. People may be faced with choices in situations such as interacting with health care workers, in dealing with local environmental issues, in responding to media reports on policy matters such as the generation of power, in reviewing technical information in the workplace, and so on. Typically, key actors in such situations are faced with controversy, choice and prioritisation. In order to engage with these kinds of situations, it is therefore necessary for people to have some understanding about how arguments are constructed and supported in scientific settings. In particular, people need to be able to appreciate the potential uses of, and limitations in the use of specialist scientific knowledge to support viewpoints. We see this as an important goal in the science education of those destined to study science at a specialist level, as well as those who are not. We imagine that young people are well able to analyse the quality of arguments in a variety of situations, and are able to recognise when arguments do not stand up to scrutiny or are not supported by evidence. This is a normal part of social life. However, there is evidence that students are not particularly skilled at recognising, constructing and evaluating arguments when the context in question is scientific. In particular, there is strong empirical evidence that, by the end of compulsory science education, many students draw upon rather naive epistemological knowledge in interpreting issues with a science dimension (for a recent review, see Désautels & Larochelle, 1998). Many students appear to assume a simple correspondence between entities in scientific explanations, and objects and events in the material world: they are naïve realists. Such students do not appear to recognise that, in many cases, proposing an explanation involves drawing upon theoretical entities (from the third world) that are not observable or taken for granted features of phenomena (from the first world). They argue, for example, that debates about the existence of enhanced global warming due to the use of hydrocarbon fuels can be resolved simply and unproblematically by collecting and looking for correlations in data (from the first world) about atmospheric temperature and hydrocarbon use. They do not appreciate that scientific measurements of atmospheric temperature and enhanced global warming are based upon mathematical models of the behaviour and functioning of the atmosphere (from the third world). When encountering situations where expert scientific opinion is equivocal, students who assume that scientific knowledge claims can be ‘proved’ by simple empirical investigations have little choice but to attribute differences of opinion to a lack of appropriate data, or personal bias or incompetence on the part of experts. This can be illustrated with reference to a recent study carried out by Rosalind Driver, John Leach, Robin Millar and Phil Scott (1996). The purpose of the study was to investigate how 16 year old students interpret the internal workings of scientific communities, and the external relations of science with society. Of course,

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students of this age generally have minimal first-hand experience of the world of professional science, and it was therefore decided to investigate students’ interpretations of information presented to them. Two scenarios were written with a view to making the social interactions of scientific communities and other groups explicit. In each case, the focus was upon a situation in which experts disagreed. The first scenario described the Wegener controversy, and as such addresses aspects of the internal functioning of scientific communities. The second scenario presented arguments about the legalisation of food irradiation as a method of food preservation in the UK, and therefore involved issues of broad interest outside scientific communities. Each scenario involved teaching students something about the background to the dispute. Then, an argument was presented where experts reached different conclusions based upon the same empirical evidence. In the Wegener context, 13 groups of 4 students worked to address the following questions: Why do you think the geologists in the 1920s did not all agree? What do you think would have been needed in the 1920s to enable all the geologists to reach agreement? Why do you think the majority of geologists in the 1920s reached a decision which we now think is the wrong one? In the Food Irradiation context, students also worked in 3 groups of 4. In this case, however, they were presented with three possible choices as to why two scientists did not agree about the legalisation of food irradiation. These choices were written following piloting: They do not have all the facts. Once you have all the facts, then an answer to the question would be clear. They have all the facts they need. No matter how many facts you have, you always have to make a judgement about what the facts mean. The scientist working for the food industry is influenced by what is profitable for the industry. The reasons given by students for differences of opinion between experts, and their possible resolution, were similar in both cases. Generally speaking, students gave empirical explanations for the disagreements and their resolution. These arguments tended to focus upon the quantity, quality or nature of the available evidence. For example, several groups argued that the rejection of Wegener’s ideas in the 1920s was primarily due to a lack of sufficient quality evidence: S:

All their evidence, it wasn’t rock solid [laughs].

I: What kind of evidence would have been rock solid? What kinds of things would convince someone? S:

Accurate measurements.

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The ground moving

S:

They didn’t have satellite pictures that they couldn’t see how it was changing.

S:

They couldn’t measure it.

S: If you put a laser from a mountain over here and a mountain over there and see if you could attach it to the other side and see the amount of time it takes it from getting from one to the other... Maybe they’d be able to see if they were moving back.

(From Driver et al., 1996, p. 124.) In the case of food irradiation, similar arguments that the dispute could be resolved simply by collecting empirical evidence were voiced: S:

If there was some hard facts that showed it was safe.

S: I think actually if they did proper tests and they had more facts and they did it on a large group of people - they’d probably find out, wouldn’t they. S:

When you’ve found out definitely what it does and if it’s dangerous.

S: They’ve got some facts, but they are not very accurate, are they? They did not come up with any figure or anything.

(From Driver et al., 1996, pp.130-131.) Of course, there are many situations where empirical information might well support one opinion more than another, and it is appropriate that students learn something about the implications of data for knowledge claims in their science education. However, in the examples presented above the students are over-ambitious in their views about the role of empirical evidence in resolving disputes. In the Wegener examples, many students seemed to assume that continental drift only came to be accepted when measurements “proving” that the continents were moving became available. (Although such measurements, if available, might “prove” that movement is happening now, they would not prove that Wegener’s ideas about the origins of the shapes of the continents were correct.) In the food irradiation case, students did not seem able to conceive of how decisions about food safety might be made in the absence of controlled experiments comparing the health of matched populations where the only difference was the inclusion of irradiated food in the diet. There was little evidence, in either the Wegener or Food Irradiation contexts, of students standing back from the evidence presented in the teaching materials, and assessing it as a body of evidence which supports or does not support a knowledge claim. We think that the science curriculum might usefully introduce students to more sophisticated, accounts of the role of empirical investigation in resolving disputes. They might, for example, consider a range of approaches to empirical investigation which move beyond the stereotypical controlled experiment and consider how scientists such as epidemiologists, geologists and astronomers collect

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and interpret data. This would hopefully allow students to recognise the kinds of evidence upon which knowledge claims encountered in their future lives were based. Although the majority of the explanations offered by students for the emergence and resolution of disputes were focused upon the empirical work that had been done, most groups also offered social explanations. Students seemed to view dispute as a taken-for-granted feature of everyday life, and consequently accepted that scientists were likely to have different opinions. Students tended to refer to disagreements between individual scientists, making no mention of the role of scientific institutions in the validation of scientific knowledge. However, some students did pick up on points made in the introductory material about the institutional allegiances of Wegener and the scientists debating food irradiation: S: He’s not even a geologist... S: ...You know, like rivalry... because he’s not like one of them. Like an outsider coming in and like butting in on them. S: He didn’t understand it enough. He just basically... He know about the weather. That’s all they thought, but he actually wanted to know about other things as well.

(From Driver et al., 1996, p. 127.) S: He’s bound to protect his own job. S: They’re bound to go for whichever gets most money really. S: If they’re saving millions with irradiation they’re going to carry on with irradiation.

(From Driver et al., 1996, p. 131.) Although the students in this study appeared to make rather naive interpretations of the social functioning of science, we see no reason why more sophisticated portrayals of the functioning of scientific communities would not be understood, if presented through the curriculum. Through a case study approach, students could be introduced to some of the social and institutional processes by which scientific knowledge is judged as reliable. In addition, students’ knowledge of the range of empirical methods used by diverse groups such as geologists, nutritionists and epidemiologists could be broadened. Interestingly, in the U.K., the role of institutional processes in the validation of knowledge are being given increasing exposure in the general news media. The scientific work generally held responsible in the UK for bringing risks associated with eating British beef, or GM foods, to public attention was initially discounted in news programmes on the grounds that it had not been through a process of peer review. The fact that students recognise that professional scientists live and work in a social milieu that in many respects, is no different from familiar social situations provides a useful entry point for teaching about the social and institutional nature of science. Students appear far less familiar with institutional aspects of science, however, and these would need to be introduced through teaching.

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There is now a wide literature about the kind of content that might be included in the science curriculum with the aim of teaching students something about the relationships between the work of scientists, and broader social concerns (see, for example, Solomon & Aikenhead, 1994; Cross & Price, 1992). However, much less work has been carried out which investigates the effectiveness of pedagogy at promoting students’ understanding in this area. Cross and Price (1992) present a characterisation of the types of skills required by students to judge social issues: Skills for understanding the argument; Skills for judging the expert; Skills for making independent investigations in the literature or in the field; Skills for participation in democratic ways of influencing decision-making. However, much remains to be done to characterise what these skills are, how they are learnt and how they might be taught. One thing, however, is clear: the skills identified by Cross and Price have a strong epistemological dimension in that they involve making judgements about arguments and claims on the basis of evidence. Students are required to develop personal understandings of ideas from Popper’s third world, and use those understandings in developing or evaluating arguments. In this case, conceptual learning has to involve learning something of the epistemology of ideas from the third world so that evidence and arguments are evaluated appropriately. This was one aim of a study that we recently carried out in collaboration with Rosalind Driver and Colin Wood-Robinson (Leach, Lewis, Driver, & WoodRobinson, 1996). We investigated how students drew upon information about prenatal screening for cystic fibrosis in order to present and justify opinions about it. In this part of the paper we address findings from the study about students’ abilities at constructing and evaluating argument in scientific contexts. Data were collected from three classes of students aged 15-16 ( students, working in 19 small groups of 3 or 4). In the first instance, students were shown a video which we had made to present background information about CF. Particular issues about CF were included in the video if they had a bearing on issues that relate to prenatal testing for the condition (such as the early onset of CF, the life expectancy of CF sufferers, the inheritance of CF, the procedures used for both prenatal screening for CF, and screening for carrier status). Students then completed an activity which was designed to test their understanding of the information that was presented in the video, and to correct misunderstandings. Next, students listened to an audiotaped drama in which a couple discuss the possibility of accepting prenatal screening for their unborn child, having discovered that they were both carriers of CF. In the drama, the couple raise a number of issues that might influence their decision, some of which relate to the future of the child, others of which relate to the process of prenatal screening itself. Finally, small groups of 3 or 4 students were presented with a sheet, on which the couple in the drama had supposedly started to write the advantages and disadvantages of each course of action. The students had to complete this process of recording advantages

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and disadvantages, and interviewers prompted them about issues that were raised in the drama that were not discussed by the group. Until this stage, the lesson was essentially a carefully planned teaching intervention which aimed to introduce students to a scientific issue that involves choice, prioritisation and the appropriate use of conceptual knowledge, in some detail. The data that were collected during this phase of the lesson suggested that, generally speaking, the students understood the background conceptual information that was presented in the video, and were able to pick out most of the issues raised by the couple in the drama that might influence their choice about whether to go ahead with prenatal screening. By the end of the group discussion, these ideas appeared to be part of the “common knowledge” of the whole group (Edwards & Mercer, 1987). In the next activity, students had to work in their small group to articulate an opinion about whether the couple should go ahead with prenatal screening for their unborn child. These discussions were audiorecorded and transcribed in full. In addition, an interviewer talked to the group about their discussion, and this was also recorded and transcribed. It should be emphasised that we expected students to hold varied and diverse opinions about this question, and that we viewed all opinions as valid. Rather than judging the opinions voiced by students, we were interested in the ways in which opinions were justified and argued for. Group discussion was a major feature of the research approach used. This was for two reasons. Firstly, in order to get access to students’ thinking about prenatal screening it was necessary to engender situations where they would articulate their thinking on particular issues. Secondly, and perhaps most importantly, we believe that it is only through articulation of viewpoints and engagement with opposing arguments that people clarify their thinking on particular issues (Barnes & Todd, 1977). Within the transcripts of group discussions, we see many cases where students are influenced by their peers. We would argue that students could not engage with issues such as prenatal screening without the opportunity for discussion work. Opposing viewpoints were noted in about half of the small groups, and the transcripts from these groups were particularly useful in characterising how opinions were justified. Mercer (1996) has characterised three ways of talking and thinking in small groups. Disputational talk involves short exchanges between students which are characterised by individual decision-making or disagreement between students. There are no apparent attempts to pool ideas to reach decisions, to warrant claims or to offer constructive criticism to ideas raised by others. Cumulative talk involves speakers in building positively and uncritically upon everything that is said in discussion. In exploratory talk, speakers engage in critical but constructive discussion about each other’s ideas. When challenges are made, they are backed up with argumentation and alternative viewpoints are suggested. Mercer suggests that in exploratory talk “knowledge is made more publicly accountable and reasoning is more visible in the talk.” (p. 104). We find this characterisation of group discussion very useful in describing the styles of talk noted in the small groups. Although this probe was not designed to

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allow for analysis of group discussion styles, there appear to be at least 4 groups using exploratory talk. The talk of these groups was peppered with statements of the form “If a then b”, as is illustrated by the following extract: S: Yeah, and also how the parents bring up the baby as well. If they’re bringing it up to be sensible about the condition and, you know, respect that they’ve got it... Yeah, it just depends on what they think they’d do, do they think that they’re going to terminate, they would terminate if they found out? Cos if they feel that then they wouldn’t be able to cope with a CF sufferer then you know they should have a test. But if they feel that they’ll love it so much that no matter what then they shouldn’t.

(School B Group 1 Line 24.29) Some groups explicitly discussed the disadvantages of a chosen course of action: S:

Yeah, they should have the test but they shouldn’t have an abortion

(...) S:

It’s a lot of discomfort for Sue as well.

(...) S:

She might feel pressurised into having one..

(...) Yeah, she might feel guilty for having an abortion cos its something that could be lived with (...)

(School A Group 6 Lines 19.9-19.16) The talk of other groups appeared much more like Mercer’s disputational talk, discussion being characterised by individual students restating viewpoints again and again, no attempt being made to justify statements or present rational arguments to counter opposing points of view. It is interesting to note that, within this small sample, groups using exploratory talk tended to be comprised of girls whereas those using disputational talk tended to be comprised of boys. It did not appear valid to distinguish examples of cumulative talk and disputational talk in these transcripts. In some cases, the style of talk was cumulative in that contributions were accepted uncritically. Students in these groups maintained similar positions throughout discussions, however, and consequently the need to make arguments in support of particular viewpoints did not arise. Although there is evidence that the genetic basis of inheritance is poorly understood by students (Lewis, Leach, Driver, & Wood-Robinson, 1996; WoodRobinson, Lewis, Driver, & Leach 1996), the students with whom we worked appeared able to understand the genetic basis of CF and engage with a range of issues relating to prenatal screening. A significant majority of students were able to evaluate these issues and justify particular points of view about prenatal screening. We see this as providing evidence that many young people in the age range of 15 -

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16 have the intellectual resources to address subject matter such as prenatal screening for CF in the curriculum. In addition, there is evidence that students’ learning of genetics concepts can be enhanced when those concepts are introduced through curricular activities seen as socially relevant by students (Zohar & Nemet, 1998). On the basis of this evidence, what can be claimed about conceptual change? Perhaps the most obvious point to make is that learning scientific content, such as genetics or plate tectonics, has an epistemological dimension. As well as understanding the technical contents of scientific content, students often need to appreciate the extent to which that content is underpinned by empirical evidence, and the issues involved in drawing upon that content to support a position on social, ethical, political or economic questions. Although students’ content knowledge was generally adequate for making sense of the information provided, their knowledge about how such content knowledge ought to be drawn upon to inform decisions was more limited. In other words, although the students in these studies appeared able to understand content in the third world, fewer of them drew upon epistemological features of that content, whether to account for the reasons for dispute between scientists or to justify opinions about an issue such as prenatal screening. We would argue that an important part of learning scientific concepts is learning what counts as appropriate use of the concepts in specific situations. Models of conceptual change therefore need to be able to explain how learners become able to recognise what counts as appropriate use of conceptual knowledge in the broad range of situations in which it might be appropriate to use that knowledge. Students’ responses to the questions posed in the reported studies were typically limited and poorly articulated. It appeared that, generally speaking students were answering questions that they had not thought about before, and that their responses were tentative. We do not take this as evidence that the students held strong epistemological knowledge that would be resistant to change following teaching. Rather, we imagine that students might well change their responses to our questions following teaching that opened up epistemological questions, and modelling the ways in which members of scientific communities might address those questions. To this extent, we think that any conceptual change metaphor which portrays students’ conceptual knowledge (and associated epistemological knowledge) as changing between relatively stable forms would misrepresent the structure of students’ epistemological knowledge and the way in which that knowledge changes as a result of teaching. These issues are developed in section 2.2. 2.2. Students draw upon different epistemological knowledge in different situations, and for this reason it makes no sense to refer to students’ epistemological knowledge in isolation from the situations in which that knowledge becomes manifest. In much research on conceptual change in science education, students’ knowledge is characterised in terms of mental models that are used in various situations. It is assumed that we can ascertain learners’ underlying mental constructs by referring to

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their responses to interview questions. An alternative perspective views students’ responses to interview questions as situated practice, and there is evidence that students give radically different accounts of natural phenomena depending upon the situations in which questions are asked (e.g. Schoultz, Säljö, & Wyndhamn, in press). There have been a number of studies of students’ epistemological understanding in science. The picture that emerges, put very simply, is that many students appear to draw upon naive inductivist knowledge when interpreting and using scientific information in a variety of situations. In terms of theories of conceptual change, however, it is not appropriate to work at this simplistic level. How do we interpret the fact that many students appear to draw upon a naive inductivist epistemology in various contexts? Does this mean, as some have claimed, that such students are “naive inductivists”, and will reason in similar ways across a whole host of situations? Alternatively, is it that an individual’s reasoning is likely to vary substantially between contexts? The answer to such questions is of considerable importance to our understanding of the role of students’ epistemological knowledge in conceptual change. In recent years, a few researchers have attempted investigations of the epistemological knowledge that underpin students’ actions in learning situations by posing questions to students in specific contexts. This work can be exemplified by considering a question recently administered to 738 European science majors aged 16-20 (Leach et al., 1998; Leach, Millar, Ryder, & Séré, 2000). The question was designed to find out how students interpret the relationship between theoretical knowledge claims and empirical data in an experimental situation where there is no agreed consensus. A situation is described where scientists at a conference are debating two different models of superconductivity, both of which are consistent with the available data. In the first part of the question, students are asked to comment upon the scientists’ different interpretations of the data. Choices are presented relating to empirical consistency between models and data, internal features of the models, and the radical relativist notion that there is no way in principle that different models can be evaluated against each other. In the second part of the question, students are asked what the scientists should do next, and are given choices which focus on resolving the conflict by collecting more data (with no reference to the underlying models), resolving the conflict by considering the underlying models, or deciding that there is no way in principle to judge one model as better or worse than the other and agreeing to differ. In the final part of the question, students are presented with four choices about how to interpret a similar data set. Again, the choices focus on data (with no reference to the models), internal features of the models, and a radical relativist response. In order to administer this question to a multilingual sample, a closed-response format was used (with all the methodological shortcomings that this entails). The closed-response items were generated from students’ open responses to pilot questions. For the purpose of analysis, responses were categorised into three groups:

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Data-focused: students tend to assume that all questions in science can be resolved so long as scientists have access to a large enough data set of sufficient quality. For example, students stated that the most useful of two competing models of superconductivity could be identified easily so long as enough data was available. Theory and data related: students tend to assume that what scientists know, the data that they have and the experiments that they do all have the potential to influence each other. For example, students stated that decisions about the usefulness of competing models of superconductivity would be informed by both internal features of the models and empirical data. Radical relativist: students recognise the problems associated with making knowledge claims on the basis of empirical data. They therefore conclude that it is up to each scientist to believe what they want to following empirical work. For example, students suggested that there was no way of evaluating empirically which of two competing models of superconductivity was most useful. These broad representations of scientific epistemology correspond to others identified in the literature (Désautels & Larochelle, 1998). The three parts of this question relate to one context, and the three situations described on each part of the question are very similar. If students have epistemological knowledge that is not context-dependent, then their responses to the three parts of the question would be expected to be coherent. If students’ responses were not coherent across the three parts of the question, either the question is not valid for identifying students’ epistemological knowledge, or alternatively the students do not use epistemological knowledge across similar contexts. Analysis of responses provide evidence that students did not answer each part of the question consistently. Furthermore, 33% of the sample used all three forms of reasoning on at least one occasion, and 83% used theory and data related and data focused reasoning on at least one occasion. [Due to ambiguities in the interpretation of some of the closed-response statements, we did not feel confident to attribute some student responses to any of the three forms of reasoning identified.] We remain cautious about findings from the study, mainly due to the inherent difficulty of interpreting the significance of students’ choices of closed response statements. Given all these limitations, however, we take this study as providing tentative evidence that relatively advanced science students do not draw upon epistemological knowledge consistently between contexts. Interestingly, recent work by Brickhouse et al. (2000) presents similar findings based upon qualitative methods. It therefore makes little sense to talk about individual students’ knowledge based on the assumption that students hold general “epistemological knowledge”, such as “naive inductivism”, that are drawn upon in the context of subject matter learning. Rather, it is more appropriate to consider student’s domain-specific knowledge as having associated epistemological dimensions.

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3. IMPLICATIONS FOR FUTURE RESEARCH ON EPISTEMOLOGICAL KNOWLEDGE AND CONCEPTUAL CHANGE

It is worth reflecting for a moment upon the research methodology being used in studies such as the ones described above, and the kind of knowledge that is being elicited. In the first instance, we would highlight the difference between studies that investigate students’ explicit statements about philosophical questions about science, from studies that investigate students’ actions (or their statements about actions) in a given context. If we are interested in the role of students’ epistemological knowledge in their subject matter learning, termed “epistemologies in action” by Désautels and Larochelle (1998), it makes sense to collect data in situations where students are engaged in subject matter learning, or alternatively in contexts that are very similar to those encountered by students in subject matter learning. This increases the likelihood of eliciting epistemological knowledge similar to that which students use during subject matter learning. Indeed, there is evidence that although many professional scientists make apparently naive statements about “the epistemology of science” in general, they make very sophisticated statements about epistemological matters in their own disciplines, and their own research fields within the discipline (Samarapungavan, 1992). The second methodological issue that we would highlight is the distinction between studies that elicit explicit statements from students about epistemological issues, and studies which make inferences about students’ tacit epistemological knowledge on the basis of their actions. There is certainly evidence that what adolescent students say about epistemological questions in given contexts is different from what they do when required to act (e.g. Rowell & Dawson, 1983). If adolescent and post-adolescent science do indeed use different epistemological knowledge when interacting with different examples of scientific subject matter, this has important implications for future work on conceptual change in science. In the context of epistemological knowledge, it becomes necessary to conceptualise learning as a process of becoming able to use epistemological knowledge in the same way as more experienced members of scientific communities in specific situations, rather than developing global representations of scientific epistemology. It also becomes even more important for research methodology to take the issue of context seriously. If claims are to be made about the role of students’ epistemological knowledge in their learning of domain-specific knowledge, it becomes necessary to select contexts for research that relate closely to the situations in which students typically learn and use domain-specific knowledge. Furthermore, if general claims are to be made about students’ epistemological knowledge it is necessary to carry out investigations across a broad range of conceptual contexts, rather than over-generalising from students’ responses in one or two situations. Our understanding about the role of students’ epistemological knowledge in conceptual change in science is currently at the stage of providing some insights into the epistemological knowledge drawn upon by students as they encounter various kinds of subject matter knowledge. There is some limited evidence that older students draw upon a range of epistemological knowledge in different contexts, though in many cases students’ use of epistemological knowledge is very different

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from that of experienced members of scientific communities. It would be interesting to explore further possible differences between students and “experts” in the use of epistemological knowledge in relation to subject matter. A further area for research, with obvious educational significance, relates to the feasibility and practice of teaching students to use their epistemological knowledge in given situations in a more ‘expert’ way. 4.

ACKNOWLEDGEMENTS

The studies reported in section 2.1 were supported by the Economic and Social Research Council (Grant R0002386), and The Wellcome Trust. The study reported in section 2.2 was supported by the EC (Project PL-95-2005), and conducted in collaboration with Robin Millar, Jim Ryder, Marie-Geneviève Séré, Dorte Hammelev, Hans Niedderer, and Vasilis Tselfes. We thank Jim Ryder for helpful discussions about this chapter. REFERENCES Barnes, D., & Todd, F. (1977). Communication and learning in small groups. London: Routledge and Kegan Paul. Bereiter, C. (1994). Constructivism, socioculturalism and Popper’s World 3. Educational Researcher, 23, 21-23. Brickhouse, N. W. (1990). Teachers’ beliefs about the nature of science and their relationship to classroom practice. Journal of Teacher Education, 41, 53-62. Brickhouse, N. W., Dagher, Z, R., Shipman, H. L., & Letts, W. J. IV (2000). Teaching about the nature of science in a college astronomy course. In R. Millar, J. Leach, & J. Osborne (Eds.), Improving science education: the contribution of research, Buckingham, UK: Open University Press. Cross, R. T., & Price, R. F. (1992). Teaching science for social responsibility. Sydney: St. Louis Press. Désautels, J., & Larochelle, M. (1998). The epistemology of students: the “thingified” nature of scientific knowledge. In B. Frazer & K. Tobin (Eds.), International handbook of science education. Dordrecht, The Netherlands: Kluwer Academic Publishers. Driver, R., Asoko, H., Leach, J., Mortimer, E., & Scott, P. (1994). Constructing scientific knowledge in the classroom. Educational Researcher, 23, 5-12. Driver, R., Leach, J., Millar, R., & Scott, P. (1996). Young people’s images of Science. Buckingham, UK: Open University Press. Edwards, D., & Mercer, N. (1991). Common knowledge: the development of understanding in the classroom. London: Methuen. Hodson, D. (1993). Philosophic stance of secondary school science teachers, curriculum experiences, and children’s understanding of science: Some preliminary findings. Interchange, 24, 41-52. Jenkins, E. W. (1999). School science, citizenship and the public understanding of science. International Journal of Science Education, 21, 703-710. Layton, D., Jenkins, E., Macgill, S., & Davey, A. (1993). Inarticulate science? Perspectives on the public understanding of science and some implications for science education. Driffield, UK: Studies in Education Ltd. Leach, J. & Scott, P. (1999, August). Teaching and learning science: linking personal and sociocultural perspectives. Paper presented at the European Association for Research on Learning and Instruction, Göteborg, Sweden. Leach, J., Millar, R., Ryder, J., Séré, M-G., Niedderer, H., Paulsen, A. C., & Tselfes, V. (1998). Survey 2: Students’ images of science as they relate to labwork learning. Leeds, UK: Centre for Studies in Science and Mathematics Education. Leach, J., Millar, R., Ryder, J., & Séré, M-G. (2000). Epistemological understanding in science learning: the consistency of representations across contexts. Learning and Instruction, 10, 497-527.

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Leach, J., Lewis, J., Driver, R., & Wood-Robinson, C. (1996). Young people’s understanding of, and attitude to, “the new genetics”. Working Paper 3: Opinions on, and attitudes towards, genetic screening A: prenatal screening for cystic fibrosis. Leeds, UK: Centre for Studies in Science and Mathematics Education. Lewis, J., Leach, J., Driver, R., & Wood-Robinson, C. (1996). Young people’s understanding of, and attitude to, “the new genetics”. Working Paper 2: Understanding of basic genetics and DNA technology. Leeds, UK: Centre for Studies in Science and Mathematics Education. Mercer, N. (1996). The guided construction of knowledge. Clevedon, UK: Multilingual Matters Ltd. Popper, K. (1972). Objective knowledge: an evolutionary approach. Oxford: Clarendon Press. Rowell, J., & Dawson, C. (1983). Laboratory counterexamples and the growth of knowledge in science. International Journal of Science Education, 5, 203-215. Ryder J, & Leach, J (1999). University science students’ experiences of investigative project work and their images of science. International Journal of Science Education, 21, 945-956. Samarapungavan, A. (1992, April). Scientists’ conceptions of science: a study of epistemic belief. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA. Schoultz, J., Säljö, R., & Wyndhamn, J. (in press). Heavenly Talk: Discourse, artifacts, and children’s understanding of elementary astronomy. Human Development. Shamos, M. (1995). The myth of scientific literacy. New Brunswick, NJ: Rutgers University Press. Shen, B. (1975). Scientific literacy and the public understanding of science. In S. B. Day (Ed.), Communication of scientific information (pp. 44-52). Basel: S. Karger AG. Solomon, J., & Aikenhead, G. (1994). STS education: International perspectives on reform. New York: Teachers College Press. Tiberghien, A. (1996). Construction of prototypical situations in teaching the concept of energy. In G. Welford, J. Osborne, & P. Scott (Eds.), Research in science education in Europe: Current issues and themes (pp 100-114). London: Falmer Press. Wood-Robinson, C., Lewis, J., Driver, R., & Leach, J.(1996). Young people’s understanding of, and attitude to, “the new genetics”. Working Paper 3: Understanding the genetics of cells A: The discussion task. Leeds, UK: Centre for Studies in Science and Mathematics Education. Ziman, J. (1980). Teaching and learning about science and society. Cambridge: Cambridge University Press. Zohar, A. & Nemet, F. (1998, November). Fostering student’s argumentation skills through bio-ethical dilemmas in Genetics. Paper presented at ERIDOB (European Researchers in Didactics of Biology) conference, Göteborg, Sweden.

INTUITIVE RULES: THE CASE OF “MORE A – MORE B” RUTH STAVY, PESSIA TSAMIR & DINA TIROSH Tel Aviv University, Israel

Abstract. In our work we have observed that students tend to react similarly to a wide variety of conceptually unrelated situations in science and mathematics. We suggest that many students’ responses, which the literature describes as specific alternative conceptions, could be interpreted as evolving from a small number of intuitive rules. In this article we present and discuss one such rule: More A-more B that is reflected in students' responses to comparison tasks. Each of these comparison tasks asks to compare two objects, which differ in a certain salient quantity with respect to another quantity B ( or ). Our findings show that in such cases, students tend to respond inadequately, according to the rule More A (the salient quantity)- more B (the quantity in question). The findings also indicate that awareness of this intuitive rule may serve as a powerful tool for analyzing and predicting students' incorrect responses to given comparison tasks.

1. INTRODUCTION

A major finding of research on students’ conceptions and reasoning is that students often hold persistent conceptions, which are not in line with accepted scientific notions. There have been several explanations for this phenomenon, a dominant one of which has been the alternative conception paradigm. According to it the child takes an active, constructive role in the knowledge acquisition process and brings to the learning situation alternative, internally coherent, robust and persistent conceptions (e.g. Driver, 1994, Fischbein, 1987; Novak, 1984). It is suggested that alternative conceptions could be made more scientifically-oriented via a planned process of conceptual change (Driver, 1994; Posner, Strike, Hewson, & Gertzog, 1982) Recent research findings provide evidence that students tend to respond inconsistently to tasks related to the very same mathematical or scientific concept (Clough & Driver, 1986; diSessa, 1993; Noss & Hoyles, 1996; Nunes, Schliemann, & Carraher, 1993; Tirosh, 1991). This challenges the alternative conception paradigm that perceives students alternative conceptions as internally consistent. In our work in science and mathematics education, we have observed that students react in similar ways to a wide variety of conceptually non-related tasks that differ with regard either to their content area and/or to the required reasoning, but share some common, external features. We have so far identified four types of responses, two related to comparison tasks (More A - more B and Same A - same B), and two to subdivision tasks (Everything comes to an end and Everything can be divided endlessly). We suggest that these responses are specific instances of a small number M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 217-231. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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of intuitive rules that direct our responses in many situations. In this paper we describe and discuss the first intuitive rule “More A -more B”. The rule “More A - more B” is often used in carrying out comparison tasks. We shall present some examples of the use of this rule in various areas in science and mathematics education. The first section discusses equality situations and the second addresses inequality situations. 2.

EQUALITY SITUATIONS

The cases that are grouped under this title involve situations in which two systems differ in one quantity (quantity A) but are equal in another quantity (quantity B). Subjects are asked to compare the two systems with regard to quantity B. Clearly, the use of the rule “More A - more B" in these cases leads to incorrect responses. We shall describe instances of the use of this rule when the equality in quantity B is: (1) Directly observable, (2) logically deducible, or (3) scientifically deducible. 2.1.

2.1.1.

Directly Observable Equality

Angle

Angle is a main concept in geometry. It is often defined as the union of two distinct rays, which have a common endpoint. Reference to this concept is made from very early on in school (in many countries even at the kindergarten level). One may therefore ask: How do people make informal judgments about the equality of angles? Let us refer to the following drawings:

In both these drawing (Figure 1), angles and are vertical, and thus equal. The equality of the two vertical angles, and in the first drawing appears as selfevident. Indeed, when this drawing was presented to eighth and ninth grade students (aged 14-15), and they were asked to determine if angle is smaller than, equal to or larger than angle 95% of them argued that the two angles were equal and the

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level of intuitive acceptance of this judgment was extremely high (Fischbein, Tirosh, & Hess, 1979). In another study, the very same drawing was presented to students in grades K, 2, 4, 6, and 9 and they were asked the same question. Most students at these grade levels (84%, 78%, 91%, 91% and 99% respectively) correctly argued that angles and were equal (Tsamir, Tirosh, & Stavy, 1997). The immediate impression one has when looking at angles and in the second drawing is that angle is larger. When the second drawing was presented to the same group of K, 2, 4, 6, 9 grade students, and they were asked the same question, the percentages of students who knew that these angles are equal were substantially lower (13% 12% 62%, 68% and 82% respectively). A substantial number of the younger students (grades K to 4) and some of the older students argued that angle was larger. This claim was accompanied by the explanation that “angle is larger because its lines are longer”. In this case the difference between the two angles in quantity A (the perceived length of the arms) affected students’ judgment of quantity B (the size of angles and ). Perceptual effects of the length of the arms on students’ judgments was reported in several other studies investigating the development of students’ conception of angle (e.g., Foxman & Ruddock, 1984; Noss, 1987). 2.1.2.

Time

Children's understanding of the concept of time is often analyzed via their ability to compare the duration of pairs of events. In one of Piaget’s experiments (Piaget, 1969) he presented children with two figures, one large and one small, that ran a race starting from a common point. Both figures ran for the same duration, but the larger figure ran faster and thus covered a larger distance. Piaget found that young children (aged 4-9) often argued that “the large figure took more time”. These responses were explained by Piaget as follows: When comparing the duration of two events, children often make their judgments according to only one of two relevant factors: speed or distance. As young children are unable to coordinate the various variables involved, they determine time according to only one of them - in this case distance. According to our thesis concerning the role of the intuitive rule “More A - more B”, we may alternatively posit that when young children are asked to compare the duration of two events they often base their judgments on scientifically irrelevant perceptual factors. In this study one of the participating figures was larger than the other. This larger figure also was the one that traveled further. Students’ responses to the effect that the larger figure traveled for more time may well have been influenced not only by the observed difference in distance, but also by the difference in size of the two figures. Confirmation for this comes from a study on children’s conception of time, conducted by one of our students (Hakham-Aharon, 1997). She presented children in grades K-6 with two tasks, one tested the effect of the size of a moving object, and the other, the effect of the speed/distance traveled. She used Lego trains in both these tasks. In the first task, the children were first presented with two identical Lego

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trains. The two trains travelled at the same speed on two parallel tracks. They were connected to the same battery and the same switch was used to turn them on and off. The researcher turned the switch on, and turned it off when the trains approached the end of the tracks (after traveling about one meter). The researcher explicitly showed and emphasised that the switch controlled both trains. The children were asked if the trains reached the end of the rail at the same time, and if not, which came first. All children at all grade levels answered, correctly, that both trains arrived at the same time to the end of the tracks, explaining that “the trains are the same”. Then, in front of the children, the researcher rearranged the Lego bricks of one of the trains, making it taller than the other train. Subsequently she asked: “If I now turn on the switch and let the trains travel, will they reach the end of the tracks together?” Clearly, the change in the height of the train neither affect the time it moves nor its speed, as both trains are controlled by the same switch. A substantial number of participants argued, in line with the intuitive rule “More A - more B” that “the taller train is faster” (40%, 54%, 48%, 34% and 50% in grades K, 1, 2, 4, 6, respectively) or “the shorter train is faster” (29%, 23%, 26%, 9% and 13% in grades K, 1, 2, 4, 6, respectively). Here, A is the height of the train and Bthe time it travels ( and relate to the regular and to the modified trains respectively). Typical responses were: “The taller train travels faster because it is taller/heavier”, or “The shorter train travels faster because it is shorter/lighter”. Children in the sixth grade related to “scientific” factors such as air-resistance and balance to justify their incorrect judgments. For instance: “The train with the tower is taller, therefore the air hinders its movement.” These results show that indeed, students’ responses to the time duration task were affected not only by the observed difference in distance, but also by the differences in size of the two moving objects. Another series of studies, which was conducted by Levin (1977, 1979, 1982) on the nature and the development of time concept in young children, also confirm that when children are asked to compare two equal duration, they are affected by perceptual factors. In one of these studies (Levin, 1982), the researcher asked nursery school children and kindergartners to judge whether two lights were lit for the same duration, or which of the two had been on for longer. The lights were switched on for the same duration but differed in size and/or brightness. Levin’s findings indicated that children tended to attribute longer duration significantly more often to the larger than to the smaller light, to the brighter than to the dimmer light, and to the larger and brighter than to the smaller and dimmer light. She concluded that this phenomenon may be based on a mediation mechanism of “Any more is more time”, which could be regarded as an application of our rule with regard to time. 2.2.

Logically Deducible Equality

In many comparison situations, the equality in quantity B is not directly observable though it can logically be deduced through concrete or formal operational schemes. We shall show some examples demonstrating that in such situations students are also affected by the intuitive rule “More A - more B.”

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We shall first refer to conservation, one of the major concrete operational schemes. In a typical conservation of quantity tasks children are asked to compare the (equal) amounts of water in the two differently shaped cups. Children up to about age five or six pay attention only to the relative heights of the water in the two cups, arguing that “there is more water in the taller cup” (Piaget & Inhelder, 1974). This well-known task, and other, similar ones are often used in an attempt to determine students' conceptions of certain concepts (area, weight, volume, etc.). In this type of study, children often argue that “More A (the height of water in the cups) means more B (amount of water)”. According to our thesis such reasoning could be attributed to the application of the intuitive rule “More A - more B”. In these tasks, unlike the ones presented in the previous section, the children were aware of the equality of the two systems in respect to quantity B (amount of water) at the initial stage of the experiment. Yet, unlike in the previous section, after the manipulation, the equality in quantity B could no longer be directly observed, but could be logically derived through the use of the conservation scheme. We shall describe several instances of the use of this intuitive rule in conservation tasks. In all of them, the equality in quantity B is logically deducible via the conservation scheme. 2.2.1.

Surface Area

Livne (1996) presented biology majors in grades 10-12 (ages 16-18) with the following task. Two opposite faces of a rectangular-shaped box were folded in the way described in Figure 2.

Is the surface area of the unfolded box larger/smaller/equal to the surface area of the folded box? Explain your choice.

Livne found that only 60%, 58%, and 48% of the biology majors in grades 10, 11, and 12 respectively conserved the surface area. About a third of the students in each of these grades claimed that the surface area of the unfolded box was larger than that of the folded one. A typical explanation was: “The unfolded box is longer, therefore its surface area is larger.” Others, who claimed that the surface area of the folded box was larger, explained that “The more folds - the larger the surface”. Clearly, these two types of explanations are instances of the use of the rule “More A (length of box/number of folds) - more B (surface area).

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R. STAVY, P. TSAMIR & D. TIROSH Expansion

Megged (1978) studied children’s understanding of the invariance of weight during the process of heating water.

In this case, as can be seen in Figure 3, the volume of heated water is larger than that of unheated water. The weight, however, remains constant. Many children aged six to ten argued that “the heated water is heavier because its volume is larger.” Proportion, unlike conservation, is a formal, operational schemes. It is widely used in mathematics, science and everyday life. Proportion could be defined as an equality of two ratios, namely, Piaget and his collaborators and many others (e.g. Piaget & Inhelder, 1967) extensively studied the development of proportional reasoning. Many common responses to various tasks involving proportional reasoning could be reinterpreted in light of the intuitive rule: More A - more B. Here we relate to fractions and concentration tasks. 2.2.3.

Fractions

Research revealed that when students were asked to compare two equal fractions, they often concluded that one of them was larger since its top and bottom numbers are larger (e.g., 4/6 is bigger than 2/3 because 4 is bigger than 2 and 6 is bigger than 3). 2.2.4.

Concentration

Stavy, Strauss, Orpaz and Carmi (1982) presented children with two cups of sugar water of the same concentration. One cup was full of water and two teaspoons of water were added and mixed in. The other cup was half full of water and one teaspoon of water was added and mixed in. The children were asked whether the taste of the sugar water in the two cups would now be the same or different, and if it was different in which cup did they expect the sugar water was sweeter. It was found that the majority of the children aged five to eight claimed that the cup with more

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sugar was sweeter or that the cup with more water was sweeter or that the cup with more water and more sugar was sweeter. In all cases included in this section, the equality could be deduced by the logical schemes of conservation or proportion. However, many students incorrect responses to these tasks share the structure “More A - more B”. In the conservation case, the use of the rule was probably elicited by salient differences in a another quantity. In respect of proportion, the use of the rule could be elicited either by relating to the nominator or to the denominator or to both, as both changed in the same direction. Interestingly, it seems that the intuitive rule could be activated not only by obvious perceptual differences, but also by salient differences between symbols associated with perceptual images (e.g., numbers). 2.3.

Scientifically Deducible Equality

In this section we described three comparison tasks, taken from different scientific domains. In these cases, students were asked to determine whether two systems are equal in a certain quantity. The systems were equal with regard to the related quantity. This equality could neither be perceptually observed nor logically derived but could only be scientifically deduced. In these cases, many students were prompted by perceptual differences in another quantity and argued that “More A more B”. 2.3.1.

Free Fall

The following task is often presented in physics lessons: Two matchboxes, one full of sand and the other empty, are held at the same height above the ground, in the same manner. They are both dropped at a specific instance. Will the matchboxes hit the ground at the same time? If not, which will hit the ground first?

Children and many adults claim that the heavier matchbox will be the first to hit the ground. Resembling tasks were presented to various groups of students, including college students in first year physics, and similar reactions were reported (Gunstone & White, 1981). However, when the experiment is carried out, it is obvious that the boxes reach the ground at the same time. The response that the heavier matchbox will reach the ground faster is often interpreted as an evidence of an alternative conception of free fall according to which the falling time of an object is directly related to its weight. We interpret this response as an instance of the intuitive rule More A (weight) - more B (speed). 2.3.2.

Infinite Sets

Consider the following two line segments, which are described in Figure 4:

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In your opinion, is the number of points in line segment CD smaller than/equal to/larger than/ the number of points in line segment AB? Explain your answer.

According to the Cantorian set theory, which is the most commonly used theory of infinity today, any two line segments contain the same number of points. If you ask students and adults to answer this question, you will realize that many claim, with great confidence, that: “Line segment CD contains more points than line segment AB, as it contains all points in line segment AB and additional ones” (Tirosh, 1991). This response was interpreted as an evidence of an application of students’ ideas of finite sets to infinite ones. We interpret this response as an application of the intuitive rule More A - more B, to this specific task. We argue that here, much like in the case of the free fall, subjects are impressed by salient, scientifically irrelevant information and consequently respond in line with the intuitive rule More A (longer segment) - more B (more points). 2.3.3.

Size of Cells

Consider the following two tasks: Is the size of a muscle cell of a mouse bigger than/equal to/ smaller than/ the size of a muscle cell of an elephant? Yes/No. Explain your choice. A kitten grows into an adult cat. Is a liver cell of a kitten bigger than/equal to/smaller than/ a liver cell of an adult cat? Yes/No. Explain your choice.

The correct answer to both these tasks is “equal to”. In fact, most cells of most organisms from minuscule nematode worms to enormous whales, are roughly 10 micrometers in diameter. These two tasks were submitted to about 60 students each in grade levels 7 to 12. Figure 5 shows that the majority of the younger students (Grades 7 and 8) incorrectly claimed that larger animals have larger cells. Common justifications in all grade levels were: “According to the dimensions of elephants and those of mice, it is obvious that the muscle cells of mice are smaller than those of elephants”; “The mouse is smaller than the elephant”; “The kitten cells grow as it grows”; “The liver of the kitten grows and consequently its cells have to grow”.

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3. INEQUALITY SITUATIONS

In the previous sections we presented examples of comparison situations in which many students responded in accordance with the rule: “More A - more B”. The application of this rule in all these cases led them astray: they concluded that because In all these situations this conclusion was erroneous because In this section we relate to two other types of comparison situations in which the application of the rule “More A - more B” leads to incorrect judgments: 1. Inverse ratio between quantities A and B ( but ). 2. The relations between A and B are not fixed. This happens when and for certain intervals, yet not in others (in these intervals either or ), or when there is no fix relationship between A and B. 3.1.

Inverse Ratio Between A and B

Consider the following two tasks: 1)

Is

smaller than/equal to/larger than ?

2)

Is 0.1 smaller than/equal to/larger than 0.01?

Clearly, in both cases, the first fraction is larger than the second one. However, young children tend to argue that the second fraction is larger: “3 is larger than 2, therefore 1/3 is larger than 1/2” (e.g., Pitkethly and Hunting, 1996), or, similarly, that “hundreds are bigger than tens, therefore 0.01 is larger than 0.1” (Nesher & Peled, 1986). Obviously, these responses are in line with the intuitive rule: “More A - More B”. Consider another task: Consider the following two sugar solutions: Solution I is prepared by mixing one teaspoon of sugar into one cup of water.

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R. STAVY, P. TSAMIR & D. TIROSH Solution II is prepared by mixing the same sized teaspoon of sugar into half a cup of water: Is the sweetness of these two solutions the same or different? If different, in which cup is the sugar water sweeter?

Studies exploring students’ responses to this task reported that some young children (aged 4-8) claimed that “the more water - the sweeter” (e.g., Stavy, 1981). A more frequent response, however, in these cases is “The same (amount of sugar) - The same (sweetness).” Such “Same - same” responses are discussed elsewhere (Stavy & Tirosh, 2000). These three tasks are often referred to as “inverse ratio tasks”. In such tasks, students are asked to compare two ratios (e.g., fractions, concentration and temperature). The numerators, in each task, are the same while the denominators are different. In these cases, some young children who had not yet acquired the proportion scheme incorrectly claimed that “The larger the denominator - the larger the ratio”. The application of the intuitive rule “More A - more B” is manifested to a larger extent in the first two tasks. A possible explanation of this difference in the application of the rule is that in the first two tasks the differences in the denominators are very salient so that the “equal” answer seems impossible. Therefore, children who have not yet acquired the proportion scheme can hardly claim anything else. However, in the concentration task, the similarity between the numerators (one teaspoon of sugar) is salient, and is associated with the quantity children are asked about (sweetness). Consequently, many students argue, incorrectly, for equality. The same behavior (responses of the type: “larger denominator- larger ratio” was reported by researchers who studied the development of logical schemes (i.e., Noelting, 1980a, 1980b; Shayer & Adey, 1981; Strauss & Stavy, 1982) 3.2.

3.2.1.

The Relationship Between A and B is Not Fixed

Temperature

Figure 6 describes the rise of temperature of water with time of heating. Several studies conducted in different countries report that students in different grade levels tend to argue that “The longer you heat, the higher the temperature” (e.g., Andersson, 1979). Children know, from their daily experience, that the temperature of an object rises when heated (i.e., “The more you heat - the warmer it gets”). This experience is consistent with the intuitive rule: “More A - more B”. The first part of the graph describes this linear relationship. Children assume that this relationship between duration of heating and temperature will continue, namely that “the more you heat - the higher the temperature”. There is no reason for them to assume that the relationship breaks down at a certain point. In fact, only formal knowledge related to heat, temperature and change in the state of matter would lead to a correct response.

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Other examples in which the relationship between A and B is not fixed can be found in other contexts in science, including growth curves of populations in biology and sociology, velocity of enzymatic reaction with concentration of substrate in biochemistry, just to mention few. Similarily, in mathematics some properties hold for certain number systems but break down when the realm of numbers is extended. For instance, when comparing two natural numbers by means of the number line, one could argue that the number that is further removed from zero is the larger number (the further - the larger). However, when applied to real numbers, this rule may incorrectly lead to, for instance, a statement that -5 is larger than -2 as “it is further from zero”. The rule “the further - the larger” holds for all natural numbers but not for all real ones.

3.2.2.

Mathematical Expressions

Some of our collaborators designed specific tasks to examine the role of the intuitive rule “More A - more B” in students’ responses to comparison tasks involving mathematical expressions (Kopelevich, 1997; Rapaport, 1998; Shohet, 1994; Zagury, 1997). Here we shall report only on some of their findings. Rapaport presented students in grades 9 to 12 with comparison tasks of algebraic expressions. Three such tasks were as follows:

Table 2 shows that the vast majority of the students in each of these grade levels gave incorrect judgments to these tasks. These responses are in line with the rule “More A - more B”. Common justifications were: “4 is larger than 2, therefore 4x is

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larger than 2x”; “3 is larger than 2, therefore ”; “5 is greater than 3, therefore is greater than ”; “I reduced the x, and compared the numbers”. These students did not consider the possibility of negative values of x, although they have learnt about negative numbers in schools.

4.

DISCUSSION AND EDUCATIONAL IMPLICATIONS

In this paper we related to many content domains in both science and mathematics. We have shown that students supplied “More A - more B” responses to various scientific and mathematical tasks. How can this behavior be explained? All the tasks described so far are comparison tasks. In each of them, the student is asked to compare two objects (or two systems) which differ in a certain, salient quantity The student is asked to compare the two objects or systems with respect to another quantity B, where is not greater than (that is, or ). We have shown that comparison tasks in which the two objects or systems are perceptually different with respect to a certain quantity A elicit a specific pattern of response ( because ). We believe this response is directly activated by immediate perceptual differences in quantity A (e.g., length, mass, etc.) or by salient differences between symbols associated with perceptual images in this quantity (e.g., numbers). Our claim is that a subject’s cognitive system is affected by the perceptual differences in quantity A, so that s/he comes to regard this quantity as the significant one in the problem. It seems that our cognitive system tacitly assumes that the two objects differ in the same direction as quantity A with regard to other quantities as well. This assumption could evolve from a more general tendency to extrapolate. In the case of the intuitive rule “More A - more B”, the response is extrapolated from Even though this extrapolation is valid in many situations it is not in others. We regard “More A - more B” as a basic, logical cognitive scheme that is undiscriminantly used, resulting in overgeneralizations. Our interpretation can account for many of the observed, alternative conceptions in science and mathematics education. Two main strengths of this approach are: (1)

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it accounts for many of the observed, alternative conceptions in science and mathematics education, and (2) it has a predictive power. The predictive power of the intuitive rules seems to have a great pedagogical value. Teachers can use their knowledge about the intuitive rules in various ways. For instance, they can create tasks that are most likely to be “easy” (i.e. the correct response is in line with the intuitive rule) or “difficult” (i.e. the correct response clashes with the intuitive rule). Such categorization of tasks could then serve to develop sequences of instruction suitable for various teaching approaches. Here we shall briefly demonstrate how knowledge about the intuitive rules could assist teachers in constructing a sequence of instruction in line with the conflict teaching approach. In the conflict teaching approach, students are first given a task known to elicit an incorrect response, and next are presented with a situation that contradicts their initial response. Such a presentation may raise students’ awareness of the inadequacy of their initial response (e.g., Piaget, 1980). Applied to intuitive rules, a conflict can be generated by first presenting students with a “difficult” task, known to forcefully trigger one of the intuitive rules, leading to incorrect response. Then, contradiction may be created in several ways, for instance, by presenting them with an contradicting experimental results. For instance, in respect to free-fall, Myers (1998) presented students in Grade 8 with two identical, plastic boxes, one filled with small stones and the other empty. She held the boxes at the same height above the ground, in the same manner. The students were asked to predict whether the boxes would hit the ground at the same time, and if not which would hit the ground first (assuming that the boxes were dropped at the same instant). Myers found that about half of the participants incorrectly predicted that “the heavier (the box) – the faster (it falls)”. Then, she dropped the boxes in front of the students, asking them to describe what they saw. Later, a questionnaire was administered including essentially the same free-fall task, albeit with two balls, identical in size and shape but differ in weight. Practically all students, who previously observed that the two boxes hit the ground at the same time, responded correctly. In this case the conflict was created by presenting students with evidence that could directly be observed. These evidence led them to change their initial responses to ones that are in line with the scientific concepts. It is important to note that in many cases, presenting students with such contradicting evidence are not so effective. Furthermore, there are cases in which it is impossible to present students with direct evidence that contradict their initial response. In this chapter we presented one way to apply knowledge about the intuitive rules to science teaching. Other attempts are described in several, recent publications (e.g., Stavy & Tirosh, 2000; Tsamir, Tirosh, Stavy, & Ronen, 2000). Since this approach has only recently been suggested, more efforts should be invested in studying its potential to science and mathematics education. REFERENCES Andersson, B. (1979). Some aspects of children’s understanding of boiling point. Cognitive Development Research Seminar. Leeds, UK: University of Leeds.

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Clough, E. E., & Driver, R. (1986). A study of consistency in the use of students’ conceptual frameworks across different task contexts. Science Education, 70, 473-496. Driver, R. (1994). Making a sense of secondary science. London: Routledge. Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Dordrecht, The Netherlands: Reidel. Fischbein, E., Tirosh, D., & Hess, P. (1979). The intuition of infinity. Educational Studies in Mathematics, 12, 491-512. Foxman, D., & Ruddock, G; (1984). Concepts and skills: Line, symmetry and angle. Mathematics in School, 13, 9-13. Gunstone, R. F., & White, R. T. (1981). Understanding of gravity. Science Education, 65, 291-299. Hakham-Aharon, A. (1997). The influence of the intuitive rule “more of A – more of B” on children’s concept of time. Unpublished Master’s thesis, Tel Aviv University, Israel. (In Hebrew) Levin, I. (1977). The development of time concepts in young children. Reasoning about duration. Child Development, 48, 435-444. Levin, I. (1979). Inference of time related and unrelated cues with duration comparisons of young children: Analysis of Piaget’s formulation of the relation of time and speed. Child Development, 50, 469-477. Levin, I. (1982). The nature and development of time concepts in children: The effects of interfering cues. In W. J. Friedman (Ed.), The developmental psychology of time (pp. 47-85). New York: Academic Press. Livne, T. (1996). Examination of high school students’ difficulties in understanding the change in surface area, volume and surface area/volume ratio with the change in size and/or shape of a body. Unpublished Master’s thesis. Tel Aviv University, Israel. (In Hebrew) Kopelevich, S. (1997). Wrong use of the intuitive rules “more of A – more of B” in power. Unpublished Master’s thesis, Tel Aviv University, Israel. (In Hebrew) Megged, H. (1978). The development of the concept of density among children ages 6-16. Unpublished Master’s thesis. Tel Aviv University, Israel. (in Hebrew) Myers, S. (1998). Effects of conceptual conflicts on using the intuitive rule ‘more of A – more of B’ in grade students. Unpublished Master’s thesis, Tel Aviv University, Israel. (In Hebrew) Nesher, P., & Peled, I. (1986). Shifts in reasoning. Educational Studies in Mathematics, 17, 67-79. Noelting, G. (1980a). The development of proportional reasoning and the ratio concept. Part I: The differentiation of stages. Educational Studies in Mathematics, 11, 217-253. Noelting, G. (1980b) The development of proportional reasoning and the ratio concept. Part II: Problem structure in successive stages: Problem-solving strategies and the mechanism of adaptive restructuring. Educational Studies in Mathematics, 11, 331-336. Noss, R. (1987). Children’s learning of geometrical concepts through LOGO. Journal for Research in Mathematics Education, 18, 334-362. Noss, R., & Hoyles, C. (1996). Windows in mathematics education. Dordrecht, The Netherlands: Kluwer Academic Publishers. Novak, J. D. (1984). Learning how to learn. Cambridge: Cambridge University Press. Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge: Cambridge University Press. Nunez, R. (1993). Big and small infinities: Psycho-cognitive aspects. Proceedings of the 17th International Conference Psychology of Mathematics Education (Vol. 2, pp. 121-128). Ibaraki, Japan. Piaget, J. (1969). The child’s conception of time. New-York: Basic Books. Piaget, J. (1980). Experiments in contradiction. Chicago, IL: University of Chicago Press. Piaget, J., & Inhelder, B. (1974). The child’s construction of quantity. London: Routledge & Kegan Paul. Piaget, J., & Inhelder, B. (1967). The child’s conception of space. New York: Norton. Posner, G. J., Strike, K. A., Hewson, P. W., & Gertzog, W. A. (1982). Accommodation of a scientific conception: Towards a theory of conceptual change. Science Education, 66, 211-217. Rapoport, A. (1998). Use of the intuitive rule “more of A – more of B” in comparing algebraic expressions. Unpublished Master’s thesis. Tel Aviv University, Israel. (In Hebrew) Shohet, N. (1994). The dominance of the natural numbers in high school students reference to algebra. Unpublished Master’s thesis, Tel Aviv University, Israel. (In Hebrew) Shayer, M., & Adey, P. Towards a science of science teaching: Cognitive development and curriculum demand. London: Heinemann Educational Books.

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Stavy, R., Strauss, S., Orpaz, N., & Carmi, G. (1982). U-shaped behavioral growth in ratio comparisons, or that’s funny I would not have thought you were u-ish. In S. Strauss & R. Stavy (Eds.), U-Shaped behavioral growth (pp. 11-36), New York: Academic Press. Stavy, R., & Tirosh, D. (in press). How students (mis-)understand science and mathematics: Intuitive rules. Teachers College, Columbia University, USA. Strauss, S., & Stavy, R. (1982). U-shaped behavioral growth: Implications for theories of development. In W. W. Hartup (Ed.), Review of child development research (pp. 547-599). Chicago, IL: University of Chicago Press. Tirosh, D. (1991). The role of students’ intuitions of infinity in teaching the Cantorian Theory. In D. Tall (Ed.), Advanced mathematical thinking (pp. 199-214). Dordrecht, The Netherlands: Kluwer Academic Publishers. Tsamir, P., Tirosh, D., & Stavy, R. (1997). Intuitive rules and comparison tasks: The grasp of vertical angles. In A. Gagtsis & G. Markides (Eds.), Proceedings of the first Mediterranean conference: Mathematics education and applications (pp. 269-276). Nicosia, Cyprus. Tsamir, P., Tirosh, D., Stavy, R., & Ronen, I. (2000). The intuitive rules theory, a diagnostic tool in mathematics and science education. In A. Gagtsis & G. Markides (Eds.), Proceedings of the second Mediterranean conference on mathematics education (Vol. 1, pp. 327-346). Nicosia, Cyprus. Zagury, S. (1997). Use of the intuitive rule “more of A – more of B” in ordering negative numbers. Unpublished Master’s thesis, Tel Aviv University, Israel. (In Hebrew)

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CONCEPTUAL CHANGE IN MATHEMATICS: UNDERSTANDING THE REAL NUMBERS

KAARINA MERENLUOTO & ERNO LEHTINEN University of Turku, Finland

Abstract. In this chapter some special features of mathematical knowledge are considered in order to better understand the nature of conceptual change in this domain. In learning mathematics, every extension to the number concept demands, not only accepting new concepts, but new logic as well. This new logic more or less contradicts the prior fundamental logic of natural numbers. Therefore, misconceptions and learning difficulties are possible at every enlargement. To understand the problems students have in the conceptual change pertaining to the enlargement of the number concept a test was administered to 564 students (mean age 17.3) from randomly selected Finnish upper secondary schools. The test included identification, classification and construction problems in the domain of rational and real numbers. We found that changes of number conceptions, which was measured through questions in the domain of rational and real numbers, was not adequately carried out by the majority of the students who had just finished their first calculus class. While working on the tasks on the more advanced numbers they spontaneously used the logic and general presumptions of natural numbers or based their answers on their everyday intuition. The number concept of the majority of these students seemed to be based on the spontaneous logic of natural numbers but had also fragmented pieces of more advanced numbers. The students tended to overestimate the certainty of their answers when they used the logic of natural numbers even if it was erroneous.

1.

INTRODUCTION

The crucial idea in the theory of conceptual change is the radical reconstruction of prior knowledge which is not adequately taken into account in traditional teaching. In educational contexts, mathematics is considered as forming a hierarchical structure in which all new concepts logically follow from prior ones, which allows students to enrich their knowledge step by step (Dantzig, 1954). The transitions from the domain of natural numbers to the domains of more advanced ones are often treated quite implicitly in the teaching process. These extensions are primarily treated as enlargements which make new kinds of operations possible. Whereas, even from the mathematical point of view, they are more like new kinds of constructions or revisions. The set of natural numbers, for example, is understood as a subset of real numbers or even “thrown out” in the construction of enlargement and replaced by corresponding more advanced numbers (Landau, 1960). 1. 1.

The Real Numbers

The notion of real numbers is one of the most complex and profound concepts in mathematics. As constructs of advanced mathematics they are purely abstract and M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 233-257. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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totally inaccessible to our senses and possible to see only with our mind’s eye (Sfard, 1991). Mathematicians have different kinds of rigorous constructs for these numbers, the most familiar are those where real numbers are presented as limits of a sequence or a cut of the number line. These constructs are, however, relatively new in the history of mathematics: the rigorous definition for real numbers was developed at the end of century. The core problem in this slow development of the concept was the dichotomy of continuous and discrete quantities. The fundamental idea of numbers since Antiquity was their discrete nature as a collection of objects, whereas the continuous quantities were not measured by numbers but by lines. Tobias Dantzig, a mathematician, describes the dichotomy between these with musical terms, saying: The harmony of the universe knows only one musical form – the legato; while the symphony of number knows only its opposite – the staccato. All our attempts to reconcile this discrepancy are based on the hope that an accelerated staccato may appear to our senses as legato. (Dantzig, 1954, p. 169)

Real numbers have their far reaching sources in two of the most obvious aspects of nature – multiplicity and variability – the possibility of repetition and continuity (Boyer, 1959). The concept of limit was already used in Antiquity, for example in the so-called exhaustion method used by Archimedes, but because of the dichotomy between the continuous and discrete it led to paradoxes (Boyer, 1959; Dantzig, 1954) which disturbed mathematicians’ still in century (Russell, 1993). In the century Newton and Leibniz, the inventors of differential calculus, defined the concept of continuity but these definitions were based on the intuition of motion. Newton’s theory dealt with continuous quantities but postulated the infinite divisibility of space and time, Leibniz justified the limit by continuity. Their theories were, however, open to the same kind of critique as in earlier centuries. Numbers had not become sufficiently abstract and symbolic to be used for defining the concept of continuity. The vague intuition of motion, however, although fruitful in having suggested the investigations which produced the calculus, was found, in the light of further development in thought, to be quite inadequate and misleading in the history of the concept of continuity (Boyer, 1959, p. 295). The development from the concept of limit based on continuity, to the rigorous definitions where continuity is based on limit, took two hundred years. Moreover when the rigorous definition of mathematical continuity was finally at hand, at the end of the century, it was based not on the intuition on motion, but on the logically developed theories of real numbers (Boyer 1959, p. 293). The theory of real numbers integrated two fundamentally different kinds of knowledge: the discrete and the continuous. And it succeeded because the theory was not based on the intuition of reality but on what was logically consistent. In other words this theory was not formed by enriching the prior thinking of continuity with the thinking of numbers, but by radically changing the quality of argumentation. In the present curriculum and discussion the system of numbers is divided into sections according to the different types of numbers. But historically there was no such distinction before the development of the theory of real numbers made it necessary. By 1800 various types of numbers had become so familiar that even

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though they had no logical basis there was not too much concern about the soundness of their properties. Thus the theories of natural numbers, irrational numbers and real numbers all evolved over roughly the same period: at the end of the nineteenth century. And when these rigorous definitions were formed they were defined in reverse order compared to the teaching order of the ordinary curriculum (Kline, 1980). From this perspective the seemingly complete hierarchy of numbers in school mathematics is a formal system defined from today’s perspective and does not correspond to the authentic cognitive construction of mathematical theories over the course of history (Boyer, 1959; Kline, 1980). Although attempts to draw conclusions from the collective development of mathematical concepts to the individual problems of learning should be careful, the history of these concepts indicates that a gradual enrichment in the concept development is not always possible. From the point of view of conceptual change the long development period of these concepts is due to the fact that on the advanced level of mathematics the initial thinking of numbers has been integrated with the knowledge belonging ontologically to another domain in which the characteristic feature is continuity (Boyer, 1959; Kline, 1980; see also Rudin, 1953). In this integration the historical dichotomy of the continuous and the discrete is combined to an abstract theory of real numbers which is based on the logical consistency of thoughts. Because of that integration the process of the conceptual change in enlarging the number concept to the domain of real numbers is a particularly radical one: the number concepts before and after the change are incommensurable. These concepts have a long and complicated history and are difficult for students today (Tall & Schwartzenberger, 1978; Tall & Vinner, 1981; Sierpinska, 1987; Cornu, 1991; Dreyfus, 1991; Williams, 1991; Kaput, 1994; Fischbein, Jehiam, & Cohen, 1995; Lehtinen, Merenluoto, & Kasanen, 1997; Szydlik, 2000). 1.2. The Initial Thinking of Numbers

There is evidence to claim that mathematics is a distinct domain already in the innate cognitive mechanism (Gallistel & Gelman, 1992). Gallistel and Gelman (1992) argue that infants’ numerically relevant responses to sets of inputs are supported by a skeleton of nonverbal counting and relate to numeral reasoning principles. The term “domain-specific” refers to a domain that consists of a given set of principles, the rules of their application and the entities to which they apply (Gelman, & Brenneman, 1994). Many researchers (Starkey, Spelke, & Gelman, 1990; Spelke 1991; Carey & Spelke, 1994; Gelman & Brenneman, 1994, KarmiloffSmith, 1995) argue that human reasoning is guided by a collection of innate domainspecific systems of knowledge. According to this hypothesis, each system is characterised by a set of core principles that define the entities covered by the domain and support the reasoning about those entities. The fact that this “mechanism” concerning the development of numbers is based on the idea that quantities are separate and discrete is important to this article. This separate nature of small quantities seems to be one of the basic ontological presumptions of the

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naive framework theory of numbers. By the terms separate and discrete we mean the instinctive feeling that there is a one-to-one relationship between the numbers and physical objects and that there is always a “next number”, “next quantity” (Hartnett & Gelman, 1998) and some kind of space between them. This quality of numbers is also found in the writings of Aristotle (see Boyer, 1959). The notion of the next number or a successor is a fundamental feature in the set of natural numbers (Landau, 1960) and together with the principle of one-to-one correspondence with objects they “are woven into the very fabric of our number system” (Dantzig, 1954, p.9). When children learn to recite number words they form specific theories where they find the one to one correspondence of number words and the objects in the counting process. In the experiences of the everyday cultural context they develop beliefs that for every object there is a next object. In formal mathematical instruction these beliefs and prior conceptions are strengthened and it is also necessary to strengthen them. The very fundamental idea of a successor is necessary for learning the notion of natural numbers. However it seriously conflicts with the understanding of the very character of both rational and real numbers (Kieren, 1992). In the domains of rational and real numbers the principle of a successor is not defined, but infinite successive division is possible. The problems resulting from the ontological shifts (Chi, Slotta, & de Leeuw, 1994) in learning begin very early because fractions are learned very early in the course of mathematics curriculum (Kieren, 1992). Because the notion of a successor is still always valid whenever operating with natural numbers and integers, this enlargement demands a construction of a parallel mental model for “numbers” and the ability to consciously move between these different models. Innate principles can foster learning but they can also serve as barriers to learning. If what is to be learned does not share the same basic assumptions as the available knowledge, then there is a high risk that the information meant to foster new learning will be assimilated to what is known and, therefore, will be misinterpreted (Gelman & Brenneman, 1994). Hartnett and Gelman (1998) found that even 5-7 year old children were able to discuss that it is not possible to write the largest natural number by relying on this kind of intuition of the next number. Further Wistedt and Martinsson (1996) found that after a short philosophy course, even 11 year-olds were able to discuss successive division on quite a high level of understanding. The children had considerable difficulties, however, when the structure of prior knowledge did not support the new information to be learned. This was the case when children were asked to sort fractions, were they were prone to use the same logic they had learned to use in sorting natural numbers (Hartnett & Gelman, 1998; Stafilidou & Vosniadou, 1999). According to the Neuman’s study (1998) this kind of mistaken transfer from natural numbers lead to the result that only a few seventh graders understood that there is an infinite number of fractions between any two different fractions. These procedures were difficult because of the constraining nature of the intuition of the “next” number. Another problem is that the concepts of advanced mathematics there is a high level of abstraction and complexity but in the students everyday life the level of abstraction is comparative low (Hatano, 1996). Besides that the operations based on small whole numbers

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seem to be accompanied with a feeling of self-evidence and intuitive acceptance even leading to overconfidence (Fischbein, 1987) then it might act as an obstacle for conceptual change in more advanced mathematics, where learners do not see or understand the reason to change their prior thinking or logic even though it would be necessary. 1.3.

Two Kinds of Continuity

The concept of continuity based on the concept of limit is the core concept of real numbers. The initial thinking behind these concepts is, however, attached to knowledge belonging to a very different category than the initial knowledge of natural numbers (Tall, 1991). In the case of numbers, the first intuition of continuity is based on repetition and comes when children learn to say number words. When they have learned the logic of the number words in the base ten system, they stop their counting and say something like “and so on” which means they have understood the mechanism of the continuity by repetition. According to Dantzig (1954) this is even a child’s first intuition of infinity: they understand that what has been said once can always be repeated. The fundamental feature of the continuity of numbers is based on repetition of discrete actions or objects. From a learners’ point of view this kind of continuity is very different from the one that is meant when speaking of everyday continuity which usually is attached to the continuity of motion. The general idea of the continuity of motion is one of the basic features of the physical world and even very small children grasp it at some intuitive level (Spelke, 1991). This idea is vague, dynamically and instinctively understood in the context of motion or time, but not with numbers. The two continuities mentioned above have different ontological features, where the previous is more like composition of objects and the later more like a process (see Chi, Slotta, & de Leeuw, 1994). 1.4.

Characteristics of Mathematical Concepts and Conceptual Change

It seems to be very typical of those mathematical concepts which demand a radical or demanding conceptual change that their rigorous definitions have been formulated relatively late compared to how long they have operationally been used (Lehtinen, 1998). It is also typical that they are first learned in operations and that structural understanding comes later. Thus these mathematical concepts are possible to comprehend either as processes or products, operational or structural, where this two-sided nature is seen as a dichotomy (Dubinsky, 1991; Harel & Kaput, 1994) or as duality (Sfard, 1991, Sfard & Linchevski, 1994). For example, it is possible to understand the number +2 as an operation ‘add two’ or as structural concept where it represents an integer and a rational number in the hierarchy of real numbers. Sfard and Linchevski’s (1994) theory of mathematical concept formation explains this process through a three staged theoretical model. This theory is based on the epistemological nature of mathematical concepts as abstract constructions which are inaccessible to our senses. Secondly it is based on the dual nature of the concepts as

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operational and structural where the operational naturally precedes the structural. The three phased process of concept formation through interiorisation, condensation and reification is explained as degrees of structuralisation of the concept (Sfard, 1991, p. 19). At the interiorisation, the learner performs operations on lower level mathematical objects and becomes more familiar with these processes. A transition to the stage of condensation in the concept formation is indicated when the learner arrives at a point where he can think about what would happen without actually carrying out the process. In the condensation stage, complicated processes are condensed into a form that becomes easier to use and think about. In this stage the learner becomes able to combine processes, make comparisons and generalise. The stage of reification, according to this theory, usually occurs as a sudden shift (Sfard, 1991), where the learner understands the concept as a “fully -fledged” object (p. 19): both structural and operational. The theory of reification with its descriptions of different phases in the concept formation explain the question “what spurs the transitions from one level to another?” According to this theory a new concept is firstly learned in operations and algorithmic processes. The phase of condensation is a result of sufficient practise where the learner begins to be skilful with the processes. The structural level seems to require a lot of practise but also profound mathematical thinking where the learner actively focuses his (her) attention also to the relations between the objects. In order to see a process as an object one needs to try to manipulate it as a whole. But it is the hardest for learners to attain. The theory of reification is formed from a mathematical point of view, and those who know the concept are able to recognise the stage of development in the answers of the learners. It does not, however, pay very much attention to the students initial thinking or prior knowledge, where the students are struggling to understand a concept from their prior point of view. For this reason equally essential, however, is the question: “what hinders the transitions?” The theories of conceptual change (Chi, 1992; Chi, Slotta, & de Leeuw, 1994; Vosniadou, 1994, 1996; Vosniadou & Ioannides, 1998; diSessa, 1993) answer the latter question by the relationship between the prior knowledge and the new information. They describe it as one of the most crucial factors in determining the quality of learning. The theories resemble each other in that they present two levels of difficulty in the conceptual change. The easier level means the enrichment of one’s prior knowledge. In this case the prior knowledge is sufficient for accepting the new specific information. The student needs only to add the new information to existing knowledge. Conceptual change that is more difficult is needed when the prior knowledge is not sufficient for the new information but needs reconstruction. These theories differ in the way that they explain the students’ prior knowledge and in the way they define the changes. In the theory presented by Chi (1992, 1994) the concepts belong to different categories. The conceptual change in this frame of reference means a change in the categorisation of the concept. The learning of scientific concepts, where a radical conceptual change is necessary, is based upon the learning the ontologically new scientific category for the concept and then reassigning the initial concept to this new category (Chi, 1992). In the theory presented by Vosniadou (1994, 1998), prior knowledge is represented by a naïve framework theory. The essential feature of this framework theory is it’s coherency.

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According to this theoretical view the conceptual change from naive assumptions and epistemological beliefs to the scientific understanding of the concept is described as different levels of synthetic models. There the synthetic mental model refers to situations where students attempt to synthesise the currently accepted scientific information with the system of their initial concept (Vosniadou & Ioannides, 1998). Misconceptions or synthetic models are built when students are presented with scientific explanations which are highly inconsistent with the intuitive explanations they have constructed on the basis of their everyday experience (Vosniadou, 1996). The framework proposed by diSessa (1993) explains the quality of prior knowledge in the “weakly organised knowledge systems” like the physical concepts of everyday experiences. The intuitive knowledge according to this view is composed of rather small knowledge structures, that act largely by being recognised in a physical system. These explanations may be self-explanatory; something happens “because this is the way things are”. One description of the explanations is causality. The learners acquire a “sense of mechanism - mechanism – a sense how things work, what sorts of events are necessary, likely, possible, or impossible” (diSessa, 1993, p. 106). The changes in this way of thinking is described as changes in the explanations: they cease to be self-explanatory and start to change to much more complex knowledge structures with scientific explanations. Because of the complexity and profound nature of the concept the concept of real numbers by high school students is on a totally different level compared to the respective concept of professional mathematicians. Students in upper secondary school level use real numbers for the basic courses of calculus. The concept of real numbers described in a typical upper secondary level curriculum in Finland is more like a foundation on which the mathematical construction of real numbers will be based in advanced mathematics learning. The essential components of this preliminary concept of real numbers are: the hierarchical nature of real numbers, where irrational and rational numbers, integers and natural numbers are understood as sub sets, secondly the compact nature of the number line, where the points represent the real numbers, where the irrational numbers fill the “gaps” between rational numbers and thirdly the concepts of limit and continuity which are traditionally taught in the context of functions. The enlargements of the number concept demand drastic changes to the initial understanding of numbers, especially on the level of structural understanding. It is possible that the harmonious whole and logical structure of numbers appears logical and continuous only to mathematical experts. For students who are approaching the concepts from a fundamentally different point of view, it appears as fragmentary and discontinuous (Lehtinen, Merenluoto, & Kasanen, 1997; Lehtinen, 1998). In this article we are interested in the conceptual change from the students’ prior thinking of numbers to the more advanced enlargement of the number concept. In order to describe the changes we explore the theory based on the duality of mathematical concepts (Sfard, 1991, 1994) together with the theories of conceptual change (Chi, 1992; Chi, Slotta, & de Leeuw, 1994; Vosniadou, 1994; Vosniadou & Ioannides, 1998; diSessa, 1993). In this combination, the experts’ view of the development of number concept is represented by the theory of reification. The students’ view is represented by different theories of conceptual change. On the basis of the historical

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development of the number concept we assume that the problem of prior knowledge is more complex than the empirical examples described in the literature on conceptual change. Thus different theories are needed to explain this complexity. The aim of the study is to describe the problems of conceptual change in the enlargement of the number concept to the preliminary concept of real numbers and to find out the quality of the changes and the role of prior knowledge in the learning process. 2.

2.1.

METHOD

Participants

The participants were 564 students of extended mathematical courses from 24 randomly selected Finnish upper secondary schools (mean age 17.3 years). There were 344 (61.0%) boys and 218 (39.0%) girls. 2.2.

Materials

The test consisted of identification, classification and construction problems in the domain of rational and real numbers. The students took the test in March 1998 in an ordinary class situation supervised by their mathematics teacher. The real number concept of the students was tested in three main dimensions: 1) formal hierarchy and facts of real numbers 2) the density (no gaps nature) of the number line 3) concepts of the limit and continuity of a function. We also asked the students to estimate their certainty about their answers to the questions on a scale from 1 to 5, where 1 meant that their answer was a wild guess and number 5 that they were absolutely sure, as sure as 2.3.

Scoring Procedure

There were basically two kinds of questions/problems in the test. First there were questions where the answers were predominantly based on remembering the formal knowledge of given numbers and sets of numbers. There were problems which demanded handling the numbers or identification their status in the hierarchy of real numbers. These were also the identification tasks, where the students were given pictures of functions and asked to identify if the function was continuous or had a limit at the given point. There were also a construction task where the students were asked to sketch a function which is discontinuous at a given point and had a limit at another point. The second kind of questions we called critical questions. In these questions the students were asked to explain their answer in their own words and these were questions unfamiliar to the students compared to the questions they traditionally faced in mathematics. Qualitative analyses were carried out on the answers to the critical questions to reveal the nature of their answers. In this databased qualitative analysis we scored the answers according to the abstraction level

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identified in the answer (see Sfard, 1991; Goodson-Espy, 1998; Cifarelli, 1988). The pre-level of answers were ones where the students used the logic of natural numbers on the domain of rational /real numbers, or based their answers on their everyday concepts and experiences. These were answers based on students’ initial thinking of numbers or continuity. Those answers where the students identified at least one feature of the more advanced level of the concept were called the recognition level, even though these answers still had mistakes or deficiencies. The level where the students explained their answer with clear operational arguments was scored on the re-presentation level. The answers where there were hints of some structural understanding we scored on the structural abstraction level. All the answers were scored on a scale ranging from 0 to 4, so that a correct or most advanced level of answer was scored 4, pre-level answers scored 1, and no answer 0. The estimations of certainty that ranged from 0 to 5, where 0 meant no answer, were multiplied by to set them on the same scale. We also formed a bias variable to estimate the students’ confidence of their answers by subtracting the performance scores from the certainty scores on this variable the positive scores respond to overestimation of confidence, whereas the negative scores correspond to underestimation of confidence. 3.

RESULTS

3.1. The Formal Knowledge of the Hierarchy of Numbers

From the viewpoint of the theories of conceptual change the hierarchical understanding of numbers seems to be a very demanding process. In one of the questions the students were asked to write all those domains of numbers to which eight given numbers belonged (Table 1). One fifth, 23.3%, of the students either did not answer the questions or identified given numbers only on the basis of their superfluous characters, as whole numbers, fractions, decimal and “square” numbers. Only 26.9% identified all the numbers as real numbers and only 6.6% of the students presented a correct a complete hierarchy for the numbers. Thus the majority gave only partially correct answers. Some of the students had systematic models in their hierarchy presentations: 19.7% of the students presented models where the domain of rational numbers was systematically missing, and in 17.5% of answers both the domains of rational and natural numbers were missing. The others seemed not to have any systematic method to their answers. The identification of irrational numbers was the most difficult: 21.8% of the students identified as a rational number and 20.7% the number 2.3131... as an irrational number, for example. The main problems in defining the hierarchy were the domain of rational numbers and the identification of irrational numbers. For example, where 49.8% of the students classified the number 12 as a natural number, 64.4% classified it as an integer and 62.8% as a real number, but only 22.0% identified it also as a rational number. From the perspective of conceptual change it is noteworthy that the estimations of certainty were statistically significantly higher on the domain of natural numbers

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and integers than on the more advanced domains regardless of the correctness of the answers.

The problems with more advanced numbers and in number manipulations were obvious also in other tasks demanding number handling. We found that more than one third of the students spontaneously used the logic of whole numbers in operations. For example, when asked how many integers there are on the number line between numbers and one third counted only the integers between -5 and 8; they did not interpret the irrational number as a multiplier. The students had problems also with common operations, only 31.3% identified the number

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as an integer or natural number. The “square” numbers were difficult for all the students. For example, in the hierarchy tasks using the numbers 12 and the difference in certainty estimations was statistically significant . In fact, the means of certainty estimations attached to were on the same level as the ones attached to irrational numbers. In the task where the students were asked to write an example of an irrational number in a decimal form, only 25.5% gave a correct answer. More than half (53.2%) of the students gave it as a rational number, complex number or even negative number. The formal knowledge of the hierarchy of the numbers seemed to be in a state of confusion in the answers of most of the students and they also had problems with handling the irrational numbers in operations. While 8.5% of the students gave at least a partial correct answer to all the hierarchy questions, only 3.7% gave an incorrect or no answer to all of them. The great majority, 87.8%, wavered in their answers; they seemed to remember some isolated facts of the hierarchical knowledge. For these reasons the formal knowledge of the hierarchy of real numbers seems to represent an enrichment kind of learning, based on the remembering of facts. They did not really have structural awareness of the hierarchy of real numbers although a few of the students with high achievements in mathematics showed some intuition of structural abstraction of the hierarchy. 3.2.

3.2.1.

The Number Line

The Points of the Number Line

Mathematically, the points of the number line represent the set of real numbers so that for every real number there is a corresponding point on the number line. The students’ representation of the number line was tested with questions pertaining to the points and density (compact nature) of the number line. The students were asked to estimate if the given statements pertaining to the points of the number line were correct. These statements were: the points of the number line represent rational numbers/ irrational numbers/ real numbers. In the questions referring to the points of number line they were asked to compare the points of the number line and the set of rational numbers and define if their cardinality was the same (Table 1). They were also asked also to compare the sets of real and rational numbers. These two questions were logically the same, but the students answered them very differently Only 35% of the students gave a correct answer to both of these questions and only 11.8% (a mean) gave an explanation where they explained that rational numbers are a sub set of real numbers. The fragmented nature of the knowledge about the number line was represented the diversity in the answers where only 13.3% of the students systematically gave correct answers to all these questions, but only 6.7% did not answer or gave an incorrect answer to all of them, the remaining 80.0% wavered in their answers. According to these results the points of the number line did not seem to represent the real numbers to the majority these

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students. They seemed to understand the number line as a representation of rational numbers, integers, decimal numbers or even positive whole numbers. 3.2.2.

The density of the number line

The answers to questions pertaining to the density (compact nature) of the number line refer to the same direction. Two different kinds of questions were asked in the domain of both rational and real numbers: the questions about density and limit (see Table 2, questions 1 and 3). The discrete nature of the students’ comprehension of the number line was obvious in those pre-level level answers where many students (mean 30.5%) based their answers on the spontaneous logic of whole numbers. On the density of rational numbers they gave an answer of six or seven numbers between the two given fractions (3/5 and 5/6) and on the density of real numbers they answered that between the numbers 0.99 and 1.00 there was either zero or one real number on the number line. In the limit questions (see Table 2, questions 2 and 4) they based their answers on the fundamental intuition of whole numbers: they answered that 4/5 is the next fraction after 3/5 or that the number 0.999... is the closest to 1.00. There were students who, on the recognition level, identified the infinite density of the rational- and real-number line. To the density question some of them gave an indefinite answer such as “many”, “ infinite” without any explanation, and to the limit question they gave uncertain answers like “that kind of number does not exist” or an inaccurate answer like A clear difference was seen on the representation level where, in density questions, the students clearly referred to the use of operations for adding to the density or explained their answer where they stated that it is not possible to define the next number with operational arguments, such as “...because it is always possible to make them more exact” , “ ...add decimals”. In the limit questions they explained that “...it is not possible to define such a number, because there are an infinite amount of them” or “you can always make it closer” . These answers refer to the awareness of potentially adding more numbers on the number line based on the logic of repetition, which represents operational understanding. There were only a few of students who, in their answers, gave hints of structural abstraction of the number line, for example “.. there are an infinity of numbers because it is possible to write all the rational numbers in fraction form” or “it is not possible to define the next, because the principle of the next number is valid only on the domain of natural numbers or integers”. A few of the students even identified the abstraction of limit on the number line, for example “it is not possible to define the closest, because it is a limit”, “..there is no limit in how close it can get” . These questions seemed unfamiliar to the students because almost a quarter (mean 22.7%) did not answer the questions about density and still more (mean 39.3%) did not answer the questions about limit (Table 1).

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On the basis of the percentage distributions, the operation of adding the density between two given numbers (questions 1 and 3) seemed more familiar than the questions of the “next” number (questions 2 and 4). There were significantly more users of pre-level logic in the answers to the question of the next number (mean 40.5%) compared to the question of density (mean 30.0%), the difference was significant The concept of the compact nature of the number line seems to have the two levels of difficulty that theories of conceptual change describe, where adding the density was easier than the question about the successor. It seems that an enrichment kind of change seems to be sufficient, when the students “add” new numbers between given numbers on the number line. This enrichment does not seem to demand restructuring of prior knowledge, but the students seem mostly to use the same type of logic that children use when they learn to enumerate the number words. The logic used is based on the logic of repetition and upon the fundamental intuition of “the next”, though the numbers are closer to each other. However, understanding the compact nature of rational and real numbers, where it is not possible to define the next number but that between any two rational or real numbers there is an infinity of numbers, demands a radical revision in one’s prior thinking. The estimations of certainty and their relatively high standard deviations refer also to the unfamiliar nature of this kind of questions (Table 2). The overestimation of confidence in these answers refers to a situation where the students were possibly not aware of the quality of their answers. The under estimation of confidence in the advanced level of answers refers to newly accepted change in thinking. The fragmented nature of students’ answers was again seen in the diversity in the answers (10.5% of the students gave at least a recognition level of answer to all these four questions and 36.3% an incorrect or no answer to all of them) where 53.2% students wavered in their answers. The fundamental presumption of always having the next number is one of the basic epistemological beliefs students have in their number concept, and it is hard for them to imagine a situation where it can not be defined. Because the participants were students of extended mathematical courses in upper secondary school they had a lot of experience with numbers and operations. It is therefore likely that most of them would have remembered that it is possible to divide fractions infinitely had they been reminded. The results refer, however, to a situation, where this knowledge of fractions constitutes an isolated piece of knowledge. When the students read the word “next” they spontaneously used the logic with which had more experience. In order to arrive at the correct answer of “it is not possible to define the next number” the students had to consciously ponder the question at some earlier time. Adding to the density of the number line seems to require the enrichment of the prior knowledge and the students seem to be able to give correct answers even though their thinking of numbers is still based on the discrete nature of the number line. Accepting the logic that it is impossible to define the “next” number demands a radical, but most of all, conscious reconstruction of one’s prior thinking. This difficulty was seen in some of the answers, where the students on one hand wrote “it is not possible to define the next” but on the other hand continued trusting on the

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actual existence of this kind of number, “...but it is the one which is the closest”, “...the one which has most of 9’s”, “...I do not know but it has a lot of nines.” In spite of the fragmentary quality of the advanced knowledge of the students it is important to notice that their prior knowledge was based on their knowledge and experiences of natural or whole numbers and has a clear coherence: numbers have an order, every number has a successor, and the successor means that you add one to the previous number. Because of the coherent nature of their prior knowledge and thinking based on the logic of whole numbers, the theory of Vosniadou (1994, 1998) explains well the role of prior knowledge in the answers of the students. Their number concept on these advanced levels of numbers seems to be synthetic, where they have not restructured their thinking of numbers, but added fragmented pieces of the system of more advanced numbers. 3.3.

The Concepts of Limit and Continuity of a Function

The mathematical concept of continuity is based on the concept of limit. It’s possible that a function has a limit, but is not continuous at a certain point. But it is not possible that a function is continuous at some point without having a limit at the same point. The concept of limit is traditionally taught in the context of functions together with the concept of continuity and it is not taught before the second year of upper secondary school, when the students are about 17 years of age. The teaching of this kind of continuity encounters the students at an “untouched” level. This concept of continuity seems to be founded upon a different kind of process than the continuity presented as the density of the number line. The students have experienced continuity in their everyday life connected with motion, time or direction. There were three kinds of tasks pertaining to the continuity and limit of a function: identification, construction and explanation tasks. In the identification tasks the students were asked to identify if a given function had a limit or was continuous at a given point. In the construction tasks they were asked to sketch a function which was defined at every real number, was discontinuous and had a limit at given points. In the explanation tasks they were asked to explain in their own words what is meant by continuity and limit. A correct answer to the identification (Table 3) of the continuity tasks was given by 54.1% of the students and 39.4% gave a partially correct answer to all of the identification questions. The problem with these last ones was the “broken” function which was continuous from the mathematical point of view but which, for 24.8% of the students, did not present the features of everyday continuity based on direction. The conflicting role of prior knowledge concerning limit not as a presumption to continuity but as a bound was obvious in the identification tasks, where only 6.5% of the students gave correct answers and 68.4% identified the limit as a bound. In the construction task 23.4% of the students did not even try, 30.2% sketched a function that was classified on the pre-level because the students sketched a function based on the everyday intuition, where the limit stops the continuity. The continuity based on everyday thinking of a “broken” line was seen in the drawings where the discontinuity point of the function

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was presented as a point where the function was not defined. Only 3.0% of the students gave a correct answer where even the equation was correctly written. Because the identification of continuity seems to be primarily based on the everyday intuition of an unbroken line the students scored quite high in this task, but underestimated their certainty which is an indication of the difficulty of these concepts. Also the percentage distribution of those who did not answer to these questions are an indication of the difficulty of the concepts. There were significantly more who did not answer in the questions about the limit or the construction task than in the questions about the identification of the continuity.

The written answers indicate that it is also possible to give mathematically correct answers based on guessing. In the answers to the explanation tasks (Table 4) the thinking of the students was more obvious and it was easier to estimate their level of the understanding the concept. The limit is a presumption to the continuity but in the explanations of many students these two concepts, however, seemed to be in a strikingly conflicting state, where the limit stops the continuity. On the pre-level level of answers in the explanation tasks the students described the continuity as a cause of something that “does not stop” or “continues pretty long and terribly far”, “the value grows towards infinity” or based on same direction: “the numbers continue in the same way”, “it continues its course”. In all these explanations the continuity is based on the dynamics of motion although the students were not very sure of what is continuous (a line, an equation or a graph). In the corresponding explanations concerning the limit the students gave explanations where the continuity was bounded by the limit “it’s the place where the graph ends”, “ it is the value where you can not go further, a stop-sign” or they described it as the maximum or minimum of a function where “it is the value where the function has its

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maximum or minimum” or even a poetic answer “the place of the hills and valleys of a function” .

Although mathematically the function has a limit also at these points these answers were classified as pre-level because the students did not recognise the limit at the continuity points of the function but their answer were based on their prior intuition of the word limit as a boundary which at these points limits the function from having higher (or lower) values. The explanations on the recognition level (Table 4) were clearly based on the dynamic of continuity caused by motion, “the function does not jump over the numbers”, by operation of drawing, “it is possible to draw without lifting the pen”, or the dynamics of breaking, “a function does not break very much”. In all these answers there was either a clear intuition of motion as a cause of continuity or the students described the continuity as a result of drawing based on an everyday operation. Although the explanations were clearly based on everyday intuition of continuity there was, in these answers, a different dimension of continuity compared to the previous level. These answers were closer to the mathematical continuity that is defined at a point. The students had kept their previous thinking of motion as a cause of continuity, but now the place of continuity was “in the middle” which was closer to the mathematical continuity defined at a point. In the case of the concept of limit, these were the answers where the students identified the abstraction of

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successive division of the concept of limit and explained this abstraction as dynamical approaching. These answers were still very indefinite and vague, but there was a clear change compared to the previous level, “...it gets closer to a value “, “the graphs approach the point but do not hit it”, “the value of the function gets closer but never reaches”. Some answers even had a hint of magic “an equation approaches some value but never reaches it, circles in the neighbourhood”. Although the students had recognised the abstraction of successive division, the answers were tied to dynamics of motion. The intuition of a limit as a boundary was still there but instead of explaining the limit as a “stop” sign, the boundary was explained as something that is forever possible to get closer, but never reach. The re-presentation level of answers were those where the students had diverged from motion as the cause of continuity and struggled closer to mathematical expression, although it was not correct. They tried to describe the unbroken continuity as a graph “a function has a value y for every value of x”, “a function is continuous everywhere and can have all the values of the number line”. The responses of these students were not mathematically correct, however, there was a change of explanations from the dynamics of motion to the context of function. From a perspective of concept change this level represents a transition level for the student. On this level the students still seem to be relying on the prelevel intuition of continuity - not of motion but of an unbroken line without the dynamics of motion. In the case of limit these were the answers where the students explained the limit in more exact terms, the operation of approaching was described as a dependence between a variable and the function, for example “a function approaches a value while x gets closer to some value” . It is not until on the level of structural abstraction where the students begin to explain the continuity based on the limit conception that we can see an essential conceptual change has happened or is beginning to happen. These were answers where the students explained that “a function is continuous if it has at that point a left hand and right hand limit that are the same and the same as the value of the function” or “the function has a limit and a value at the points where it is continuous and they are the same”. There were very few students who, based on their written answers, were on that level of abstraction. Likewise in the case of limit, only a few seemed to have some structural intuition of the limit concept although the answers were not exact “it’s based on the limits if the function is continuous at some points” or “it is the value that the value of the function approaches when the variable approaches a certain value, there are also one-sided limits” . The difficulty of these concepts was obvious in the percentages of answers and in the estimations of certainty and it seems that only the students with high scores in mathematics were able to explain these concepts in an advanced level. What is noteworthy from the conceptual point of view is that in the case of continuity the students are able to give mathematically quite a high level of answers just by relying on their pre-level intuition of continuity as something that does not have “gaps”. The difficulty was again obvious also in the fragmented nature of the answers: when 12.6% of the students gave a pre-level or no answer to all the questions concerning the continuity and limit and 7.1% gave at least a recognition level of answer to all of them, but 80.3% of the students wavered in their answers. The correlation between

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the tasks were highest between the explanation and construction tasks than between the identification and construction task and lowest between the identification and explanation task . The certainty estimations refer to the same direction where the students overestimated their certainty in the pre-level of answers and under estimated their certainty in the more advanced level of answers (Table 4). The general tendency to underestimate the certainty in these questions, which were in the context of functions compared to the questions about the numbers (Tables 1 and 2) where there was a respective general tendency to overestimate the certainty, refers also to the overall difficulty of the context of function and to the familiar nature of numbers to the students. From a conceptual change point of view it seems that as far as the continuity is thought of as something without gaps and the limit as something that is possible to dynamically get closer to but never reach, the enrichment of the prior knowledge is sufficient. Although the answers of the students are close to the mathematical continuity, the everyday intuition of an unbroken line supports the student but leads to restriction of understanding where they do not mention the limit as a presumption for continuity. Respectively, in all these answers where the students referred to approaching and not reaching, there remains the pre-level based intuition of a restrictive and dynamic nature of the limit. The students give different kind of causes or explained the mechanism of continuity or limit in most of their answers. The majority of the answers seemed to be based on a vague intuition of the dynamics of motion or approaching. It seems to de different when compared to the prior knowledge that was distinguished from the answers to the questions of numbers and the number line: less coherent and more concentrated on causal explanations. For these reasons the theory presented by diSessa (1993) seems to explain the nature of the students prior knowledge. In the different levels of answers the development of explanations from self-explanatory level to a little more complex level with some scientific explanations was also indicated. 4.

DISCUSSION

Our empirical results support the assumption which was based on historical evidence. The results refer to the two-level difficulty defined by the theories of conceptual change. Where the most difficult questions were those pertaining to the concept of limit either on the number line or of the function. The results also refer to the strong, and sometimes restrictive nature of prior knowledge (Vosniadou, 1994; diSessa 1993). The majority of students had not restructured their prior system of beliefs to understand these concepts even on the preliminary level. Their comprehension of the hierarchy of the number system was confused, many of the students spontaneously used the logic of natural numbers in the domain of rational numbers. Continuity based on the concept of limit was practically unknown to them. Their real number concept seems to be a mixture of fragmented pieces of advanced logic and of powerful pieces of pre-level logic based on finite processes and everyday experiences. As such we could call their number concept synthetic. The difference between the difficulty of the operational and structural understanding

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(Sfard, 1991; Sfard & Linchevski, 1998) in the concepts was also obvious in our data, where the highest means of underestimation of confidence were attached to the answers having some hint of structural thinking in them. Further, the results refer to the possibility that the moderate operational understanding of these concepts, the synthetic models of the students, seem to be an obstacle to further conceptual elaboration: the need of the revision of their concepts does not even occur to the students. The majority of the students did not have any connections between the different components of the preliminary concept of real numbers and their spontaneous thinking of numbers seemed to be based on whole numbers (not integers). In the notion of real numbers the concepts of the density of the number line and the concepts of continuity and limit are combined (see figure 1). In order to understand the structure of this combination one has to make a radical reconstruction of one’s prior knowledge and this reconstruction seems to be very complicated and difficult to undertake. The concept of mathematical continuity is already difficult per se because it is defined by the limit concept, and in the students’ prior thinking these concepts seem to be in conflict with each other: the limit stops the continuity (see Merenluoto & Lehtinen, 2000). Moreover, the abstraction of approaching and not reaching seems to be connected to the dynamics of everyday motion in the students answers where the “unattainable” limit even had a hint of magic. These answers of the students were based on an abstraction of motion, not on numbers. In the theory of real numbers the same abstraction is described as a static situation where you can have numbers as close to the limit as you please. In other words it is possible for the distance from the limit to be smaller than any given positive number. This abstraction is difficult for the majority of the students who seemed to base their spontaneous thinking of the numbers and the number line on the discrete nature of whole numbers. These concepts are difficult and complicated but it is also possible that the insufficient number concept of the students does not give an adequate foundation for understanding them. Another reason for this difficulty seems to be the fragmented nature of the students’ mathematical knowledge. The transfer of the limit concept from the abstraction of density of the number line to the concept of the limit of the function seems to be very difficult. Only a couple of students identified the abstraction of the limit in the questions pertaining to the density of the number line (see also Sierpinska, 1987). The initial thinking concerning the numbers and continuity seems to be a different kind of knowledge, which was obvious in the students’ explanations (see figure 1). In the questions pertaining to the numbers, the students gave descriptions of knowledge based on a seemingly coherent system of knowledge (see Vosniadou, 1994). The points of the number line for the majority of students did not represent the real numbers but their thinking seemed to be more or less on the level of a framework theory based on a static coherence of whole numbers. The prior thinking pertaining to the concept of continuity and limit, however, seemed not to be static but dynamic, with the students thereby explaining the cause of continuity and limit. To an even greater extent the students’ fragmented explanations appeared to be the initial stages of conceptual development described by diSessa (1993).

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Every enlargement of the number concept demands the learner to accept new knowledge and a new kind of logic attached to numbers, while the former is still valid every time when operated on the domain of the previous numbers. This means that the enlargements of the number concept demand a construction of a parallel model for the “numbers” and an ability to move freely between the models. According to Vosniadou the conceptual change (Vosniadou & Ioannides, 1998) does

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not necessarily mean that the expert has lost the initial concepts that a child is operating with. In mathematics the enlargements of number concept are specially demanding because the prior knowledge is not necessarily abandoned, but the learner has to take another point of view. In the case of mathematical continuity, however, the attachments to motion and time need to be abandoned in the advanced level of mathematics where the continuity is defined by numbers, as a static state of affairs. This domain–specificy of mathematics makes the conceptual change in the enlargements of number concept demanding, because the basic operations and fundamental truths of natural numbers do not cease to be valid whenever one is operating on the domain of natural numbers. In addition to the high complexity of the concepts, the symbolic language of mathematics tries to describe all concepts in a very economical way. However, all the concepts get their meaning from a large, and often highly abstract, system of interrelated ideas. The concept of real numbers is one of the many mathematical concepts which cannot be understood on the basis of prior formal knowledge but the very understanding of the concept presuppose the construction of this abstract systemic environment (see Russell, 1996; Rudin, 1953; Landau, 1960). The results also refer to the possibility that it might be reasonable to teach the abstraction of limit first in the familiar context of the number line and after that build the connections between the limit on the number line and the limit of a function, where the context was so much more difficult for the students. This conceptual change seems also to be the kind of change which demands a radical change of the ontological category (Chi, 1992), which seems to explain the difficulty in integrating the two different kinds of knowledge of numbers and continuity and also the change in the quality of argumentation (see figure 1). This kind of change seems not possible through any acquisition mechanism such as deletion or addition, discrimination or generalisation, because these kind of operations cannot transform the substance-base type of knowledge to the abstract kind of knowledge typical of advanced mathematics (see Ohlsson & Lehtinen, 1997). In order to succeed the students need to learn about the abstract nature of mathematical concepts where the logical consistency is more important than the physical intuition. In addition they need to reassign the concepts of numbers and limit to this new ontological category. In this reassignment they need to actively abandon the connections of motion in the concepts of continuity and limit and base them on numbers. This means a radical change to the viewpoint of numbers: after the change natural numbers are seen as a sub set of real numbers. This kind of radical conceptual change is too difficult for students to achieve by themselves and deliberate pedagogical arrangements are needed (Chi, 1992; Lehtinen & Ohlsson, 1999). The early development of numbers is thoroughly dealt with in the research of learning but there is comparatively little research dealing with the later extension of number concept. These findings suggest important theoretical considerations for planning learning environments which better support the process of the conceptual changes of the students: the need for revision of prior knowledge needs to be made explicit for the students. The students need to be well aware that they are operating on a different domain of numbers which is based on a new kind of logic. The deeper knowledge of the history of calculus and a critical discussion of its foundations

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could help students orient to this new domain and cope with the idea of real numbers that seems to conflict cognitively with many principles of elementary mathematics. In general, we assume that the difficulties students have in the acquisition of new areas of mathematical knowledge, like extensions of number concept, are not only due to the increasing complexity of the knowledge, but also to situations where prior knowledge systematically supports the construction of misconceptions. Theoretical approaches developed in the conceptual change tradition could help mathematics educators to recognise those situations and develop more explicit methods for supporting adequate conceptual revisions in students. REFERENCES Boyer, C. B. (1959). The history of calculus and its conceptual development (2nd ed.). New York: Dover Publications. Carey, S., & Spelke, E. (1994). Domain-specific knowledge and conceptual change. In L. A. Hirschfeld & S. A. Gelman (Eds.), Mapping the mind. Domain specificity in cognition and culture (pp. 169200). Cambridge, MA: Cambridge University Press. Chi, M. (1992). Conceptual Change within and across Ontological Categories: Examples from Learning and Discovery in Science. In R. Giere (Ed.) Cognitive models of science. Minnesota Studies in the Philosophy of Science (pp. 129-186). Minneapolis, MN: University of Minnesota Press. Chi, M., Slotta, J., & de Leeuw, N. (1994). From things to process: A theory of conceptual change for learning science concepts. Learning and Instruction, 26, 27-43. Cornu, B. (1991). Limits, In Tall, D. (Ed.) Advanced mathematical thinking (pp. 153 – 166). Dordrecht, The Netherlands: Kluwer Academic Publishers. Dantzig, T. (1954). Number, the language of science (4th ed.) New York: The Free Press. Dreyfus, T. (1991). Advanced mathematical thinking processes. In D. Tall, D. (Ed.) Advanced mathematical thinking (pp. 25-41). Dordrecht, The Netherlands: Kluwer Academic Publishers. Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.) Advanced mathematical thinking (pp. 95-123). Dordrecht, The Netherlands: Kluwer Academic Publishers. Fischbein, E., Jehiam, R., & Cohen, D. (1995). The concept of irrational numbers in high-school students and prospective teachers. Educational Studies in Mathematics, 29, 29- 44. Fischbein, E. (1987). Intuition in science and mathematics. An educational approach. Dordrecht, The Netherlands: D. Reidel Publishing Company. Gallistel, G. R,. & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 4374. Gelman, R., & Brenneman, K. (1994). First principles can support both universal and culture-specific learning about number and music. In L. A. Hirschfeld, & S. A. Gelman (Eds.) Mapping the mind. Domain specificy in cognition and culture (pp 369- 390). Cambridge: Cambridge University Press. Goodson-Espy, T. (1998). The roles of reification and reflective abstraction in the development of abstract thought: transition from arithmetic to algebra. Educational Studies in mathematics, 36, 219245. Cifarelli, V. (1988). The role of abstraction as a learning process in mathematical problem solving. Unpublished doctoral dissertation, Purdue University, IN. Hartnett, P., & Gelman, R. (1998). Early understanding of numbers: paths or barriers to the construction of new understandings? Learning and Instruction, 8, 341-374. Harel, G., & Kaput, J. (1991). The role of conceptual entities and their symbols in building advanced mathematical concepts. In D. Tall (Ed.) Advanced mathematical thinking (pp. 82-94). Dordrecht, The Netherlands: Kluwer Academic Publishers. Hatano, G. (1996). A conception of knowledge acquisition and its implications for mathematics education. In P. Steffe, P. Nesher, P. Cobb, G. Goldin, & B. Greer (Eds.) Theories of mathematical learning (pp. 197 - 217). Mahwah, NJ: Lawrence Erlbaum Associates.

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Kaput, J. (1994). Democratizing access to calculus: New routes to old roots. In A. J. Schoenfeld (Ed.) Mathematical thinking and problem solving (pp. 77-155). Hillsdale, NJ: Lawrence Erlbaum Associates. Karmiloff-Smith, A. 1995. Beyond modularity. A developmental perspective on cognitive science. Cambridge, MA: MIT Press. Kieren, T. (1992). Rational and fractional numbers as mathematical and personal knowledge: implications for curriculum and instruction. In G. Leinhardt, R. Putnam, & R. Hattrup (Eds.) Analysis of arithmetic for mathematics teaching (pp. 323-371). Hillsdale, NJ: Lawrence Erlbaum Associates. Kline, M. (1980). Mathematics. The loss of certainty. New York: Oxford University Press. Landau, E. (1960). Foundations of analysis. The arithmetic of whole, rational, irrational and complex numbers (2nd ed.). New York: Chelsea Publishing. Lehtinen, E. (1998, November). Conceptual change in mathematics. Paper presented at the Second European Symposium on Conceptual Change. Madrid, Spain. Lehtinen, E., Merenluoto, K., & Kasanen, E (1997). Conceptual change in mathematics: From rational to (un)real numbers. European Journal of Psychology of Education, 12, 131-145. Lehtinen, E., & Ohlsson, S. (1999, August). The function of abstraction in deep learning. Paper presented at the European Conference for Research on Learning and Instruction, Göteborg, Sweden. Merenluoto K., & Lehtinen E. (2000) The “conflicting” concepts of continuity and limit, a conceptual change perspective: Proceedings of the Conference of the International Group for the Psychology of Mathematics Education, T. Nakahara & M. Koyama (Eds), Hiroshima University, 3, 303-310. Neumann, R. (1998). Schülervorstellungen bezüglich der Dichtheit von Bruchzahlen. Mathematica didadtica. Zeitschrift für Didaktik der Mathematik. 21, 109-119. Ohlsson, S., & Lehtinen, E. (1997). Abstraction and the acquisition of complex ideas. International Journal of Educational Research, 27, 37-48. Russell, B. (1993). Introduction to mathematical philosophy. New York: Dover Publications. Russell, B. (1996). The principles of mathematics (2nd ed.) London: Norton & Company. Rudin, W. (1953). Principles of mathematical analysis. London: McGraw-Hill diSessa, A. (1993). Toward an epistemology of physics. Cognition and Instruction, 10, 105-225. Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36. Sfard, A, & Linchevski, L. (1994). The gains and pitfalls of reification - the case of algebra. Educational Studies in Mathematics, 26, 191-228 Sierpinska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics, 18, 371-397. Spelke, S. E. 1991. Physical knowledge in infancy: Reflections on Piaget’s theory. In S. Carey & R. Gelman (Eds.) The epigenesis of mind. Essays on biology and cognition (pp. 133-170). Hillsdale: NJ: Lawrence Erlbaum Associates. Stafilidou, M., & Vosniadou, S. (1999, August). Children’s believes about the mathematical concept of fraction. Abstracts. Proceedings of the European Conference for Research on Learning and Instruction, Göteborg, Sweden. Starkey, P., Spelke, E,. & Gelman, R. (1990). Numerical abstraction by human infants. Cognition, 36, 97127. Szydlik, J. E. (2000). Mathematical beliefs and conceptual understanding of the limit of a function. Journal for Research in Mathematics Education, 31, 258-276. Tall, D. & Schwarzenberger, R. (1978). Conflict in the learning of real numbers and limits. Mathematics Teaching 82, 44-49. Tall, D. (1991). The Psychology of Advanced Mathematical Thinking. In Tall, D, (Ed.) Advanced mathematical thinking (pp. 3-24). Dordrecht, The Netherlands: Kluwer Academic publishers. Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151-169. Vosniadou, S. (1994). Capturing and modelling the process of conceptual change. Learning and Instruction, 4, 45-69. Vosniadou, S. (1996). Towards a revised cognitive psychology for new advances in learning and instruction. Learning and Instruction, 6, 95-109. Vosniadou, S., & Ioannides, C. (1998). From conceptual development to science Education: a psychological point of view. International Journal of Science Education, 20, 1213 – 1230.

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Williams, S. R. (1991). Models of limit held by college students. Journal for Research in Mathematics Education, 22, 219-236. Wistedt, I., & Martinsson, M. (1996). Orchestrating a mathematical theme: eleven year olds discuss the problem of infinity. Learning and Instruction, 6, 173-185.

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CONCEPTUAL CHANGE IN HISTORY

MARGARITA LIMÓN Autónoma Universidad, Madrid, Spain

Abstract. The question dealt with in this chapter regards the extent to which results from research on conceptual change in science education can be applied to other domains, and in particular that of history. In order to answer this question, we must examine the peculiarities of history and history teaching and their possible implications for conceptual change. The chapter is divided into three parts. The first part consists in a discussion of the characteristics of history concepts and how they may influence students’ prior knowledge. Particular attention is paid to second-order concepts (evidence, cause, explanation, empathy, etc.) that seem to play a crucial role in history understanding. In the second part, the peculiarities of history as a discipline and their implications for history teaching and learning are reviewed. The third part deals with the comparison between conceptual change in history and science. The characteristics of students’ prior knowledge and the goals of conceptual change in history and science are compared. Finally, some general conclusions are discussed.

1.

INTRODUCTION

Most of research on conceptual change has been developed using tasks with scientific content. Consequently, most of the theoretical models developed for describing and explaining conceptual change relate to science. However, to what extent can these models and the research results about conceptual change in science be applied to the description and explanation of conceptual change in other domains? In this chapter I shall consider this question in relation to history. The question leads to further questions: what are the peculiarities of history as a discipline and history learning and teaching, and how do they influence conceptual change in this domain? Let us first deal with this issue, before going on to discuss some similarities and differences between conceptual change in science and history. In Section 2, I shall review the characteristics of historical concepts and how they influence students’ prior knowledge and history understanding. In Section 3, I shall introduce some epistemological characteristics of history as a discipline and discuss how they should influence the goals of high school history learning and teaching in relation to the conceptual change process. Finally, Section 4 is concerned with the way the peculiarities of history can influence conceptual change in this domain, and includes a comparison of conceptual change in science and history. Before going on, and in order to avoid ambiguity, some clarification is necessary with regard to the terms used in the text. Domain is understood as subject matter. Thus, when I refer to the history domain, I am referring to history as an academic subject. M. Limón, & L. Mason (Eds.), Reconsidering Conceptual Change: Issues in Theory and Practice, 259-289. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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Conceptual change is understood as a process through which the individual’s prior knowledge is modified to a greater or lesser extent by new information. As a result of this process, various outcomes are possible: knowledge enrichment, reassignment of concepts within the individual’s conceptual network of the topic, partial or total revision of the individual’s prior knowledge, partial or total restructuring of the individual’s prior knowledge, and so on. This process may take place in different contexts, but in this paper I shall focus on school learning, and particularly high school learning (12 to 18-year-olds). In this context, I shall consider conceptual change as the process through which students’ prior knowledge is intended to be changed by new information introduced by the teacher. Thus, conceptual change will be understood as an instructional strategy to promote weak or strong modifications of students’ prior knowledge. In accordance with this particular definition of conceptual change, by prior knowledge I refer to the conceptual, procedural and conditional knowledge activated by each individual when a learning task or new information is presented. Prior knowledge includes prior domain-specific knowledge and prior topic-knowledge (related to the particular task in hand). In this chapter, I shall refer to students’ domain-specific prior knowledge about history. 2. STUDENTS’ PRIOR KNOWLEDGE ABOUT HISTORY

2.1. Characteristics of Historical Concepts and Students’ Prior Knowledge

As pointed out above, there has been very little research with regard to students’ ideas on particular historical concepts. Consequently, our knowledge about students’ prior knowledge in this domain is somewhat limited. However, some studies have been carried out on causality and the way students understand causes and explanations in history (Lee & Rogers, 1978; Portal, 1987; Shemilt, 1987; Lee, Dickinson, & Ashby, 1998, Jacott et al., 1998; Voss et al., 1994; Britt et al.1994); on text comprehension and the use and interpretation of sources and evidence (Shemilt, 1987; Rouet et al., 1998; Ashby & Lee, 1987a; Limón & Carretero, 1998, Wineburg, 1998; VanSledright & Kelly, 1998; VanSledright & Frankes, 2000); on history problem-solving and reasoning (Wineburg, 1991; Pontecorvo & Girardet, 1993; Kuhn et al., 1994; Limón & Carretero, 1999); on empathy (Shemilt, 1984; Ashby & Lee, 1987b; Portal, 1987, Yeager et al., 1998); and on students’ epistemological beliefs (Boscolo & Mason, 2001). A few studies have dealt with the understanding of particular historical concepts (e.g. Levstik & Pappas, 1992; Berti, 1994; Limón, 1997; Alonso Tapia, in press), or have examined the understanding of particular events (e.g. McKeown & Beck, 1990; Beck & McKeown, 1994). In the last decade, some European research projects have been developed to examine students’ view of history, how useful they find it and how it is conceived as part of their identity as citizens (e.g. Angvik & Von Borries, 1997; Ross, 1999; 2000). History teaching in Europe, and its problems in different European countries, have also been dealt with (e.g. van der Leeuw-Roord, 1998).

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I shall not attempt here to undertake a detailed review of the above work; rather, I shall reflect briefly on the peculiarities of history concepts and how they are taught, making some reference to results from the body of research available. A first difference between research on students’ understanding of the concepts of science and of history is that, in the case of science, it is easier to identify concepts relevant to its understanding and to explore students’ ideas about them. Historical concepts, on the other hand, are frequently presented, not in an isolated way, but within a narrative or a factual account, so that they are implicit, rather than explicit, and students must therefore infer their meaning. For example, the Roman Empire is a topic commonly taught in schools: students are presented with maps illustrating the territories under Roman control at a given time; reference is made to important personalities, such as Julius Caesar, Nero or Trajan; there are descriptions of the way people lived under the Roman Empire, and the causes of its fall are listed. Nevertheless, it is not usual for the concept of empire to be explicitly introduced. Another characteristic of historical concepts (Limón, 1997; Carretero,& Limón, 1995, for a review) is that they change their meaning over time, and may have different meanings when applied to different historical situations. For instance, the concept of democracy at the time of Pericles was not the same as it is now. Empire, when used to refer to the Roman Empire, does not mean the same as it does when we speak of the USA’s empire. Concepts such as revolution (Limón, 1997), nation (Berti, 1994), war, power or society are other examples. In contrast, physics concepts referred to in textbooks or teachers’ lessons, such as power or gravity, always have the same meaning, and are usually defined explicitly. Today, physicists do not argue over the definition of power (even if they did so in the past) and while it is true that scientists may debate the meaning of some concepts of quantum mechanics, there is total consensus on the concepts included in high school science curricula. Such agreement is far from having been achieved with regard to many historical concepts, due to the epistemological characteristics of history as a discipline. Historical concepts are ill-defined categories. As will be outlined in Section 3, many historical concepts are not defined in the same way by historians with different historiographical standpoints. Consider, for example, the concept of revolution. The frontier between a revolt and a revolution is not particularly clear (Porter & Teich, 1986). According to Rosch (1978), economic revolution is a subordinate category of the category of revolution. Is Internet causing a revolution? Was the discovery of fire a revolution? What criteria -spatial, temporal, etc.- should be used to define the term “revolution”? When concepts are diffuse, as is the case of history concepts, individuals tend to use prototypes employing examples with which they are familiar (Martorella, 1991; Limón, 1997). Moreover, given the polysemic nature of history concepts, in the examples usually familiar to students, the concepts have different meanings, and this constitutes an additional difficulty for constructing reliable and solid global representations of concepts. Most historical concepts are abstract. No physical manipulation of objects can be provided to explain or illustrate them. In the case of science, particularly in the domain of physics, objects can be manipulated, and personal experience with objects provides a source of knowledge for students. In fact, some misconceptions or

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alternative conceptions appear to have their origin in such intuitive knowledge. But experiments cannot be carried out to measure revolutions or democracy, or to explain possible causes of a particular war. We cannot design an experiment in the classroom to see what would have happened if the Boston Tea Party had not taken place. Lee, Dickinson and Ashby (1998) have suggested that it may be unrealistic to expect consistency in students’ approaches to the enormous range of substantive content offered by history. They also point out that, given the wide variation of content presented, the consistency of the content actually taught to students is itself questionable. Furthermore, as content is frequently introduced in a narrative style, students’ seem to develop beliefs and ideas regarding particular historical events, more than in relation to the concepts involved in them. Further research is needed on the extent to which the presentation format and the diversity of content may influence the consistency and coherence of students’ ideas, beliefs or representations. However, it is difficult for students to develop consistent and coherent ideas when they are faced with textbooks full of names and dates totally unknown to them. No explanation is provided, and there are frequently unexplained leaps in time and space. Let us consider an example taken from a Spanish textbook for seventh grade students (aged 13). It refers to “Al-Andalus”, the name the Arabs gave to the territories under their control in the Iberian Peninsula. The fragment shown below is part of the section on “The Political Development of Al-Andalus”. As a test example, readers might try to assess their understanding of this text. If your topic knowledge is low or zero, your experience as you read will be similar to that of naïve students. After the conquest, Hispania became an Islamic province. The Moslems, after the Battle of Guadalete, occupied the whole of the Iberian Peninsula except for the mountains in the north. At first, Al-Andalus was a dependency of the Damascan Omeya caliphs. After he Abasian rebellion an Omeya, Abd-al-Rahman I, fled to Al-Andalus and proclaimed himself an independent emir (around the mid-VIII century), breaking off relations with Baghdad. In 929, the emir Abd-al-Rahman III proclaimed himself caliph, becoming independent of Baghdad and assuming full political and religious authority. During this period, the Christian population remained north of the River Duero. At the end of the X century, when Hisham I was in government, his Prime Minister Almanzor launched numerous attacks against the Christian people; Barcelona, León and Santiago de Compostela were sacked. He was defeated by the Christians in 1002 at Calatañazor (Soria). On his death, the caliphate went into crisis, and was divided in 1031 into small kingdoms called taifas. This allowed the Christian population to advance, and they gradually drove the Moslems out of Al-Andalus, though Granada remained unconquered until 1492. (Alambique Group 2000, p. 126.)

Who were all these Arab caliphs named in the text? What was a caliph? How was the Moslem’s government organised? What was the role of religion in the caliphs’ territories? None of these questions are explained in this textbook fragment, and the reader may have asked some of them while reading it. Different types of numbers (Roman, Arabic) are employed; students are assumed to able to deal with both.

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There are numerous references to Moslem dynasties (Omeya, Abasian...) unknown to students, or to places (Baghdad, Damascus, Guadalete, Calatañazor, River Duero, Barcelona...). Some of them are in the Iberian Peninsula and others are very far away. There is no map to accompany the text. There are quite considerable chronological jumps. Abd-al-Rahman I and III are mentioned, but what happened to the second? After reading the text, what is your understanding of “political development”, as the section is entitled? Perhaps one of the most well-supported results from research on students’ prior knowledge in history is that students’ ideas and representations interact with what Lee, Dickinson & Ashby (1998) have called second-order concepts. For these authors, examples of second-order concepts would be evidence, cause, or empathy: ...‘Second-order’ means something more than a higher order of substantive concepts ordering other substantive concepts within a field; the higher order to which reference is being made is a meta-level, in terms of which the discipline is given epistemological shape. (p.228)

In their view, this interaction between second-order concepts and substantive concepts frustrates any efforts to construct models of how these ideas and naïve concepts develop. But, what are these second-order concepts? 2.2.

Meta-Concepts in History and Students’ Prior Knowledge

These concepts can be said to refer to a meta-level, and act as axes around which students organise their substantive knowledge about history. These meta-concepts1 are closely related to students’ epistemological beliefs about what history is and what history learning means. As Lee, Dickinson & Ashby (1998) have also noted, asking students, particularly younger ones, direct questions about the nature of historical knowledge and the philosophy of history, such as what history actually is, what it means to give explanations in history, what is good evidence in history, what a source is, etc., may not be very helpful for exploring their understanding and ideas. These authors therefore propose that, in dealing with such questions, it may be more appropriate to explore second-order concepts. These concepts are likely to be tacit, not only in the sense of being unspoken and implicit, but also because they concern matters students often never confront. To the list of concepts such as evidence, cause, explanation and empathy, I would add time, space, change, source, fact, description and narration. These can be grouped and related as in Figure 1. Describing, explaining, understanding and narrating the past are central goals of history. And each goal corresponds to a different view of history. History as chronicle looks for an objective description of historical events or facts. History as narration looks for a subjective account or a subjective explanation of facts and events, or both. Subjectivity is not avoided: it is intrinsic to the nature of narration.

1

The terms “meta-concepts” and “second-order concepts” are considered as interchangeable throughout this chapter.

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History as explanation looks for explanations of change; explanation involves the identification of causes. Intentional explanations are based on intentional causes. The motives of historical characters provide an example of intentional causes (Carretero et al., 1997; Jacott et al., 1998; Voss et al., 1994). For example, if it is said that “the expulsion of the Moriscos from Spain in 1609 was due to the personal interests and feelings of the Duke of Lerma, the King’s court favourite at that time”, this would be an intentional explanation, based on an intentional cause: Lerma’s feelings and personal interests. On the other hand, structural explanations look for structural causes: social, political, economic or ideological. If it is said “the expulsion of the Moriscos from Spain in 1609 was due to the need to show religious coherence to the Pope, a key ally of Spain in her attempts to control her territories in the south of the Italian Peninsula”, this would be an example of a structural explanation based on political causes. History as comprehension involves understanding the subjective views of those that lived in the past. It focuses on how people felt, thought and behaved in former times. The four views approaches to history outlined above rely on evidence if accounts, narratives or explanations are to be constructed. Such evidence comes from sources discovered by historians. As discussed in the next section, not all sources are equally acceptable for historians working from different perspectives in history. Time and space are meta-concepts present in all views of history and all types of historical content. Historical time is a somewhat complex concept (Thornton &Vukelich, 1988; Carretero, Asensio & Pozo, 1991). It concerns not only when facts or events happened, but also duration, and the relationships between present, past and future. Duration refers to how long events took to occur, or to how much time different historical periods occupied: Prehistory, the Ancient World, the Middle Ages, the Renaissance, the Enlightenment, etc. Students must be able to realise that such epochs differ widely in the time they span. There is no comparison, for example, between the duration of the period referred to as Prehistory and that of the Renaissance era. Historical time also includes the dimension of the individual. Each one of us is part of the time line. Representations of individuals in the present, past and future in the time line and in their historical context form part of the understanding of the time concept: where one is located in the time line, how much time one’s life or that of one’s relatives might occupy, and so on. Space is also present in every historical fact or event. History can be classified according to the space to which it refers: a village, a region, a country, a continent, or the world. The way in which these meta-concepts are defined and understood forms the basis of historical knowledge. Even if it is true that many students have never been confronted with these matters, their beliefs and ideas about them develop implicitly through history lessons, textbooks or the view of history transmitted by their social context. These meta-concepts mediate students’ understanding of substantive concepts and events in history. Let us consider an example from my own research. I

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asked students2 about the possibility of reconciling alternative views presented in a research task about the discovery of America. One of the alternatives supported the view of the conquerors, the other the natives’ view. Alternatives were presented as coming from different textbooks. One girl, a seventh-grader, said: No, it is impossible to reconcile these views. Nothing is the same! They’re totally different. If these are real textbooks, what a mess the world is in!” (Student #245, Limón, 2000).

This girl believes textbooks should say exactly the same thing. Otherwise, they are wrong, so imagine what might happen if we rely on what they say! Underlying her response is her view of history as a true account of facts. She considers that history can be objective, so that only one view is true. If we find discrepancies it means the book is wrong. Someone is lying. In the same study, students were also asked: “Do you think students in Latin America will learn the same as you about the discovery of America?”. These are some of the answers students gave: Yes, because it is a very important issue. (Student #249, seventh-grader). Yes, because although the years pass, history is always the same. (Student #252”, seventh-grader) Yes, because they have to pass an exam. If they pass the exam, it means they know what’s in the textbook. (Student #400, tenth-grader).

The first answer illustrates how content selection in the history curriculum may bias students’ view of history, and how much relevance they give to the topics studied. “Only what I study is important” appears to be the underlying belief expressed. The second answer reveals the student’s conception of history as immutable, with no different views possible. VanSledright and Brophy (1992) found similar conceptions of history in their sample. The third response is the most striking. For this student, exams guarantee that all students are assessed in the same content. In this case, history is also seen as unchangeable, so that the same content will be taught all over the world. None of these students has shown much empathy. They seem to be unable to consider the perspective of Latin-American students, and how this event might be viewed on the other side of the Atlantic. Their representation of the “discovery of America” and the content they have studied is limited by their view of history, history textbooks and history learning. They might show more understanding of empathy if they were more directly questioned about alternative views, but their beliefs about history and history learning leave no space for recognising alternative views. History metaconcepts appear to act as a sieve for students’ understanding of history curriculum content. But, how do historians understand these meta-concepts?

2

The sample was made up of 302 seventh-graders and 367 tenth-graders. All were pupils at Spanish public schools.

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3. HISTORY AS A DISCIPLINE: SOME IMPLICATIONS FOR HISTORY LEARNING AND TEACHING

3.1. Epistemology of History: What is History?

It is not my aim in this section to enter into the realm of historiography, nor to defend a particular view of history, but rather to describe some of the features of history as a discipline that should be taken into account in its learning and teaching. A review of historiography (e.g. Collingwood, 1946; Braudel, 1969; Bloch, 1949; Carr, 1961; White, 1973, Le Goff & Nora, 1974; Cohen, 1978; Ricouer, 1983; Burke, 1991, Hobsbawm, 1997) reveals that actually defining history is far from easy, since the definition itself involves a particular view of it. For example, Fevre (1953) considered history as “the science of men, but of all men”. In this way, he was openly rejecting a positivist definition of history that considers it as the science that studies historical facts, or the Marxist view of history that stresses the analysis of socio-economic structures (macrostructure), rather than the actions of individuals (microstructure). Etymologically, “history” means research. A traditional distinction between history as rerum gestarum - an account of things that happened -, and history as res gestae - things that happened - juxtaposes the subjective and objective senses of history. History as narration, as an account of things that happened, involves the subjectivity of the historian that built the account. On the other hand, as Howsbawm (1997) points out, even if texts written by historians are subjective, the facts these texts were based on can be verified. If this is not the case, we cannot refer to such a text as history, though perhaps as literature. For Hobsbawm, then, history is both subjective and objective. This subjectivity-objectivity controversy is not the only one widely discussed among historians and philosophers of history. A characteristic of historiography throughout the twentieth century has been the lack of agreement among historians over the question of what history is, over its object of study and over its methodology. Different schools have defended different views. Table 1 presents a simplified overview of these differences. From a positivist point of view, history should study historical facts. Historians should look for evidence that leads to a reconstruction of the past that is as precise as possible. This would be the goal of history: to reconstruct the past so to discover “the truth” about what happened. This reconstruction should be objective. There is no room for the historian’s interpretation of those facts. What is stressed, in the positivist view, is the relevance of historical method to find evidence and to work with documents. Two dates stand as landmarks in the development of a challenge to the positivist approach. The first is 1929, when the journal Annales d’Histoire Economique et Sociale was founded in Strasbourg by Marc Bloch and Lucien Fevre (Stoianovich, 1976). The second is 1950, when the IX World Conference on Historical Sciences was held in Paris. It was at this conference that these new conceptions of historiography were presented. For the representatives of the so-called School of

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Annales, history is the study of men in society. All men, even those not belonging to the upper classes, are part of history and should be studied. For philosophers of history such as Bloch and Fevre, the supreme value given by the positivists to official documents meant that historians were studying only the view of the dominant political classes, biasing our view of the past and constraining a more complete understanding of it. Historians begin their search for evidence from a hypothesis, a critical view of a specific problem, so that history cannot avoid the subjectivity introduced by a particular historian’s interpretation. This does not mean that history is absolutely subjective. Hypotheses built by historians must be demonstrable through evidence, and able to be falsified. Otherwise, history would be no more than fiction, literature. Thus, history cannot be a mere narration of facts. Historians should look for problems to be solved through historical research. The Marxist view of history had great repercussions in historiography throughout the twentieth century, and continues to do so - in a modified way - as we enter the twenty-first. The materialist view of history focused on the analysis of the means of production. Class war would constitute the engine of history. Historians supporting the Marxist view have concentrated on the role of social and economic structures in past societies, to explain, for example, how it was possible for capitalism to come about. Relationships between social and economic structures and conditions, on the one hand, and individuals’ consciousness, on the other, are dynamic, and therefore subject to analysis. One of the goals of history would be to show how social and economic conditions can change individuals: their way of life, ideology, opinions, beliefs, and so on. Quantitative history (cliometrics) considers history as the study of quantitative variables that may be relevant to an explanation of the past. For instance, the quantification of social, economic and demographic indicators can offer historians the possibility of more objective comparisons and a clearer picture of how people lived in the past. In economic analyses of past societies, statistical indicators become crucial. The School of Mentalities was considered by some as an extension of the School of Annales. However, the School of Mentalities is interested in how individuals or social groups saw themselves in the particular contexts in which they lived. The goal of history would be the understanding of the past, achieved through the comprehension of people’s feelings, motives, thinking, ideas, etc. To avoid presentism and to develop empathy would be a crucial skill of historians in their descriptions of the particular conditions and contexts of the past. The last fifteen or so years have seen a proliferation of studies on the private life of particular groups (e.g. Duby, 1985). Due to the influence of positivist perspectives, and also to the School of Annales, the Marxist view and Quantitative History, this traditional feature of history has been undervalued, and to some extent removed from the practice of history. Nevertheless, during the late 1970s and the 1980s, work such as that published by Ricouer (e.g. 1983, 1991) and White (e.g. 1973, 1987) have supported a revival of narration as an integral part of history. Narrative discourse is much more than a mere vehicle of knowledge transmission. Discourse is not neutral. For Ricouer,

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historical events have the same structure as narrative discourse, and this constitutes the difference between natural phenomena and historical events. Narration is what distinguishes history from other sciences. Ricouer considers that individuals make history, are in history, and are themselves historical beings. Therefore, subjectivity and narration are intrinsic to the nature of history. History as a discipline generates several controversies, some of them closely related, that are the subject of heated debate, and are far from being solved. Below is a brief summary of some of them: The conception of history, and what should be studied. The two right-hand columns of Table 1 summarise the different views regarding this point. The methodology of history. Is there a specific method historians should follow in the analysis of documents? Which sources are valid? Positivists and Marxists, for example, defend the idea of a specific method for history. And while the positivists place a high value on official documents, the School of Annales and the School of Mentalities would accept a wider range of evidence. Representatives of quantitative history would not advocate a particular method, simply stressing the need to use statistics and economic indicators to obtain the necessary data. Objectivity-subjectivity of history. Is history objective or subjective? The different historiographical positions described above and in Table 1 indicate how each one would answer this question. Positivists are at one of the extremes: history must be objective. Those that defend history as narration are at the other pole: history cannot be objective. An intermediate position would consist in arguing that historians interpret evidence, and that they are therefore subjective to some extent; however, hypotheses and theories should be developed following a method, and based on evidence. Facts occurred, and we know about them thanks to evidence we find from the past. This would be the “objective” part of history. The individual-society controversy. Should history attend to individuals, how they felt, how they thought and how they lived or, on the other hand, should it analyse social and economic structures and relationships? Should historians look for patterns in history? Are there general laws or models that can explain what happened in the past and predict, to some extent, what will happen in the future? The School of Annales, the School of Mentalities and advocates of History as Narration stress the importance of individuals in history . History is the study of men. In contrast, positivists, Marxists and those representing quantitative history would argue that history should focus on social and economic structures, even though, for example, quantitative social and economic indices may be useful for describing how some particular groups lived. The Marxist view of history provides a general model of the development of social and economic structures. Also, although the School of Annales and the School of Mentalities are interested in individuals, some models could be developed to explain the behaviour of social groups.

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What is history useful for? Most of the positions reviewed consider, regardless of other goals, that history should explain the past, but their concept of explanation is not always the same. For the School of Mentalities, explanation involves an empathic understanding of people: what they felt and thought, their motives, etc. Intentional explanations are important for them. On the other hand, the Marxist and School of Annales approach is mainly concerned with causal explanations, though they differ with regard to what is explained and how. For positivists, there is no need to explain, just to give an accurate account of facts. What it means to explain in history is a highly controversial issue into which, for reasons of space, I shall not delve any deeper here. Related to the difficulties of defining explanation in history is the concept of time. For example, how much time should elapse before historians develop an explanation? Which temporal frame of reference should explanations use; that of individuals, of groups, of institutions, of structures? Time. Time is at the core of history. Carr (1961) defines history as a continuous process of interaction between the historian and the facts, a never-ending dialogue between present and past. But what is the nature of these relationships? Chronology is a part of history, but historical knowledge is not based only on dates. For instance, it is impossible to fix the date of the beginning of Britain’s Industrial Revolution. A particular event is a reflection of what was happening in a society, a reflection of more general processes and of the context in which it took place. The incidents at La Bastille reflected what was happening in pre-Revolutionary France. Braudel (1966) stated that history works with different time scales: days, years, centuries, and so on. He distinguished three planes of analysis on which the historian works, and which involve different time scales. Chronicles, mere accounts of facts put together, is the first of these planes. The second is concerned with longer-lasting events, such as the French Revolution or World War I, where the unit of time may be 10, 20, 50 years or more. Events are explained and related, free of anecdotal detail. Finally, a third plane is for events or phenomena that covered much longer periods of time - one or more centuries -, examples of which would be Feudalism or the Renaissance. As can be seen, the landscape of historiography is somewhat complex as outlined up to now. Many of the controversial issues relate to history meta-concepts (see Figure 1). In contrast to what textbooks often reflect, history is much more than a mere account of dates, facts and explanations in terms of causes and consequences presented as a true representation of what happened in the past. Nevertheless, writers of textbooks and history curricula appear reluctant to introduce different views of history or any type of reflection upon what history is and why it can be useful for students.

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3.2. Implications for History Learning and Teaching: What Should Be the Goals of High School History Teaching?

What goals should conceptual change in history pursue? According to the definition of conceptual change used throughout this chapter, its goals in history will depend on how high school history teaching is conceived. Thus, before addressing the question regarding the goals of conceptual change, let us consider some of the objectives that, in my opinion, history teaching should set. I shall focus on three aspects: epistemological features of history and what history learning means, skills to be trained, and concepts that should be taught. 3.2.1. Teaching Epistemological Features of History and What History Learning Means

A first conclusion to be drawn from the previous section is that history can be viewed from many perspectives. From an epistemological point of view it is open to discussion, and there is no dominant position that is generally accepted by the community of historians. Therefore, history teaching should try to provide a broader picture of what history is. As illustrated above, many students consider there is only one true history: the one that is written in their textbook, and which should be studied by students the world over. One goal to be pursued by history teachers would be to enrich what students think history is, how it is built, who builds history and why . A problem history teachers complain about is the lack of motivation shown by their students. One of the aspects that may affect students’ motivation to study history is how far they consider history to be useful for them, and to what extent they feel involved in historical content. History teachers should encourage reflection and discussion on this point. Historiographers and historians themselves disagree on this matter. Those that consider it is possible to observe some patterns argue that history can contribute to predicting (to some extent) the future, or the future behaviour of society. To understand the present, it is important to understand the past. In general, though, history is essential for individuals and society to develop an identity, and for transmitting social values and ideology. History allows individuals to learn about their roots, where they come from, but at the same time it provides a collective identity. Nationalism offers a good example of how history becomes essential for developing national or group identity. Such aspects may explain why there is often great controversy over the historical content to be included in the school curriculum. Many examples can be provided, but I shall refer to one from my own country. In the late 1990s, the central government of Spain tried to reform the content included in the official curriculum to be studied by all Spanish students aged 12 to 16. There was a move to include more topics from the history of Spain as a whole, to the detriment of regional and local history. The argument was that many Spanish children studied mainly the history of their autonomous region, and that more attention should be given to issues that affected the history of Spain, and which many considered to be more relevant for providing students with a basic knowledge

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of history. Of course, the regional governments, particularly those of Catalonia and the Basque Country, disagreed, and a social debate ensued over what historical content should be included in the compulsory programme, and what students really knew about Spanish history. Leaving aside the anecdotal aspects of the example, what I intend to illustrate is that history is part of our identity, which is why it awakens so many feelings and passions. Consider, for instance, the Palestinian-Israelian conflict and the passions and feelings aroused over Jerusalem, or over Macedonia in the Greeks. The existence of “Official history” and “Unofficial history” (see, e.g. Wertsch & Rozin, 1994) is another aspect of history as identity. Hobsbawm (1997) pointed out the risks of “manipulating” history, and the distortion to which passions may lead. History may become an instrument that is employed for indoctrination. This controversial side of history also derives from the impossibility of reconstructing exactly what happened in the past. Who is right? Is a neutral account of what happened possible? Each historical event is unique, even though, for some historians, patterns can be extracted from them. The question of subjectivityobjectivity in history is central, and, as we saw above, remains open to debate. History is a vehicle not only for ideology, but also for teaching values. These values are often implicit in the narrative with which students are presented. Let me illustrate this point with two excerpts from two old Spanish history textbooks for primary school pupils (aged 9 to 11). Both refer to the Arabs, what they were like and how they lived during the period in which they occupied the Iberian Peninsula (from 711 to 1492). One of these books was used in schools during the Second Republic (1931-1939); the other was used from 1943 until the 1960s, during the regime of General Franco that followed his victory in the Civil War. Try to guess which one is from the Republic period (with a socialist government) and which one is from the Franco era. Excerpt 1: ...The Moors loved neither Our Lord Jesus Christ nor the Virgin Mary. The Moors believed in a man called Mohamed. Mohamed said: “Kill our enemies wherever you find them.” And a Moorish king told them to devour all the Christian people until none of them could be found.” (Serrano de Haro, p. 40)

Excerpt 2: ...The Arab people were lazy and melancholic, but with an impressive and ardent imagination. Every little obstacle discouraged them, but they carried out the most difficult enterprises with extraordinary courage and decision. They were cunning, hypocritical and vindictive. They were apparently prepared to suffer any kind of humiliation in order to accomplish their objectives.” (Dalmau-Carlés, p.346)

As the reader can see, these excerpts present particular views of the Arab people, referred to as “Moors” (a term that has acquired a pejorative sense in the Spanish language). Intolerance is being implicitly transmitted in both. Often, after reading this kind of text students were asked to answer questions such as: “Were the Moors

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good people? Why?” The first text belongs to the Franco period, and even though it is only short excerpt, it is evident how religion is mixed with history, with the clear purpose of indoctrinating children in the Catholic religion and its values. The second excerpt is from the Republican period. What is striking on reading the Republican text is that the description of Arab people is as biased and pejorative as those found in textbooks published under the Franco government. My interpretation is that this was Spanish society’s view of Arab people in the period in which the books were used, independently of people’s political ideas. Today these texts are considered totally unacceptable, because our society has changed its values. The point I wish to underline through this example is how social values are reflected and transmitted through the history that students study. It is something of which society and teachers should be conscious. Therefore, what history should be taught? In my view, what school history teachers should consider as a goal of their classes is to encourage students to ask themselves about the following matters: the nature of history (“what is history?”), objectivity-subjectivity, the transmission of values and ideology, the purpose of history, and so on. One way of doing so would be to explore and work with metaconcepts, encouraging them to reflect on these and helping them to develop their own answers. Of course, students will be given a view by textbooks, parents, and society in general; but one of the most important goals of history teaching is to make it clear that this is only one view. There is not only one “true” history , and this is not a problem, it is simply the way history is. A more general aim would be to teach students to be able to analyse historical situations from multiple perspectives and levels of analysis, and to be conscious that they are receiving society’s values and identity through the accounts they read. Normal science as defined by Thomas Kuhn is the paradigm accepted by the majority of the scientific community, and therefore the dominant one. Historical content taught in schools should likewise be based on a wide consensus, but given that history involves transmission of identity, values and ideology, such a consensus is difficult to attain, and is often not the goal pursued. 3.2.2.

Teaching Skills for History Understanding

In accordance with the overview of different historiographical positions and the goals I have suggested in relation to the introduction of the epistemological features of historical knowledge in high school, certain skills would appear to be particularly relevant for history learning. Let us briefly consider some of the most important. Relativistic thought. Relativistic thought has been proposed as a post-formal stage of cognitive development (Kramer, 1983; Sinnott, 1984; Kramer & Woodruff, 1986). Kramer (1983) cited three features of relativistic thought: a) awareness of the relativistic nature of knowledge, b) acceptance of contradiction, and c) integration of contradiction into the dialectical whole. Kitchener (1983) proposed three levels of cognitive processing when people are faced with ill-defined problems , those that have more than one possible solution. At the first level, cognition, individuals

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compute, memorise, read, solve problems, etc. At the second, metacognitive level, individuals monitor their own progress when they are engaged in these first-order tasks. At the third level, epistemic cognition, individuals reflect on the limits of knowing and the criteria of knowing. Epistemic assumptions influence how individuals understand the nature of problems and decide what kinds of strategies are appropiate for solving them. These epistemic assumptions appear to be reflected in students’ reflective judgement stages. Reflective judgement is defined as the reasoning about the basis for knowing in relation to ill-structured problem-solving (Wood, 1983). Kitchener and Fischer (1990) presented a model of the development of this judgement, summarised in Table 2.

The attainment of Stage 5 (knowledge is uncertain and must be understood within a context: thus, it can be justified by arguments within that context) and Stage 6 (knowledge is uncertain, but constructed by comparing and coordinating evidence and opinion on different sides of an issue) fits quite well with some of the goals I have suggested history teaching should pursue. Historical knowledge is indeed uncertain, and must be understood within a context. To compare and co-ordinate evidence from multiple representations and opinions to justify different views or explanations -often contradictory- of a historical event is essential if history is considered as something more than a mere account of facts. Although some data appear to indicate that these final stages of cognitive development take place during late adolescence and adulthood (Kitchener, 1983), there is also evidence to suggest that sustained practice may facilitate their attainment (Kitchener et al., 1993).

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Narration, argumentation and problem-solving skills. Table 1 showed how some historiographical positions consider history as narration, while others view it as problem-solving or take the history-as-chronicle standpoint. Although these positions are rather difficult to reconcile, all of the views they represent are valid, and can be taught in high school. Practice in all of them should be provided, as it can contribute to the development of relevant skills for students. For example, teachers might suggest possible topics to be researched. Imagine the topic chosen is “society under feudalism”. The “problem” could be introduced by a film related to the topic (e.g. Robin Hood), followed by some questions about how people lived, asked by the students themselves. In this way, “problems” could be defined, and students would have to solve them, plan their strategies for dealing with them, look for evidence, etc. Some procedures and self-regulation skills applied to this domain could be trained: determining the goals of the problem, searching for information, selection of evidence, planning of searches, evaluation of results, etc. Students could also be asked to write a chronicle of events related to the topic that took place during feudalism, and by way of conclusion of the unit, they could write a narrative incorporating their view of the topic. In this way, they would also discover the differences between the various views on how to construct history. Analytical and integrational reasoning skills. Some of our previous research findings (e.g. Carretero & Limón, 1995; Limón & Carretero, 1998; Limón & Carretero, 1999) indicated that, on solving the historical problem presented, our historians sample was able to analyse the situation presented by distinguishing economic, social, political and ideological levels of analysis. They also contextualised the problem using their background knowledge about the period to which the problem referred. These results suggest that such skills are useful for problem-solving in history. Although the purpose of high school history teaching is not to train professional historians, a reasonable goal would be to teach students to look at different planes of analysis in a historical situation. This could constitute a first step towards building or evaluating multi-causal explanations. Integration of knowledge and contextualisation of situations also appear to be highly relevant skills. History teaching programs are often presented too chronologically, and lessons frequently focus too closely on particular areas or countries. For instance, lessons on the French Revolution explain what happened in 1789 and in the early Napoleonic period in France, but students are often not introduced to what was happening in other countries at the same time. They tend to look at historical events as though they were isolated facts, being unable to contextualise them in time and space, nor to integrate other knowledge they have. In my own view, one of the goals of history teaching should be to give students practice to help them relate events and situations and put them in context. 3.2.3.

Teaching Concepts for History Understanding

Although further research is needed, what the present results appear to support is that students’ understanding of substantive historical content is often filtered by their

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history meta-concepts and epistemological beliefs about history and its learning. On the other hand, these concepts would seem to provide, at least in theory, a good vehicle for introducing a richer view of history and its methodology. Thus, to deal with them explicitly seems to be a necessary goal for promoting history understanding. In particular, the concepts of time and space are crucial. As pointed out in Section 1, frequently history concepts -such as empire, revolution or democracy- are not taught explicitly, but rather within an account of a particular episode, and as a result, they may not receive as much attention from students as they should. History learning assessment should place more emphasis on such concepts: what teachers tend to evaluate is how much correct information students remember from the textbook accounts, but it is unusual to ask students to compare the types of concepts mentioned above in different historical situations, in order to give them meaning or relate them to others. In general, more attention should be paid to the teaching of history concepts. Also, as history contents are usually presented in a narrative way, students’ representations of particular events -such as the French Revolution or the American War of Independence- maintain this narrative or sequential structure. This can be an obstacle, or at least a difficulty, for students in their attempts to create a network of the concepts involved in the topic. For instance, with regard to the French Revolution, students may be able to talk about or write a sequence of the main events, but it would probably be much more difficult for them to elaborate a conceptual map in which they would have to represent their view of what a revolution is, or to reflect their understanding of the French Revolution, explaining the relationships among concepts such as monarchy, republic, bourgeoisie, nobility, peasants, craftsmen, sans-culottes, Enlightenment, church, etc. Further research is needed to assess how content presentation can affect students’ representations. Finally, although history curricula and history textbooks often include too many dates and names of characters, it is true that these are also part of history content, and that it may be necessary for students to remember at least the most important dates, events and personalities. 4.

CONCEPTUAL CHANGE IN HISTORY AND SCIENCE

4.1. Students’ Prior Knowledge about History and Science and Conceptual Change

Research on misconceptions and students’ ideas and beliefs about science has provided some results that characterise naïve science, particularly in relation to physics. Table 3 presents a summary of some of these results, comparing them with the few research results we have about students’ knowledge in history. Before discussing some differences and similarities between students’ prior knowledge in science and in history, some general remarks should be made about Table 3. First of all, even though there is an enormous body of research on science concepts, we are still a long way from having a clear picture of students’ prior

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knowledge about science. The characteristics of students’ previous ideas and beliefs are not yet clear. For instance, there is still no agreement over whether they are fragmented or coherent -indeed, the issue is hotly debated (see, for example, the chapters by diSessa and Vosniadou in this volume). More research is necessary, though Table 3 attempts to summarise some general points that would probably be accepted by a majority of researchers. Secondly, students’ prior domain-specific knowledge is only a part of their prior knowledge, and cannot be considered in isolation. It is for practical reasons that I refer here only to students’ prior domain-specific knowledge. However, a wider perspective is needed in order to develop theoretical models of conceptual change that work in the classroom. Thus, such models should focus not only on students’ prior knowledge, but also on its interaction with prior skills (e.g. learning strategies, thinking skills, self-regulation), prior attitudes and prior motivation. Also teacherlearner interaction and the context in which learning takes place must also be taken into account. Thirdly, research on students’ prior knowledge in history is extremely scarce. Thus, the contents of Table 3 are quite provisional and tentative. In fact, Table 3 is simply a reflection of my own view of a possible comparison between students’ prior knowledge in science and history. My aim is to promote further discussion on the topic, and in no way to present a prescriptive and exhaustive comparison. 4.1.1. Some Differences between Students’ Prior Knowledge about Science and about History

Differences between students’ prior knowledge about science and about history result mainly from the different epistemological nature of science and history, and to the way science and history are taught. The differences related to the nature of science and history knowledge have been partly dealt with in Sections 2 and 3 of this chapter. For example, students’ misconceptions about science concepts often have their origin in their experience of the physical world: how objects move, fall, etc. As such direct experience is not possible in history, students’ prior knowledge about history may have its origin in their social context (what they have heard from parents, relatives, friends, the mass media, teachers, etc.) and in school teaching. Also, misconceptions in science have often shown themselves to be useful and predictive for everyday life. This has been proposed as an explanation for their resistance to change. However, given the nature of history, the knowledge students may develop about concepts such us empire, democracy, war or revolution can be considered as fairly useless for everyday life. Their ideas about a particular event such as the French Revolution are not helpful for predicting anything in the real, day-to-day world. In this sense, they should therefore be less resistant to change, but since history is a vehicle for social values, ideology and identity, the so-called “affective entrenchment” of students’ prior knowledge about history, particularly for certain topics, is strong. We might say, therefore, that prior knowledge is very difficult to change because individuals do not want to change it (Limón, in press).

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In the context of science, students’ misconceptions are incorrect. School scientific content is considered a well-defined domain : there is a correct answer. Nevertheless, once again because of the nature of the discipline, there is no “correct history”, no single and unchangeable history. In a recent study (Limón, 2000), I asked some Spanish sixth and ninth-graders whether they considered Napoleon’s brother, Joseph I, as a legitimate king of Spain. Two possible views were presented to them. One of them offered arguments close to the version Spanish textbooks often suggest: Napoleon tricked the Spanish king, Charles IV and his son, the Crown Prince, for them to renounce their rights in favour of his brother. But the Spanish population saw the trick, and rebelled against the French army. The alternative version states that there was evidence that both Charles IV and his son signed a legal document renouncing their rights. Most of the students, even though they saw that both views were supported by arguments and were contradictory, maintained that Napoleon’s brother was not a legitimate Spanish king. Some of them said he could not be a Spanish king because he was a foreigner, or because the Spanish people did not want him. But although we might find evidence and arguments counter to these answers, it cannot be said that they are defending an incorrect view. A second group of differences between students’ prior knowledge about science and history is concerned with the way they are taught. As already pointed out in Section 1, in contrast to science concepts, those of history are usually taught, not independently, but within an account embedded in a narrative format. Students’ must infer their meaning, which may be different in different historical contexts. This constitutes an additional obstacle to the learning of historical concepts, and may explain why students do not show much consistency in their initial understanding. The huge number of concepts textbooks tend to introduce may also contribute to students not paying too much attention to the understanding of history concepts. Moreover, teachers’ insistence on assessing their students by asking them to reproduce textbook contents only serves to compound the problem. As regards the influence of history’s narrative format, more research is needed on the topic, though students’ representations are almost certainly affected. To use the language of computers, information may be “saved” in a sequential format, focusing on facts, dates, names and events, and following the rhetorical structure of a narrative: beginning, development and end. When students are asked to show their understanding of what happened by writing an explanation or by presenting their conceptual network in the form of a conceptual map, they would have to transfer the information they have saved to a different format. This process of transfer would make enormous demands on students. On the other hand, science teaching focuses more on teaching explicitly scientific concepts, such as mass, weight, force, energy, and so on. Relationships between concepts tend to be more explicitly indicated than in history lessons, where chronological order and narrative style guide the presentation of content. To what extent these differences in content presentation may influence students’ representations and understanding is a question to add to the research agenda.

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4.1.2. Some Similarities between Students’ Prior Knowledge about Science and about History It is often pointed out that many of the ideas students have about scientific phenomena have their origins in their daily life experience, where they are useful, relevant, and can be used to predict the nature of phenomena (Driver et al., 1985; Driver et al, 1996). In fact, everyday life also plays a role in students’ knowledge about history. Frequently, students’ ideas about particular events or concepts are presentists. That is, present day values, ideology and schemes are applied to the past without taking into account that they were different at that time. Such presentism indicates a lack of empathy. For instance, in the study I referred to above (Limón, 2000), in which I asked students whether Napoleon’s brother was a legitimate king of Spain, some of them said “no, because he was not elected by people”. This answer shows, apart from their lack of understanding of how any monarchy works, that they have applied to the past situation what they know from the present day about how political representatives (though not kings) obtain their positions: they are elected. They probably also think every citizen was allowed to vote at that time, which once again constitutes a wrong application of their knowledge. These are clear mistakes that show a lack of empathy and of contextual changes across time. In these cases, it can clearly be said that students’ intuitive ideas about history are incorrect. Context also plays a role in students’ ideas about science and about history. In the case of history, the contextualisation of concepts and events according to the time and place in question are essential for a proper understanding, as can be seen in the example described above, in which students were unable to distinguish present from past context. However, in order to understand the importance of that decision for Napoleon, and why he might do such a thing, it is also necessary to know what was happening in Europe at that time. In the case of students’ ideas about science, it has also been shown how they have difficulties in differentiating the school context, where they are asked to apply the content they have been taught there, from the everyday life context, where misconceptions may be valid. Some authors (e.g. Caravita & Hallden, 1994) have suggested that to obtain conceptual change would involve teaching students to differentiate between contexts. This could be a valid goal for conceptual change both in science and in history. Epistemological beliefs about what history is and what history learning means are closely related to second-order concepts, which seem to work as a filter for history understanding. Students’ understanding of these meta-concepts is often implicit, as is the case with most misconceptions. Recently, research on epistemological beliefs in science and what science learning means has shown that such beliefs may also be essential for science understanding (e.g. Carey et al., 1989; Hofer & Pintrich, 1997; Mason, 2001, Leach and Mason’s chapters, this volume). In some cases, it has been shown they may explain why students do not change their prior ideas about science.

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Finally, the nature of students’ ideas about science and about history is still uncertain. This is a common problem in both areas of research. Even though some progress has been made in this area, further research is needed to describe more accurately students’ prior domain-specific knowledge. Researchers have debated whether students’ prior knowledge about science is consistent or not, coherent or not, stable or unstable, and the extent to which it is entrenched. In my opinion, consistency, coherence, stability, entrenchment, particularly affective entrenchment,

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and certainty may be viewed as features that characterise students’ domain-specific prior knowledge. These features might be understood as continuums. Table 4 offers a summary of them and the extreme points of the continuums they represent. But not all domain-specific knowledge has the same level of specificity. For example, knowledge about Roman houses is more specific than knowledge about how Roman people lived. Knowledge about oxidation-reduction reactions in chemistry is more specific than knowledge about chemical reactions in general or the nature of matter. For conceptual change purposes, and to characterise domainspecific prior knowledge that must be changed, it is relevant to know its degree of specificity. By way of an example, in a study I designed about the expulsion of the Moriscos from Spain in 1609 (see Limón & Carretero, 1998; Limón & Carretero, 1999), specialists in that historical period were posed a quite specific problem on the topic. One of the purposes of the task was to record participants’ changes of their initial answer. Although some of them noticed that certain data presented in the task were contradictory to their prior knowledge, and they recognised the reliability of these data, at the end of the task they said that they would not change their initial ideas, since the problem in question was only one particular case. How many particular cases would they have needed to change the positions based on their domainspecific prior knowledge? Although they accepted making changes to their knowledge about the content of the problem studied, they were not prepared to make wider changes. This may also be happening with younger, non-specialist students, and may explain some failed research attempts to achieve conceptual change. When students are faced with a specific task about a scientific phenomenon, they may change highly-specific knowledge, but this may not be sufficient to make them change higher-order ideas or beliefs, with a greater degree of generality. They may not be able to generalise or transfer the changes achieved. Thus, although the conceptual change task may be working, with some changes being produced, they are not the changes researchers or teachers are aiming for. Further research is needed to study how the degree of specificity-generality of individuals’ domain-specific prior knowledge may interact with the level of specificity-generality demanded by the conceptual change task. The certainty trait refers to students’ degree of certainty about their knowledge. It allows us to locate on the continuum weak beliefs, which individuals cannot justify and that indicate they are not certain at all, and, at the other extreme, solid knowledge, strongly entrenched. As in the case of the other traits, further research would be needed to describe and locate intermediate points of the continuum. If domain-specific prior knowledge is highly uncertain (a mere weak belief), inconsistent, incoherent, unstable, low affective entrenched and highly specific, it is likely that conceptual change would not be very difficult to achieve. On the other hand, if individual’s domain-specific prior knowledge is highly certain, consistent, coherent and stable, strong affective entrenched and general, it will be very difficult to be changed. Of course, predictions about the likelihood of conceptual change are not so clear when individuals’ domain-specific prior knowledge does not show a clear extreme

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pattern, but rather a combination of intermediate points. Further research is needed to be able to make such predictions. The nature of domain knowledge may also contribute to differences between the features of individuals’ domain-specific prior knowledge: affective entrenchment is often high in the history domain, but appears to be lower in physics, though these tendencies may vary across particular tasks and particular individuals. For example, let us imagine two scientists that have been working for a long time in a particular area, and who support opposing theories. If they are asked to solve a particular problem, whose results are conflicting for both of them, their domain-specific prior knowledge will likely show high levels of affective entrenchment. Other questions for the research agenda concern how domain-specific knowledge acquisition might change these traits, in what direction, and how this might influence conceptual change. The domain-specific prior knowledge features shown in Table 4 do not represent a closed or exhaustive list. Features could be added or deleted in the future. It is merely a theoretical proposal to promote further discussion that may contribute in the future to a more accurate picture of domain-specific prior knowledge. Moreover, it is also necessary to develop effective assessment tools. 4.2.

Goals of Conceptual Change in History and Science

What are the goals that conceptual change in history and science should pursue? What kinds of changes should be promoted in history? Should it be taught differently from science? As we have seen throughout this chapter, there are epistemological differences between history and science that involve some differences related to: a) students’ acquisition of domain-specific prior knowledge, b) the way science and history are taught, and c) the skills to be developed in each discipline. These differences mean that some of the changes to be achieved through conceptual change also differ to some extent. For example, as discussed above, second-order concepts in history appear to act as a sieve for understanding other substantive content. Dealing with these concepts would appear to be an essential goal of history teaching. Modifying them would constitute an important step on the road to conceptual change -in both science and history-, though it is in the latter case that the matter is more urgent, and in which it should be given priority by teachers and those that design curricula. In the course of the chapter, some differences between science and history have been discussed with regard to the understanding of particular concepts. Although the two domains share the goal of changing students’ inadequate understanding of particular concepts, differences between students’ prior knowledge may involve differences in the way it can be changed. Some traditional strategies for conceptual change, such as the presentation of alternative views to create a conflict, may constitute an excellent vehicle for helping students to develop skills such as relativistic thought, argumentation, analysis and integration of information,

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contextualisation and empathy understanding, all of which are essential for history learning. Another central goal of conceptual change in history is the modification of students’ attitudes, values and ideology. Although modification of certain attitudes may also be a goal of conceptual change in science, it is far more necessary in relation to history. The narrative style usually found in the presentation of historical content may influence students’ representations, in which content tends to be ordered sequentially, with the concepts embedded, and sometimes hidden, in the narration. This may lead to difficulties in the understanding of concepts and for establishing relationships among them. If students are asked to elaborate a conceptual map of particular concepts presented through narration, they may have to change the “format” of their initial representation, and to do so they will have to retrieve information in a different way from that in which it was “saved”. Although further research is needed to confirm this hypothesis, a possible goal of conceptual change in history would be to help students enrich their initial representations by developing conceptual relationships. This would involve changing their initial representation format (the way the information is “stored”). Clear goals to be set for conceptual change in both the history and science domains are to make explicit to students what must be changed, to help them to understand the usefulness of such changes, and to make them feel involved in the task. It is in this way that intentional conceptual change (Sinatra & Pintrich, 2002) can be promoted. As it has been shown in this chapter, some of the goals related to conceptual change are common to history and science, though many differ considerably. Further research and theoretical progress is needed to explain how the particular conditions leading to conceptual change in history might be satisfied. 5.

CONCLUSIONS

Finally, let us consider some general conclusions regarding our initial question about the extent to which conceptual change models in science, especially physics, could be applied to other domains, and particularly to history. Firstly, as I have tried to show in this chapter, there are important epistemological differences between science and history that lead to differences in the teaching goals and skills to be developed in the two domains. These differences mean that the models available from science cannot be applied to the question of conceptual change in history. Nevertheless, these models have been of great help in promoting research, opening up comparisons among domains, and generating questions that contribute to making progress in the field. Secondly, we do not yet have an accurate picture of individuals’ domain-specific prior knowledge, either in science or in history. The picture we have in the case of history is especially vague. To be able to explain conceptual change processes, it appears essential to obtain a clearer view of domain-specific prior knowledge, to

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develop efficient tools for its assessment and to identify more precisely how conceptual change should be promoted. Thirdly, it is important to remember that domain-specific prior knowledge is only a part of students’ prior knowledge, and that this prior knowledge interacts with motivation, learning, thinking and self-regulation, all of which appear to play a role in the achievement of conceptual change. Further research in different domains is necessary to provide data that may be useful in identifying more precisely the similarities and differences of conceptual change across domains, and in developing suitable models that are able to take account of such similarities and differences. REFERENCES Alonso Tapia, J. (1997] August). New tasks for assessing how students 12-14 years-old understand historical causality. How do such students understand the role of causal factors that produced the Industrial Revolution in Britain? Paper presented at the Euroepan Conference for Research on Learning and Instruction, Athens, Greece. Angvik, M., & von Borries, B. (1997). Youth and History. A comparative European survey on historical consciousness and political attitudes among adolescents. Hamburg, Germany: Körber Stiftung. Ashby, R., & Lee, P. (1987a). Discussing the evidence. Teaching History, 48, 13-17. Ashby, R., & Lee, P. (1987b). Children’s concepts of empathy and understanding in history. In C. Portal (Ed.), The history curriculum for teachers (62-88). Lewes, UK: The Falmer Press. Beck, I. L., & McKeown, M. G. (1994). Outcomes of history instruction: Paste-up Accounts. In M. Carretero & J. F. Voss (Eds.), Cognitive and instructional processes in history and the social sciences (pp. 237-257). Hillsdale, NJ: Lawrence Erlbaum Associates. Berti, A. E. (1994). Children’s understanding of the concept of the state. In M. Carretero & J. F. Voss (Eds.), Cognitive and instructional processes in history and the social sciences (pp.49-75). Hillsdale, NJ: Lawrence Erlbaum Associates. Bloch, M. (1952). Introducción a la Historia. Mexico: Fondo de Cultura Económica. (Original work published in French, 1949). Boscolo, P., & Mason, L.(2001). Writing to learn, writing to transfer. In P. Tynjälä, L. Mason, & K. Lonka (Eds.), Writing as a learning tool. Integrating theory and Practice (pp. 83-104). Dordrecht, The Netherlands: Kluwer Academic Publishers. Braudel, F. (1966). Las civilizaciones actuales [Le monde actuel, histoire et civilisations]. Madrid: Tecnos. Braudel, F. (1969). Écrits sur l’histoire [Writings about history]. Paris: Flammarion. Britt, M. A., Rouet, J. F., Georgi, M. C., & Perfetti, C., A. (1994). Learning from history texts. From causal analysis to argument models. In G. Leinhardt, I. Beck, & C. Stainton (Eds.), Teaching and Learning in History. Hillsdale, NJ: Lawrence Erlbaum Associates. Brophy, J. (1992). Fifth Grade US history: How one teacher can arrange to focus on key ideas in depth. Theory and Research in Social Education, 20, 141-155. Burke, P. (Ed.) (1991). New perspectives on historical writing. Polity Press. Carey, S., Evans, R., Jay, E., & Unger, C. (1989). “An experiment is when you try and see if it works”: A study of seventh grade students' understanding of the construction of scientific knowledge. International Journal of Science Education, 11, 514-529. Caravita, S., & Halldén, O. (1994). Re-framing the problem of conceptual change. Learning and Instruction, 4, 89-111. Carr, E. H. (1961). What is History? London: Pellican. Carretero, M., Asensio, M., & Pozo, J. I. (1991). Cognitive development, causal thinking and time representation in adolescence. In M. Carretero, M. Pope, R. J. Simmons, & J. I. Pozo (Eds.), Learning and instruction. European research in an international context (Vol. 3, pp. 27-48). Oxford, UK: Pergamon Press. Carretero, M., & Limón, M. (1995). Construcción del conocimiento y enseñanza de las Ciencias Sociales y la Historia In: M. Carretero, L. Jacott, M. Limón &, A. López-Manjón, Construir y enseñar: las Ciencias Sociales y la Historia (pp. 31-56). Madrid: Visor.

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Carretero, M., López-Manjón, A., & Jacott, L. (1997). Explaining historical events. International Journal of Educational Research, 27, 245-253. Cohen, G. A. (1978). Karl Marx’s theory of history: a defence. Oxford, UK: Clarendon Press. Collingwood, R. G. (1946). The idea of History. London: Oxford University Press. Dalmau-Carlés, J. (1936). Enciclopedia Ciclico-Pedagógica. Grado Medio [Pedagogical Encyclopaedia for primary school]. Gerona, Spain: Dalmau-Carlés & Pla. Driver, R., Guesne, E., & A. Tiberghien (Eds.) (1985). Children's ideas in science. Milton Keynes, UK: Open University Press. Driver, R., Leach, J., Millar, R., & Scott, P. (1996). Young people’s images of science. Buckingham, UK: Open University Press. Equipo Alambique Editex (2000). Historia. 2° curso de ESO [History. 2nd. Course of Secondary School]. Madrid: Editex. Fevre, L. (1953). Combats pour l’histoire. Paris. Hobsbawm, E. (1997). On history. London: Weidenfeld & Nicholson. Hofer, B. (2001, April). “How do I know what to believe?” Learning online: Epistemological awareness and Internet searching. Paper presented at the annual meeting of the American Educational Research Association, Seattle, WA. Hofer, B. K., & Pintrich, P. R. (1997). the development of epistemological theories: Beliefs about knowledge and knowing and their relation to learning. Review of Educational Research, 67, 88-140. Jacott, L., López-Manjón, A., & Carretero, M. (1998). Generating explanations in history. In J. F. Voss, & M. Carretero (Eds.), Learning and reasoning in history (pp. 307-330). London: Woburn Press. Kitchener, K. S. (1983). Cognition, metacognition and epistemic cognition: A three-level model of cognitive processing. Human Development, 4, 222-232 Kitchener, K. S., & Fisher, K. W. (1990). In D. Kuhn (Ed.), Contributions to Human Development: Vol. 21. Developmental perspectives on teaching and learning thinking skills (pp. 48-62). Basel, Switzerland: S. Karger AG. Kitchener, K. S., Lynch, C. L., Fischer, K. W., & Wood, P. K. (1993). Developmental range of reflective judgment: the effect of contextual support and practice on developmental stage. Developmental Psychology, 29, 893-906. Kramer, D. A. (1983). Post-formal operations? A need for further conceptualization. Human Development, 26, 91-105. Kramer, D. A., & Woodruff, D. S. (1986). Relativistic and dialectical thought in three adult age-groups. Human Development, 29, 280-290. Kuhn, D., Weinstock, M., & Flaton, R. (1994). Historical reasoning as theory-evidence coordination. In M. Carretero & J.F. Voss (Eds.), Cognitive and instructional processes in history and the social sciences (pp. 377-402). Hillsdale, NJ: Lawrence Erlbaum Associates. Le Goff, J., & Nora, P. (1974). Faire l’histoire [Making History]. Paris: Gallimard. Lee, P. , Dickinson, A., & Ashby, R. (1998). Researching Children’s ideas about history. In J. F. Voss,& M. Carretero (Eds.), Learning and reasoning in history (pp. 307-330). London: Woburn Press. Levstik, L. S., & Pappas, C. C. (1992). New directions in studying historical understanding. Theory and Research in Social Education, 20, 369-385. Limón, M. (1977, August). Exploring historical concepts understanding: students’ ideas and explanations about the concept of revolution. Paper presented at the meeting of the European Association for Research on Learning and Instruction, Athens, Greece. Limón, M. (2000). Motivación y cambio conceptual: implicaciones para el aprendizaje y la enseñanza de las Ciencias Naturales, la Historia y la Etica en la E.S.O. [Motivation and conceptual change: implications for science, history and ethics learning and teaching ]. Madrid: CIDE. Limón, M. (in press). The role of domain specific in intentional conceptual change. In G. M. Sinatra & P. R. Pintrich (Eds.), Intentional conceptual change. Mahwah, NJ: Lawrence Erlbaum Associates. Limón, M., & M. Carretero, M. (1997). Conceptual change and anomalous data: a case study in the domain of natural sciences. European Journal of Psychology of Education, 12, 213-230. Limón, M., & Carretero, M. (1998). Evidence evaluation and reasoning abilities in the domain of history : an empirical study. In J. F. Voss & M. Carretero (Eds.). Learning and reasoning in history. London: Woburn Press. Limón, M., & Carretero, M. (1999). Conflicting data and conceptual change in history experts. In W. Schnotz, S. Vosniadou, & M. Carretero (Eds.). New perspectives on conceptual change (pp. 137160). Amsterdam: Pergamon/Elsevier.

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Martorella, P. (1991). Knowledge and concept development in social studies. In P. Shaver (Ed.), Handbook of research on social studies teaching and learning (pp. 370-384). New York: Macmillan. Mason, L. (2001). Verità e certezze. Natura e sviluppo delle epistemologie ingenue [Truth and certainty. Nature and development of naïve epistemological beliefs]. Roma: Carocci. McKeown, M. G., & Beck, I. L. (1990). The assessment and characterization of young learners’ knowledge of a topic in history. American Educational Research Journal, 27, 688-726. Pontecorvo, C., & Girardet, H. (1993). Arguing and reasoning understanding historical topics. Cognition and Instruction, 11, 365-395. Portal, C. (1987). Empathy as an objective for history teaching. In C. Portal (Ed), The history curriculum for teachers (pp. 89-102). Lewes, UK: The Falmer Press. Porter, R., & Teich, M. (Eds.) (1986). Revolution in history. Cambridge: Cambridge University Press. Ricouer, P. (1983). Temps et récit [Time and Narrative]. Paris: Editions du Seuil. Ricouer, P. (1991). Narrative identity. In D. Wood (Ed.), On Paul Ricouer: Narrative and interpretation. London: Routledge. Rosch. E. (1978). Principles of categorization. In E. Rosch & B. Lloyd (Eds.) Cognition and categorization (pp. 27-48). Hillsdale, NJ: Lawrence Erlbaum Associates. Ross, A. (Ed.) (1999).Young citizens in Europe. Proceedings of the first Conference of the Children’s Identity and Citizenship in Europe Thematic Network. London: University of North London. Ross, A. (Ed.) (2000). Developing identities in Europe: Citizenship education and higher education.. Proceedings of the second Conference of the Children’s Identity and Citizenship in Europe Thematic Network. London: University of North London. Rouet, J. F., Marron, M. A., Perfetti, C. A., & Favart, M. (1998). Understanding historical controversies: students’ evaluation and use of documentary evidence. In J. F. Voss & M. Carretero (Eds.), Learning and reasoning in history (pp. 95-116). London: Woburn Press. Serrano de Haro, A. (1943). Yo soy español: el libro del primer grado de Historia [I am Spanish: the book for the first grade of history]. Madrid: Paraninfo. Shemilt, D. (1984). Beauty and the philosopher: empathy in history and classroom. In A. K. Dickinson, P. J. Lee, & P. J. Rogers (Eds.), Learning history (pp. 39-84). London: Heinemann Educational Books. Shemilt, D. (1987). Adolescent ideas about evidence and methodology in history. In C. Portal (Ed.), The history curriculum for teachers (pp. 39-61). London: The Falmer Press. Sinatra, G. M., & Pintrich, P. R. (Eds.) (2002). Intentional conceptual change. Mahwah, NJ: Lawrence Erlbaum Associates. Sinnott, J. D. (1984). Postformal reasoning: The relativistic stage. In M. L. Commons, F. A. Richards, & Armon, C. (Eds.), Beyond formal operations. Late adolescent and adult cognitive development (pp. 298-325). New York: Praeger. Stoianovich, T. (1976). French historical method: The Annales paradigm. Ithaca, NY: Cornell University Press. Thornton, S. J., & Vukelich, R. (1988). Effects of children’s understanding of time concepts on historical understanding. Theory and Research in Social Education, 16, 69-82. van der Leeuw-Roord, J. (Ed.) (1998). The state of history education in Europe. Hamburg, Germany: Körber-Stifttung. VanSledright, B. A., & Brophy, J. (1992). Storytelling, imagination and fanciful elaboration in children’s historical reconstructions. American Educational Research Journal, 28, 495-519. VanSledright, B. A., & Kelly, C. (1998). Reading american history: The influence of using multiples sources on six fifth graders. The Elementary School Journal, 98, 239-266. VanSledright, B. A., & Frankes, L. (2000). Concept-and-strategic knowledge development in historical study: A comparative exploration in two fourth-grade classrooms. Cognition and Instruction, 18, 239-283. Voss, J. F., Carretero, M., Kennet, J., & Silfies, L. N. (1994). The collapse of the Soviet Union: A case study in causal reasoning. In M. Carretero & J. F. Voss (Eds.), Cognitive and instructional processes in history and the social sciences (pp. 403-430). Hillsdale, NJ: Lawrence Erlbaum Associates. Wertsch, J. V., & Rozin, M. (1998). The Russian revolution: Official and unofficial accounts. In J. F. Voss & M. Carretero (Eds.), Learning and reasoning in history. London: Woburn Press. White, H. V. (1973). Metahistory. Baltimore, MD: John Hopkins University Press. White, H. V. (1987). The content of the form: narrative discourse and historical representation. Baltimore: John Hopkins University Press.

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Wineburg, S. (1991). Historical problem solving: A study of the cognitive processes used in the evaluation of documentary and pictorial evidence. Journal of Educational Psychology, 83, 73-87. Wineburg, S. (1998). Reading Abraham Lincoln: An expert/expert study in the interpretation of historical texts. Cognitive Science, 22, 319-346. Yeager, E. A., Foster, S. J., Maley, S. D., Anderson, T., Morris, J. W., & Davis, O. L. (1998, April). The Role of empathy in the development of historical understanding. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.

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CONTENT AND CONCEPTUAL CHANGE: A COMMENTARY

RICHARD WHITE Monash University, Australia

Abstract. This is a commentary on the chapters by Stavy, Tsamir, and Tirosh, Leach and Lewis, Merenluoto and Lehtinen, and Limón. The chapters address two important questions: Is each topic idiosyncratic, or are there principles that apply across a number of topics? Does conceptual change require a different type of knowledge that enables learners to see a subject and the topics within it in a new way? The chapters find common ground in recommendations for teaching to promote conceptual change: attention to epistemology, alternative views, sources of beliefs, linking within and between topics, and diverse forms of testing.

1.

INTRODUCTION

The chapters in this section deal with subtle aspects of subject matter that need to be taken into account in any consideration of conceptual change. Teachers naturally have always been interested in the content that they aim to pass on to their pupils, but their understanding of it is generally more that of the scientist, mathematician, historian, or linguist than that of the learning theorist and educational psychologist. Until recently, learning theorists themselves had little to say about content. Prominent writers on learning such as Ausubel (1968), Gagné (1965), Bruner (1960), and Skinner (1968) did not make fine discriminations between disciplines, nor between topics within a discipline. Nor was content a variable in research. In almost all research before the mid-1970s on teaching and learning, subject matter was no more than a necessary vehicle. In the many experiments that compared one teaching method with another, any topic was as good as another. Another characteristic of this research was lack of interest in differences between learners in what they believed. Behaviourism took no account of differences in topics or in learners’ beliefs. Before its onset there were studies of the psychology of content. An example is Judd’s investigation in the first decade of the twentieth century of the influence of knowledge of refraction on ability to spear fish. The few early studies did not, however, lead to continuing interest in content. While, at least in the United States, behaviourism was dominant, Piaget was investigating young children’s beliefs about specific phenomena, such as the way the moon appears to follow you as you walk. Decline in satisfaction with behaviourism and the rise in interest in Piaget’s work, which became evident in the 1960s, lifted interest in content and in individual’s beliefs. Replications of Piaget’s observations became common, especially in topics that form part of science and M. Limón & L.Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 291-297. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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mathematics such as conservation of number, mass and volume, classifications, and sequencing by size. Later, studies of situated cognition in mathematics learning (e.g. Lave, 1988; Nunes, Schliemann, & Carraher, 1993) not only emphasised the importance of context but also directed further attention to content. In science, studies of students’ beliefs mushroomed (Pfundt and Duit, 1994, provide a bibliography of several thousand studies). The initial studies in science were descriptive, in which researchers reported elucidations of students’ beliefs. They uncovered many instances where students’ conceptions were at odds with scientists’ portrayal of the world, and often where they differed from what they had been taught in school. The next phase of research was to see how alternative conceptions could be displaced by the scientists’ portrayal. This proved to be much more difficult than the researchers had imagined. Even when students acquired the scientific explanation, they often kept their original contradictory beliefs as well (Brumby, 1979; Gunstone, Champagne, & Klopfer, 1981). In some contexts, such as formal school tests, they could respond with the scientific view, while in less formal out-of-school contexts they would rely on the earlier belief. Content-general principles for change in belief, such as the much-cited statement of Posner, Strike, Hewson, & Gertzog (1982) that it requires dissatisfaction with the present belief and that the new belief must be intelligible, plausible, and fruitful, did not lead to practical methods of intervention. It is not easy, for instance, to make people dissatisfied with an ingrained belief that must have been suiting them quite well for a long time. The difficulties that researchers experienced in their attempts to bring students’ conceptions into line with those of scientists stimulated interest in how alternative beliefs form in the first place. Although differences exist between theories of early learning, such as those of Carey (1985) and diSessa (1988), all accept the obvious principle that children form their ideas through interactions with the physical world. Play, in which they push, pull, drop and throw things, gives them notions of force and motion. Other experiences lead them to ideas of solids and liquids and gases, of living and non-living, and of plants and animals. Of course social transmission also has an effect. Parents, other adults and older children, stories and television, all present the child with interpretations of the world that might not be scientific. A point to note is that topics vary in their openness to both experience and social transmission. White (1994) attempted to codify this variation by defining dimensions of content. One dimension is how open a topic is to common experience, and another is how abstract it is. White argues that students are less likely to come to the classroom with beliefs about topics for which they have had little experience or that are abstract. White’s theme is that where a topic stands on the set of dimensions should influence how it should be taught, and how alternative conceptions might be addressed. White’s analysis is a step towards a sophisticated appreciation of subject matter and its teaching and learning. It deals with an important question: Is each topic idiosyncratic, or are there principles that apply across a number of topics with similar properties? The chapters in this section carry the sophistication further not only by providing positive evidence about that question, but also by opening up

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another important issue: Does conceptual change require a different type of knowledge that enables learners to see a subject and the topics within it in a new way? Though all four chapters bear on both questions, that by Stavy, Tsamir, and Tirosh is more directly concerned with the idiosyncratic nature of topics, and those by Limón, Leach and Lewis, and Merenluoto and Lehtinen more with knowledge that leads to a new perception. 2.

IDIOSYNCRACY VERSUS HOMOGENEITY OF TOPICS

I criticised above early research for treating content as homogeneous rather than as a variable that should affect the method of teaching. It would, however, make teaching even more difficult than it is if topics were totally diverse. That would require researchers to investigate every separate topic to discover, and then to try to counter, the alternative beliefs that students are likely to hold about it. Consequently one would hope that even if content is not psychologically homogeneous some regularities exist and can be found. That is, there is a half-way position, a balance between uniformity and individualistic chaos. Regularities lie behind Piaget’s stages of operational thought, where conservation is a general principle that applies to several quantities. They also appear in diSessa’s (1988) phenomenological primitives and in Bliss and Ogborn’s (1994) prototypes. In proposing that “a small number of intuitive rules…direct our responses in many situations”, Stavy, Tsamir, and Tirosh make it clear that they, too, intend to identify “phenomenological primitives”. They mention four that their research is to focus on, and provide details about their study of one, the notion that more of one variable will be accompanied by more of another, or as they put it more succinctly, ‘More A, more B.’ In diverse situations Stavy et al. found that many students implement the More A, More B rule. This is useful for teachers to know, since there will be many topics where the rule will lead to fallacious expectations, interpretations, and beliefs. Alerted to this, teachers would be prepared in advance to head off error. Teaching to counter More A, More B might be an explicit part of the curriculum, with students learning about situations where the rule does not apply. Some such situations are important in themselves. An example is where people take excessive quantities of analgesics or other medicines in the belief that the more they take the better the effect. Not so important, but an example that interests me personally, is a belief I once had that the more I knew about a subject the more I would feel that I understood it; I now appreciate that after a certain amount of knowledge is gained, an appreciation can grow that one’s understanding is less complete than one had thought. It is interesting to see More A, More B thinking occur in a topic so different from the examples that Stavy et al. describe. 3.

KNOWLEDGE THAT SUPPORTS NEW PERCEPTIONS

Many authors (e.g. Fensham, 1988) have discussed the tension between teaching science to produce future scientists and teaching it to produce a generally informed

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community. Of course, for either aim an outcome of deep understanding of science is desirable. In their chapter, Leach and Lewis assert that knowledge of the epistemology of science is essential for that understanding, but further, that such knowledge is required for conceptual change. Past attempts to promote conceptual change (I think that conceptional would be a more accurate word) employed demonstrations, logic, and debates about alternative views, all of which deal with much the same type of information as the alternative conceptions they address. But does conceptual change require a different form of knowledge that brings students to see the subject in a new way? This deep question should stimulate much discussion and empirical investigation. Epistemological knowledge, though nothing like the knowledge of phenomenological primitives, shares with them the property of being relevant to many topics. Leach and Lewis join many predecessors in pointing out that science curricula commonly ignore epistemological issues. That neglect may be even more prevalent in other school subjects. It may be responsible for a widespread perception of students that science consists of established facts, and that it is not continually being not just extended but also revised. This perception leads students to ignore social aspects of problems. Leach and Lewis argue that students need a broader view of science. A broad view of science should include understanding of how opposing views are resolved. Mitchell (1992) provides extracts from a lesson that illustrates how a teacher might model this. In the lesson students put forward their notions on the source of reaction forces on objects lying on a table, and on the size of the forces. The teacher manages a debate of the notions, guides the students towards means of testing the validity of the various notions, and brings the debate to a clear conclusion. Leach and Lewis point out that a broader view of science requires more than understanding of resolution of arguments within science; it extends to understanding of how people deal with social questions that involve science. To teach about that, we shall need detailed case studies. The choice of appropriate topics is not simple. To keep students’ interest they must be recent and contentious. Suitable examples may be cloning, genetically modified foods, control of greenhouse gases, and use of nuclear energy for generation of electricity. Keeping teachers informed and supplied with useful data about these topics is not a trivial challenge. Nor is information the only need. Teachers would have to learn skills that differ from those honed for clear exposition of subject matter. For students, framing and weighing arguments differs from learning scientific facts and laws. Leach and Lewis note that these needs require new lines of research. These include comparisons between students’ expressed epistemological beliefs and their actual behaviour in diverse contexts, comparisons of students’ and experts’ use of epistemological knowledge, and attempts to teach students to use epistemological knowledge expertly. Most difficult of all would be studies that go on to check whether training in use of epistemological knowledge leads to facility in conceptual change. The great bulk of work on conceptual change has focussed on science, particularly physics. In considering conceptual change in mathematics and history,

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Merenluoto and Lehtinen and Limón provide a contrast that identifies issues that are specific to disciplines and ones that span them. Like Leach and Lewis, Merenluoto and Lehtinen are concerned with epistemology. Their chapter on conceptional learning in mathematics shows that curriculum designers and teachers need to appreciate how the epistemology of the number system interacts with the psychology of learning. The tasks that Merenluoto and Lehtinen gave to senior school students brought out deficiencies in understanding of the key notions of continuity and limit. Without that understanding, there must be further shortcomings in understanding of fractions. Merenluoto and Lehtinen point out that counting, which develops through early experience and training, leads to the notion of a specific successor, a “next number.” That notion is an example of what diSessa terms a phenomenological primitive. Like “More A, more B” and the others that Stavy, Tsamir and Tirosh identified, the notion of next number though important for early development can later impede proper understanding. The belief that there is a next number cuts across the notion that there is an infinite number of real numbers between any pair of numbers. This belief and More A, more B are at least two obstacles that cause the notorious difficulty that learners have with fractions. The issue for researchers, curriculum designers and teachers is what to do to overcome these obstacles. Merenluoto and Lehtinen suggest that the abstract notion of limit should be developed from the image of the number line with which most students will be familiar, and then the idea of limit from the number line should be extended to the even more difficult notion of limit of a function. This does not appear a trivial piece of pedagogy. Nor does their further recommendation that teachers make explicit to students the reasons why they need to revise their prior knowledge of numbers. They also suggest that knowledge of the history of calculus (and presumably of other topics in mathematics) would assist conceptional change. Obviously these are topics for research. Although Merenluoto and Lehtinen do not say so, another inference that might be drawn from their analysis of understanding of real numbers is that the process of pushing mathematical topics to ever younger students might have gone too far. There are two aspects to this. One is that the curriculum is so full that excessive time has to be spent on drill with algorithms, leaving insufficient time for explanations and the careful building up of understanding. Nor is there time to deal effectively with conceptional change. The other aspect is that children are meeting advanced concepts at an age when they have not developed correspondingly advanced skills of learning that may be necessary for reflection on the concepts and consequent understanding of them. Both aspects imply the need for thoughtful reappraisal of mathematics curricula. Much teaching in mathematics concentrates on drill on algorithms. Merenluoto and Lehtinen call for attention to concepts such as continuity and limit. Limón makes a parallel recommendation for history: some of the time spent on narrative teaching of events should be reallocated to developing understanding of “second order” concepts such as evidence, explanation, and cause. Limón points out that such concepts differ from those in science in being less sharply defined, more

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abstract, and less permanent in time. While these characteristics should make it easier to change students’ beliefs about them, students are likely to have stronger emotional attachments to historical concepts than they do to scientific ones. National pride may be involved. A possibly out of date example is British and French students’ notions of empire. It would have been extremely difficult to get a British student in 1900 to shift to an Indian’s or a Boer’s view of empire. Although it has not been invariably successful, the use of experiments and demonstrations to show the superiority of one explanation over another remains attractive for attempts to change beliefs in science. Experiments and demonstrations are not an option in history, where sympathetic presentation of alternative interpretations of an event might be tried. There is no shortage of examples from recent events: American and Vietnamese views of their war, Israeli and Palestinian positions, Republicans and Nationalists in Ireland, Serbs and Croats in Bosnia. 4.

COMMON GROUND ON TEACHING FOR CONCEPTUAL CHANGE

Despite important differences between the natures of scientific, mathematical, and historical knowledge, the four chapters in this section lead to similar recommendations about teaching to promote conceptual change. All call for less attention to superficial acquisition of content and more to deeper general concepts. This should include the epistemology of the subject, which receives almost no time in elementary or secondary school curricula (and all too little in tertiary). Alternative views have to be taken seriously, and students brought to recognise the sources of their beliefs. Poor linking between topics, and between propositions that the teacher or text presents and personal experience, seems to accompany shallow and dogmatic views, so promotion of rich patterns of links across knowledge should provide readiness for conceptual change. It is a truism that testing shows students what they are supposed to learn, so tests must encompass understanding of concepts, epistemology, recognition of alternative explanations, and linking. Fortunately, the work on alternative conceptions and conceptual change has thrown up a diversity of appropriate testing methods, such as concept mapping (Novak & Gowin, 1984), interviews about events and instances (Osborne & Fryberg, 1985), predictionobservation-explanation, drawings, fortune lines, and Venn diagrams (White & Gunstone, 1992). These recommendations are the basis not just for conceptual change but for generally good teaching. That is hardly surprising, because conceptual change is the essence of learning. REFERENCES Ausubel, D. P. (1968). Educational psychology: A cognitive view. New York: Holt, Rinehart & Winston. Bliss, J., & Ogborn, J. (1994). Force and motion from the beginning. Learning and Instruction, 4, 7-25. Brumby, M. (1979). Problems in learning the concept of natural selection. Journal of Biological Education, 13, 119-122. Bruner, J. S. (1960). The process of education. Cambridge, MA: Harvard University Press. Carey, S. (1985). Conceptual change in childhood. Cambridge, MA: MIT Press. diSessa, A. (1988). Knowledge in pieces. In G. Forman & P. B. Pufall (Eds.), Constructivism in the computer age (pp. 49-70). Hillsdale, NJ: Lawrence Erlbaum Associates.

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Fensham, P. J. (1988). Familiar but different: Some dilemmas and new directions in science education. In P. J. Fensham (Ed.), Development and dilemmas in science education. London: Falmer. Gagné, R. M. (1965). The conditions of learning. New York: Holt, Rinehart & Winston. Gunstone, R. F., Champagne, A. B., & Klopfer, L. E. (1981). Instruction for understanding: A case study. Australian Science Teachers Journal, 27, 27-32. Lave, J. (1988) Cognition in practice: Mind, mathematics, and culture in everyday life. Cambridge: Cambridge University Press. Mitchell, I. J. (1992). The class level. In J. R. Baird & J. R. Northfield (Eds.), Learning from the PEEL experience. Melbourne, Australia: Monash University Faculty of Education. Novak, J. D., & Gowin, D. B. (1984). Learning how to learn. Cambridge: Cambridge University Press. Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge: Cambridge University Press. Osborne, R. J., & Freyberg, P. (1985). Learning in science: The implications of children’s science. Auckland, New Zealand: Heinemann. Pfundt, H., & Duit, R. (1994). Bibliography: Students’ alternative frameworks and science education ( ed.). Kiel, Germany: Institute for Science Education, University of Kiel. Posner, G. J., Strike, K. A., Hewson, P. W., & Gertzog, W. A. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Science Education, 66, 211-227. Skinner, B. F. (1968). The technology of teaching. New York: Appleton Century Crofts. White, R. T. (1994). Dimensions of content. In P. J. Fensham, R. F. Gunstone, & R. T. White (Eds.), The content of science. London: Falmer. White, R. T., & Gunstone, R. F. (1992). Probing understanding. London: Falmer.

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PART IV

INSTRUCTIONAL PRACTICES TO PROMOTE CONCEPTUAL CHANGE IN THE CLASSROOM

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DEVELOPING EPISTEMOLOGICAL THINKING TO FOSTER CONCEPTUAL CHANGE IN DIFFERENT DOMAINS

LUCIA MASON

University of Padova, Italy

Abstract. This chapter focuses on the development of personal epistemologies as an essential condition for conceptual change. Starting from the distinction of the terms “knowledge” and “belief in literature, it introduces first the epistemic level of cognition which affects learning. Key issues from cognitive development and educational psychology research on general representations about the nature of knowledge and knowing are then presented. Further, findings from research on beliefs in specific domains - science, maths and history - are described. Data from studies with students at different school levels illustrate how specific beliefs may act as resources or constrain conceptual change. This is followed by core arguments on the relationship between epistemological beliefs and knowledge revision. The chapter continues with three examples of effective instructional interventions in powerful learning environments on the refinement of students’ epistemological beliefs in the three domains already considered. Finally, some concluding remarks underline the importance of developing epistemological thinking, pose some open questions and provide suggestions for future research.

1.

PERSONAL EPISTEMOLOGIES

For a long time cognitive psychology has recognised and widely examined two types of knowledge influencing the accomplishment of a task or activity: declarative and procedural knowledge. The first is knowledge about the domain in which one is cognitively involved, the latter is knowledge about strategies that can be used, which is relatively independent of the domain. More recently, research on cognitive processes has also recognised the existence of a third type of “intuition” influencing learning and problem-solving, i.e. “beliefs”, “epistemological beliefs" in particular. Research on conceptual change has begun to explore if, and to what extent, epistemological beliefs have a role in restructuring knowledge, although this exploration has mainly been carried out in science (see Leach & Lewis, this volume). I will now briefly consider the construct of beliefs, and epistemological beliefs. 1.1.

Knowledge and Beliefs

The terms “knowledge” and “beliefs” are often used interchangeably, with no difference in meaning. “Knowledge” is usually intended in a more rigorous way, M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, pp. 301-335. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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whereas “beliefs” are much less controlled, as has been clearly pointed out (Pajares, 1992). Do the two terms refer to two different concepts or are they just synonyms that can be used interchangeably? It is not easy to answer this question as the difference between the two constructs may be quite subtle. In cognitive psychology Abelson (1979) has identified some features that differentiate knowledge systems from beliefs systems, although they share other features, which have been identified by Nespor (1987) in analysing teachers’ beliefs. Summarising all distinctions between the two constructs, it can be said that beliefs are more “open”, in that it is less clear what comprises a belief system and what does not, compared with a knowledge system. Beliefs are also of a more affective and evaluative nature than knowledge. As underlined by Fenstermacher (1994), knowledge has a higher epistemological status than beliefs, as it is constituted by justified assertions and supported by evidence. In the social psychological literature, knowledge is also intended as information without evaluative components, whereas beliefs are associated with “affect”, that is feelings, emotions and evaluations accompanying information (Dole & Sinatra, 1994). For instance, one may believe that nuclear power is very dangerous and a high-cost production, and that alternative sources of power with much less negative impact on the environment can be used. An assertion like “There are alternative sources of power less potentially harmful to the environment” (p. 249) may be considered as knowledge, whilst commitment to the truth of the assertion is considered as beliefs. Beliefs are the building blocks of attitudes. Underlying an individual’s attitude towards nuclear power is a set of interconnected beliefs. Perception of the difference between knowledge and beliefs, whose constructs do not have clear semantic boundaries, has been investigated by Alexander and Dochy (1994) with American university students (undergraduates and graduate) and faculty (educational researchers). Articulated perspectives on knowing and believing emerged. Knowledge was considered as factual and verifiable, whereas beliefs were considered as personal and value-laden, and also changeable for external (e.g. experience) or internal (e.g. doubting) stimuli. Similar distinctions were found by Alexander and colleagues in two cross-cultural studies, one involving American and European (Dutch) students and experts (Alexander & Dochy, 1995), the other involving American and Asian (Singaporean) students and teachers (Alexander, Murphy, Guan, & Murphy, 1998). It is interesting that American, European and Asian participants share important aspects when distinguishing between knowledge and beliefs. Knowledge was described in terms of what is factual, experiential and learned as a result of school instruction. Beliefs were described in terms of feelings, values, subjective or personal, and idiosyncratic truths that are not proven, but to which one is strongly attached. The terminology is quite problematic, given the fuzzy boundary between knowledge and beliefs, and this difficulty is reflected in this volume. Leach and Lewis argue about “epistemological knowledge”. They prefer the term “knowledge”, when referring to implicit representations that inform respondents’ various actions. Since they consider these representations as “profile-like”, in that individuals draw upon different epistemological knowledge in different situations, they do not use the term “beliefs” which, according to them, may suggest some sort

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of commitment on the part of respondents. In this chapter, I prefer not to use the term “knowledge” when referring to representations about the nature and acquisition of knowledge, but the term “beliefs”. I think the affective and evaluative nature of these representations, which a student may have a strong, coherent commitment towards, should be included, thus the term “beliefs” seems to be more appropriate, at least in this perspective. 1.2.

Epistemological Cognition

The epistemological belief is a particular type, which has been defined as “socially shared intuitions about the nature of knowledge and the nature of learning” (Jehng, Johnson, & Anderson, 1993, p. 24). Most studies about epistemological beliefs have developed since the 90s, however, apart from pioneering work by Perry (1968) in the 50s and 60s, there is also earlier reference in research on the analysis of the different levels an individual may be cognitively involved in. In 1983 Kitchener discussed a three-level model of cognitive processing to give a more complete account of ill-structured problem-solving processes. The first level of this model is the cognitive one: individuals are involved in basic tasks related to perception, computing, memorisation, etc., through which they construct their world knowledge. The second level is metacognitive: individuals are involved in monitoring their own cognitive processes, for instance applying a memory strategy. The third level is epistemic: individuals are involved in reflecting on the nature of a problem and the truth value of different solutions. It refers essentially to knowledge and limitations, degree of certainty and criteria of knowing. Therefore it does not concern the procedures to be adopted to resolve a problem, but rather if the problem itself is solvable and under what conditions. Through this level of epistemic cognition we reflect on the limitations of solution strategies, and how a solution can appear true, when reasoning about problems necessarily leads to an entirely correct solution. In 1983 Schoenfeld also pointed out the existence of a system of beliefs that drives students’ behaviour when trying to solve mathematical problems, since problem-solving performance cannot be seen as purely cognitive. The author revealed that students’ beliefs about what is useful in learning maths affected the cognitive resources available to them when learning in this domain, making a large portion of stored information inaccessible when the beliefs did not facilitate understanding, but rather impeded it. By examining four different frames that underlie misconceptions in science, mathematics and computer programming, which all share some structural similarities, Perkins and Simmons (1988) argued an epistemic frame, that is a system of coherent schemes regarding the validation of knowledge assertions in a domain. For instance, an epistemic frame implies that a theory should be sustained by a number of facts as evidence of its truth value. Greeno (1989) referred to “personal and social epistemologies” as factors that guide our mental activities, since thinking and learning are situated in contexts of beliefs about knowledge and cognition which differ between individuals and groups.

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Assuming personal epistemologies highlights the role of “theories” about knowledge, knowing and learning, which are developed by students and affect their learning processes and products. Over the last decade research on epistemological thinking has flourished along different lines, which cannot all be reviewed here. However, it should be pointed that not all scholars refer to personal epistemologies as systems of coherent and consistent representations evolving through a logical sequence of structures, as is the case in most of the literature on developmental psychology (e.g. Moshman, 1994, 1998). A number of scholars, mainly in educational psychology, refer to personal epistemologies as a set of different beliefs that are not necessarily organised into cognitive structures and can even be orthogonal (e.g. Schommer, 1990, 1994a, b). Some researchers in science education claim that students use different epistemological beliefs in different contexts as they do not reason consistently about science and scientific knowledge across a wide range of contexts (e.g. Leach, Millar, Ryder, & Séré, 2000; Leach & Lewis, this volume). It should also be noted that in developmental psychology literature personal epistemologies include representations about knowledge, and reasoning and justification processes concerning knowledge only. On the other hand, in educational psychology and educational research literatures, personal epistemologies often include representations about knowledge acquisition, that is learning, so the construct has a wider and less pure meaning. As well as the different conceptualisations about the nature and components of personal epistemologies that can be found in the various lines of research, a shared common point can also be identified, that is the influence of convictions about knowledge and knowing on thinking and understanding. What are these convictions? To answer this question, research on epistemological thinking, as part of cognitive development, and on epistemological beliefs generally, and in different domains, will be introduced in the following sections. 2.

COGNITIVE DEVELOPMENT AND EPISTEMOLOGICAL THINKING

The research interest of cognitive development psychologists in pre-school years has focused on children’s theory of mind (e.g. Astington, Harris & Olson, 1988; Wellman, 1990). Adults believe that the mind, which differentiates people from other entities, includes components such as perception, belief, emotion, feeling, desire, intention, will and knowledge (D’Andrade, 1987). To some extent also children need to understand what comprises the mind and how it works, in order to understand the everyday events in which people act. Research has revealed that children first understand that the mind exists and is connected with the physical world, although at the same time being separate from it, that it represents objects and events more or less accurately, and that it actively mediates interpretations of reality. Understanding this latter aspect of the mind corresponds to the highest level of the theory of mind. It concerns the essential constructivist nature of our mental activity, implying an epistemology of uncertainty and doubt, which is based on the assumption that the difference between views and conceptions is intrinsic to the knowing process (e.g. Chandler, 1988).

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Research underlines that the most advanced levels of development of the theory of the mind are closely related to the more sophisticated levels of development of epistemological thinking. Many aspects of cognitive development which go beyond formal operations in the Piagetian sense, have usually been investigated by interviewing children, adolescents and adults about the justification of knowledge in general, and/or the epistemic characteristics of their theories or reasoning. Reflective judgement (King & Kitchener, 1994), relativistic thinking (e.g. Leadbeater, 1986; Chandler, Boyes, & Ball, 1990), dialectical thinking (e.g. Benack & Basseches, 1989), and argumentative reasoning (Kuhn, 1991) are all aspects of epistemic cognition that have been examined more or less systematically. Kramer (1983, 1989) identified three fundamental features of post-formal thinking as depicted by scholars who examined it, despite divergences in their analyses regarding epistemological thinking. These features are: 1) relativism: understanding that knowledge is not certain and absolute and that conceptual tools used to acquire knowledge affect construction of knowledge of the world; the individual’s own view is considered one of many potentially true representations; 2) acceptance of contradictions: awareness of contradictory information and aspects of the world; 3) integration: ability to synthesise conflicting views and conceptions in an integrated and consistent whole. These characteristics of post-formal thinking are based on recognising multiple representations of reality and the need for doubt, which imply an awareness that in a continuously evolving, and at times contradictory world, knowledge is neither certain nor absolute. According to most scholars in the field, post-formal thinking develops from adolescence, not before, and proceeds through adulthood. From childhood to adulthood epistemological thinking appears to develop as follows (Moshman, 1998): objectivism: knowledge is certain and absolute, has a right-wrong format. When justification is considered, it is conceived in terms of appealing to observation or an authoritative source of knowledge. This epistemic stance of naive realism is the most common in children but can also be found in adolescents and adults; subjectivism: knowledge is intended as ambiguous, uncertain, idiosyncratic, contextual and/or subjective; any strong justification is conceived as possible since each individual holds his/her own truth. As pointed out by Chandler (1987, 1988), the emergence of sceptical doubt is typical in adolescents. Adolescent epistemology of generic doubt can lead to both scepticism (no sources of absolute or indubitable knowledge) and dogmatism (faith in some omniscient non-criticisable authority); rationalism: there are justifiable norms of inquiry and in some cases some knowledge claims are more strongly justified than others. Rationalism does not mean returning to less advanced beliefs in absolute and certain truths or refusing insights concerning context and subjectivity, but rather being aware that justification of knowledge requires active reflection processes about the

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nature and aim of knowing. Rationalism permits definition, explanation and justification of standards for evaluating the individual’s own, and other’s reasoning, as well as understanding the reasons underlying the individual’s own beliefs and attitudes. This epistemic stance develops in the course of late adolescence and adulthood. The issue that children and young adolescents can only believe in knowledge as certain, absolute and unproblematic has been criticised in the light of evidence that it may be possible to develop a constructivist stance on knowledge, and how it is elaborated, at an earlier age. This will be discussed below when introducing research on the development of students’ science epistemologies (Smith, Maclin, Houghton, & Hennessey, 2000). It is worth noting that in the developmental psychology literature, the development of epistemological thinking is conceived in terms of a logically evolving sequence of cognitive structures comprising coherent representations, which can characterise a level or stage of the cognitive development, or as a cognitive process. As will be seen in the next section, epistemological beliefs have also been considered as a set of different beliefs not necessarily organised into cognitive structures, or even that they are not activated in consistent and stable ways across contexts. 3.

GENERAL AND DOMAIN SPECIFIC EPISTEMOLOGICAL BELIEFS

This section introduces key issues from research on students’ general epistemological beliefs, as well as research on beliefs about specific areas of knowledge and learning. The former are usually investigated in educational psychology in relation to learning outcomes, the latter in educational research regarding curriculum domains. Given the space constraints of this book, this section is not intended as a comprehensive review of all extant research in these areas. Rather, it is a review of few illustrative studies of various aspects of students’ general epistemological thinking at different ages, and specific epistemological thinking in science, mathematics and history. 3.1.

General Epistemological Beliefs

A systematic research program on the relationship between epistemological beliefs and learning has been carried out by Schommer (e.g. 1990, 1993), who proposed considering this construct as comprising different, more or less independent dimensions that do not feature a level or stage sequence since students may be naïve in some beliefs, but not others. More recently (Schommer, 1994) also proposed viewing these beliefs as a frequency distribution rather than a single point along each continuum. Using the Epistemological Questionnaire, an instrument comprising 63 items to be rated on a Likert-type scale, she assessed two epistemological dimensions on the nature of knowledge, which at the extremes of the continuum are:

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belief in simple (isolated and unambiguous items of information) or complex (set of interrelated concepts) knowledge; belief in certain (absolute and stable) or uncertain (continuously evolving) knowledge; and two dimensions on the acquisition of knowledge (learning), which at the extremes of the continuum are: belief in quick (quick or not all) or gradual (slow process) learning; belief in fixed (unmodifiable) or malleable (improvable) ability to learn. Based on Schommer’s instrument, other questionnaires have been developed to assess epistemological beliefs, for instance the Epistemic Beliefs Inventory by Schraw, Dunkle and Bendixen (1995). It should be underlined that students’ convictions about the nature and acquisition of knowledge affect reading comprehension (Schommer, 1990; Schommer, Crouse, & Rhodes, 1992) and drawing conclusions from two different texts on the same topic (Schommer, 1990; Kardash & Scholes, 1996), as well as metacomprehension (Schommer, 1990; Schommer, Crouse, & Rhodes, 1992), ill-defined problem-solving (Schraw, Dunkle, & Bendixen, 1995) and transfer of learning (Jacobson and Spiro, 1995). In all these studies, less advanced epistemological beliefs are associated with lower performances and more sophisticated beliefs are associated with higher performances. For instance, the more students believe in certain knowledge and quick learning, the more they wrote inappropriate absolute conclusions derived from reading hypothetical material (Schommer, 1990). In almost all existing educational psychology literature epistemological beliefs are of a general nature, that is, they regard representations about the nature of knowledge and learning, which have been investigated on a general plane, independently of domains. As well as beliefs about knowledge and learning in general, beliefs about specific areas of knowing have also been assessed and examined, particularly in the three domains which the remainder of this section will focus on. 3.2.

Epistemological Beliefs about Science

The ways students view science, its objectives, methods and purposes, as well as their attitudes towards science at different school levels has been widely investigated (e.g. Aikenhead, Fleming, & Ryan, 1987; Grosslight, Unger, Jay, & Smith, 1991; Larochelle & Desautels, 1991; Lederman, 1992; Linn, Songer, & Lewis, 1991). An important aspect that differentiates the studies in this field is their contextual or noncontextual nature, that is, the use of questionnaires or interviews to ask students questions within the particular context of a scientific activity, or the use of the same instruments to ask questions generally, without referring to a specific activity in which beliefs about the nature and acquisition of science could emerge. Students could be asked questions such as “What is a scientific theory?” or “What is an experiment?” in either a decontextualised manner, or while involved in carrying out a particular task or activity.

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As an illustrative example of decontextualised research we refer to the study by Carey, Evans, Honda, Jay and Unger (1989). Through clinical interviews, before and after the implementation of a teaching unit aimed at developing the constructivist view of science, the authors asked seventh-graders questions outside any framing context about: the nature/purpose of science and scientific ideas; the nature of a hypothesis; the nature/purpose of an experiment; how scientists do their work, the source of their hypotheses and how they decide which experiments to perform; when and why scientists change their ideas and what they do when they get unexpected results from their tests; the relationship between scientists’ ideas and the rest of the work they do. Students’ answers were coded on the basis of the degree to which they defined and differentiated ideas, experiments and data one from another, and the degree to which they articulated and understood the relationship between those elements. Three general levels of response were identified: level 1: students do not show a clear distinction between scientistss ideas and activities. They believe that an activity is performed to achieve the activity itself and that the goal of science is to discover facts about reality and invent new things; level 2: students show a clear distinction between ideas and activities. They believe that an experiment is performed to verify the rightness of an idea and that refusing or revising an idea is possible on the basis of the results. However, students do not recognise that a revised idea covers old and new data and believe that the goal of science is to understand how things work; level 3: as in the previous level, students clearly differentiate between ideas and experiments and believe that an experiment is aimed at verifying or exploring ideas, and that unexpected results influence the development of ideas. They also understand the cyclic nature of science and believe that its goal is to construct more profound explanations of the world. A hypothesis for instance, at level 1 is an idea or guess; at level 2 it is still an idea or guess, but also something that can be tested, which is clearly related to an experiment or phenomenon. At level 3 a hypothesis is also a tool for interpreting the results of an experiment and is developed on the basis of those results. Again using scientists’ work as an example, there is no idea at level 0 that scientists seek information or have a purpose in their tasks. At level 1 students mention observing, thinking or exploring, however, not guided by questions or phenomena. At level 2 students recognise that ideas and questions guide scientists’ activities, and at level 3 students believe that scientists have ideas and perform experiments to verify if they are right or wrong. The results of the experiments are the basis of evaluation and development of ideas. Driver, Leach, Millar and Scott (1996; Leach & Lewis, this volume) have underlined that through the decontextualised approach it is impossible to know what students have in mind when answering a general question. They could refer to

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specific examples in their answers but they remain undeclared. With respect to the question “What is an experiment?”, for instance, the term “experiment” can be interpreted by an interviewee in different ways. Scientists themselves perform different kinds of experiments for different purposes, and in everyday language there are alternative meanings for the term, therefore several legitimate interpretations. A second critical issue is that using decontextualised questions researchers can obtain information about students’ “expoused” views and not those they express implicitly when in action, as they can assert one thing while doing another. It has also been shown that students’ beliefs about the nature of science can refer to “distal” or “proximal” knowledge. The first concerns the processes and products of professional science, while the second concerns students’ personal understanding, beliefs and commitment to the scientific knowledge that they perform and encounter, not as generated by scientists (Hogan 2000). An example of contextualised research on the nature of science and scientific enterprise (e.g. Hammer, 1994; Roth & Riychoudhury, 1994; Ryder, Leach, & Driver, 1999), is the cross-sectional study by Driver, Leach, Millar and Scott (1996) carried out with students aged 9-16. They were asked specific questions in the following three areas: 1) the purpose of scientific work; 2) the nature and status of scientific knowledge; 3) science as a social enterprise. Six probes were developed as research tasks to investigate images of science in context. These not only provided material as a basis for semi-structured interviews, but also oriented students to the topic to be examined by stimulating them to think about issues and questions within particular contexts and providing opportunities for reflection. For instance, the probe about the purpose of scientific work comprised eleven questions about natural and social phenomena (school science and real science activities). Among them, some questions were tested empirically (e.g. “What kind of fabric is waterproof?” or “Can any metal be made into a magnet?”) and others were not (e.g. “Which is the best programme on TV? or “Is it wrong to keep dolphins in captivity?”, p.73). Pairs of students were asked to consider the scientific questions and say whether they were in fact scientific or not, and why. The interviewer then discussed their choices with them. Finally they were asked: “In general, what makes a question a scientific question?” (p. 74) to see whether they held any general representation of the features of science. The probe about the social nature of science, which was prepared for 16-year-old students only, consisted of a 30 minute audiotape and accompanying booklet to be followed according to what they had heard. The oral and written material introduced two controversies: one about Alfred Wegeners’ hypothesis of the continental drift in the 1920s geology community; the other about a more recent issue in the UK regarding the generalised irradiation of food. The first controversy allowed students’ representations about internal scientific issues to be investigated, in particular how scientific communities reach a consensus about phenomena. The second controversy allowed the external social relations of science to be investigated, in particular how society comes to a practical decision about an issue involving scientific knowledge. Students in groups

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of four were asked to discuss the reasons underlying disputes between scientists, and how to solve them. The methodological procedure ensured that students’ answers and views would be based on specific examples and the situations they called to mind, thus avoiding difficulties in interpreting responses to general questions asked without reference to any framing context. 1. Purposes of scientific work. Students’ answers reflected three features of their image of science: empirical testing: younger students saw it as a simple process of observations leading to obvious outcomes. Older students were more aware that testing implies finding out mechanisms or testing theories; domain of investigation: students of all ages tended to include physical and biological phenomena in scientific domains and exclude social phenomena. Younger students referred more to their science experience at school while older ones referred to a wider set of experiences, also showing the beginning of an awareness of ethical issues not scientifically examinable; characteristics of scientific work: younger students had a stereotyped image of scientists and did not distinguish between their personal and professional affairs. For most students aged 12-16 scientists address problems of social relevance. At the age of 16 a small number conceived scientific work as collaborative and taking place in different settings, such as hospitals and industrial laboratories. 2. Nature and status of scientific knowledge. The simplest image of scientific knowledge was that of a number of events in the world with little differentiation between evidence and explanations. The most sophisticated image was that of a theoretical model of events to be evaluated on the basis of evidence. More specifically, the term “theory” was increasingly understood by older students as a generalised question, especially at 16 years. The most common image was that of a correlation of specific variables and there was very little evidence that students recognised the conjectural nature of theories. For the majority, a theory comprised entities to be mapped on to world events, in a non-problematic way. 3. Science as a social enterprise. Students of all ages showed little awareness of the role of internal and external social factors in the development of scientific knowledge. However, at the same time, they referred to ideas in everyday life regarding controversies and their resolution to propose solutions to scientific disputes. Their ordinary social experiences provided rich material for preparing accounts based on ideas of bias, rivalry, vested interests, etc., as well as ideas on how controversies may be solved, which were frequently superficial and naïve. For instance, to solve the problem of disagreement between scientists they proposed repeating the same debatable experiment in the same laboratory as a joint test, or a form of adjudication by involving an independent unbiased arbitrator. Trying to summarise the outcomes of both types of research on pre-university students’ epistemologies about science, it can be said that they tend to see science in terms of manufacturing artefacts that are generally useful for the well-being of humankind. Scientific explanations are conceived as being derived inductively from

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data since the conjectural nature of scientific theories tends not to be appreciated by students who believe that theories emerge from observing facts and change according to the extent to which scientists can use more powerful instruments in their work. In addition, younger students in particular do not differentiate between theories and evidence as separate entities and have difficulty evaluating the former in the light of the latter. In this regard it should be pointed out that Samarapungavan (1992) provided evidence that young children (age 6-11 years) may be able to use four epistemological criteria in theory-choice tasks: range of explanatory power, non ad-hocness of explanation, empirical consistency, and logical consistency. In two different contexts of ideas, the Earth in Space and colour changes when using indicators, 85%-90% of children in that age range were able to make, and explain theory-choices in terms of those criteria. Samarapungavan acknowledged that her findings did not lead to an assertion that to be able to choose the better of two theories using the above criteria, means being able to use these criteria in science learning. However, the findings indicate that even young students can actually apply criteria in a given context, but cannot in other contexts. To conclude, what has also emerged from a recent study by Leach, Millar, Ryder and Séré (2000), and clearly argued by Leach and Lewis in this volume, should also be underlined. That is, students can draw upon different epistemological representations in different contexts. More than 700 European upper secondary school and undergraduate students, in their answers to five written survey items, revealed three distinct forms of epistemological reasoning called “data-focused reasoning”, “radical relativist reasoning” and “knowledge and data-related reasoning” (italicised in the original). Their use of these forms was not consistent and stable across various contexts, in that students reasoned differently in response to different questions. diSessa, Elby and Hammer (in press) have also argued that epistemological beliefs should not be considered as coherent systems of stances. Through a micro-causal analysis of these beliefs in action, they showed in a case study how the outcome is affected by different stances and strategies activated by a university student when dealing with learning in different contexts. The concluding section will focus again on the question of whether beliefs are to be considered as consistent and stable across a broad range of situations and tasks, or as situated and contextual. 3.3.

Epistemological Beliefs about Maths

Students’ epistemological beliefs about maths have not been investigated to the same extent as their beliefs about science. However, a number of studies have pointed out that they can hold convictions about this discipline which are not adaptive to meaningful learning. Two decades ago Schoenfeld (1983) began to highlight the interaction between cognitive and affective factors in learning maths at school, and argued about beliefs underlining students’ performance when involved in problem-solving and other activities. In a study carried out with high school students by means of a questionnaire (Schoenfeld, 1989), it emerged that students were highly motivated, perceiving mathematics as an interesting subject which

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helped them to think logically and which could be mastered if they worked at it, since hard work was considered the reason for success in this domain. However, at the same time, the “dark side of the picture” was that students showed the “rhetoric” of maths, whilst the reality of their classrooms appeared quite different. Problems they were asked to solve were just exercises in which they had to routinely apply, as quickly as possible, the procedures and formulas taught. Exceptions were only peripheral tasks that students considered enjoyable but recreational, rather than being important to their learning. They believed that normal homework and test problems should be solved in a few minutes, if not, they should not waste time on them, as they would never find the solution. More precisely, they believed that if a problem could not be solved in less than 12 minutes, it was impossible. Moreover, although in geometry they claimed that proof and constructions were closely related, in reality their performance showed that they did not take their proof-related knowledge into account in construction problems. Even if they could assert that maths helps to think logically and requires creativity, they claimed that this discipline involved rote memorisation to be learned as they were used to doing. Schoenfeld suggested that students separate school mathematics, that is the discipline experienced in the classroom, from abstract mathematics, the discipline of discovery and creativity heard about but never practised. The author (Schoenfeld, 1988) also underlined that even “well-taught" mathematics courses ( grade geometry class) leading students to do well in standard performance measures, could fail in terms of the perspectives they elaborated about the nature of the discipline. Although students were proficient in applying certain procedures, they developed beliefs that acted as constraints in constructing mathematical knowledge, since they showed convictions that: constructive geometry is separate from deductive geometry. That is, empirical aspects have nothing to do with the formal. When trying to make a construction, they thought it essential to follow the sequence of steps carefully; the form of a mathematical answer is what counts. Students tended not to recognise the importance of the coherence and correctness of an argument and were concerned about the form of the written argument. In other words, the form of the expression, for instance if the abbreviations were correct, was considered as important as the substance of the discipline; all problems can be solved in a few minutes. It is a waste of time to think about a problem that does not appear to be easily understandable; it is better to give up as it is impossible to reach a solution; students are passive consumers of mathematics produced by others. They cannot make sense of it by themselves, so facts and procedures must be memorised blindly to be able to apply them correctly. Lester and Garofalo (1982) identified representations about maths and mathslearning in elementary school children who believed that: the difficulty of a maths problem is due to the size and quantity of the numbers; all problems can be solved through performing one arithmetical operation, in rare cases two;

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the operation to be performed is determined by the key-words of the problem, usually introduced in the last sentence or in the question, thus it is not necessary to read the whole text of the problem; the decision to check what has been done depends on how much time is available. Silver (1985) also analysed some beliefs described by Schoenfeld, for example there is only one correct way to solve a problem, and that just a few minutes are required to solve any problem. He also highlighted the different approach to problem-solving by students who believe that they should consider the underlying structure of a problem and by those who believe that they should consider surface details introduced in the text. Lampert (1990) described students’ common view of mathematics - developed by practising this discipline for years in the classroom - in terms of certainty, and fast and correct answers that become true when accepted by the authority of a teacher. Doing maths means strictly following rules provided by the teacher, and knowing maths means remembering and applying those rules correctly. Belief in the role of real-world knowledge on problem-solving has been widely investigated by De Corte and Verschaffel (1989, De Corte, Verschaffel, & Op ’t Eynde, 2000; Verschaffel, De Corte, & Lasure, 1994, 1999). They found that upper primary school students considered important the choice of the operation to be computed and did not refer to their common-sense knowledge or the realistic context of a given problem. In their basic study (Verschaffel, De Corte, & Lasure, 1994), students were asked to solve two series of problems. The first introduced standard problems requiring the application of one or more arithmetic operations (e.g. “Steve has bought five planks, each 2 meters long. How many 1-meter planks can he saw out of these planks?”, De Corte, Verschaffel, & Op ’t Eynde, 2000, p. 700). The other series introduced problems whose mathematical modelling assumptions were problematic given the reality of the contexts used in the problem statements (e.g. “Steve bought four planks of 2.5 meters each. How many 1-meter planks can he saw out of these planks?”, p. 700). Only 17% of all reactions to the “problematic” questions were realistic. The answers could be realistic or non-realistic, but accompanied by realistic comments. Reusser (1988) showed that students believed that all word problems can be solved, even absurd problems (e.g. “There are 125 sheep and 5 dogs in a flock. How old is the shepherd?”) when presented in ordinary classroom contexts. Students tend not to ask themselves whether a given problem is solvable or not. The relationship between university students’ general epistemological beliefs and their comprehension and metacomprehension of a text about statistics were investigated by Schommer, Crouse and Rhodes (1992). They found that belief in the dimension of certain/uncertain knowledge predicted comprehension: the less students believed that knowledge is simple, the more they comprehended the text. In addition, the dimension of simple/complex knowledge predicted metacomprehension: the more they believed that knowledge is simple, the more they overestimated their comprehension.

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Belief in the critical role of large numbers in determining the difficulty of a problem was examined within a wider research on the relationship between metacognitive awareness and maths problem-solving by Lucangeli, Coi and Bosco (1997). They found that poor maths problem-solvers in fifth-grade believed more that the size of numbers determines the difficulty of a problem. They also had less metacognitive awareness and made more computational and procedural errors compared with good problem-solvers. In a recent study Mason (2001a) used the instrument prepared by Kloosterman and Stage (1992), the Indiana Mathematics Belief Scale (translated and adapted), to identify Italian high school students’ beliefs about maths and maths problemsolving. Significant differences emerged in relation to gender and grade. Girls, more than boys, believed in the importance of understanding concepts, not only the application of procedures for meaningful learning. In addition, from the first ( grade) to the final grade ( grade) of high school (there are five grades in the Italian high school) there was a decrease in students’ belief in the usefulness of maths as well as their own ability to solve problems that were not solvable in a short time. Finally, correlations between some students’ beliefs and their grades in maths emerged, although modestly. Higher grades in maths were associated with students’ beliefs in their ability to solve time-consuming problems, the importance of understanding concepts, the value of effort and hard work, and the usefulness of the discipline. In this study individual interviews have also been carried out with a selected sample of students (across the five grades) holding the most advanced or naïve beliefs emerging from the scale. What follows is drawn from students’ answers, and reveals how their beliefs may be either adaptive or maladaptive to learning and understanding in the domain. This should lead us to consider the need to help students reflect on their convictions in order to change their attitude and approach to the discipline and, in turn, their performance. The first are examples of beliefs about the importance of understanding in maths: In maths if the result’s always the same you can write without thinking very much, the result comes out the same. If you have to waste too much time understanding, explaining things to yourself, you give up. If you don’t remember the formulas for solving maths problems, you can’t solve them. Yes, yes, you could, but taking a long time and with a lot of intelligence. This is why it’s much better to remember formulas than to understand things. (Giacomo, grade) You should understand, otherwise if you don’t understand a maths problem, it means that you can’t understand and solve others. You need to understand all the procedure. I try to understand it, the result is relative. I believe that it is important that the procedure is correct. You need to figure out how to do exercises, to have an idea about the theory. Maths is also reasoning, thinking, awareness of what you are doing, understanding the steps you are following, explaining your actions and what you write. (Carlo, grade)

The following are examples of beliefs about the usefulness of maths: I always try to link school to practical life. In practical life I’ll never need to know sine and cosine, that is, I don’t see their usefulness in everyday life. Instead other school subjects give a lesson for life, such as philosophy, I mean that they are very important. I like philosophy very much because thanks to other people who have studied human experience I can base my own thinking and develop my own beliefs. I believe that maths is only a mental exercise. You also do a mental exercise when you translate from

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Latin, but in this case it’s not only a mental exercise but also knowledge of our roots, whereas in maths it’s only a mental exercise. Maths is only useful to exercise the mind to reason and to avoid your brain getting lazy, but nothing more. (Francesca, grade) I have chosen this school because I like maths very much. I think it is one of the most important subjects because it’s not only useful to shopping, but also for solving all everyday problems. Even expressions and equations give you more knowledge about everyday life. To give you a trivial example. In a recipe there’s a certain amount of salt. If you do not remember how much salt you have to use, you can work it out through an equation: a litre of water is to X, that is salt, as a kilo of flour is to baking powder, and so on. It seems trivial but maths is applicable to every kind of action, every practice of everyday life. (Corinna, grade)

3.4.

Epistemological Beliefs about History

Students’ epistemological beliefs about history have been investigated even less than maths - as well as other aspects of cognitive and instructional processes in this domain (Carretero, Jacott, Limón, López Manión, & Leon, 1994), but the outcome of this research is interesting and rich in implications for teaching and learning (Carretero & Limón, 1993; Leinhardt, Beck, & Stainton). Two studies on the nature of history and historical method have been carried out with Italian students. In the first study (Bombi, Ajello, 1988) elementary and middle school children were asked interview questions such as: “What is history?”; “How do people who write books find out about the things they write about”?. In answering the first question most students did not show a very advanced view of the discipline as a narration of events happening in the past. Their answers to the second question regarding methods of knowledge construction, revealed naïve beliefs. In most students’ representations, information tout court and historical knowledge coincided. According to more mature beliefs, sources of knowledge were also conceived as self-evident, thus interpretative action was not recognised. Only very few students with more sophisticated beliefs maintained that historians have to formulate hypotheses when trying to reconstruct the past. In the second study by Bozzo, Morra and Pierimarchi (1989), elementary school students were administered a questionnaire about knowledge construction in history, such as: “Nowadays we know many things about the civilisations of ancient populations like the Maya, Aztecs, Incas. How do we know about them?”; “Historians know for sure that Columbus’s voyage to America really did take place. Maybe, in earlier times other voyagers (Vikings, Irish) went to America, but historians are not sure about that. Why are they sure about Columbus’s voyage but not about Viking and Irish voyagers?”. According to their level of correctness and complexity, the answers were assigned to different categories. Tautological answers, which did not add any element to the question, just reformulated it. Descriptive answers, which gave information about the historical event but without saying how historians know. Some answers vaguely referred to the existence of documents, such as archaeological finds, exhibits in museums or written documents. The few more sophisticated answers described historians’ work as collecting and interpreting documents.

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In an interview study with Swedish high school students, Halldén (1993) explored their conceptions of history. They believed that history essentially means knowing what happened in the past and understanding how things in the present are as they are. Considering the possibility of impacting historical development through individual actions, students believed themselves to be a “small cog in a big wheel” (p. 321) or believed that becoming a politician was a way of personally influencing the course of history. Regarding the possibility of understanding and explaining what happens and has happened, some students denied the possibility of arriving at historical explanations of events, and others believed in this possibility and referred to the need to collect evidence of events and happenings to be able to form a coherent whole. A clear outcome of this study was students’ tendency to personify when describing historical events, consequential to their beliefs about what makes history and what comprises an explanation in history. Within a wider investigation of young Europeans’ ideas about learning and history teaching, Limón and Carretero (1997b) gathered data about 991 Spanish high school students and their representations of the meaning of history and sources of historical knowledge. It emerged that the students mainly considered history as showing “the background of the present way of life and explaining today’s problems” or as “a means of mastering my (their) life as part of historic changes” and as a chance “to learn from failure or success of others”. These students did not tend to conceive history as “something dead and gone, which has nothing to do with present life”. Significant gender differences showed that girls more than boys believe that history explains today’s problems and they believe less that history is just a school subject. Moreover, significant differences related to performance in the domain revealed that students with better grades in history were more likely to report that through the discipline they have the chance to learn from the failures and success of others and, comparatively, believe less in history as a school subject or “something dead and gone”. These Spanish students also maintained that they trusted most the presentation of history as in museums and historical places, followed by TV documentaries and historical documents and sources. Although they do not like them very much, textbooks were also considered reliable, as well as teachers’ accounts. On the other hand, they had little trust in fictional films and historical novels. Significant gender differences showed that boys trusted TV documentaries and fictional films more than girls, while girls had a greater trust in adults’ accounts and historical novels. In addition, significant performance differences revealed that those with better grades in history were likely to trust all sources of knowledge more than those with lower grades. Through interviews, not only focused specifically on their beliefs about history and historical knowledge, Vansledright and Brophy (1992) collected data on fourth graders who were not yet exposed to systematic instruction in United States history. Half the interviewees believed that historians gather information directly by questioning living witnesses of events in the recent past. If there were no living witnesses, they could use books, diaries and other written material. Students did not clearly differentiate the work of historians and archaeologists. None of them were familiar with the interpretative nature of historical studies believing that historians collect purely factual information by means of purely scientific methods. To be able

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to resolve historical disagreements, they believed that it is necessary to go back to collect more and better information or ask “the” authority for a final adjudication. Limited recognition of the interpretative nature of historical work also emerged in Wineburg’s (1991) research with American students. In particular, he examined what it means for historians and high school students to read a historical text. They were asked to think aloud while reviewing the same set of texts about the American Revolution. Wineburg noted how the two groups read the text from different epistemological stances which model and guide the meaning drawn from the text. Experts comprehended not the literal or inferred text when reading, but the “subtext” (italicised in the original), that is a text with hidden and latent meanings, both a “rhetorical” and human “artefact”. Comprehension of the text implies going beyond the words and sentences expressed to capture underlining purposes, intentions, motives. On the contrary, students believe that in historical texts they can find “straight” information, “facts”, and do not perceive a text in terms of a social instrument produced for a social end. Therefore, they approach a text without seeking the author’s intentions and purposes or situating it in a social context. Beliefs about rational understanding in history have been investigated in the U.K. by Lee, Dickinson and Ashby (1996) within the CHATA (Concepts of History and Teaching Approaches) project with students aged 7-14. Based on their previous work, the authors assumed that they would find children have tacit ideas acting as resources or obstacles for certain kinds of thinking. Through interviews and penciland-paper responses they identified the following beliefs: it is not possible to explain the past (action, institutions, practices) as it is not intelligible; people in the past were inferior from an intellectual and moral point of view and behaved in absurd ways which justify contempt; to understand the past means giving a stereotypical account of people’s situations, intentions, values and purposes; taking into account the specific situation in which people lived in the past, but these are conceived in modern terms; the specific situations of the era being considered are no longer seen in modern terms since beliefs, motives and values of people living in the past are different from those of today; in giving an explanation of problematic actions or institutions it is necessary to situate it within a context of beliefs and take into account that today concepts used to understand human actions (goals, values, habits, etc.) are different from those of past situations. Lee, Dickinson and Ashby (1996), among several other aspects, have also examined children’s beliefs about causal explanation in history and have found the following patterns of progression: a) they do not distinguish between information and explanations; b) explanation is linked to purpose, such as wanting to make things occur; c) explanation is conceived in terms of wants, but these have to be strong since wants are linked to outcomes by the mediation of morale or strength of volition; d) explanation means to find causal antecedents.

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Lee, Dickinson and Asby (1998) also investigated children’s ideas about the possibility of different explanations for the same event. They were asked “How can there be two different explanations of the same thing?” and other questions on whether one could be better than the other, how they could evaluate if one was better than the other, and how they could check to find out if either explanation was good or bad. The authors’ analysis led to the identification of four categories of response: 1) responses which maintained that only one explanation could be correct; 2) responses that conceived the possibility of two, interchangeable and discrete explanations; responses that resulted in unifying two different explanations to give a better 3) one, but without indicating any relationship between them; 4) responses which stated that one explanation made the other happen or was necessary to it. Few children showed that they knew any strategy to test whether an explanation was good, with the exception of checking the truthfulness of its statements. From an epistemological point of view, for most of the children causes were on the same level as statements of fact. Many younger children proposed “looking it up in a book” or “finding out what most books said” (p. 248). Among students of 10 years and over it was common to find the belief that there is no way of checking which explanation is better since explanations are only opinion. In any case, by “opinion” they referred to anything from mere whim to sustained hypothesis. A few older students, aged 14 years, proposed counter-factual thought experiments and comparisons with similar phenomena occurring at different times or places in order to evaluate explanations. More sophisticated views were found among college students by Voss, Wiley and Kennet (1998) who studied their perceptions of history and historical concepts. The authors found that undergraduates tended to consider history as not being controlled by historical laws. However, they did consider the importance of human activity, either on the part of individuals or institutions. Historical facts, to be used to write narratives, were believed to be the result of historians who put the information together. Accounts were believed to be different because of differences between historians and the times they lived. Historical changes were conceived as involving multiple causes and not simple causal relationships. Moreover, history was perceived as different from natural sciences with regard to the role of laws and the investigator, as well as the stability of factual information. 4. RELATIONSHIP BETWEEN EPISTEMOLOGICAL BELIEFS AND CONCEPTUAL CHANGE The previous section has introduced key aspects of research on personal epistemologies from the developmental and educational psychology perspective, as well as research on beliefs about the nature and acquisition of knowledge in three different domains. The section which now follows will outline the links between beliefs and the process of conceptual change, after introducing. Is conceptual change affected by belief in certain, absolute, simple knowledge, made up of isolated facts

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and delivered by authority, or belief in complex, tentative, interconnected and evolving knowledge, that can be rationally constructed by individuals? It is not difficult to hypothesise that these beliefs may have a different influence on knowledge revision. Qian and Alvermann (1995) have examined the role of beliefs about the nature of knowledge and learning (using Schommer’s questionnaire) in knowledge restructuring by text reading. High school students who held alternative conceptions on motion read a text introducing the Newtonian theory of motion, which contradicted their impetus theory. The authors found that epistemological beliefs predicted conceptual change. The more naïve were students beliefs about knowledge and learning, the less likely they were to revise their conceptions. More precisely, two beliefs were important predictors of knowledge restructuring, that is belief in simple and certain knowledge and belief in quick learning. Windschitl and Andre (1998) have investigated the relationship between epistemological beliefs (also assessed by Schommer’s questionnaire) and the learning environment with respect to conceptual change. University students learned about the cardiovascular system in two different simulation environments. In the more traditional one (the objectivist) they had to use simulations following prescribed steps given in written instructions to solve a number of problems. In the more innovative environment (the constructivist), following a thematic instructional guide, students could formulate their own hypotheses as possible solutions to the same questions given in the other setting. It emerged that the constructivist learning environment was more effective than the objectivist in producing conceptual change. It is particularly interesting that students’ epistemological beliefs interacted with the type of instruction. Students with less advanced beliefs on the nature and acquisition of knowledge reached higher results in the traditional setting in which they followed the given instructions on how to use simulations. On the contrary, students’ with more sophisticated beliefs performed better in the innovative setting in which they explored the new conceptual material. The authors have indicated that less epistemologically mature students, who believe in certain and simple knowledge, are more comfortable and motivated in a learning environment that helps them proceed step by step, since it is more aligned and consistent with their learning approach. More epistemologically mature students instead, who believe in complex and uncertain knowledge, were more tuned in the environment that asked their active construction of new knowledge. Mason (2000) also studied the role of epistemological beliefs in relation to conflicting information (Chirm & Brewer, 1993; Limón & Carretero, 1997a; Limón Luque, 2001) about a controversial scientific topic, the extinction of dinosaurs, and a historically controversial topic, the construction of the great pyramids in Egypt. For both topics two theories were introduced: the first was familiar with what the students (eighth graders) already knew. The second, alternative theory, was preceded by presenting anomalous data, that is evidence supporting it, but conflicting with the familiar theory. Students’ change in theory was strongly mediated by acceptance of anomalous data in that the more they perceived the data as valid and inconsistent with the theories held, the more they accepted the alternative theories. In addition, acceptance of anomalous data was associated with

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one dimension of students’ epistemological beliefs (assessed by Schommer’s questionnaire), although not strongly, and greater for the scientific topic. This dimension included both beliefs about the nature of knowledge, as certain versus evolving, and beliefs about the source of knowledge, as handed down by authority versus derived from reason. This outcome indicates that the more students believe in the unstable nature of knowledge, the less likely they are to refuse information contradicting their prior conceptions and, as a consequence of anomalous data rejection, to keep their theory about the topic. On the contrary, the more students believe in the changing nature of knowledge, the more likely they are to accept anomalous data and change their theory. A qualitative analysis (Mason, 2001 b) of students’ justifications for motivating their initial theory preference, anomalous data acceptance or rejection, as well as their final theory preference, revealed that epistemological belief in the authoritative source of knowledge was one of the reasons they mostly appealed to. Scientists, teachers and books were mostly considered in terms of fundamental sources of believable knowledge as in the following examples: I’m not entirely convinced about this theory because I have never studied it at school. (Sara) I’m quite sure that this theory is true since I have been taught about it. (Stefania) It’s truthful, things really happened in that way, it is written in all the books. (Enrico) I believe that these new suppositions have been made thanks to scientists’ deeper study and research. (Giuliana)

Although few, there were some students who were sceptical about the possibility of knowing for sure about a topic or doubted scientists’ work, as in the following examples: I don’t know if the data are valid and acceptable because everything happened so long ago that it’s not possible to say if one event happened before or after another, or at the same time. (Andrea) I think that even scientists could be wrong when they say that. (Marco)

The interactive dynamics between students’ epistemologies and their learning concepts in the process of knowledge revision in science domains have been underlined (Strike & Posner, 1993). There are some studies on this interaction which are relevant to the argument developed here. Songer and Linn (1991; Linn & Songer, 1993) found that middle school students with a dynamic view of science, who were following a CLP (Computer as Lab Partner) curriculum, learned more integrated knowledge than those with a static view, showing an understanding of the principles underlining many thermodynamic phenomena. The dynamic view led to belief that scientific ideas develop and change, and that to learn these ideas implies understanding their meaning and the relations between them. The static view, on the other hand, led to holding opposing beliefs about science and science learning. Integration of knowledge supported by more advanced beliefs (assessed by

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Schommer’s questionnaire) about the dimensions of certainty/uncertainty and simplicity/complexity of knowledge was also found in high school and college students by Rukavina and Daneman (1996). Relationships between epistemological beliefs about scientific models and the construction of diagrammatic models of plate tectonic phenomena and inference-making was considered in a study by Gobert and Discenna (1997). While students’ beliefs about scientific modelling did not differentiate their generation of diagrammatic models, the data collected revealed that those with more sophisticated beliefs about science transferred more of what they learned when reasoning on other plate tectonic phenomena, showing richer inferences on the basis of the models they constructed. Hammer (1994) pointed out how beliefs about the structure and content of physics knowledge, and physics learning, influenced university students’ approach to learning and problem-solving and what they learned within the context of an introductory physics course. In a study with Taiwanese eighth graders, Tsai (1998) found that those who held more constructivist epistemologies about science tended to have a more active attitude toward learning and use more appropriate strategies for learning science than peers with more empiricist beliefs. In a review of literature on the relation between secondary school students’ learning by conceptual change and their epistemological beliefs about science, Qian and Alvermann (2000) have highlighted that those with immature beliefs are less likely to achieve an integrated understanding of particular science concepts, and are less likely to change their conceptions. A question that should be asked at this point is: why are epistemological beliefs and conceptual change so closely linked that the former can positively or negatively affect the latter? To answer this question Mason (in press) has proposed considering beliefs about the nature of knowledge and knowing as “thinking dispositions” in Stanovich’s (1999), terms, that is intentional-level psychological attitudes that are activated at a higher level of cognition than the algorithmic level in reasoning tasks. These dispositions act as resources or constraints on change conceptions in that they do, or do not, lead to developing the intention of knowledge revision. Less advanced beliefs seem not to contribute to engagement in self-controlled conscious and goaldirected actions, whose goal is a new state of one’s own understanding of phenomena and events, that is, a goal of knowledge that produces restructuring of existing knowledge and higher levels of understanding. More advanced beliefs seem to activate and support students’ deliberate efforts to produce conceptual change, on a cognitive and motivational plane. A student who believes that knowledge is absolute, certain and simple, composed of information items to be learned in isolation and reproduced as such, and what is known remains stable otherwise the truth would not exist, is much less likely to engage in a conceptual change process than a student who believes that knowledge is tentative and evolving, what is true today may be rejected in the future in the light of new evidence, and meaningful learning requires establishing connections between concepts and integrating them consistently. In other words, students with more sophisticated beliefs may benefit from them as they act as thinking dispositions contributing towards their awareness that what they already know is incompatible with a new conception or perceiving the potential of new information. Thus, this student can engage in a knowledge

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problem, whose solution is represented by a better understanding of a phenomenon or event. It is more likely that a student processes new information in greater depth when trying to compensate for a knowledge gap. Awareness of the changes occurring in one’s own conceptual structures is implied by the successful integration of new and pre-existing knowledge, which has been intentionally pursued. A student with less mature epistemological beliefs may not be helped to engage in a process of theory change as he or she does not pursue the goal of knowledge revision. This goal cannot be pursued since the student tends not to perceive any conflict of information and is unaware of the need to restructure conceptions. Awareness of the need to revise knowledge is, instead, a necessary precondition for the conceptual change process (Mason, in press). 5.

DEVELOPING EPISTEMOLOGICAL THINKING FOR CONCEPTUAL CHANGE

It has been argued that epistemological beliefs may affect conceptual change by sustaining or impeding it. Researchers who have investigated beliefs about the nature and acquisition of knowledge, both in general or in particular domains, have clearly pointed out that their construction is strongly influenced by the ways teachers introduce concepts and assess classroom learning. Thus, a question arising at this point is: can interventions in novel learning environments at school successfully develop students’ epistemological beliefs about a particular subject, as a crucial condition for conceptual change? To answer this question positively, three examples of effective instructional intervention on the refinement of students’ epistemological beliefs in science, mathematics and history will be introduced in the following parts of this section. 5.1.

An Example about Scientific Beliefs

From the research in science presented above (see 3.2.) it emerges that it is necessary to stimulate students to move from their limited scientific epistemologies, of an objectivist and unproblematic nature, toward a sophisticated constructivist view. A recent study evaluating the impact of elementary science experiences on sixth graders’ naïve epistemologies about science has been carried out by Smith, Maclin, Houghton and Hennessey (2000). They started with the premise that young students have difficulty elaborating a problematic view of science, and assumed that their naïve epistemology would develop in an appropriate learning environment in which they could generate, evaluate and resolve competing knowledge claims. In this context two similar groups were compared. They learned in different instructional settings with the same teacher throughout elementary school. One environment featured a more traditional pedagogy aimed at helping students enjoy science and see its connection with everyday life (comparison class). The other environment was characterised by a coherent constructivist pedagogy whose main goal was to help students strive for personal understanding (constructivist class). The more traditional intervention was focused on giving children the opportunity to:

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be involved in personally meaningful topics; do hands-on activities; explore outdoor realities; discuss in groups; watch videotaped TV programs about science; participate in two annual school-sponsored science fairs that required them to formulate hypotheses, carry out experiments and draw conclusions; read standard texts. The constructivist class acted as a community of learners (in Brown and Campione’s, 1994, terms) in which the children were engaged in experiments and dialogue to make sense of their own, and other’s ideas. The intervention was focused on giving them the opportunity to: express their own ideas; provide reasons to sustain their views; participate in small group or whole class discussions; monitor the intelligibility, plausibility and fruitfulness of their ideas; represent their thinking externally; read to find information in books useful for their explorations and sense-making activities; reflect on the nature of learning and the nature of science. To summarise, the constructivist environment differentiated from the more traditional one as the children were responsible for their own inquiry in authentic contexts (originally italicised), as well as representing their ideas in various ways. They were also asked to consider generative topics (originally italicised), that is, issues of great significance from the disciplinary point of view. They were involved as a community of learners in social dialogue, listening, contrasting, negotiating, sharing and raising questions about their own ideas and other’s conceptions. They were also involved in metacognitive discourse aimed at stating their own ideas, giving reasons to support an idea, examining the implications of the idea, temporarily abandoning an idea to consider a rival conception, reflecting on the status of conceptions (in terms of intelligibility, plausibility and fruitfulness of their own and other’s conceptions), evaluating the consistency and generalisability of a set of ideas. The more traditional environment was mainly based on problem-solving and critical thinking, rather than notions of knowledge construction in a community of learners, and supported metacognitive development and conceptual change. The teacher’s role in the constructivist environment was to provide students with opportunities of expressing their own ideas and articulating the reasoning which sustains them; to introduce the idea of consistency of thinking and model-consistent and inconsistent thinking; to enhance metacognitive discourse between students asked to reflect upon, and monitor the status of, their own and other’s conceptions; and to present historical examples of conceptual change over time. The two similar groups were interviewed using “The Nature of Science Interview”, previously developed (Carey et al., 1989) to assess their domain-specific

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epistemological theories1. This interview includes questions about the goals of science, the nature of scientific questions, purpose of experiments, the role of ideas in scientists’ work and processes of change in scientific ideas (Smith et al., 2000, pp. 412-413). The significant differences in students’ scientific epistemologies which emerged as results are, according to the question clusters: Goals of science. The majority of learners in the comparison classroom expressed notions of doing things and collecting information. In the constructivist classroom, ideas not mentioned at all in the previous group were expressed by a large percentage of students, who represented science goals as understanding and developing ideas. Type of questions. Asked to give an example of the type of question scientists ask, most students in the comparison classroom referred to questions about concrete objects or perceptible events, followed by those who referred to procedural and relation questions (e.g. “Does listening to music affect how quickly you do your homework?”, p. 371). On the other hand, the majority of children in the constructivist classroom mentioned explanatory (e.g. “What causes disease?”, p. 383), metacognitive (e.g. “Why am I doing this experiment?”, p. 371) and theoretical, unobservable entity questions (i.e. entities such as atoms, forces and germs). Nature and purpose of experiments. To an overwhelming extent, learners in the comparison classroom viewed experiments in terms of answering unproblematic questions, trying things out and finding cures. Students in the constructivist classroom expressed these views much less frequently and, in contrast, made explicit their ideas of experiments as means of testing and developing ideas. Nature of change processes. The most frequent belief among students in the comparison class was that scientists keep or give up an idea after a single experiment or simple observation. No learners in the constructivist class held this simplistic belief, instead they thought that change involves developing ideas, finding complex evidence or better explanations, or is forced by prior conceptions. It should be underlined that consistency and coherence analyses of children’s answers for the four clusters of questions revealed that they develop networks of ideas expressed consistently and coherently. Learners in the constructivist class clearly showed a more knowledge problematic epistemology of science than peers in the comparison class. This epistemology was based on their awareness that scientists often deal with “deep” explanatory questions, that many scientific beliefs are not simple and absolute, right or wrong. Rather, beliefs must be evaluated by more complex criteria and different perspectives can be proposed. Therefore convincing evidence and arguments through social interactions are necessary to support one perspective over another. This study shows how a powerful instructional environment can stimulate and sustain the shift from an objectivist to a more constructivist science epistemology. The students too are younger than those normally conceived in most literature as 1

The authors assumed that even in young children concepts are organised in intuitive theories, that is in quite coherent explanatory systems of conceptions, and that concepts in theories undergo conceptual change (e.g. Carey, 1985).

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capable of refined epistemological thinking. Although the question of whether the refinement of students’ scientific epistemologies positively affects their conceptual change has not been addressed in this study. Other work regarding the science teacher’s practice in the constructivist class has also shown that it enhanced students’ knowledge of science topics (Hennessey, in press; Beeth & Hewson, 1999). 5.2.

An Example about Mathematical Beliefs

One outcome of the research on maths presented above (see 3.3.) was students’ belief that real-world knowledge is irrelevant to solving mathematical word problems. Interestingly, De Corte, Verschaffel and Op ’t Eynde (2000) have pointed out that in some studies (with individual interviews) a significant number of students showed an awareness that conventional answers, typical of the school context, are different from those appropriate to real situations, and were able to justify why they did not use realistic considerations in problem-solving, as clearly expressed by a student (p. 701): I know all these things, but I would never think to include them in a maths problem. Math isn’t about things like that. It’s about getting sums right and you don’t need to know outside things to get sums right.

Considering that the entrenched belief turned out to be very resistant to change, Verschaffel, De Corte and Lasure (1999) implemented an experimental programme about realistic modelling in the typical context of a fifth-grade classroom. The intervention consisted of five teaching/learning units of about two and half hours each over a period of around two weeks. The essential characteristics of this intervention were the following: a set of more realistic problem-solving situations replaced “the impoverished and stereotyped diet of standard word problems given in traditional maths classrooms” (p. 185). Each was aimed at making children focus on realistic and stereotyped solutions in applying maths, as well as complexities implied in realistic mathematical modelling; teaching methods also differentiated from the usual didactic practice in that children worked mainly in mixed-ability groups and used class discussions to compare ideas, comments and possible solutions proposed by the groups. The final individual assignment was also discussed by the whole class; new socio-mathematical norms regarding the role of the teacher and students in the maths classroom, as well as what could be considered a good mathematical problem, a good procedure for solving a problem or good answer were established. An example of a realistic and challenging problem used to apply the heuristic “use your real-world knowledge” is as follows (De Corte, Verschaffel, & Op ’t Eynde, 2000, p. 715): Wim would like to attach a swing to a branch of a big old tree. The branch is 5 meters high. Win has already made a suitable wooden seat for his swing; now he is going to buy some rope. How many meters of rope will he have to buy?

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Results confirmed researchers’ hypotheses. Children in the experimental programme produced significantly more realistic responses to 10 matched pairs of items than peers from the control group. The items included a standard problem to be solved by applying the most obvious arithmetic operation, and a less obvious and problematic problem which required realistic considerations of the context referred to in the problem statement. In addition, the children who followed the programme were more able to apply realistic considerations not only to the learning items (similar to those in the experimental programme) but also to the near-transfer items. Finally, the positive effect of the experimental programme was lasting since at the retention test more realistic responses were again given by those children, even in the case of the far-transfer items. Moving from these encouraging findings on the feasibility of changing beliefs about the role of real-world knowledge in maths problem-solving, De Corte, Verschaffel and Op ’t Eynde (2000) designed a novel learning environment. It was not only aimed at helping children develop more adaptive beliefs and attitudes toward maths learning and mathematical problem-solving, but also aimed at helping them learn an overall cognitive self-regulatory strategy to be used when solving maths application problems. The teacher’s role was mainly to stimulate and scaffold students to engage in cognitive and metacognitive activities underlying the model of competent mathematical problem-solving. As the learners became more competent and able to take responsibility for their own learning and problem-solving, the teacher gradually withdrew encouragement and support, that is, the more the students became selfregulated, the less the teacher gave external regulation. The effectiveness of this environment was tested with some fifth-grade classes after a series of 20 lessons planned by the research team in collaboration with the classroom teachers. Results indicate that the environment positively affected, although not as strongly as expected, different aspects of children’s mathematical modelling ability, cognitive self-regulation, beliefs about maths and problem-solving performance. Students’ improved performance in solving word problems, through the development of their beliefs about the discipline and how to learn, is perhaps the more important outcome of these studies. Change in beliefs about the domain means advancement of competence in that domain. Similar results on the effectiveness of an instructional intervention on the development of fifth graders’ beliefs about themselves as maths learners and about maths and mathematical problem-solving, as well as improvement in their problem-solving performance have also been obtained by Mason and Scrivani (2001). 5.3.

An Example about Historical Beliefs

From the research on history presented above (see 3.4.) it emerged that even high school students have difficulty recognising the constructive, subjective and argumentative nature of historical work and believe that the sources of knowledge used by historians are self-evident. Boscolo and Mason (2001) have investigated the

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development of historical beliefs in fifth graders within a wider study on the effectiveness of writing as a learning tool in conceptual change processes. Individual writing was used by students in the experimental group as a tool to express, reflect and reason on ideas, descriptions and explanations, monitor and communicate their own understanding in the process of knowledge construction in history. Voss and Wiley (1997) pointed out that cognitive restructuring in history may occur in three ways: (a) restructuring conceptions and beliefs about events; (b) restructuring the concept of historical explanation; (c) restructuring epistemological beliefs about the role of the historian and the nature of history itself. One of the purposes of the study was to see whether writing in the service of learning would facilitate understanding of a new history topic through restructuring at all levels as outlined by Voss and Wiley; that is, content, type of explanation, beliefs about the nature of history and the historian’s role. In addition, the study aimed at seeing whether writing would increase students’ awareness of the concepts they had learned. A curriculum unit on geographical discoveries, in particular the discovery of America, was implemented in the history class lasting about ten weeks, with weekly sessions of one hour and fifteen minutes each. For both groups, experimental (writing) and control (no writing), the instructional activity was based mainly on the use of written historical documents to help students learn not only the new contents about events, but also how historical accounts are constructed, that is to understand the historian’s job as a scientist. In some cases, the documents presented different interpretations of the same historical event to give students the opportunity to reflect on the non-existence of “pure” facts, but rather on biased interpretations of the facts. Students in both groups read, examined and discussed the same historical documents, but only those in the experimental group systematically used writing to make what they had read the object of their reflections. From the beginning of the history activity the experimental group teacher made the children aware that notetaking, commenting on, reasoning and reflecting upon ideas, expressing doubts, synthesising what has been learned, could all be writing activities. Writing for learning was systematically carried out individually, while at the same time the control group was engaged in drawing or writing summaries about the topics as dictated by the teacher. In the experimental group at the beginning of each session the teacher and children used what they had written as a link with the previous session. The following are examples (Boscolo & Mason, 2001) that illustrate how, through the writing activity, learners reflected on two texts that portrayed American natives in conflicting ways. In the third example the idea that the writer’s aim is to support Spanish settlers’ actions seems to appear, and it is taken further in the fourth but absent in the first two. We have read two totally different things. I think that they are so different because the Indios behaved differently towards las Casas and Sepúlveda, so they thought of them in different ways and wrote that. (Federica) In my opinion the writers had different informers and they wrote two texts that are conflicting. (Anna)

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L. MASON One document is more balanced and objective, the other justifies that they wanted to kill the natives. Sepúlveda judged people according to two scales. On the highest there were the Spanish people, on the lowest the natives as their servants. (Alessandro, p. 95) The document by Sepúlveda wants to explain why natives are inferior to Europeans. According to him, natives are slaves by nature. As they had never come in contact with the life and culture of Europe, they are considered stupid and wild. Although it is known that these people are able to do things that Europeans cannot, they are judged stupid and inferior all the same so Europeans could do anything they wanted to them. In my opinion, the second document written by Bartolomé de las Casas is totally different as we read that natives were not stupid and primitive. The documents are so different because the two authors had totally different points of view about what was happening between Europeans and natives and each of them wrote what he believed. (Jacopo, p. 95)

The following examples were comments written after reading a document about the first ship-load of slaves taken by Columbus, which impressed the children a lot. While in the first there is reference to the characteristics and tools of the natives, in the second a first attempt to contextualise the event appears. Thinking about the document I think that Columbus could exploit the natives because they were peaceful and did not have weapons, only wooden swords with a stone tip. (Francesca) I believe that Columbus was able to take men as slaves and treat them in the way described in the document because in the past poor people or people from another countries were considered as animals or disposable things. This happened only in the past whereas nowadays poor people can get by one way or another. Now there is more freedom than in the past and there is a law that says that everyone is free. (Silvia)

The next texts are examples of students’ reflections on a document introducing Pope Alexander VI’s bull in which they read that he would give land to those who arrived in America. The students tried to make hypotheses about why the Pope was so interested in “the new lands”. Both are of a personalised nature. We have read the document about the Pope and I think he was so interested in the new territories because he could teach the natives about his religion and make many new people Christian. (Matteo) My opinion on the document is that if the Pope was a good person he was interested in the inhabitants to make them Christians since that was his job. Instead if he was cruel he was interested in wealth and in the inhabitants because they had to pay him. (Francesca)

Before and after implementation of the curriculum unit, students were asked openended written questions on epistemological beliefs about the historian’s work and knowledge construction in the domain: “What is history?”; “How do the people who write history books know about the past they write about?”, “What problems can historians have when they try to understand the past?”, “Is it possible to explain the same fact which happened in the past in different ways? Why?”, “If there are two different explanations of the same fact in the past, how is it possible to understand which is the better?”. Students’ answers underwent a qualitative analysis and were assigned to different categories: low, middle or high level. Moreover, a pre- and

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post-instruction task, “the Livia task”, taken from Kuhn, Weinstock and Flaton (1994, p. 384), was given. It introduced two historians’ conflicting accounts of the fictitious “Fifth Livia War” and was used to see whether students could perceive differences in the accounts. They were asked to “Describe what the war was about and what happened”. Giving children the opportunity to reflect on the documents they read through writing was effective in cognitive restructuring at the three levels outlined by Voss and Wiley (1997). Learners in the experimental group reached higher levels of conceptual understanding of the events examined (by changing prior conceptions), shifted more from an intentional to an economic cause to explain the discovery of America (see Carretero et al., 1994), showed a greater metacognitive awareness of what they had learned and advanced their epistemological beliefs more. Experimental group students’ answers to the last two questions were much more sophisticated at the end of the instructional intervention than those given by the control group. Learners with more advanced epistemological beliefs justified why several explanations can be given for the same historical fact by referring to the different theories that historians may hold when interpreting the past: “Historians have their own theories and points of view, and they write what they think about an event, they interpret it”. Before the intervention, they had mainly referred to the fact that there are many different ways to explain: “There are many words, so many explanations can be made using different words”. The experimental group also progressed more than the control group in saying how it is possible to decide which of two explanations of the same historical fact is the better. At the end of the history activities, more frequently than the control group, they maintained that more investigation is necessary to collect evidence for, or against, the given explanations: “It is necessary to study more, and for years, to investigate and look for further evidence until the things become more certain”. At the beginning they mainly said that it is necessary to ask an expert, or see which explanation is richer, longer or more meaningful: “An expert can say which is right”, “The explanation that is richer in information is true”, “If an explanation is longer, it is the most correct”, “The explanation that seems more truthful is the correct one”. In addition, only the experimental group significantly improved their performance in the “Livia task”. They recognised, more than the control group, the conflict between the two historians’ accounts of the “Livia war”, and that it was not possible to say what happened. The two groups did not differ in their answers to the first three questions. All learners but one maintained that history is about studying and knowing what happened in the past. Most students in both groups, at the beginning and end of the intervention, said that historians study what is written in books or use ruins or documents. To the third question, most students in both groups maintained, at both the beginning and end, that historians may not always find remains, or be unable to decode very old documents or not find enough evidence. It should be noted that the general questions may not have been an adequate means for eliciting young students’ beliefs about history. Interviews could allow a more accurate picture of what they think about the nature of the discipline and knowledge construction in the domain.

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This study, which was not only specifically focused on the development of epistemological beliefs about history, shows that even young students like fifth graders can be helped to refine at least some aspects of their representation of the historians’ work. If they have the opportunity not only to read historical documents, but also to systematically write about them to make hypotheses, construct explanations, interpret events, they can experience the tools of the historian’s work and be aware of the constructive nature of the work in this domain. At the same time they can improve their knowledge and understanding of historical facts. Other studies not specifically focused on students’ historical epistemologies have indicated that elementary school children can learn and use methodological, metacognitive and explanatory procedures to interpret historical events (Fasulo, Girardet, & Pontecorvo, 1999). For instance, working autonomously in small groups and guided by a set of questions on the analysis of a photograph illustrating the inside of a Viking house, fourth graders faced key issues of historical methodology. They discussed in depth source reliability, manipulations that transform findings in the source, generalisability from single cases, interpretation of the past and comparison with the present (Fasulo, Girardet, & Pontecorvo, 1998). 6.

CONCLUDING REMARKS

In this chapter it has been argued that conceptual change in different domains can be fostered through the development of epistemological thinking. Students construct representations about the nature and acquisition of knowledge, in general and regarding specific domains, which have a strong impact on thinking and understanding. Epistemological beliefs may act as resources facilitating conceptual change or as constraints impeding it in that these beliefs may, or may not, guide students to intentionally pursue the goal of knowledge revision. Through examples from science, maths and history education it has also been shown that in powerful learning contexts students can be stimulated and supported to develop their naïve epistemological beliefs as an essential condition for conceptual change. Giving them opportunities to refine these beliefs has a double purpose. First, they can reach the highest levels of development of their theory of mind that are represented by a constructivist epistemology. Second, students can develop and refine thinking dispositions crucial to fostering learning through knowledge revision. Flourishing research on students’ epistemologies has left the fundamental question of the nature and structure of personal epistemologies open to theoretical and methodological investigation. Hopefully, greater clarity of this crucial point will lead to adopting a clearer terminology for referring to the epistemic plane of cognition. From this chapter, and the one by Leach and Lewis in this volume, it emerges that there are scholars (e.g. Smith et al., 2000) who consider these epistemologies as theory-like structures, that is, coherent structures in which representations about knowledge and knowing are qualitatively restructured during development. There are scholars (e.g. Schommer, 1994) who consider these epistemologies as a set of beliefs that are not necessarily aligned in all dimensions,

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so a student may have more advanced beliefs in one dimension, and less advanced in another. There are also scholars who consider these epistemologies as profile-like representations that vary according to specific contexts, in that a student draws upon different epistemologies in different situations (e.g. inductivist in one and constructivist in another). It therefore makes little sense to talk about their epistemological stance without reference to a specific situation. Further research should explore in greater depth the nature and structure of epistemological views and the kind of revision they undergo during development. Different ideas about epistemological views lead to different implications for teaching to think on the epistemic level of cognition. In addition, it is worth exploring the reciprocal interaction between personal epistemologies and conceptual change. It may be speculated that not only advanced beliefs about the nature and acquisition of knowledge facilitate knowledge revision, but also that changing conceptions about phenomena and events in a domain contribute to refining general beliefs about knowledge and knowing. REFERENCES Abelson, R. (1979). Differences between belief systems and knowledge systems. Cognitive Science, 3, 355-366. Aikenhead, G., Fleming, R. W., & Ryan, A. G. (1987). High school graduates’ beliefs about sciencetechnology-society. 1: Methods and issues on monitoring student views. Science Education, 71, 145161. Alexander, P. A., & Dochy, F. J. R. C. (1994). Adults’ views about knowing and believing. In P. A. Garner & P. A. Alexander (Eds.), Beliefs about text and instruction with text (pp. 223-243). Hillsdale, NJ: Lawrence Erlbaum Associates. Alexander, P. A., & Dochy, F. J. R. C. (1995). Conceptions of knowledge and beliefs: A comparison across varying cultural and educational communities. American Educational Research Journal, 32, 413-442. Alexander, P. A., Murphy, P. K., Guan, J., & Murphy, P. A. (1998). How students and teachers in Singapore and the United States conceptualize knowledge and beliefs: Positioning learning within epistemological frameworks. Learning and Instruction, 8, 97-116. Astington, J. W., Harris, P. L., & Olson, D. R. (1988). Developing theories of mind. New York: Cambridge University Press. Beeth, M. E., & Hewson, P. W. (1999). Learning goals in an exemplary science teacher’s practice: Cognitive ansd social factors in teaching for conceptual change. Science Education, 33, 738-760. Benack, S., & Basseches, M. A. (1989). Dialectical thinking and relativistic epistemology: Their relation to adult development. In M. L. Commonns, J. D. Sinnott, F. A. Richards, & C. Armon (Eds.), Adult development: Vol. 1. Comparisons and applications of developmental models (pp. 95-112). New York: Praeger. Bombi, A. S., & Ajello, A. M. (1988). La rappresentazione della storia nei bambini [History representations in children]. Orientamenti Pedagogici, 35, 17-27. Boscolo, P., & Mason, L. (2001). Writing to learn, writing to transfer. In P. Tynjälä, L. Mason, & K. Lonka (Eds.), Writing as a learning tool. Integrating theory and practice (pp. 83-104). Dordrecht, The Netherlands: Kluwer Academic Publishers. Bozzo, M. T., Morra, S., & Pierimarchi, S. (1989). Il concetto di documento storico nella scuola elementare [The concept of historical document in the elementary school]. Scuola e Città, 40, 345350. Brown, A. L., & Campione, J. (1994). Guided discovery in a community of learners. In K. McGilly (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice (pp. 229-270). Cambridge, MA: MIT Press/Bradford Books. Carey, S. (1985). Conceptual change in childhood. Cambridge, MA: MIT Press.

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Mason, L. (2000). Role of anomalous data and epistemological beliefs in middle students’ theory change on two controversial topics. European Journal of Psychology of Education, 15, 329-346. Mason, L. (2001a). High school students’ beliefs about maths, mathematical problem solving, and their achievement in maths: a cross-sectional study. Manuscript submitted for publication. Mason, L. (2001b). Responses to anomalous data on controversial topics and theory change. Learning and Instruction, 11, 453-483. Mason, L. (in press). Personal epistemologies and intentional conceptual change. In G. M. Sinatra & P. R. Pintrich (Eds.), Intentional conceptual change: Mahwah, NJ: Lawrence Erlbaum Associates. Mason, L., & Scrivani, L. (2001, August). “Maths gives less, but more correct answers”: Students’ epistemological beliefs about maths and their development in the classroom. Paper presented at the European Conference for Research on Learning and Instruction. Fribourg, Switzerland. Moshman, D. (1994). Reasoning, metareasoning, and the promotion of rationality. In A. Demetriou & A. Efklides (Eds.), Intelligence, mind and reasoning. Structure and development (pp. 135-150). London: Elsevier. Moshman, D. (1998). Cognitive development beyond childhood: Constraints on cognitive development and learning. In W. Damon (Series Ed.) & D. Kuhn & R. Siegler (Vol. Eds.), Handbook of child psychology: Vol. 2. Cognition, language, and perception (5th ed., pp. 947-978). New York: Wiley. Nespor, J. (1987). The role of beliefs in the practice of teaching. Journal of Curriculum Studies, 10, 317328. Pajares, F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62, 307-332. Perkins, D. N, & Simmons, R. (1988). Patterns of misunderstanding: An integrative model for science, math, and programming. Review of Educational Research, 58, 303-326. Perry, W. G. Jr. (1968). Forms of intellectual and ethical development in the college years: A scheme. New York: Holt, Rinehart and Winston. Qian, G., & Alvermann, D. (1995). Role of epistemological beliefs and learned helplessness in secondary school students’ learning science concepts from text. Journal of Educational Psychology, 87, 282292. Reusser, K. (1988). Problem solving beyond the logic of things: Contextual effects on understanding and solving word problems. Instructional Science, 17, 309-338. Roth, W.- M, & Roychoudhury, A. (1994). Physics students’ epistemologies and views about knowing and learning. Journal of Research in Science Teaching, 31, 5-30. Rukavina, I, & Daneman, M. (1996). Integration and its effect on acquiring knowledge about competing scientific theories from text. Journal of Educational Psychology, 88, 272-287. Ryder, J., Leach, J., & Driver, R. (1999). Undergraduate science students’ images of the nature of science. Journal of Research in Science Teaching, 36, 201-220. Schoenfeld, A. H. (1983). Beyond the purely cognitive: Beliefs system, social cognition, and metacognition as driving forces in intellectual performance. Cognitive Science, 7, 329-363. Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of “well taught” mathematics classes. Educational Psychologist, 23, 145-166. Schoenfeld, A. H. (1989). Explorations of students’ mathematical beliefs and behavior. Journal for Research in Mathematics Education, 20, 338-355. Schommer, M. (1990). Effects of beliefs about the nature of knowledge on comprehension. Journal of Educational Psychology, 82, 498-504. Schommer, M. (1993). Epistemological development and academic performance among secondary students. Journal of Educational Psychology, 85, 406-411. Schommer, M. (1994). Synthesizing epistemological belief research: Tentative understanding and provocative confusions. Educational Psychology Review, 6, 293-319. Schommer, M., Crouse, A., & Rhodes, N. (1992). Epistemological beliefs and mathematical text comprehension: Believing it is simple does not make it so. Journal of Educational Psychology, 84, 435-443. Schraw, G., Dunkle, M. E., & Bendixen, L. D. (1995). Cognitive processes in well-defined and ill-defined problem solving. Applied Cognitive Psychology, 9, 523-538. Silver, E. A. (1985). Research in teaching mathematical problem solving: Some underrepresented themes and directions. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 247-266). Hillsdale, NJ: Lawrence Erlbaum Associates.

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Smith, C. L., Maclin, D., Houhgton, C., & Hennessey, M. G. (2000). Sixth-grade students’ epistemologies of science: The impact of school science experiences on epistemological development. Cognition and Instruction, 18, 349-422. Songer, N. B, & Linn, M. C. (1991). How do students views of science influence knowledge integration?, Journal of Research in Science Teaching, 28, 761-784. Stanovich, K. E. (1999). Who is rational? Studies of individual differences in reasoning. Mahwah, NJ: Lawrence Erlbaum Associates. Strike K. A., & Posner G. J. (1993). A revisionist theory of conceptual change. In R. A. Duschl & R. J. Hamilton (Eds.), Philosophy of science, cognitive psychology, and educational theory and practice (pp. 147-176). New York: SUNY Press. Tsai, C.-C. (1998). An analysis of scientific epistemological beliefs and learning orientations of Taiwanese eighth graders. Science Education, 82, 473-488. Vansledright, B., & Brophy, J. (1992). Storytelling, imagination, and fanciful elaboration in children’s historical reconstructions. American Educational Research Journal, 29, 837-859. Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4, 273-294. Verschaffel, L., De Corte, E., & Lasure, S. (1999). Children’s conceptions about the role of real-word knowledge in mathematical modelling: Analysis and interpretation. In W. Schnotz, S. Vosniadou, & M. Carretero (Eds.), New perspectives on conceptual change (pp. 175-189). Amsterdam: Pergamon/Elsevier. Voss, J. F., & Wiley J. (1997). Conceptual understanding in history. European Journal of Psychology of Education [Special issue], 12 (2), 147-158. Voss, J. F., Wiley, J., & Kennet, J. (1998). Student perceptions of history and historical concepts. In J. F. Voss & M. Carretero (Eds.), International Review of History Education: Vol. 2. Learning and reasoning in history (pp. 307-330). London: Woburn Press. Wellman, H. M. (1990). The child’s theory of mind. Cambridge, MA: Bradford/MIT Press. Windschitl, M., & Andre, T. (1998). Using computer simulations to enhance conceptual change: The roles of constructivist instruction and student epistemological beliefs. Journal of Research in Science Teaching, 35, 145-160. Wineburg, S. (1991). On the reading of historical texts: Notes on the breach between school and academy. American Educational Research Journal, 38, 495-519.

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SCIENCE LEARNING THROUGH TEXT: THE EFFECT OF TEXT DESIGN AND TEXT COMPREHENSION SKILLS ON CONCEPTUAL CHANGE

MIRJAMAIJA MIKKILÄ-ERDMANN

University of Turku, Finland

Abstract. This study examined how a traditional text design, compared to a conceptual change text design, supports readers with varying text comprehension skills in learning photosynthesis. The study is theoretically motivated by the research on conceptual change and text comprehension. Two hundred eleven-year-old participants were first given a conceptual understanding pre-test concerning photosynthesis and two tests on text comprehension skills. In the next session, participants were randomly given a traditional text or a conceptual change text and a conceptual understanding post-test. The experiment took place in a normal classroom setting, and the participants were allowed to make use of the text while answering the conceptual understanding post-test. Conceptual change was measured through critical distinction questions and generative questions. In these questions, the participants in the conceptual change text design group outperformed the participants in the traditional text design group. Furthermore, on critical distinction questions, both high-level and low-level readers profited from the conceptual change text design. Hence, a conceptual change text design which systematically points out the differences between possible misconceptions and the science knowledge to be learned helped the learners to construct a relevant mental model concerning photosynthesis and so facilitated conceptual change.

1. INTRODUCTION

1.1. Conceptual Change Learning - a Challenge for Instructional Practice and Textbooks The purpose of this study was to investigate how different texts support readers with varying text comprehension skills in learning difficult scientific concepts that contradict their prior knowledge. This kind of learning process can be called conceptual change in which learners continuously have to revise their preinstructional naive theories in response to new, contradictory scientific ideas (Chinn & Brewer, 1993; Vosniadou, 1994; Vosniadou & Ioannides, 1998; Vosniadou & Schnotz, 1997). The realisation that learners do not come to school as empty vessels but have rich prior knowledge representations of a more or less systematic nature, has important implications for the design of science instruction and textbooks (Ioannides M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 337-356. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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& Vosniadou, 1998, p. 1223). The problem is, first, that pre-instructional theories, and in particular those differing from the scientific ones, seem to be invisible to teachers, textbook writers and even the learners themselves (Roth, 1990). Second, pre-instructional knowledge seems to be very persistent because children have tested their naive theories in everyday contexts where they seem to work and do not see any relevance in changing their conceptions. Hence, it can be suggested that a lot of science learning proceeds through enrichment. A learner adds new information to an existing theoretical explanation on the level of specific theories, without changing the framework theory (Vosniadou, 1994, p.46). Children have been taught, for example, about photosynthesis many times at school, but they still think that plants have external sources of food like human beings (Mikkilä, 2001; Roth, 1987, 1990;). In Vosniadou’s (1994, p.46) terms, children seem to have a specific theory about how a plant gets its food through its roots, and a framework theory according to which plants and animals are similar concerning nutrition (see Mason & Boscolo, 2000; Roth, 1990). Hence, in learning photosynthesis, revision-like conceptual changes are needed, and these can be considered the most difficult and significant type of conceptual change. This often requires systematic instruction (Chinn & Brewer, 1993; Hatano & Inagaki, 1997; Vosniadou, 1994; Vosniadou & Schnotz, 1997). In sum, instructional interventions are needed which make learners aware of their implicit prior knowledge and provide a meaningful experience to motivate them to understand the limitations of their explanations and to change them (Vosniadou & Ioannides, 1998, p. 1224). Science textbooks can be seen as an unexplored resource in promoting conceptual change in science classrooms. 1.2.

Problems of Learning from Textbook Text

Most of the learning occurring in the school context, even in science classrooms, happens with the help of texts. They are still one of the main methods of science instruction. Hence, the role of textbook text in fostering conceptual change learning may be essential. They have, however, been criticised for their inability to promote high quality learning, such as conceptual change (Guzzetti, Snyder, & Glass, 1992; Guzzetti, Snyder, Glass, & Gamas 1993; Roth, 1990; Roth et al., 1987). In particular, the knowledge organisation, and also the lack of explanatory coherence of the textbook texts (see Beck, McKeown, Sinatra, & Loxterman, 1991), has been the target of criticism. Science textbooks traditionally present the discipline as a series of related but fairly discrete topics (e.g. plants, animals, and cells). There are normally few or no connecting textual units between different topics. Thus, the target of science textbooks seems to be the coverage of many concepts (in-breadth) instead of concentration on some of the central conceptual contents (in-depth) (Guzzetti et al., 1993; Mikkilä & Olkinuora, 1994; Roth, 1990; Roth et al., 1987; Stinner, 1995). This approach towards designing science textbooks can also be seen on the level of the science text itself. The most common science text type is namely the expository, non-refutational text which presents facts in a list-like fashion rather

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than explains them. Furthermore, the links between concepts presented in the text are often not made explicit, a fact that presupposes a great deal of inference and causes problems for learners who lack prior knowledge or whose prior knowledge interferes with, rather than facilitates, the acquisition of new knowledge (Beck et al., 1991; Guzzetti et. al., 1993) It is, in fact, a common problem that elementary school pupils often have difficulties in learning from expository texts (Vauras, Kinnunen, & Kuusela, 1994). After reading an expository text, they are often able only to reproduce the textbase (van Dijk & Kintsch, 1983), i.e. the information that is directly expressed in the text, as the author has organised and structured it, without constructing a mental model, i.e. without understanding the topic in a more profound way. However, normally the target of science learning is learning from text that can be defined according to Kintsch (1986, 1988) as the construction of an adequate mental model of the phenomenon described in the text. There is, however, evidence that textbook texts often fail to support this target in learning because they concentrate on delivering facts rather than on conceptual understanding (Beck et al., 1991; Guzzetti et al., 1993; McNamara, Kintsch, E., Songer, & Kintsch, W., 1996). In the case of a demanding science text, more is required for understanding than just the ability to reproduce the text itself. In the comprehension process, the reader must contribute information that was not explicitly stated in the text from his or her own prior knowledge about the domain in question. Hence, considerable active inferencing may be required to link the text to the reader’s prior knowledge. The result of such inferencing is the mental model. In the construction of a mental model, the reader integrates the information provided by the text and often reorganises and restructures it in terms of his or her understanding of the knowledge domain as a whole rather than the particular text just read (McNamara et al., 1996). Furthermore, in the model of Kintsch (1988), the knowledge base of the learner is conceptualised as an associative network. To construct even a single proposition an appropriate framework must be retrieved from one’s store of knowledge and its slots must be filled in the way indicated by the text (Kinsch, 1988). However, texts differ in how they indicate which kind of frame must be actualised and in how to fill the slots. The research done on conceptual change may give us new insight into why even good readers who do a great deal of inferencing during reading may construct inappropriate mental models of the text under study. The design of the text, which refers to the organisation of knowledge in the text and how the possible conflict between prior knowledge and to-be-learned knowledge is taken into account, may play an important role in helping the reader to build relevant mental models concerning the domain. It can be suggested that the text will set the reader in the right direction for constructing and editing mental models from the text and from his or her prior knowledge. In sum, enrichment or revision processes, i.e. conceptual change, may be enforced through text design. Moreover, it is suggested that especially low-performing readers, i.e. readers who have problems in constructing mental models from text, need support on the part of the text design in overcoming the problems of interfering prior knowledge.

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In sum, it seems to be very difficult to support science learning, for example, concerning photosynthesis, through a standard expository, non-refutational science text design that does not pay any attention to misleading pre-instructional notions but rather enriches them. 1.3. Conceptual Change Learning through Text-Cognitive Conflict is not enough

The research conducted on reading in the area of science content has indicated although the results are, to some extent, equivocal - that a text can affect conceptual change processes under two conditions: either when the text is refutational or when the text is used in combination with other strategies producing a cognitive conflict (Guzzetti et al., 1993). The so-called cognitive conflict approach, which originates from Piaget (see Posner, Strike, Hewson, & Gertzog, 1982), first involves identifying the learners’ current state of knowledge, and then tries to bring these conceptions into confrontation with the scientific knowledge, so that learners can replace their preexisting ideas with scientifically accepted ones (Chinn & Brewer, 1993; Posner et al., 1982). However, the problem seems to be that even when students are confronted with contradictory information, they are often unable to achieve meaningful conflict or even to become dissatisfied with their prior conceptions. They will ignore or reject the new knowledge when this is possible (Chinn & Brewer, 1993). Hence, simply presenting a cognitive conflict in the learning situation seems to be inadequate for promoting conceptual change in a radical sense, in particular in young learners (Caravita & Halldén 1994; Limón & Carretero, 1997; see also Chann, Burtis, & Bereiter, 1997). In accordance with this, some limitations can be found in the studies aiming to facilitate conceptual change through cognitive conflict provoked by a science text. The refutational texts used in the experiments often consist of some counterintuitive statements which are then refuted (e.g. Alvermann & Hague, 1989), or else the texts are like a typical expository science text in which only conceptual change sections, e.g. diagrams, are inserted (Wang & Andre, 1991). Furthermore, refutational texts are often used in combination with other instructional activities like activation of prior knowledge (Alvermann, Smith, & Hynd, 1985; Hynd & Alvermann, 1986), so that it is very difficult to find out what is the main text effect. 1.4. Metaconceptual Awareness, Conceptual Change and Learning from Text

One essential question in designing science texts seems to be, how to make readers aware of the possible conflict between their prior knowledge and knowledge presented in the text. In particular, from the conceptual change perspective, we are challenged to think about the activation “path” of knowledge in the process of text comprehension. Could it be possible to hinder the activation and interference of inappropriate prior knowledge through text? According to Kintsch (1988), there are construction-integration processes that act in a bottom-up and top-down way in the

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various phases of reading. The reader activates knowledge in order to construct different mental representations (van Dijk & Kintsch, 1983; see also Schnotz, 1993). It can be suggested that when the framework theory of the learner is inappropriate, the knowledge presented in the text is easily over-read and top-down processes may dominate. But the text design may lead the comprehension process from enrichment through bottom-up activation to revision. Furthermore, the lack of metaconceptual awareness (Vosniadou, 1994) can be one reason why young learners are unaware of the cognitive conflict. Metaconceptual awareness can be seen as awareness of the ‘theoretical’ nature of one’s thinking, i.e. of the mental models we construct and make use of in order to make sense of the world. Metaconceptual awareness in science contents also suggests an understanding of the differences between naive and scientific representations. This can be seen as an important prerequisite for conceptual change (see Vosniadou, 1994; Vosniadou & Ioannides, 1998). The study done by Alvermann and Hague (1989) has provided us with a very interesting contribution to dealing with the problem of lacking metaconceptual awareness through text. The study examined the effects of activating prior knowledge and refutation text structure on students’ comprehension of counterintuitive science material. It was found that students benefit from a text that explicitly points out incongruencies between the students’ thinking and the scientific ideas expressed in a text in the following way: If you thought that the path the marble would take would be… your ideas may be different from what the laws of physics would suggest. As you read the following text, be sure to pay attention to those ideas presented in the text that may be different from your own.

Alvermann and Hague (1989, p. 198) call this approach augmented activation, i.e. advance ‘warning’ of possible inconsistencies between the reader’s beliefs and the information in the text. It was suggested that once the incongruencies are pointed out, students would be more likely to modify or correct their misconceptions. This suggestion was confirmed in their study (Alvermann & Hague, 1989). In the present study, in accordance with Alvermann and Hague (1989), the idea of augmenting text is applied. However, in contrast to the design of their text, the augmenting text in this study (i.e. the metaconceptual text design) was not only used in the beginning of the text but throughout the whole text. It systematically tries to point out the differences between naive preinstructural and to-be-learned scientific conceptions. It is assumed that not only high-level readers but also low- level readers, who have difficulties in going beyond the text, i.e. in constructing adequate mental models, may benefit from the conceptual change text design. In sum, it is suggested that text which points out the differences between possible misconceptions and science contents can promote metaconceptual awareness and can thus assist the learner to construct a relevant mental model concerning, e.g. photosynthesis and, so facilitates conceptual change.

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2.1.

METHOD

Participants

The participants were 200 school pupils 10-11 years of age, from five primary schools that were located in socio-economically different urban areas. The children were randomly assigned to two experimental conditions. 2.2.

Materials

The effect of text design on conceptual change was measured through two versions of a text about photosynthesis. The two versions had the same content but were organised in different ways: A traditional text (TT) and a conceptual change text (CT). The traditional text was taken from a contemporary science textbook widely used in schools (Aho, Enqvist, Kytömäki, Nurmi, & Saarivuori, 1995). The TT has exactly the same content than the CT. Furthermore, it is a coherent and explanatory school text on photosynthesis. The conceptual change text was prepared for the experiment. Because of the extended explanations the conceptual change text (597 words) was slightly longer than the traditional text (441 words). The main differences concerning the text versions are as follows: 1) Macro-level organisation (specific theory approach vs. framework theory approach concerning photosynthesis (see Roth, 1990; Vosniadou, 1994); 2) text elements targeted at inducing metaconceptual awareness. Macro-level organisation. The logic behind the texts is different. The traditional text follows a topical organisation on the level of the specific theory about photosynthesis. Thus, the traditional text does not deliberately produce any cognitive conflict, i.e. it does not take into account the typical misconception concerning photosynthesis (Mikkilä & Olkinuora, 1995; Mason & Boscolo, 2000; Roth, 1990) of the role of water (“water is food” = energy-containing substance for a plant), but aims to enrich learners’ prior knowledge and starts from a description of the importance and function of water in the plant. It follows the topical pattern: a plant needs water; water goes into the plant along tubes, explanation of photosynthesis, self-sufficient/other-sufficient, the global importance of photosynthesis (see Appendix A). The conceptual change text design takes the framework theory level as an organisational aid, and uses the critical difference between plants and animals in the production of energy as its starting point, following the pattern: “Plants and animals need energy to live” ... “Plants differ from all living organisms because they can make their food by themselves.” Thus, the conceptual change text design tries to produce a cognitive conflict on the level of the framework theory. It contrasts learners’ prior knowledge with the scientific knowledge from the beginning to the end of the text. Its topical structure is as follows: all living organisms need energy, plants produce their own food, self-sufficient/other-sufficient, explanation of

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photosynthesis, self-produced sugar is photosynthesis (see Appendix B).

stored, the

global

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importance

of

Text elements targeted at inducing metaconceptual awareness. The difference between the traditional text version and the conceptual change text is also that the TT has no metaconceptual text that directly comments on how to understand the phenomenon of photosynthesis when the learner has the typical misconception. The conceptual change text version has seven metaconceptual text units such as, “How plants get their food happens in a different way than we normally think. How does the energy get into a plant? Is water food for a plant?”... “It is important to understand that a plant does not take ready-made food through its roots from the soil. So a plant does not eat but makes its food in the chloroplasts...” “Thus, water is not food for a plant but only one of the raw materials it uses to make its own food in the process called photosynthesis.” “Food chains help us to understand how energy circulates in nature.” “It is important to learn that plants can make their food by photosynthesis and do not take it in through their roots from the soil.” “When you are learning about photosynthesis it is useful to think of the difference which exists between plants and animals concerning how they get their food.” “The most important thing to understand about photosynthesis is that only plants can absorb light energy for food and produce oxygen as a by-product.” 2.3.

Conceptual Understanding Test

The conceptual understanding test concerning photosynthesis consisted of 11 openended essay-type questions, used in the pre-test and the post-test, which can be categorised as follows: 1) Retention questions requiring fact finding: the answers were explicitly stated in the text (e.g. “What are tubes?”); 2) inferential text comprehension questions also based on the text, demanding understanding of essential subelements of the concept photosynthesis (e.g. “What are chloroplasts?”); 3) critical distinction questions (see Hatano & Inagaki, 1997) demanding understanding of the basic ontological distinction between animals and plants (e.g. “What does a plant/human being need to live and grow?” “Where does it come from?”); 4) generative questions (see Vosniadou, 1994) requiring the learner to solve a novel problem by constructing an adequate mental model of photosynthesis (e.g. “When we eat a potato, we get energy. How does the energy get into the potato?”). Both retention and inferential text comprehension questions were targeted at measuring comprehension on the text-base level. The critical distinction questions and the generative questions tried to tap into mental model construction and so can be used as criteria for conceptual change. Scoring. In order to compare the performance on the conceptual change test by participants who read the traditional text version and participants who read the

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conceptual change text version, a template of model answers based on the data was developed. The first step in the development of model answers was that two raters read the tests through and negotiated the following scores for different question types: 1) Retention questions were scored 0-3. Three credits were given if the fact asked about in the question was given correctly. Two credits were given if the answer consisted of relevant information but was not exact enough. One credit was given if the learner produced an isolated piece of information. In the scoring of every question type, zero means no answer was given by the learner. 2) Inferential text comprehension questions were scored on a scale of 0-5 because this corresponded better with the nature of the data and worked well. The highest score (5) was given if the learner produced a text-based explanation of photosynthesis. Four credits were given if the participant produced an almost perfect explanation of the process but made a few mistakes. Three credits were scored for an answer that only explained the end result of photosynthesis. Two credits were given when the answer revealed that the learner had understood part of the process. One credit was given for an isolated fact. 3) Critical distinction questions were scored on a 0-5 scale. Five credits were given if the learner understood that plants are self-sufficient. Four credits were given if the end products of photosynthesis were mentioned in the answer. Three credits were given if the answer consisted of a morphological definition of a plant. Two credits were given if the answer showed that the difference between plant and animal was partly understood, partly not. One credit was given for answers that suggested that a plant takes its food from the soil. Furthermore, three of the critical distinction questions were scored 0-3. Three credits were given if the pupil understood the differences between plants and animals in the production of energy. Two credits were given if the learner produced an answer which revealed that he/she thought a plant gets its food both from the soil and from the sun.. One credit was given for an explanation consisting of isolated facts. 4) One generative question was scored 0-5 (see critical distinction questions). Two generative questions were scored 0-3. The highest score (3) was given if the answer revealed an appropriate mental model of photosynthesis. Because of the open-ended nature of the questions, two raters read every paper and the interrater agreement on scoring was calculated. Interrater agreement on answers was 0.94. Disagreements were settled through discussion. 2.4.

2.4.1.

Text Comprehension Skill Tests

Science Text Comprehension Test

Text comprehension was measured by means of two tests which are dealt with separately in the following section because they are partly intended to measure different aspects of text comprehension. Firstly, a Science Text Comprehension test (ST) was used in this study. The aim of the ST is to measure both text-based

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understanding and the construction of a mental model of the topic presented in the text in the science content area. The ST is a coherent and well-written textbook-like text (245 words) on natural selection. The text was called ‘a bat is hunting in the summer night’. The first paragraph describes in a narrative way how a bat hunts and recognises first a fly and then a moth from far away with its super-sensitive ears. The text then explains how animals like the bat and its prey, such as the moth, has developed effective defence mechanisms during evolution. In the last paragraph the basic idea of evolution is summarised on a very abstract level. After reading the text, the participants were instructed to write a short summary of the main ideas of the text. They did not have the text available while summarising but reconstructed it from memory. Scoring. Two independent raters developed model answers based on the data. Through negotiation, the decision was made to score the summary task based on the science text from 1-2 that corresponded with the nature of the data. One credit (low level) was given for responses which reproduced the text base, i.e. revealed that the learner had reproduced the text in a linear way starting from the characteristics of a bat (“A bat has sensitive ears. A bat is hunting a moth.”, etc.). The answers on this level tell a story about a bat without understanding the idea of interaction between specific characteristics and the environment. Two credits (high level) were given when the answer revealed that there was an understanding of the interaction between animal and environment, and hence of the development of the species. This can be seen as a prerequisite for understanding the notion of evolution. The interrater agreement on responses was 0.80. Disagreements were settled through negotiations. 2.4.2.

Action-oriented Mental Model Test

Secondly, an Action-oriented Mental Model test (AT) was used to measure mainly the construction of a mental model, i.e. the understanding of the text on a global level. The AT (273 words) consisted of a text which described a discussion in the classroom concerning a class trip to be planned to a town near-by. The children were instructed to write a telegram (a short message) to the person responsible for the practical organisation. The telegram should be based on the text and had to include all the relevant information for the organisation of a successful class trip. Thus, the telegram should provide all the relevant information for the person and so enable her to make the practical organisations for the trip (e.g. hire a guide; order a table in the restaurant etc.). Furthermore, the participants were encouraged to make use of the text while writing the telegram. Scoring. The level of the situation model was scored 1-2. The relevant actions to be taken, which were described in the text, were scored 1-4. A sum score was calculated from these scores: those who scored 1-3 were low-level readers and 4-6 high-level readers. In the Action Oriented Text Comprehension Test, responses that scored 1 (low level) revealed that the learner had copied sentences from the text base (‘they want to go on a trip’) without constructing a mental model. The high level

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credit (2) was given for responses revealing a relevant mental model according to which it was possible to make the relevant preparations for the class trip: ‘1. Arrival 9.5, 10.00 at the railway station. Could you please organise a guide for us? Please reserve a table for 31 persons in a pizzeria. Please reserve 6 tickets for the theatre etc.’ The interrater agreement was 0.70. Disagreements were settled through negotiations. 2.5.

Procedure

Both the text comprehension tests and the conceptual understanding pre- and posttest were conducted in a classroom situation. In the first session (45 min), the learners were given the text comprehension tests. In the second session (45 min), the pupils did the conceptual change pre-test. In the third session (post-test 45 min) the pupils were randomly given one of the text versions and a conceptual change test concerning photosynthesis in a classroom situation. They were then instructed to study the text as they normally do when working on their assignments. It was possible for them to make use of the text while answering the questions. The children were told that the target of learning is not memorising but understanding. There was no time limit, but it took approximately one hour to read the text and answer the questions. The treatment conditions were as follows: 1. Traditional text design group; 2. conceptual change text design group. 3.

3.1.

RESULTS

Conceptual Understanding Pre-test

A t-test was performed for every question type, and the results show that there were no statistically significant differences in the quality of prior knowledge between the treatment groups in the conceptual understanding pre-test concerning photosynthesis. Both groups showed a typical misunderstanding concerning the difference in the energy production of plants and animals which has been documented in the research literature (“a potato gets its energy from the soil through roots”; “a plant gets its food from the water and from the sun”) (e.g. Mason & Boscolo, 2000; Mikkilä & Olkinuora, 1995; Roth, 1990). 3.2.

Retention Questions

In the following, the sum scores of every question type are used in the analyses. The three-way ANOVAs (repeated measures) analysing the interaction between text design and text comprehension tests on different question types are presented separately because the tests aim to measure different aspects of text comprehension. First, a three-way ANOVA was performed for each question type including between-subjects factor of text design and levels of text comprehension measured

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through the Science Text Comprehension test (ST). Both means and standard deviations of each question type in the pre-and post-test are presented in Table 1.

A 2 x 2 x 2 repeated measures ANOVA for Science Text Comprehension test (highlevel readers vs. low-level readers) x Condition (conceptual change design vs. traditional text design) x pre-test/post-test change was conducted on retention questions which were mainly designed to measure performance on the text-base level. The ANOVA showed only symptomatic main effect for condition, favouring the traditional text design treatment. A significant main effect for the change from pre-test to post-test was observed, Furthermore, a significant interaction effect was gained for condition and for the change of the scores from the pre-test to the post-test on retention questions, On the whole model level there was no interaction effect. The post hoc test (LSD), on the 0.05 level of significance indicated, however, that subjects with high scores on the Science Text Comprehension Test in the traditional text treatment group performed significantly better on retention questions than high-level readers in the conceptual change treatment group. Moreover, subjects with low scores on this Science Text Comprehension test profited from the

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traditional text design on retention questions. Low-level readers in the traditional text condition group responded better on the retention questions than low-level readers in the conceptual change treatment group.

A 2 x 2 x 2 ANOVA was also conducted for the Action-Oriented Text Comprehension text (high level vs. low-level readers) x Condition (traditional text vs. conceptual change text) x pre-test/post-test change on every question type. Table 2 shows the means and standard deviations. On retention questions, the ANOVA showed a significant main effect for text design condition, favouring the traditional text design group, There was also a significant main effect for the text comprehension test, and for the change of the scores from pre-test to post-test, No interaction effect was found at the whole-model level. The post hoc (LSD) analysis revealed that the low level readers profited from the traditional text design in answering the retention questions. The low-level readers in the traditional text design group scored

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significantly better in the retention questions compared to those in the conceptual change design group. 3.3.

Performance on Inferential Text Comprehension Questions

Inferential text questions were designed to measure inferential, but still to a great extent, text-based comprehension. Repeated measured ANOVAs (ST x Condition x pre-test/post-test change) on inferential text questions showed no significant main effect for text condition. There was, however, a significant main effect for science text comprehension test, and for the difference in the pretest/post-test scores, No interaction effect was found at the whole-model level. The post hoc analysis (LSD) revealed a significant difference between high-level readers in the conceptual change group and in the traditional text design group. The high-level readers in the conceptual change condition outperformed high-level readers in the traditional text design condition. The three-way ANOVA (AT x Condition x change from pre-test to post-test) on inferential questions produced a significant main effect for the text comprehension test, favouring the high-level readers, There was also a significant main effect for the change of the scores from pre-test to post-test There were no interaction effects on the whole-model level. 3.4. Performance on Critical Distinction Questions

Critical distinction questions were targeted at the construction of a mental model concerning the difference between plants and animals. An ANOVA (ST x Condition x pre-test/post-test scores) on critical distinction questions showed a statistically significant main effect for condition and for the change from pre-test to post-test, Furthermore, there was a significant interaction effect of text condition and change of scores from pre-test to post-test, Participants in the conceptual change group performed significantly better on critical distinction questions than the subjects in the traditional text design group. Moreover, the post hoc (LSD) analysis showed a significant difference between high-level readers in the conceptual change group compared to those in the traditional text design group. Furthermore, an interesting result is that the low-level readers in the conceptual change condition significantly outperformed the low-level readers in the traditional text design condition as well as the high-level readers in the traditional text design condition. In sum, the conceptual change text design seems to help both low and high level readers to respond to questions that require an understanding of the ontological difference between plants and animals. Furthermore, an ANOVA (AT x condition x pre-test/post-test) on critical distinction questions showed statistically significant main effects for condition, and for pre-test/post-test change on the scores of critical distinction questions, Moreover, an interaction effect of condition and text comprehension test was obtained,

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In addition, the post hoc analysis (LSD) showed a statistically significant difference between the low-level readers in the traditional text design group and in the conceptual change group. Furthermore, the high-level readers performed better in the conceptual change group than the high-level readers in the traditional group. Moreover, it was found that the low-level readers in the conceptual change group scored significantly better on critical distinction questions than the high-level readers in the traditional design group. 3.5.

Performance on Generative Questions

A three-way ANOVA (ST x Condition x pre-test/post-test change) was performed on generative questions measuring the construction of a mental model concerning photosynthesis. Significant main effects were found for science text comprehension test, and for the change of the scores from pre-test to posttest, .Moreover, a significant interaction effect was obtained of text treatment and pre-test/post-test change of the scores, In addition, the post hoc (LSD) analysis showed the following tendencies. The high-level readers in the conceptual change condition performed significantly better on generative questions than the high-level readers in the traditional text condition. It seems that the low-level readers did not find support from the text design in answering the generative questions that required generating a mental model concerning photosynthesis. An ANOVA concerning the Action oriented Text Comprehension Test, condition and pre-test/post-test change was also conducted on generative questions. A main effect was observed for the change of the scores from pre-test to post-test, In addition, a significant interaction effect of text treatment and pre-test to post-test change was obtained, 4.

DISCUSSION

The purpose of this study was to investigate how a text design supports the learning of difficult scientific concepts in learners with varying reading skills. The results indicate that a conceptual change text design is superior to the traditional text design in promoting conceptual change concerning photosynthesis. Conceptual change was measured through critical distinction questions and generative questions, which encouraged the learners to build an adequate mental model of photosynthesis. However, the traditional text led to better performance on retention questions, which to large extent, required fact-finding. Hence, the traditional text design seems to support traditional school learning. But if the target of instruction is to convey a deeper understanding and conceptual change concerning the domain, then the conceptual change text design works better. When looking at the results, an interesting question is how did low-level readers profit from the conceptual change design? Two question types, critical distinction questions and generative questions, were used as criteria for conceptual change. A positive result was that, on critical distinction questions, both low and high level

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readers profited from the conceptual change text design which uses metaconceptual text as an augmenting tool in order to point out the differences between naive preinstructional and scientific conceptions presented in the text. Hence, low-level readers and high-level readers in the conceptual change group outperformed the parallel groups in the traditional text treatment. However, in the case of generative questions, which demanded the construction of a mental model concerning photosynthesis and text-independent problem-solving, low-level learners did not obtain any support from the conceptual change text in answering generative questions. It can be suggested that motivational factors may also play a role among low-level readers explaining why they did not profit from the conceptual change text in answering generative questions. The influence of motivational orientation on conceptual change through text design will be dealt with in future studies. Although the results of this study are both theoretically and pedagogically interesting, there are some limitations that must be dealt with in future studies. First, how stable are conceptual changes? A delayed test would give us an answer to this question. It could in fact be suggested that, in order to produce stable changes, the whole instructional process has to be designed from the conceptual change perspective. A textbook could, however, perhaps play a more important role as a pedagogical resource in the complicated process to facilitate conceptual changes than many of us think. Second, in order to be able to explain how successful the conceptual change text was in intensifying the metaconceptual awareness of the learner, a qualitative analysis of the learning process and a stimulated recall interview would be necessary. Third, the role of pictures in supporting conceptual change is an interesting question for future studies. There is already evidence that pictures may support mental model building in the field of science (Gyselinck & Tardieu, 1994; Schnotz & Mikkilä, 1991; Weidenmann, 1989). It can be suggested that pictures may positively influence the conceptual change. Visualisations may function as an augmenting activation and so enforce metaconceptual awareness. There are, however, prerequisites which must be met, for example, metaconceptual picture design must be developed. The pictures have to be constructed from the perspective that learners may have misconceptions that can be enriched through pictures. For example, in the visualisations concerning photosynthesis, the problems of plants’ and animals’ energy production must be dealt with simultaneously. Moreover, the integration between text and pictures must be well established: direct references to the pictures and explicit legends could be helpful. An interesting question is also that of how different readers make use of pictures. There is evidence that sometimes pictures may be helpful for low-performing learners as a compensating medium in mental model construction (Weidenmann, 1988). However, there are also results indicating that learners are not able or do not find it necessary to make use of pictures when learning new topics (Hannus & Hyönä, 1999). Pictures can also produce cognitive overload for low-level readers. Process analysis of picture comprehension may be useful.

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The results of this study may be helpful for teachers, textbook authors and publishers. For many years, the target for textbook authors has been to write a school text according to readability standards: expository, non-refutational texts consisting of short sentences often lacking explanatory coherence and metaconceptual text. Thus, traditional textbook texts are often very dense and incoherent. According to this study, a longer and metaconceptually more explanatory text can offer support even, to some extent, for low-level readers in learning difficult science contents. To conclude, for a learner, the process of becoming aware of a possible mismatch between his/her ideas and the science contents to be learned through a text can be seen as an essential factor in promoting conceptual change. However, in order to achieve this i.e. to produce radical changes, the whole instructional process should be planned so that it supports conceptual change. Hence, textbooks and also the pedagogical interaction should be designed with the aim of making the misconceptions visible and helping the learners to experience and solve the cognitive conflict. Textbooks that follow a metaconceptual text design in connection with multimedia environments and a collaborative learning setting could offer teachers a tool, in the everyday classroom situation, for solving the problems of dysfunctional prior knowledge. REFERENCES Aho, L., Enqvist, S., Kytömäki, P., Nurmi, J., & Saarivuori, M. (1995). Verne 4. Primary science textbook for Finnish comprehensive school. Porvoo, Finland: WSOY. Alvermann, D., Smith, L., & Hynd, C. (1985). Prior knowledge activation and the comprehension of compatible and incompatible text. Reading Research Quarterly, 22, 420-436. Alvermann, D. E., & Hague, S. A. (1989). Comprehension of counterintuitive science text: effects of prior knowledge and text structure. Journal of Educational Research, 82, 197-202 Beck, I. L., McKeown, M.G., Sinatra, G. M., & Loxterman, J. A. (1991). Revising social studies text from a text-processing perspective: evidence of improved comprehensibility. Reading Research Quarterly, 26, 251-278. Caravita, S., & Hallden, O. (1994). Re-framing the problem of conceptual change. Learning and Instruction, 4, 89-111. Chan, C., Burtis, J,. & Bereiter, C. (1997). Knowledge building as a mediator of conflict in conceptual change. Cognition and Instruction, 15, 1- 40. Chinn, C.A., & Brewer, W. F. (1993). The role of anomalous data in knowledge acquisition: a theoretical framework and implications for science instruction. Review of Educational Research, 63, 1-49. van Dijk, T., & Kintsch, W. (1983). Strategies of discourse comprehension. Orlando, FL: Academic Press. Glynn, S. M., & Duit, R. (1995). Learning science meaningfully: Constructing conceptual models. In S. M. Glynn & R. Duit (Eds), Learning science in the schools. Research reforming practice (pp. 3-33). Hillsdale, NJ: Lawrence Erlbaum Associates. Guzzetti, B., Snyder, T., & Glass, G. (1992). Promoting conceptual change in science: Can texts be used effectively. Journal of Reading, 35, 642-649. Guzzetti, B., Snyder, T., Glass, G., & Gamas, W. (1993). Promoting conceptual change in science: A comparative meta-analysis of instructional interventions from reading education and science education. Reading Research Quarterly, 28, 117-159. Gyselinck, V., & Tardieu, H. (1994). The role of text illustrations in the construction of non-spatial mental models. In De Jong & van Hout-Wolters (Eds.), Process-oriented instruction and learning from text (pp. 175-181). Amsterdam: VU University Press. Hannus, M., & Hyönä, J. (1999). Utilization of illustrations during learning of science textbook passages among low- and high-ability children. Contemporary Educational Psychology 24, 95-123.

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Hatano, G., & Inagaki, K. (1997). Qualitative changes in intuitive biology. European Journal of Psychology of Education, 22, 111-130. Hynd, C., Qian, G. Ridgeway, V., & Pickle, M. (1991). Promoting conceptual change with science texts and discussion. Journal of Reading, 34, 596-601. Hynd, C., & Alvermann, D. (1986). The role of refutation text in overcoming difficulty with science concepts. Journal of Reading, 29, 440 -446. Kintsch, W. (1986). Learning from text. Cognition and Instruction, 3, 87-108. Kintsch, W. (1988). The role of knowledge in discourse comprehension: a construction-integration model. Psychological Review, 95, 163-182. Limon, M., & Carretero, M. (1997). Conceptual change and anomalous data: a case study in the domain of natural sciences. European Journal of Psychology of Education, 22, 213-230. Mason, L., & Boscolo, P. (2000). Writing and conceptual change. What changes? Instructional Science 28, 199-226. McNamara, D. S., Kintsch, E., Songer, N. B., & Kintsch, W. (1996). Are good texts always better? Interactions of text coherence, background knowledge, and levels of understanding in learning from text. Cognition and Instruction, 14, 1-43. Mikkilä, M., & Olkinuora, E. (1994). Problems of current textbooks and workbooks: Do they promote highquality learning? In De Jong & van Hout-Wolters (Eds.), Process-oriented instruction and learning from text (pp. 151-164). Amsterdam: VU University Press. Mikkilä, M. 2001. Improving conceptual change concerning photosynthesis through text design. Learning & Instruction, 11, 241-257. Posner, G., Strike, K., Hewson, P. &, Gertzog, W. (1982). Accomodation of a scientific conception: toward a theory of conceptual change. Science Education, 66, 211-227. Roth, K., Anderson, C., & Smith, E. (1987). Curriculum materials, teacher talk and student learning: case studies in fifth grade science teaching. Journal of Curriculum Studies, 19, 527-548. Roth, K. (1990). Developing meaningful conceptual understanding in science. In B. Jones & L. Idol (Eds.), Dimensions of thinking and cognitive instruction (pp. 139-175). Hillsdale, NJ.: Lawrence Erlbaum Associates. Schnotz W. (1993). Adaptive construction of mental representations in understanding expository texts. Contemporary Educational Psychology, 18, 114-120. Stinner, A. (1995). Science textbooks: their present role and future form. In S. M. Glynn & R. Duit (Eds.), Learning science in the schools. Research reforming practice (pp. 275-296) Hillsdale, NJ: Lawrence Erlbaum Associates. Vauras, M. Kinnunen, R., & Kuusela, L. (1994). Development of text-processing skills in high-, average, and low-achieving primary school children. Journal of Reading Behaviour, 26, 361-389. Wang, T., & Andre, T. (1991). Conceptual change text versus traditional text and application questions versus no questions in learning about electricity. Contemporary Educational Psychology, 16, 103-116. Weidenmann, B. (1988). Psychische Prozesse beim Verstehen von Bildem. Bern, Switzerland: Verlag Hans Huber. Vosniadou, S. (1994). Capturing and modelling the process of conceptual change. Learning and Instruction, 4, 45-69. Vosniadou, S., & Schnotz, W. (1997). Introduction. European Journal of Psychology of Education, 22, 105-110. Vosniadou, S., & Ioannides, C. (1998). From conceptual development to science education: a psychological point of view. International Journal of Science Education, 20, 1213-1230.

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TRADITIONAL TEXT DESIGN Photosynthesis

A plant needs water to live and gets the water from the soil through its roots. At the same time it gets nutrients which are dissolved in the water and which the plant needs, besides the water, to grow its new cells. You can follow the path of the water in a flower if you dye the water in a glass jar. Where does the water go in a plant

If you cut the stem of the flower along its length in the coloured water, you will notice that the colour is not even. In the stem you can see little dyed dots. In these dyed places you can see, side by side, thin pipes. In these pipes, water is going through the roots to the stems and to the leaves. Water goes through the roots to the leaves as a continuous water stream. In the leaves there are little openings (stomata) from which the water steam evaporates all the time in warm conditions. From the soil, new water is absorbed all the time in the place of the evaporated water. The water evaporates but the nutrients from the water remain in the plant. Work within a leaf

A plant emerges, grows, develops and eventually dies like all other organisms. However, all plants make their building materials and their food by themselves, unlike the other organisms. The process by which a green plant makes its food is called photosynthesis. In photosynthesis a plant needs as raw materials water and nutrients. From the air the plant gets, through air openings, carbon dioxide which is needed in photosynthesis. There are chloroplasts in the leaves of the plants which have a green colour substance called chlorophyll. In the chloroplasts, carbon dioxide and water are made into sugar with the energy from the sun. As a plant photosynthesises, at the same time oxygen is released. Oxygen goes from the leaves, through air openings, to the atmosphere. All the oxygen that is in the air comes from plants. Photosynthesis

a factory: the chlorophyll of the plants Raw materials: water with its nutrients and carbon dioxide Energy: sun energy Products: sugar and oxygen A plant is self-sufficient for food unlike animals that are other-sufficient, dependent on other organisms for food. These concepts refer to an organism that survives without another organism. Plants survive, animals do not. A plant makes its own food, whereas animals get their food from other organisms, plants and animals.

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A human being can do almost everything but not photosynthesise in laboratory conditions. All the food resources and oxygen in the world are originally produced by the plants. APPENDIX B

CONCEPTUAL CHANGE TEXT DESIGN Photosynthesis

Plants and animals need energy to live and this comes from food. How plants get their food happens in a different way than we normally think. How does the energy get into a plant? Is water food for a plant? Plants make their own nourishment

Plants differ from all other organisms because they make their food by themselves. Plants can absorb the light energy from the sun that goes into food. It is important to understand that a plant does not take the ready-made food through its roots from the soil. So a plant does not eat but makes its food in the chloroplasts that are mostly in the leaves. Thus water is not food for a plant but only one of the raw materials it uses to make its own food in the process called photosynthesis. Green plants are self-sufficient because they can absorb the sun light into the food, and they do not need any other organisms to survive. Animals, like a human being, are othersufficient, because they get the energy they need from the plants. All the energy in our food comes from the plants. We get energy either through eating plants or through animals which have eaten plants. Food chains help us to understand how energy circulates in nature. A wolf gets energy through eating a rabbit, which got its energy from grass, and the grass got its energy form the sun. Energy comes into the food chain only through plants. It is important to learn that plants can make their food by photosynthesis and do not take it in through their roots from the soil. Where and how does the photosynthesis happen?

When making food, i.e. in photosynthesis, a plant absorbs light energy that goes into the food. When you are learning about photosynthesis, it is useful to think of the difference which exists between plants and animals concerning how they get their food. Plants make their food by themselves, but animals eat food made by plants. A plant needs raw materials for photosynthesis: carbon dioxide from the air and water from the soil. Water goes through pipes in the roots up the leaves. The end products of photosynthesis are sugar and oxygen. Sunlight energy is used as driving force. The chloroplasts convert water and carbon dioxide with the help of sun energy. Thus, this process is called photosynthesis (photo means light in the word). As a result, oxygen is produced, which is released into the air through the openings (stomata) in the leaves. Hence plants make their food by themselves in the chloroplasts which are in the leaves. The green colour of the plants is caused by the colour of chlorophyll.

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Where do the plants store the self-produced sugar?

The end product of photosynthesis is sugar, which is plants’ food. A plant does not use all the sugar immediately but changes it to other nutrients, which are easier to store. So fruit sugar and sugar combined with proteins circulates to the fruits, seeds and nuts. When we eat that food we get the energy we need to live. Photosynthesis as a basis for life

The most important thing to understand about photosynthesis is that only plants can absorb light energy in food and produce oxygen as a by-product. Photosynthesis is the most important factor in helping the world survive, because only green plants can make use of light energy from the sun when making food through photosynthesis. Without plants there would be no food and no oxygen in the world. Thus, all animals are dependent on plants.

COMPUTER-BASED INTERACTIONS FOR CONCEPTUAL CHANGE IN SCIENCE

MARIANNE WISER & TAMER G. AMIN Clark University, USA

Abstract. Science learning has been characterized as the construction of conceptual structures, as the appreciation of the nature of scientific knowledge, and as participation in scientific practices. Research has primarily been carried out in each of these domains separately. There is a growing body of research that addresses the interaction between these components. In this paper we seek to add to this literature by integrating our ideas with that of other researchers to begin an initial formulation of a multifaceted framework for studying physics learning using computer-based conceptual models. In this framework we distinguish two aspects of conceptual restructuring: understanding computer models and internalizing these models as a way to construe the physical world. We argue that two different types of interaction (symmetric and asymmetric) support these different kinds of restructuring. We conclude that achieving deep changes in conceptualization requires consideration of conceptualization as a component of practice.

1. INTRODUCTION

Kelly and Crawford (1996) express a prevalent view in science education: “Learning science requires novices to be initiated into the conceptual framework, epistemic dispositions, and social practices of the scientific community” (p. 693). Similarly diSessa and Minstrell (1998) have considered these three aspects of science learning as the key features of what they call benchmark lessons. Teaching physics with models, especially computer-based models and simulations, fits this mandate very well. Models make the content of physics theories more easily graspable, especially in areas traditionally difficult to learn (Smith, Snir, & Grosslight, 1992; White, 1993; Wiser, 1985). Important epistemological issues can be organized around models: What is their nature and their relationship to real world phenomena? What is their role in science? What is the nature of the laws they embody (Grosslight, Unger, & Jay, 1991; Smith, Maclin, Grosslight, & Davis, 1997; White, Shimoda, & Frederiksen, 1999)? Finally, models are central to scientific practices both in “normal” and “revolutionary” science (Giere, 1988; Hestenes, 1992; Nersessian, 1992a, 200la). In particular, computer representations play a major role in experimental work, with groups of scientists relating multiple representations and negotiating the interpretation of experimental evidence (Kozma, 2000; Dunbar, 1995). Thus, models are ideally suited to helping students become part of a scientific community by introducing them to both the contents and practices of science. (Note however that all this can be conducted without computer based models, as evidenced, for example, by the work of Lehrer and Schauble and colleagues (see e.g., Lehrer, Schauble, Strom, & Pligge, in press). M. Limon & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 357-387. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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We view the three components of science learning listed above as closely interrelated. Our work with high-school students learning thermal physics has shown that computer-based conceptual learning is a multi-faceted and lengthy process. Our work has led us to view this process as involving students’ evolving interpretations of visual representations that embody conceptual models, as well as students’ metaconceptual reflection on the practice of conceptual revision, and their application of naïve epistemological standards. But yet another aspect of this process of computer-based concept learning, which, until now, we have not addressed in our work, is student-student and student-teacher discussion. In this paper we begin to examine the interaction between concept learning and computer-based discussions. Others (e.g., Roschelle, 1996; Roschelle, & Clancey, 1992; Roth, 2001) have already begun to examine the role that discussion plays in computer-based concept learning. We follow that lead, but also extend prior accounts to accommodate some of our own findings and what we see as important findings and conceptual distinctions in the model-based concept learning literature. We base our proposals in particular on the work of Kozma, Roschelle, Smith, and White, and their respective colleagues. At the heart of our account is the claim that in attempting to integrate an account of concept learning with an account of negotiations over the meaning of representations, distinctions need to be made both with respect to the kinds of meanings being negotiated and the types of negotiations involved. 2. COMPUTER-BASED CONCEPTUAL MODELS 2.1. Overview

At the center of computer-based conceptual model approaches to the teaching of scientific concepts is the following rationale. Conceptual models show students how to envision classes of phenomena because they superimpose iconic representations of real world objects (e.g., objects being heated or weighed are represented by rectangles; objects being pushed are represented by dots; thermal probes and scales are represented on the screen), and representations of the theoretical entities inside, or applied to, those objects (e.g., heat, force, amount of matter). Conceptual models make visible core theoretical entities, which are usually too small to be observed in the (students’) real world (e.g., molecules), non-material entities (e.g., force), and properties (e.g., velocity, density), as well as the laws and causality at work in a domain. These models represent domain phenomena in simplified form, and often in idealized worlds (e.g., mechanical systems with no friction, perfectly insulated systems), isolating important variables and their interactions, and making it easier to see the behavioral implications of physical laws and to discover basic principles. As such, conceptual models are interpretations of abstract laws (Nersessian, 1992b). Thus, conceptual models provide an intermediate level of abstraction between phenomena and quantitative laws (White, 1993). For the reasons above, conceptual models are believed to help students acquire the expert theory in domains traditionally known to be difficult to master because students approach them with pre-existing conceptualizations that differ in some

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fundamental ways from scientists’. This approach has been applied in a number of domains in which students’ prior conceptions have posed obstacles to learning textbook concepts - for example, thermal physics, weight and density, and Newtonian mechanics. Our own work and our reading of the work of others who have studied the role of computer-based conceptual models in inducing conceptual change point to the fact that complex processes of conceptual revision are involved. Attempts to integrate accounts of conceptual change with descriptions of student-student and student-teacher interactions will need to grapple with this complexity. Through a selective review in the rest of this section, we make an initial attempt to identify those features of computer-based conceptual change that will need to play a role in an integrated account of conceptual change and social interaction. 2.2. Inducing Fundamental Conceptual Revisions

Smith (Smith, 2001; Smith, Snir, & Grosslight, 1992; Smith & Unger, 1997) and her colleagues view learning physics with conceptual models as conceptual bootstrapping, i.e., structural understanding in one domain (the models, constituting the source domain) is used to guide restructuring of a set of concepts in another domain (the target domain) via analogical transfer. They focus on the differentiation of weight and density, a notorious stumbling block for middle-school students, most of whom have an undifferentiated concept heavy/heavy-for-size. In their curriculum, they incorporate dots-per-box models, stripped-down visual analogs which articulate the qualitative (intensive vs. extensive) and quantitative difference and relation between weight (total number of dots), volume (number of boxes) and density (number of dots per box). Smith and her colleagues (Smith, Snir, & Grosslight, 1992) confess that in their early work on weight and density, they adopted a naive approach to using conceptual models. They had hypothesized, they say, that the models would enable students to come to differentiate weight and density. They found instead that the only students who benefited from the models were those who already differentiated weight and density, at least qualitatively, and had mastered the key mathematical knowledge embedded in the models, i.e., a concept of “per-quantity”. For these students the models reinforced, and helped quantify, the relation between weight, volume, and density. To explain the other students’ failures, Smith et al. point out that mapping from conceptual models to the target domain involves more complex processes than the kinds of inter-domain transfer generally studied in the problemsolving literature (e.g., Gentner, 1989; Gentner & Gentner, 1983) in which the target domain involves concepts that are differentiated and well understood and the general problem solutions or symbolic representations are well understood in the source problem context. In the case of weight and density, on the other hand, the domains to be mapped are initially non-isomorphic: a single undifferentiated concept of weight/density, does not map onto a model representing two extensive quantities (number of dots and number of boxes) and an intensive one (number of dots per

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box). A Catch-22 situation: One can benefit from the model only if one already differentiates! In our view, Smith et al. provide an accurate analysis of this problem; we have come up against a similar problem in attempts to induce the differentiation of heat and temperature (Wiser, 1993). In the domain of thermal physics, students initially have an undiffereritiated concept of heat-as-hotness, measured by temperature. In our earlier work on heat and temperature, in which we also used dot models (number of dots represents amount of heat and dot crowdedness represents temperature) we found that one path to conceptual change consists of anchoring the two visual representations to different aspects of the undifferentiated concept. It makes sense to students, for example, that giving the “same heat” to two different masses consists of adding the same number of dots to different size rectangles, bringing out the extensive aspect of the students’ concept. Judging which object now has a higher temperature brings out the intensive aspect of the concept, and is based on dot crowdedness. But this creates a paradox: how can one entity (heat-as-hotness) have two (incompatible) representations? With the models mapped to the concepts in this preliminary, partial way some students can then reason syllogistically: if dot crowdedness represents temperature and number of dots represent heat, temperature and heat are not the same thing (Wiser, 1993). But this is a rigorous logical process, relying on adequate epistemological understanding of scientific models, and requiring from the students a lot of theory construction without much support from the models. It is probably not within the spontaneous repertoire of the average science student and cannot be relied on, without explicit scaffolding, to produce conceptual differentiation. A few of our ninth graders could carry it out, Smith’s sixgraders could not. The mapping problem illustrated in the weight-density and the heat-temperature studies mentioned above is one case of a more general challenge faced by software and curriculum designers in any domain in which students’ preconceptions are at odds with the expert theory: how do we present the expert theory in a way that will both make sense to the students given their current conceptions and lead them to reconceptualize that domain, rather than ignore or misassimilate the information presented in the teaching models? In order to learn the expert theory from (or with) conceptual models, students must make sense of these models using the concepts, beliefs, and schemata they already have. They must understand that the models represent scientists’ interpretations of a particular domain of the physical world. They must also be able to relate the interpretation embodied in the models to their own. In Smith’s early studies, students can make sense of the stripped-down models on the basis of their mathematical knowledge (as long as they have a “per quantity” concept) but have difficulty linking them to their own knowledge of weight and density. In their later work, Smith and her colleagues, attempt to solve the bootstrapping problem by embedding the use of conceptual models in an extensive curriculum about the theory of matter (Smith, Maclin, Grosslight, & Davis, 1997). They argue convincingly, both on theoretical grounds and on the basis of their classroom findings, that the undifferentiated concept heavy/heavy-for-size is tied to and supported by, an early theory of matter (Theory of Matter 1). The concept of

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weight, which is differentiated from density, is tied to and supported by a later theory of matter (Theory of Matter 2), which is closer to the expert theory. Thus, they devote a good part of their curriculum to making the Theory of Matter 2 intelligible and convincing; the core tenets of this theory are that matter is infinitely divisible and that any amount of matter, however small, has weight. They also build up students’ intuitions for the extensivity of weight, and the relation between how packed matter is and kind of stuff, thereby inducing a proto-differentiation. Besides hands-on experiments, they use thought experiments and limiting case analyses, both conceptual tools used by physicists to construct and communicate novel theories (Nersessian, 1989, 200la). Smith and her colleagues see their models as supporting a differentiation that emerges from these other areas of the curriculum, rather than driving it. Notice, however, that within this much extended and enriched curriculum, the dots-in-box model does not function as analogy anymore, but as a “proper” physics model: the dots are labeled by the teacher as representing pieces of matter, and dot crowdedness as representing how “packed” they are. That level of interpretation is non problematic, at least for students who now believe in Theory of Matter 2. Labeling dot crowdedness “density” should not represent a major hurdle, since the word had little meaning before instruction; and linking it to kind of material is commonsense: aluminum is aluminum irrespective of object size and so is dot crowdedness. However, given the mapping problems pointed out above, we would expect that using the models to learn to coordinate weight, volume, and density, including reserving the label “weight” for the total number of dots, irrespective of their crowdedness, should be more problematic, because, in the students’ lexicon and conceptual system, “weight” is not fully differentiated from heavy for size. This is indeed what Smith et al. find. Some obstacle seems to hinder repeated efforts to use analogical conceptual models to achieve deep levels of conceptual change, where a firmly entrenched everyday concept needs to be fundamentally transformed into a scientific concept with a similar label. What we find when we examine our own studies and those of Smith et al. is that when fundamental conceptual revisions are needed for achieving scientific understanding conceptual mechanisms are not sufficient. By this we mean that mechanisms such as analogical reasoning, thought experiment, and limiting case analyses are productive tools but they fall short of achieving full conceptual revision. What is this obstacle? And how might identifying this obstacle help us characterize more fully the complex process of model-based conceptual change? We continue with our selective review in an effort to answer these questions. 2.3. Conceptualizing Microworlds Versus Conceptualizing the World

White and her colleagues have worked extensively on students’ conceptual understanding of Newtonian mechanics and electrical circuits (e.g., White & Frederiksen, 1989, 1998, 2000). They base their curricula on the THINKERTOOLS software, the main feature of which is a series of microworld simulations of the physical world that embody the Newtonian laws of motion. Adopting a

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constructivist approach to the teaching of physics, one of their central goals is to bridge the large semantic distance between physical phenomena as perceived by students and symbolic representations as understood by the physics expert. White and her colleagues have sought to do this by designing a hierarchy of computerbased models, representing more and more elaborate aspects of Newtonian mechanics (one-dimensional motion, two-dimensional motion without friction, twodimensional motion with friction, etc.). Moreover, each model is realized using multiple representations that are increasingly more abstract: an experiential representation (a dot acted upon by impulses or forces, and its resulting trajectory), a representation of intermediate abstraction that incorporates the Cartesian components of velocity (arrows and data cross) and finally, formal representations. The intermediate representations are concrete, manipulable objects that represent Newtonian variables, allowing students to induce the principles of the microworlds and establish links between experiential understanding of familiar events and formal representations (vectors; equations). White and her colleagues are aware of the obstacles presented by students’ preexisting interpretations of phenomena, but, like Smith, they recognize the potential for experiential knowledge to be productive. Thus, the multiple representations allow students to utilize experiential knowledge to make sense of idealized microworlds that behave according to laws they need to discover. White’s rationale is that students’ new understanding of mechanics can be built on pre-existing intuitions, in keeping with Minstrell’s “facets of knowledge” (Minstrell, 1989; Minstrell & Stimpson, 1996) and diSessa’s reorganization of phenomenological primitives, p-prims (diSessa, 1993). Let us examine how this strategy is implemented in the design of the models. An example of basic intuitive conception that students possess prior to instruction (we will call it the “kick preconception”) is that a kick applied to an object causes it to move in the direction in which the kick is applied, with a velocity proportional to it. White’s first model capitalizes on this belief. In it, fixed impulses are applied to objects moving in a one-dimensional, frictionless world, causing fixed increases in velocity. In this very simple microworld, events obey Newton’s laws and are also easily assimilable to students’ kick-preconception, making the intermediate representations (arrows and datacross) meaningful. Once interpreted, the intermediate representations can be imported into the next (two-dimensional) microworld, to help students make sense of events that do not conform any more to their preconception. Later, students are taught that a force such as gravity can be thought of as a series of “very tiny kicks”. Moving from one model to the next in the hierarchy, students become able to interpret a world in which a fixed continuous force causes a fixed acceleration; their initial intuition (kick preconception) has been utilized and transformed to be part of a Newtonian mode of thinking. White’s work on teaching electrical circuits illustrates further the importance and merit of taking into account not only the content of students’ initial knowledge, but also more general characteristics of the cognitive processes involved in interacting with teaching models (White, 1993). White notes, for example, that, even simplified, expert models are not necessarily the most suitable pedagogical tools. For example, experts reason about electric circuits in terms of states, a mode of physical reasoning

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that is not students’ spontaneous way of thinking about events. Students spontaneously reason in dynamic and causal terms. White and her colleagues designed a series of teaching models, centered around the concept of process, that allow students to use causal reasoning, but also to induce qualitative versions of electricity laws. They ground students’ understanding of circuit behavior in a particle model depicting the attraction and repulsion between charges, behaviors which have analogs in body experience and, at the same time, embody a fundamental law of electrostatics (Coulomb’s). The aggregate model, at the next level of abstraction, is a transport model still featuring charges, but embodying a different, more global causal mechanism--differences in voltage cause current flow. In this hierarchy the causal mechanism of one model is an emergent property of the previous model. From the aggregate model, students can induce two qualitative laws (equilibrium and a simple version of Ohm’s law, the “flow equation”) which explain steady states, and allow students to envision the causal mechanism implicit in the formal laws (Ohm’s and Kirshoff’s laws). One strength of White’s approach is certainly its representational richness. A seamless succession of representations interact with students’ knowledge to allow them to reason both qualitatively and quantitatively, in ways analogous to the scientist in each domain. However, in light of the obstacles to conceptual change pointed out above in our discussion of Smith’s work and our own, White’s work raises several intimately related questions: What is the world that the students are learning the laws of? How does their own conceptualization of the physical world, qua conceptualization of the world, interact with their understanding and manipulation of the models? How deep and broad is conceptual restructuring? Are their initial conceptions (pre-conceptions or misconceptions) erased? What do theoretical terms (e.g. force, voltage) mean to them by the end of instruction? How well do they understand that the conceptual models represent scientists’ conceptualizations of physical phenomena in the world that challenge their own? The status of microworlds vis-à-vis the physical world is a crucial issue. They are enough like it that students bring their intuitions to bear on them (as on White’s simplest models). But this may be an asymmetrical relation: the rules inferred from the microworld, like those of videogames, may not be seen as applying to the physical world. This may be especially the case for the more elaborate microworlds, the understanding of which rests on complex interactions between the interpretation of the lower level models and the various abstract representations, and whose behaviors are more directly in conflict with students’ intuitions. Grosslight et al.’s (1991) findings that students do not typically understand the nature and purpose of scientific models are relevant here suggesting that the depth of conceptual restructuring may be limited. Similarly, some of White’s results, suggesting that transfer is limited to problems similar to those modeled, with students reverting to their Aristotelian preconceptions for more difficult problems, support the need for careful consideration of how students relate epistemically their own (initial) conceptualization to those presented by the models. It is important to point out, however, that White and Frederiksen (1998, 2000) have also used the THINKERTOOLS software as the basis for a curriculum designed to help students develop expertise in scientific inquiry. This curriculum

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aims to scaffold students into rigorous participation in the key elements of scientific inquiry. The computer-based microworlds are used as easily manipulable objects of scientific investigation, where students engage in an “inquiry cycle” in which they formulate research questions, make hypotheses, design ways to investigate their hypotheses, analyze the data they collect, formulate general laws and describe causal models that characterize the microworld they are investigating, and finally, evaluate the laws and models they come up with by testing them on the real world. In addition to this inquiry cycle this inquiry curriculum also includes a “reflective assessment” component in which students are given a set of criteria with which to evaluate their own and other students’ scientific investigations. Examples of these criteria include understanding and applying relevant scientific content, being systematic and inventive, using scientific tools such as graphs and calculators appropriately, communicating well, and coordinating well with others. White and Frederiksen have shown that the inquiry curriculum does produce gains in students’ understanding of the process of scientific inquiry. This was assessed by examining how students outlined how they would investigate questions such as “what is the relationship between the weight of an object and the effect that sliding friction has on its motion?” They have also shown that the inquiry curriculum produces gains in students’ understanding of the content of Newtonian physics. The assessment in this case involved near and far transfer items in a preand post-test. This finding that teaching students about the process of scientific inquiry not only leads to gains in their understanding of, and participation in, this process but also leads to enhanced understanding of the content of physics as assessed through problem solving suggests an interaction between conceptual change and metacognitive aspects of scientific expertise. While providing evidence that suggests such an interaction, the work of White and her colleagues focuses on the role that microworld curricula can play in the learning of physics and the process of scientific inquiry as separate pedagogical goals. In addition to sharing these pedagogical goals with White, her colleagues and other researchers in this area we take a particular interest in constructing a process model of conceptual change that captures the complexity of this process. The interaction between conceptual content learning and metacognitive learning demonstrated by White reinforces the need to pursue the line of question just raised above: how does students’ understanding of microworlds as models of the physical world interact with the conceptual change taking place as they learn more about the microworld? We would like to grapple with this complexity. This aspect of the complexity of the interaction between student conceptualizations and microworld understanding can be illustrated with the first model in White’s hierarchy. In this simple microworld, a Newtonian object does behave in accordance with the student’s p-prim. That is, the event makes sense to a physicist because it obeys Newton’s laws and, when parsed in terms of the student’s concepts and causal principles, it makes sense to the student as well. Moreover, scientist and student would probably agree on a common verbal description of the event, in terms of “force” and “velocity”. However, this agreement is superficial, as the scientist and the student are using very different concepts and explanatory

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principles. Therefore, the extent of the reconceptualization achieved even at this early stage, is not clear; students have assimilated new rules and new formalisms, more in keeping with Newtonian mechanics, but have they come to conceptualize the world in terms of a Newtonian concept? Another lens through which to view this aspect of the problem of conceptual restructuring is the role of language. Most theoretical terms in Newtonian mechanics already have everyday meanings for students. Common language forces the concepts of the two users to interface. For example, the laws expressing the behaviors of the models students have to choose from in White’s studies are formulated in terms of “force” and “velocity”. Do students easily map these terms on the variables in the models? Do the labels lead students to import into their interpretation of the models their own concepts of force and velocity? How do the labels constrain the interfacing of the models and students’ pre-existing knowledge? Similar questions arise when students are told to think of gravity as a series of “kicks”; this certainly “explains” the behavior of the dots in the models, but how does this fit into how students already think about gravity? Is it difficult to accept that kicks are applied downward, especially when the dot is going upward, since students do not initially think that “real-world gravity” acts on objects moving up? Will they think that “gravity-in-the-models” is a different kind of gravity than “gravity-in-the-world”? Moreover, an emphasis on the rules embedded in computerbased representations, rather than on the conceptualization of the physical world, may make it easier for the students to treat the microworlds as “parallel worlds”, and not question their own concepts and beliefs about the real world when they conflict with the behavior of objects in the microworld. To sum up so far, the goal of teaching with microworlds is clearly the internalization of the teaching models, i.e., that teaching models become mental models of the world. Our work and that of others (e.g., Roschelle, see next section; Smith, see previous section) show, however, that teaching models do not get internalized as mental models of the world without a struggle, or when they are, that they may not have the same scope as they do for their designer. By “internalizing teaching models” we refer to a process whereby the models are transformed from being something construed to being the lens through which the world is construed. That is, understanding the internalization process will require an appreciation of the important distinction between the microworld qua microworld and the microworld as a model of the real world. To understand the process of internalization we will need to turn to a discussion of how scientific representations, especially visual representations, are understood as representations of the world. 2.4. Negotiating the Meaning of Scientific Representations

Kozma and his colleagues present an interesting perspective on the role of computer-based visual representations in science, and apply it to the teaching of chemistry (Kozma, 2000; Kozma, Chinn, Russell, & Marx, 2000). They are interested in the collective role of inquiry, discourse, representations, and tools in scientific investigations, and on the centrality of computer visual displays in each of

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these aspects of conducting scientific research. In this context, Kozma distinguishes between “signs” and “symbolic representations”: prototypical signs are instrument readings (e.g., spectrogram, map of a region of the sky provided by a telescope); prototypical symbolic representations are equations and molecular models. A major component of what scientists do, according to Kozma, is coordinate, via group discussion, multiple signs representing different aspects of a given event or phenomenon. Via these discussions, scientists co-construct a conceptual (i.e., “symbolic”) “umbrella” representation for that event and thereby converge on an interpretation of the event. Accordingly, the central focus of Kozma and his colleagues is on training students to participate in a practice that they see as central to science – negotiating the meaning of multiple representations. They note, however, that many symbolic systems used by scientists are misunderstood by students because their surface features do not correspond to the features and behaviors of the abstract scientific entities and processes in the mental models of experts (for example, to a scientist a chemical equation represents a state of dynamic equilibrium, however, a superficial interpretation of the form of an equation suggests a static end point, all chemical events stop). While symbolic representations represent theoretical, aperceptual entities (e.g., molecules, forces), they can do so more or less transparently. Kozma et al. (2000) advocate “provid[ing] students with an expressive medium in which the features of representations structure students’ thinking about the entities and processes that underlie physical phenomena [, and] connect[ing] student-generated representations to tool-generated representations during the investigations of physical phenomena” (p. 108). To support his claim, he reports that students are more successful at coordinating multiple representations of chemical equilibrium when they include a molecular model of chemical reactions (Kozma, 2000). The symbolic systems advocated by Kozma as pedagogically preferable, seem to be akin to what other researchers have called “conceptual models”, discussed in the previous sections (Smith, Maclin, Grosslight, & Davis, 1997; White, 1993; Wiser, 1986). Taking scientists’ negotiation practices as a pedagogical target is a reasonable strategy, but this strategy does not address an important aspect of the process of conceptual learning. Whereas the professional chemists Kozma observed discussed the specific molecular structure of the product of a novel reaction, the chemistry students relied on a basic molecular model to reconceptualize chemical equilibrium as a dynamic, rather than static, process. Scientists (such as those studied by Kozma) are making sense of a particular event, usually an event at the border of their understanding (i.e., of what “normal science” can explain); they are using multiple ‘signs’ as windows onto that event and may disagree on the import of these signs. But a crucial feature of their successful negotiation is that they share a “generic” understanding of the signs and symbols they use, and, most importantly, they know and share the concepts embodied in symbolic representations. Thus, scientists’ arguments aim at specifying parameters in conceptual models so as to attain a theoretically based interpretation of the event. (The situation being, of course, very different in a revolutionary phase; see e.g., Nersessian, 1992b). Students, on the other hand, who do not have at their disposal the theoretical foundations (concepts and mental models) necessary to interpret and discuss expert representations such as

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spectrograms or force vector diagrams, cannot interpret, let alone coordinate, multiple “signs” meaningfully. Thus, one must privilege conceptual models to ground both signs and more abstract symbolic representations. Moreover, in many cases (and unlike the case of chemical equilibrium), students will need a carefully orchestrated curriculum to help students assimilate the models (as demonstrated in White’s and Smith’s work, see previous section), and link the models to both signs and more abstract symbolic representations. We find that we have returned full circle back to the problem of trying to change students’ basic conceptualizations of physical phenomena. We come away from Kozma’s work, however, with greater clarity about how to tackle the problem raised at the beginning of this section - i.e., how to ensure that the conceptual models are internalized in a way that restructures students’ conceptualizations of the physical world. Kozma’s emphasis on understanding the negotiation processes whereby computer representations are assigned meanings that constitute a scientific understanding of the physical world, suggests that we begin to tackle the internalization of conceptual models as the negotiation of the meaning of representations. We will keep in mind, however, that scientists are engaged (during periods of normal science) in interpreting signs produced by instruments given a shared understanding of rich symbolic representations and of their relations to the signs themselves. In contrast, students are engaged in interpreting foreign symbolic representations of foreign concepts and conceptual relations, given a stock of concepts and beliefs which are at odds with those embodied in the computer representations, and are not necessarily explicit nor shared. Clearly, scientists and students are engaged in very different species of negotiations. Together the points raised in this section allow us to begin to identify an explanation for the limitation of a purely conceptual approach to concept learning guided by computer-based conceptual models described earlier in our review. As we will outline in the next section we see interactions between students and between student and teacher as an inherent part of this process, and protocol analysis as a crucial tool for the researcher. Individual protocols can show how the models interface with students’ preconceptions, whether or not the students’ overall conceptualization of the domain has been deeply restructured and what kinds of conceptual restructuring processes have taken place. In addition, protocols can be analyzed, not only as windows onto conceptual processes but as records of communicative exchanges in which students (amongst themselves and with their teacher) attempt to reach convergent interpretations of visual representations. In the next section we begin to outline a view of conceptual change based on computer models that incorporates both conceptual restructuring processes per se and collaborative efforts by students and teacher to reach convergent understanding of visual representations. Roschelle has already gone some distance in constructing such a framework (Roschelle, 1996; Roschelle, & Clancey, 1992). We will begin the outline of our framework by discussing his work, indicating where we believe it needs to be elaborated. This elaboration is grounded in the conclusion drawn from our review of Kozma’s work: different types of negotiations are involved with different types of representational meaning construction

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Roschelle has argued (convincingly) that conceptual change induced through the use of microworlds needs to be understood in terms of a detailed characterization of the nature of conceptual change as well as the collaborative mechanisms that allow for peers to achieve convergent understanding (Roschelle, 1996; Roschelle & Clancey, 1992). His account begins to extend, and greatly enrich, the repertoire of process components in the conceptual change literature. Following analogical mapping (e.g., Brown & Clement, 1989; Gentner, 1989; Smith, Snir, & Grosslight, 1992), thought experiment (Nersessian, 1992a; Smith, Maclin, Grosslight, & Davis, 1997), limiting case reasoning (Nersessian, 1992a; Smith, Maclin, Grosslight, & Davis, 1997; Zietsman & Clement, 1997) and the strategic triggering of pre-instruction experiential knowledge (e.g., diSessa, 1993; Smith, Maclin, Grosslight & Davis, 1997; White, 1993), Roschelle (1996) has added collaborative conversational mechanisms for converging on shared meanings. He describes the conceptual change achieved via these collaborative mechanisms in terms of the “interplay of metaphors”, following diSessa’s account of conceptual change in terms of the reorganization of p-prims. For the purpose of describing the role of collaborative mechanisms for convergence in the process of conceptual change he takes as an instance of conceptual change the construction of a novel, and productive interpretation of visual elements of a microworld via a collection of “p-prims” (“pulling”, “hinging” etc). That is, he accepts as an instance of conceptual change the achievement of a qualitative understanding of the microworld in a way that would be analogous to that of the scientist with a sophisticated understanding of the concepts of velocity and acceleration We believe that taking a revised interpretation of a microworld as an instance of conceptual change is reasonable if the purpose is to begin to think of ways to study the interaction between processes for collaborative convergence and conceptual change. However, we feel that we need to push this account further so as to understand more fully what we see to be a more challenging aspect of the process of conceptual change supported by computer microworlds. That is, once a productive interpretation of the microworld has been achieved students still need to achieve a deeper kind of understanding - i.e. to use this interpretation to revise their conceptualization of the physical world. Roschelle (1996) points out that “[the students’] new conception was not phrased in language that had the surface features of a scientific discussion of velocity and acceleration, yet it did express an analogous concept” (pp. 262-263). He also qualifies the extent of the conceptual change achieved in the case of collaborative convergence he discusses. He mentions that in a later interview the students who had converged on productive interpretations of the microworld believed that a ball tossed in the air would rise at a constant speed. Roschelle explains that in a debriefing session, the students and experimenter engaged in a negotiation using the processes of situated action as a means to converge on an understanding of the ball toss. This understanding

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integrally involved and extended the conceptual structure the students had built during these episodes [in which students participated in collaborative engagement with microworlds]. (Roschelle, 1996, p. 263.)

As we suggested above the issue of language and the application of conceptualizations to the physical world (as in the ball toss) must both be seen as related to the extent of students’ conceptual revisions. “Speed”, “velocity”, and “acceleration” are terms in the students’ everyday vocabulary. If their newly acquired conceptualizations are not expressed through these terms it is quite possible that they do not make contact with and thereby restructure their everyday conceptions. The fact that the students in Roschelle’s case study needed help extending their newly constructed conceptual understanding of the microworld to a real world problem also suggests that the conceptual revisions that took place via peer-peer collaborative convergence was limited to the microworld itself. It is interesting to consider the need for student-experimenter (or teacher) negotiation for the extension of microworld understanding to the real world in light of our earlier suggestion that different types of meanings require different kinds of negotiation. We are committed to trying to understand the process of deep conceptual revision where contact is made with prior conceptualizations of the physical world and where those conceptualizations are clearly revised as conceptualizations of the world. But, like Roschelle, we are convinced that there is a need for incorporating a treatment of social interaction into a process model for conceptual change. Thus we would like to start where he stopped and propose an integrated account of deep conceptual restructuring and social interaction. Our selective review above led us to draw the distinction between two aspects of conceptual change that is supported by microworlds: (1) microworld interpretation and (2) the utilization of this interpretation to restructure students’ initial interpretation of the physical world thereby achieving a deeper kind of conceptual restructuring. We agree with Roschelle that in considering conceptual change a situated (i.e. relational) epistemology is necessary. We also agree that an integrated account of conceptual change and social interaction is important to further our understanding of the process of conceptual learning. However, we would like to extend Roschelle’s framework with respect to both points. First, we believe that a situated epistemology suggests the need to distinguish the two aspects of conceptual change just mentioned. Second, while peer-peer interaction and the spontaneous convergence processes that Roschelle describes may be sufficient for microworld interpretation (aspect 1 above) it is not sufficient to account for aspect 2. We suggest that the asymmetry of peer-teacher interaction is necessary for this deeper kind of restructuring. The interactional processes that Roschelle describes can be interpreted as providing enhanced cognitive support for the individual’s attempts at making sense of the microworld. That is, the presence of a peer enriches the meanings brought to bear on interpreting the microworld and provides the cognitive constraints imposed by conversation and the rules of convergence that are assumed by participants in a conversation. But ultimately, the individual student arrives at an interpretation the coherence of which is constrained by her conceptual system and the features of the microworld. In this process we can say that two individuals are making sense

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together. Granted the presence of a peer may help the process along but in an important sense we are still dealing with individual sense making. In the case of deeper restructuring, the process, in an important sense, goes beyond individual sense making. That is, the power asymmetry, inherent in the fact that students are being asked to revise existing interpretations of the physical world in accordance with how the scientific community interprets it, is a component of the process that needs to be appealed to to explain students’ revised conceptualization of the physical world. Let us begin to clarify this view by describing what we see to be an analogous process in the history of science. The distinction we are trying to draw is analogous to the distinction between knowledge construction processes in “normal” and “revolutionary” science. During periods of normal science, scientists (of equal status) engage in puzzle solving, and debate experimental results in great detail, always trying to reconcile experimental results with existing concepts and models of interpretation that they share. There is strict adherence during puzzle solving to “the rules” of how physical entities are believed to interact (specified by existing models), how instruments are believed to operate, what visual displays mean, what constitutes measurement noise versus real effects etc. In periods of revolutionary knowledge building, the outcome of negotiations are much less governed by existing rules than by a social status differential or metacognitive powers of persuasion. Kuhn initially argued that the choice between competing paradigms can only appeal to socio-political factors (Kuhn, 1962). Granted, a purely cognitive account can be given of how an individual scientist arrives at an alternative perspective on a set of physical phenomena. Indeed Nersessian’s work on the role of model-based reasoning and analogical mapping in the history of science demonstrates that (Nersessian, 1992a). However, a different question is: given the presence of alternative perspectives how does one perspective come to be selected as the perspective to be adopted? Kuhn initially gave a socio-political explanation. Later he suggested appealing to five broad criteria: accuracy, consistency, simplicity, scope of application, and fruitfulness (Kuhn, 1977). But he pointed out that these criteria are imprecise and when applied individually may not lead to consistent conclusions regarding theory choice. Different values can be attached to these criteria, values that derive from an individual scientist’s history and personality. The important lesson here is that when fundamentally different worldviews are in competition, either social or metacognitive factors are brought to bear on the selection process. Our findings in our work on heat and temperature, that metaconceptual strategies were required to induce deep conceptual restructuring can be interpreted against this backdrop (Wiser & Amin, 2001). We found that it was necessary to explicitly tell students that we were presenting them with an alternative framework to theirs and that while scientists often use words similar to those in everyday use, they attach very different meanings to them. That is, we needed to make it explicit that two different perspectives on the same physical phenomena were in competition. But having clarified this point we needed to get students to adopt the scientific perspective that we were advocating. We believe that our status as teachers/researchers played a role in “persuading” students to adopt the scientific view. Also, the status of the adjective “scientific” in

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and of itself plays a rhetorical role as well. Another rhetorical move that we adopted was to take into account young adolescents’ naïve epistemology. Our metaconceptual teaching also incorporated a unit that would present the scientific perspective as an explanation of the everyday perspective thereby integrating the two conceptualizations. This can be seen as a rhetorical move that avoided leaving these young adolescents having to construct and appreciate a relativistic epistemology along with all the new ideas we were presenting to them. The important point we wish to stress here is that while it is reasonable to think of the learning that students achieved via these metacognitive factors in terms of the convergence of meaning as a result of collaboration, it is important to identify these interactions as asymmetric interactions. They aren’t the kinds of collaborations that peers of equal status engage in. An important power differential is necessary to achieve the desired learning. What we have been arguing as a distinct aspect of conceptual change - the internalization of models for the construal of the world requires, in our view, interactions between students and someone of higher status such as a teacher, researcher, or scientist. 4. CHANGING CONCEPTUALIZATIONS IN INTERACTION: ILLUSTRATIONS FROM A STUDY ON HEAT AND TEMPERATURE

In a recent study, four eighth-graders interacted with computer-based conceptual models, each other, and us; we were acting as both teachers and researchers (see e.g., Lampert, 1998). The students were told that their goal should be making sense of the models and that our goal was to find out whether and how the models helped them learn about heat and temperature. Our intervention was designed to give us rich information about the microgenetic course of assimilation of the teaching models, rather than optimize speed of learning. The instructional sessions in this study can be broadly divided into four parts. In the first part, students built their own interpretation of the models collaboratively; their own ideas about heat, heating, and temperature, as well as their molecular knowledge and domain general reasoning mechanisms, constrained their interpretations. In the second part, we presented the expert interpretation of the models, and thereby challenged students’ interpretation, as well as the concepts and beliefs it was built from. Our students could not, on their own, reconcile the expert interpretation with their own. Rather than inducing students to revise their concepts and beliefs, we characterized them as different from the scientific ones. Two labels, “everyday heat” and “science heat” helped maintain the distinction between the concepts in the two views. The epistemic relation between the two views was not presented from a relativistic standpoint, as we know that students at this age are not comfortable with it (Chandler, 1988). Instead, we related the two views causally, teaching how the feeling “hotness”, is caused by the energy that scientists call “heat”; i.e., we integrated the student view into the science view. These metaconceptual lessons constitute the third part of our intervention. In the fourth part, further exploration of the models and of thermal phenomena resumed. All through the teaching intervention, ULI (Universal Laboratory Interface, designed by

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Vernier) helped students realize that the microworlds are models of actual phenomena. 4.1. The Models

We limit our discussion here to three types of visual representations used to model an object on a hot-plate (the curriculum also included other representations of other physical situations). The amount of heat given by the hot-plate to the object is measured with a fictitious “Energy-meter” (or E-meter). The thermal probe reads the temperature at the top of the object. The E-model (Figures la and lb) represents the energy added to the object and its distribution. The molecular motion model (Figure 1c) represents molecules moving according to the amount of kinetic energy they each have. When an object is placed on a hot plate, the molecules in the bottom row of the object start moving faster because they receive energy from the hot plate. That energy is then transmitted from a row of faster moving molecules to a row of slower moving molecules. When the hot plate is removed, all the molecules end up at the same speed (simplified version of the law of thermal equilibrium). In the Es per molecule model (Figure 1d), the number of Es above each molecule represents its kinetic energy, and is proportional to the temperature at that location. The domain of heat and temperature bears strong similarities to the domain of weight and density: the student’s initial concept is perceptually-bound (heat is a physical entity with the essential property of hotness), conceptual change involves differentiation into an intensive (temperature) and an extensive concept (heat), and a radical ontological shift (from hotness to energy). Another similarity is that the expert concepts in the two domains are tied to the particulate theory of matter (temperature is average molecular kinetic energy and heat is the energy exchanged by molecules in motion). Not surprisingly our models and instructional strategies bear a resemblance to those of Smith’s. We taught students a simple version of the kinetic molecular theory of matter to serve as an anchor to the expert concepts, and our teaching models act as an analogy source, as they visually explicate the mathematical relation between heat, mass, and temperature. But our models are also causal, hierarchical microworlds, they include multiple representations and they are linked on-line to laboratory events via ULI. Thus, they share important features and goals with those of White’s (e.g., an emergent property of the molecular model becomes the causal principle of the E model). They also fulfill Kozma’s mandates (e.g., the models make sense of thermal equilibrium; the E model makes the relation between heat, mass, and temperature transparent; and ULI links signs to symbolic representations). At the same time, they privilege symbolic representations and, by linking them to actual physical events via ULI, should make the epistemic relationship between the scientific model and physical world more accessible to students. The majority (although, importantly, not all, see the section below, Content Teaching and Metaconceptual Lessons) of our sessions consisted of discussions, focusing on the interpretation of the models, as in Roschelle’s work.

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4.2. Students Negotiate Interpretations of the Models

We will now present excerpts from protocols collected during the first part of our study. They will illustrate how difficult it is for students to map the models “correctly” onto the world and to relate them to their pre-existing domain-specific beliefs. By “correctly”, we mean in the manner intended by the designer/teacher.

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4.2.1 Excerpt 1: What do the Es Represent? The first excerpt is from a session early in the study. Students had been taught a basic version of the molecular model of matter and had explored the models with the main goal of discovering their features. The theme of this session was: What do the Es represent? The excerpt illustrates several points: students do not spontaneously make contact with their domain-specific beliefs, especially when there is a potential conflict between them and the models; meaning is negotiated among students and teacher; and meaning, even when successfully negotiated, can be “wrong” from the point of view of the expert. The models on the screen are the E-crowdedness models of two different size objects on hot plates. The different “Exchanges” are consecutive parts of the session. Exchange 1 Teacher: Student

What do you see happening? The energy is coming in.

Exchange 2 Teacher:

The energy is coming in, fine, now what is the difference between energy and heat... When we asked you in the interview in the past two days what happens when you put something on the hotplate, you said heat is going to go from the hotplate into the pieces of metal. Now you’re telling me that the energy is going in. So, what do you think, shouldn’t we have had Hs for ‘heat’ or…have you thought about that?

Exchange 3 Peter: Natasha: Teacher: Peter: Teacher: Katherine: Teacher: Katherine:

The energy is heat energy. It’s not heat that’s coming out, it’s energy. It’s not heat, it’s energy, so heat’s not going in? It’s heat energy. What do you think, Katherine? It’s heat energy. It’s heat energy, so the energy and the heat are one and the same thing, do you think? Yea.

The teacher asks students to bring up the icon of the E-meter on the screen. Teacher: Natasha: Katherine: Teacher: Melanie: Teacher: Katherine: Teacher: Natasha: Katherine:

Do you think one could say that the E-meter is showing the amount of heat that’s in the object, or does that make little sense to you? It’s not as much heat as the energy. The heat energy. Melanie, what about you? It’s just showing a lot of heat energy that’s going into the object. Katherine? Both sides are showing heat energy. It’s showing heat energy, okay, but why did you, Natasha, say that it wasn’t really showing the heat, it was showing the heat energy? It’s not like heat, it’s, I don’t know…it’s not… It’s not hot.

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Teacher: Katherine: Teacher: Melanie:

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Yeah, it’s like the temperatures are like so different but the energy is not as distant as the two temperatures are. Like they still have the same amount of energy but it’s not like the same. But then five minutes ago, you told me that heat and energy were the same thing. So if they are the same thing, how come the Es are not measuring heat? They are measuring heat energy. Okay and how about heat? Melanie, do you agree with that so far? Yea.

Exchange 4 Teacher:

Students: Teacher:

Okay so you’re all comfortable with the idea that E is a unit of heat energy and the E-meter measures heat energy and when you put stuff on a hotplate, heat energy goes in and heat to some extent is different from heat energy. Okay, very good, we’ll see how all this evolves next week. So does anything measure heat on that screen? Probes. The probes. Okay.

At the beginning of this session, students spontaneously refer to Es as “energy” (Exchange 1). In a way, this is not surprising, since this label was used by the teacher in the previous session, and the E-meter icon has been called an “energy meter”. However, the students have explored the models; they have noticed the thermometer and hot plate icons and observed Es flowing from the hot plate icon and thermometer rising, and yet have made no connection between Es and heat. The teacher is the one forcing contact with pre-existing thermal conceptions (Excerpt 2). One student, Peter, resolves the issue by creating a label, “heat energy”, which, at least at the verbal level, satisfies both the student’s interpretation of Es as energy and the teacher’s point that Es must have something to do with heat. Two other students, Katherine and Melanie, adopt the label right away; the fourth student, Natasha, resists it because her concepts of heat and of energy are incompatible (energy is not hot), so that “heat energy” does not make sense to her. She uses the screen to support her point (Kelly and Crawford, 1996): the number of Es in the two objects is the same but their temperatures are different. Taking for granted (as all four students do; Exchange 4) that temperature measures heat, Es can’t represent heat. This is an example of the syllogistic reasoning we mentioned earlier as one way that some students (in previous studies) benefited from the models. But here, Natasha’s conclusion leads her away from expert understanding. Some students in previous studies concluded that, if number of dots represent amount of heat, and dot crowdedness represents temperature, temperature does not measure heat after all, but Natasha concludes that Es do not represent heat. Katherine agrees that Es don’t represent something hot but, presumably, takes the label “heat energy” to refer to the origin of the Es (they come from the hot plate) rather than to their ontological status. The teacher summarizes what she sees as a consensus among students (Exchange 4). This excerpt from our protocols contains an example of what Roschelle has called “collaborative convergence”. Roschelle’s discussion is of how two students converge on the interpretation of an arrow representing a force vector as “pulling” the represented velocity vector. His example of collaborative convergence involving the adoption of a creative metaphorical move by one student which is then taken up

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by another, can be seen to be productive from the expert point of view. In the case of “heat energy” just described the students’ creative move and subsequent convergence cannot be considered similarly productive. Many sessions followed the one from which we’ve just quoted, in which students used the word “heat energy” and enriched the concept associated with that label on the basis of simulations and ULI modeling. As illustrated in Excerpt 3 below, the more students noticed about the models, the more complex the concept of heat energy got, without getting any closer to the expert concept; this, as we will see, is because the concept heat energy is based on the uneasy union of two ontologically incompatible entities (hotness and energy). Before turning to that issue, Excerpt 2 illustrates, like Excerpt 1, that students easily agree when they interpret the behavior of the objects in the models, but not when interpreting the behaviors of their referents in the physical world. 4.2.2. Excerpt 2: The Motion of the Es. How are the Es Moving? Why are the Es Moving? What Makes the Es Move? Early in the sessions, students are watching a simulation of an object on a hot plate (E-crowdedness model.) They are asked to predict what will happen. Exchange 5 Teacher: Katherine: Teacher: Katherine: Teacher: Melanie: Melanie:

Why did you do that, Katherine? So I could see how many Es keep on going because I'm not sure. Tell us what you see. I think it's the same amount of Es but they're not moving around, I mean that they are moving, but that there [are] not more coming in. Melanie? That's what it looks like now that I think about it. They 're gonna be spread out evenly and they are pretty much doing that right now. But I didn't know that's what they were doing before.

[...]

Exchange 6 Teacher: Peter: Natasha: Peter: Natasha: Peter: Natasha:

[...]

Why do you think the Es spread? Because they wanna like… Because the Es more room like the air fills the whole room because it has the space to so because it has the space to go it'll spread out. …and the Es like they spread because like… the Es they kinda wanna be like …they… the bottom ones… Don't really know why they do it's just like… It's kind of like a law. They'll always do it. They just do.

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Exchange 7 Teacher: Katherine: Teacher: Katherine: Teacher: Katherine:

Now, if we now don't talk about the Es moving but go back to what they really represent, which is heat energy, why is the heat energy doing that? Why is it moving? Yea, why is it moving, since that's what the Es are showing you, and if you trust that the models… Because it is still warm. Because it is still warm? Yeah, it's like still warming up… well I don't know, I 'm used to it.

[...]

Exchange 8 Teacher: Katherine: Teacher: Katherine: Teacher: Katherine:

So let me go back to my first question then, what makes the energy, the heat energy, move like that, even from the bottom to the top? I don't know. Keep thinking of your other models. This [referring to the molecular motion model] is still moving, so making the heat, Es move. Okay now does that help at all explain why the Es were moving from the bottom to the top? It's passing though the molecules, that's just the only…

[...] Melanie: Teacher: Katherine:

May be the forces of the atoms, of the molecules are moving it. I don't know. Well, how do you like that idea? Does that make sense? I don't know if it does. Melanie just made it up.

Students notice Es even out after the hot plate is removed, and converge on an explanation on the basis of a p-prim-like belief (things tend to go where it is less crowded) (Exchanges 5 and 6), but their attempts at accounting causally for the behavior of the heat energy Es stand for do not lead to any agreement (Exchanges 7 and 8). 4.2.3 Excerpt 3: What is Heat Energy Anyway?

This series of exchanges illustrates the tension between Es as related to motion energy (Exchange 12) and Es as related to hotness (Exchanges 9, 10, and 11). Exchange 9 Katherine: Teacher: Katherine: Teacher: Melanie: Teacher:

The Es will just keep on going, spreading to the top. What makes you think that may be the Es will go up and… The temperature was still getting warmer but it was slowing down so… And why would it do that? Because that's what happens, the heat energy comes in when it's getting hotter and it's still warming up, so that there would be more Es. Okay, so let me restate this to make sure I've got it. Okay, you've noticed that when more Es come in the temperature goes up and since you noticed

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Katherine

that the probe there was showing an increasing temperature, it must be that more Es are going to go there. What do you think, Katherine? Um, that's what I think.

[...]

Exchange 10 They are looking at the E per molecule model, and are asked to predict the changes in the model as the object is put on the hot plate. Student: Teacher: Student: Teacher: Student: Teacher: Student: Teacher: Student: Teacher:

Student:

The energy will get higher? The energy will get higher, where? There will be different numbers all over. Okay, and that's it? Yea they're hottest at the bottom. Okay, is there anything else happening? It's getting more energy, more heat energy. What is? The thing. The object. Okay, what's happening to the molecules specifically? [...] those numbers there for the molecules are there differences between the molecules? Yes, they're at different temperatures.

Exchange 11 Teacher: Melanie: Teacher: Melanie: Katherine:

What is the relation between the probe reading and the Es? It is the temperature of it. The temperature of the Es? Yes. The energy is getting hotter. There are more Es at the top, that is why it keeps getting hotter. The warmer it is, the more heat energy, so that is why the numbers [of Es per molecule] change.

Exchange 12 Watching an aluminum bar being heated by a soldering iron, in ULI mode, the students have agreed that, after the soldering iron is removed, the molecules on the screen exchange heat energy until they all have the same number of Es per molecule. Teacher: Natasha: Teacher: Peter:

How do they [the molecules] do that? [The Es] spread out. Ok, and how do they do that? The molecules [closer to the soldering iron] are influencing the other ones.

Teacher:

Why do the faster ones [near the soldering iron] slow down [after the soldering iron is removed]? Because the other ones need energy to keep up, and like if they give that energy, then they’ll lose it.

[...]

Peter:

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In this series of exchanges, students display implicit or explicit confusion as to the nature heat energy, as symbolized by Es, and as to the nature of the relationship between Es, molecular motion, and thermometer reading. In Exchanges 9, 10, and 11, the focus is on temperature reading. In Exchange 9, Melanie and Katherine notice the correlation between Es reaching the thermometer and the thermometer rising, but do not venture a causal interpretation. In Exchange 10, they think of the number of Es per molecule as the temperature of the molecules and in Exchange 11, they mention “the hotness of the energy”. In Exchange 12, which takes place while viewing the molecular motion and the E per molecule models, the focus is on molecular motion, leading students to favor an “energy” interpretation. Notice from the excerpts above that our teaching style during this part of the curriculum was hardly didactic. This style we believe fostered collaborative convergence - often, in fact, with the teacher converging on the students’ creative ways of interpreting the computer models. Much of this was productive when limited to the world of the computer models per se. Using visual information and pprim-like beliefs, students come to agree that Es are emitted by the hot plate; that they move upward; once the hot plate is removed, they spread until their distribution is homogeneous, with their number conserved; there is a “give and take” of Es between molecules. However, relating the models to domain specific knowledge, i.e., viewing the models as models of the physical (thermal) world, an attitude which entails a fundamental conceptual restructuring of the domain, was not successfully negotiated in this manner. These problems are due, we believe, to the inadequacy of processes of collaborative (i.e. symmetric) convergence - however good computer models are - if there exists a serious ontological difference between the students’ and the scientific concepts (or, more generally, if there is a deep discrepancy between the students’ and the scientists’ conceptualizations). We believe that what we needed to induce deep conceptual restructuring was an interaction style that involved an asymmetric relationship: teacher/researcher/scientist, on the one hand, and student/research participant/layperson on the other. 4.2.4. Excerpt 4: Content Teaching and Metaconceptual Lessons

Following the session (partially) reported above, the teacher presented a scientific account of thermal conduction: electrical interactions between molecules underlie the exchange of kinetic energy between molecules. Kinetic energy was discussed at some length. Students knew that it is measured in Joules. Excerpt 4, which follows this lesson, shows that students have no trouble accepting a mechanico-electrical account of molecular behavior, while not being able to accept that Es represent heat. Exchange 13 Teacher: Peter: Teacher: Peter:

[…] What does this have to do with the models? Molecules in motion. […] So what are those Es after all? They are like Joules.

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Natasha: Teacher: Peter: Teacher: Melanie: Peter: Teacher: Katherine: Peter:

Ok. Es per molecule are a measure of how much kinetic energy each molecule has. Does this make sense to you? Yeah, it makes sense. Ok, on the other hand, Melanie and Katherine told me [earlier] that those Es could represent heat. Is that true? Did you believe that too? Es are like heat energy. Heat energy, and that’s different from heat? It is confusing. I was thinking, that since E is for energy, or the heat energy. Yeah, that’s what I was thinking too. If I said those Es were actually heat, other than, you know, I am the teacher and I’m kind of helping you, does that make sense to you? Is that right? If Es were the heat? Yea. You see, I was thinking different. I wasn’t thinking Es are like units of kinetic energy, I was thinking like the energy of the heat of the bar. That’s what you thought, OK. They were the energy from the bar. And you Melanie, what do you think? I just agree with Peter. I wasn’t thinking like the energy, I was thinking the energy in the molecules. In the molecules. What about you, Katherine? I’m not sure if I know exactly what Peter said… I am saying like the energy is coming from the bar and going into, not like the molecules’ energy, but the bar’s energy.

In this exchange (and other similar ones, not reported here), students seem to agree that the source of heat (the soldering iron) is providing “heat energy” which flows through the bar (along with “heat” or hotness) and is transformed into kinetic energy. (The asymmetry between source and recipient is a salient feature of the naïve conceptualization, Wiser and Carey, 1983.) The teacher then leads them to realize that the bar molecules around the soldering iron start moving faster because the soldering iron molecules are themselves moving fast, i.e., the process of kinetic energy transmission holds from source and recipient as well as within the recipient. Students accept this account and that Es represent kinetic energy; they become able to provide a scientific description of heat conduction in terms of molecular interactions. However, in the next session, the teacher raises the issue of hotness: Where does the feeling of hotness come from? Students fall right back into conversion mechanisms, mostly based on friction between molecules. Thus, didactic “conversations” privileging the scientist’s view, were necessary for students to learn the molecular kinetic theory; they produced real understanding, but they were not sufficient, as they left students unable to account for their core concept, heat-ashotness. In Posner et al.’s terms, we had made the new theory understandable, but not plausible. (Posner, Strike, Hewson, & Gertzog 1982). The students needed help understanding that what they meant by “heat” was different from what scientists mean by “heat”. What scientists mean by “heat” is ontologically closer to what students had started labeling “heat energy” early in our study. At the same time, in order to accept the scientific theory as a theory of “heat”,

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they also needed a way to understand how hotness (a prevalent everyday experience and the core of their own concept of heat) was related to the scientists’ heat. We designed several metaconceptual lessons to provide that help (see Wiser & Amin, 2001, for details). After discussions about multiple views, theory change, and multiple meanings of words, a session was devoted to contrasting ‘everyday heat’ and “science heat”. The “everyday view” and “science view” were then made commensurable by teaching about the physiology of temperature perception, thus changing the ontological status of hotness and integrating the two views. In the integrated view, hotness is a percept caused by “science heat” rather than a physical entity co-existing with it (Wiser & Amin, 2001). By the end of these sessions, students were much more comfortable and facile with the scientific theory, and used the labels “everyday heat” and “science heat” to facilitate communication. In these Metaconceptual lessons, as in the lesson on conduction, the teacher has an authority status. We believe that, when deep conceptual restructuring has to take place, especially when radical ontological revisions are involved, the teacher has to “step in” and present the scientific view as such, because students cannot be expected to come up with it on their own. However, direct instruction worked because it was integrated into an otherwise student-centered curriculum. Open-ended, “egalitarian” discussions and computercentered sessions brought out the students’ own beliefs and let them construct their own interpretations of the models, which paved the way toward understanding the scientific theory, although only up to a point. At that point, students’ beliefs were explicitly compared to scientific tenets and integrated within them. The “authoritarian” components of our curriculum allowed students to capitalize on what they had learned from the models and their own negotiations. The two labels (“Everyday view” and “Scientific view”) helped maintain the privileged status of the scientific theory without forcing students to reject their own beliefs or adopt a relativistic epistemology for which they are typically not ready. 5. CONCLUSION

While we have not used the word much so far in this paper we are advocating a situated approach to understanding and achieving conceptual change in science. We refer to a situated approach in the sense used by Roschelle (1996), meaning the adoption of a “relational epistemology”. Trying to understand conceptual learning while adopting a relational epistemology means that we find it more appropriate to speak of students developing conceptualizations of things rather than acquiring concepts. That is, it seems more appropriate to treat conceptualization as a relational construct. Roschelle applies this relational epistemology to students’ conceptualization of the visual elements in the microwold he uses. We are extending this to thinking of the internalization of computer-based models as a process whereby students use them to conceptualize the world (see also Roth, 2001). Figure 2 captures, in outline form, how we view the role that computer-based conceptual models play in inducing conceptual change. Figure 2a represents what we see as the first phase of the conceptual learning induced by computer-based

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interactions. Before any instruction or exposure to the computer displays students already have a variety of concepts and beliefs that constitute their initial understanding of thermal phenomena. This is represented by arrow A. During the first phase of learning symmetric, peer-peer interactions takes place in which students are collaboratively trying to make sense of the computer displays. To do this they draw on some (but not all) of their conceptual resources for making sense of thermal phenomena (e.g., hot objects heat up other objects when placed in contact with them) as well as other conceptualizations (e.g. things, like air and sugar, move from more crowded to less crowded regions) and domain-general reasoning processes (e.g., analogies, establishing correlations). The result of their collaborative sense making is represented by arrow B (e.g., hot-plate gives Es to the object; when it is removed, the Es spread out until they are distributed homogeneously in the object). We argued that making sense of the computer displays need not imply sense making with respect to the real world: in Phase 1, the computer displays are treated as microworlds only, worlds onto themselves, to which some physical laws apply, some known, some to be discovered, but not as models of the world. But of course, the models were designed with the intention that these map onto the world in specific ways. Figure 2b represents the second phase of learning in which elements of the computer displays are internalized as conceptualizations of the world. We argued that this process involves, indeed requires, asymmetric interactions between students and teachers/researchers. The T-shaped arrow, C, represents the result of this second phase. This is a highly simplified representation of what we view as a complex set of interactions. First, upon teacher’s suggestion the symbols making up the displays are mapped onto the real world and students attempt to integrate their conceptualizations of the computer displays with what they ‘know’ about the world. With this type of guidance aspects of the scientific view can be internalized as long as there is no conflict (especially ontological) between the scientific view and students’ prior concepts. For example, students quickly internalize the idea that little circles represent molecules, and that fast moving molecules make adjacent molecules move faster. Also easily accepted is the idea that Es represent energy (or at least “energy-of-some-sort”), and the number of Es per molecule represents a measure of its motion. Up to this point, the teacher acts as a catalyst, not as an authoritative source of scientific information; the student-teacher negotiations in these sessions are symmetrical. However, when it becomes clear that the students’ interpretation of the models-applied-to-the-world is not moving toward the scientific view, the teacher presents the scientific interpretation of the models, and, when ontological conflict arises between student and scientific interpretations (students not being able to internalize heat being represented by total number Es because of their entrenched view that heat is hotness), metaconceptual teaching provides an explanation of the relation between heat and hotness, that integrates the two views. Although the student view is being acknowledged and respected and the students are active participants, the teacher-student negotiations are not symmetrical in these interactions.

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An important feature of the diagram in Figure 2 is that it incorporates into our account of the process of conceptual change (driven by computer-based models) the interaction between conceptual change and an understanding of the elements of the models qua models. As we have discussed above - in particular, in our discussion of White’s work - conceptual change and metacognitive learning about scientific inquiry and practice have generally been treated as separate pedagogical targets. Our protocol analyses suggest to us that the two processes are intimately connected and our understanding of the process of conceptual learning needs to address this connection. There are a number of implications for instruction that follow from this view of computer-based conceptual learning in science. Our suggestion that different aspects of the process of conceptual change can be achieved through different types of interactions has direct implications for how computer-based models and microworlds are incorporated into learning activities. First, more realistic expectations can be formulated regarding what kind of learning can be achieved through peer-peer interaction. Second, the teacher’s role can be channeled where it is most seriously needed, getting students to use computer-based representations to construe the physical world thereby making contact with their lay conceptualizations (of the world). Indeed, the account we have given brings into focus the importance of enriching activities intended to achieve conceptual change with representationworld connections. The value of the Universal Lab Interface in conjunction with models and simulations can be seen in this light. Models of conceptual change are gradually becoming more complex, a tendency which can already be gleaned from the literature. It is likely that we will need to be more sensitive, both in our theorizing and in the instructional implications we draw, to differences across domains. Theoretical and instructional implications with regard

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to domain-specificity can be drawn from our suggestion that two types of interactions lend themselves to two aspects of conceptual change. In the domain of thermal physics students already possess an entrenched set of interconnected ideas about thermal phenomena in the world. It is this set of ideas that was the primary obstacle to helping Students map their understanding of the computer representations to the world. In our view, this obstacle was surmounted through asymmetric, metacognitive interactions between ourselves (teachers/researchers) and the students. However, no equivalent obstacle would arise in a domain in which students do not possess a rich set of ideas prior to instruction and thus the role of asymmetric interactions will be less crucial. The domain of electricity may fit such a profile. A useful gloss of the perspective on computer-based conceptual change we are proposing might be that it is a view that emphasizes conceptual change as participation in the practice of improving models of the physical world. This phrase highlights the emphasis we have been placing on understanding the interactions between conceptual change per se and modeling qua modeling, on incorporating this understanding into our curricula, and on the recognition that both processes are value-laden. Nerssesian (200l a) has advocated such an approach, although, as a historian and philosopher of science studying individual scientists’ cognitive processes during revolutionary phases of science, her attention weighs on the conceptual change, rather than the participation, component. As we hope our paper has made clear, elements of this view are embodied to a lesser or greater extent, in the work of the science education researchers we have reviewed, and of some of those we did not have space to include. We would like to conclude by pointing out that by seeing conceptualization as a component of the value-laden practice of modeling, a bridge can be established between cognitive approaches that have focused on the fine-grained analysis of conceptual structure and practice (or participation) approaches that have shifted the focus to broader units of analysis (e.g., socio-cultural activities, see Rogoff, 1997). Amin (1998) has argued, in general terms, that practice (or participation) views of learning can be compatible with a close consideration of cognitive units such as concepts. Moreover, like others (e.g., Roschelle, 1996), we are increasingly finding that in our attempt to understand the process of conceptual change we are incorporating more social interactional elements into our accounts. There is a growing need for an integrated model of conceptual change in science that draws on constructs from cognitive and practice perspectives. We view this paper as a contribution to the growing effort to meet this challenge. ACKNOWLEDGMENTS The study reported in this paper was supported in part by a grant from the National Science Foundation to the first author: Differentiation and theory change in thermal physics: The role of conceptual models and metaconceptual understanding. Contract #MDR89-50-333.

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KNOWLEDGE ASSESSMENT AND CONCEPTUAL UNDERSTANDING

JESÚS ALONSO-TAPIA

Autónoma Universidad, Madrid, Spain

Abstract. Conceptual change involves weak or radical modifications of conceptual understanding. Thus, how to assess students’ conceptual understanding becomes a key issue of conceptual change. This chapter deals with the assessment of students’ conceptual understanding, considering some implications it may have to assess conceptual change processes. It outlines the main characteristics of assessment tasks, processes and contexts that can affect knowledge construction and revision. In doing so, it is intended to widen the perspectives on conceptual understanding by considering some fctors that usually are present in classroom practice, but not always taken into account in research. For example, the kinds of assessment task employed by teachers, whether or not teachers make learning goals explicit, the design and coverage of assessment processes, the degree of feedback given by teachers or how much self-regulation is promoted by assessment tasks. I shall include some examples mainly from my own research on social sciences that will illustrate the ideas presented. Special consideration is given to analogous and transfer tasks, and to portfolio-assessment in the context of project-oriented learning. Finally, the chapter outlines a research agenda in order to go further on these topics.

1. INTRODUCTION

There is a growing interest among psychologists and educators in understanding how knowledge is acquired and represented in memory and, especially, in knowing how it changes in the light of new information and experiences, and in identifying which factors promote or hinder this change, as many recent publications, including this book, attest (Carey & Spelke, 1994; Chinn & Brewer, 1993; Dole & Sinatra, 1998; Guzetti & Hind, 1998; Siegler, 1996; Thagard, 1992). Achieving these objectives is important not only from a theoretical point of view, but also from an applied one, as teachers and educators strive to help students to understand and to change their world conceptions where necessary. Researchers and teachers, however, do not pose the problem in the same terms. The question for researchers is what factors may influence understanding and conceptual change. However, teachers ask themselves what can be done to promote them. The two questions are related, as knowing how different factors affect knowledge construction and change M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, pp. 389-413. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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can help to decide where, when and how to act to promote conceptual understanding and change. Nevertheless, the question posed by teachers forces researchers to consider the role of factors defining real contexts in order to reach a deeper understanding of the process of knowledge construction and change. In trying to produce the above mentioned effects, teachers have to confront with the problem of creating learning environments that foster and do not hinder understanding. Dealing with this problem involves considering the role of assessment. Therefore, it is important to consider which assessment conditions, i.e. which tools, procedures, criteria and contexts, are most appropriate for fostering and assessing conceptual change. In order to do so, firstly I shall discuss the main characteristics of assessment tasks, processes and contexts, and how they can affect conceptual understanding. Secondly, I shall introduce some examples from own research to illustrate the issues discussed. Finally, I shall outline an agenda for researchers to go further on these topics. 2.

2.1.

THEORETICAL FRAMEWORK

Perspectives on Knowledge, Conceptual Understanding and Conceptual Change

Given the different perspectives on conceptual change, it is necessary to make explicit which perspective I shall employ. Recently, Dole and Sinatra (1998) reviewed the contributions of cognitive psychology, science education and social psychology to conceptual understanding and, especially, to conceptual change. In this review they showed that though there are important differences between authors from different theoretical traditions, their points of view are complementary and can be tentatively integrated within a new heuristic framework. According to Dole and Sinatra, cognitive psychologists have conceptualised knowledge as memory representations in the form of scripts, frames or schemata (Anderson & Pearson, 1984; Rumelhart & Ortony, 1977; Shank & Abelson, 1977). Most of them have studied the nature and structure of these representations, though some have also studied processes of change. They have referred to these processes as assimilation - the addition of new information to existing knowledge structures and accommodation - the modification of existing knowledge structures - (Piaget, 1937); accretion - the assimilation of factual information that fits into existing knowledge structures - (Rumelhart & Norman, 1981); weak restructuring or conceptual change - the knowledge acquisitions that results from mechanisms such as addition, deletion, discrimination and generalization - (Chi, 1992); and finally, radical restructuring or conceptual change. It involves the creation of new structures to reinterpret old information or to account for new information (Vosniadou & Brewer, 1987). All these researchers, however, agree in pointing out that the mechanisms of change are not well known.

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As regards work on science education, researchers have tried to explain why so many students maintain their existing conceptions in spite of instruction, and under what conditions these conceptions change (Posner et al., 1982). In doing so, they have shown, first, that when knowledge structures are crystallized, coherent and firmly entrenched, they are highly resistant to radical change, even when confronted with data that contradict the existing theories (Chan, Burtis & Bereiter, 1997; Chinn & Brewer, 1993; Dole & Sinatra, 1998; Limon & Carretero, 1997; Posner & al. 1982). Due to such resistance, radical restructuring requires a great deal of cognitive effort, effort that will not take place: unless students are dissatisfied with previous ideas, …unless they find that the new conceptions are intelligible and make sense, …unless they perceive that the new conceptions are plausible ones, which implies that they must fit into existing and related ideas, …and unless they find that the new conceptions are open to new areas of inquiry. (Posner et al., 1982, p. 214)

Let us now consider the work of social psychologists (Eagly & Chaiken, 1993; Olson & Zanna, 1993). They have traditionally been interested in beliefs, the thoughts that people have about attitude objects, and attitudes. They were defined as dispositions to act regularly and in a particular way in relation to a class of objects, people, actions, ideas, etc., due to the positive or negative emotional valence that they have for the subject. This valence may stem from the knowledge or beliefs people have about the object of the attitude. Thus, knowledge is at the base of beliefs and attitudes, and social psychologists carried out a lot of work aimed at identifying the conditions under which this knowledge and the corresponding attitudes change (Kuhn & Lao, 1998). According to Dole and Sinatra, social psychologists have borrowed the theory and methodology of cognitive psychology to explain how attitudes and beliefs are represented in memory. However, they have been more interested than cognitive psychologists in identifying the conditions of change. Thus, Petty and Cacioppo (1986) have shown that changes in beliefs and attitudes may occur in one of two ways. First, though a process motivated by personal involvement due to one’s personal stake in the outcome or to the need for cognition and its consequences, a process called “the central route to persuasion”. Second, even if there is not a great deal of personal involvement, information characteristics may induce a peripheral shift which, depending on different factors - message comprehensibility, background knowledge, etc.-, may vanish or activate a deep change in beliefs an attitudes, a process called “the peripheral route to persuasion”. Dole and Sinatra (1998) have integrated the different approaches to conceptual understanding and change within a new model. They have pointed out that conceptual change depends on the interaction between learner characteristics, message characteristics and peripheral cues. In the first group of variables they have included existing conception characteristics and motivation to engage in the elaboration process due to dissatisfaction or cognitive conflict, to the personal relevance of the topic, to the need for cognition or to social context influences.

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They have suggested that such characteristics interact with characteristics of the message, such as its comprehensibility, coherency and plausibility. Moreover, they have also suggested that even if such interaction is not sufficient to stimulate engagement capable of producing strong conceptual change, the existence of different peripheral cues may stimulate at least weak conceptual change. From our point of view, in one way or another, all of the above approaches recognise that acquiring or organising knowledge implies constructing some sort of mental representation – ideas, scripts, schemata, beliefs, etc. Nevertheless, it is important to point out that that this construction implies two different processes. One is concept formation, that is, the construction of categorization rules by which: to render discriminably different things equivalent, to group the objects, events and people around us into classes and to respond to them in terms of their class membership rather than their uniqueness. (Bruner, Goodnow, & Austin, 1956, p. 1)

The other is concept identification, that is, the association of the rule underlying a verbal term to that term, an association that requires prior formation of the concept. Sometimes students may have formed a particular concept, as can be inferred from their reactions to exemplars and non-exemplars of it, but they do not know the verbal label. For example, they may react to the listening or reading of pronouns by looking for their referents without associating the word “pronoun” with them. Other times, they associate with a verbal label conceptions that are different from the conceptions that experts attach to that label. For example, this is the case with the concept of “alive”, which evolves from meaning “to be in motion” to “be born, to grow and to die” (Delval, 1975; Piaget, 1926). It is not difficult to associate the correct verbal label to a concept as long as a person has formed the correct categorisation rule. Thus, from our point of view, if assessment is aimed at deciding which instructional aids should be given to students in order to favour conceptual change, assessment activities should focus on the first aspect of conceptual understanding - the student’s rules for categorising phenomena. These rules become manifest in categorising or predicting behaviour, and their change can be detected if they are assessed before and after instruction. The above referred models also recognise that conceptual change depends on individual characteristics and those of information or message. However, no model considers the effect of characteristics defining real learning contexts on conceptual understanding and change, as many of the studies have not been carried out in such contexts. Of course, as long as real situations had the characteristics that, according to research findings positively affect conceptual understanding and change, they might induce these outcomes. Nevertheless, other conditions might also be necessary. One of these may be the characteristics of assessment, as will be shown next.

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Perspectives on Assessment

Recently, Dochy (2001) have distinguished two different perspectives on assessment, the testing culture (Wolf et. al., 1991) and the assessment culture. The testing culture developed around the purpose of identifying the amount of knowledge “deposited” in students’ minds. In this culture instruction and assessment are considered as separate activities. Planning of tasks, writing of items and evaluation criteria are not shared with students, and the tasks are usually unrelated to the student’s life experience. The assessment culture, on the other hand, has as its main goal to provide information –to the teacher or the student him/herself- that may help students overcome their difficulties and self-regulate their learning processes. Teachers working from each one of these perspectives create assessment contexts that can affect the extent to which students strive for understanding, and therefore, the likelihood of conceptual change. Thus, in order to promote conceptual understanding and change it is necessary to consider the characteristics of such contexts. When talking about assessment we refer not so much to assessment scores obtained by students or to the different assessment activities, but to the whole assessment process. There are different kinds of assessment activities. First, there are assessment activities aimed at identifying the prerequisites of learning - the ideas or mental representations that students bring with them, the strength and coherence of these ideas and the student’s commitment to them. Second, there are those that take place during the teaching-learning process with the aim of monitoring students’ progress and diagnosing their difficulties, or with the aim of aiding their self-assessment, self-monitoring and selfregulation. Third, there are those aimed at final or summative assessment. However, in all of these cases the assessment process may differ depending on the specific configuration of characteristics such as the extent to which assessment goals are made salient by teachers; the nature and sequence of assessment tasks; the frequency and distribution of occasions for assessment; the amount of time available for performing assessment tasks; the frequency and kind of feedback based on quality of assessment outcomes. These differences constitute one of the main contextual factors affecting students’ motivation and learning activities, on which conceptual understanding and change depends, at least partially. The existence of these differences raises some questions related to the issue under discussion: do assessment processes exert any influence on conceptual understanding and change? If so, what kind of assessment characteristics can affect these outcomes in the most positive way? Are the assessment characteristics that supposedly best foster conceptual understanding and change also adequate for showing this change? Are these kinds of task commonly used by teachers for assessing their students? If not, how can we promote their use by teachers so that assessment improves conceptual understanding and change? These are the questions that will be dealt with, mainly in relation to assessment in history and geography.

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J. ALONSO-TAPIA 3. ASSESSMENT CONDITIONS FAVOURING CONCEPTUAL CHANGE

In order to answer the first question -whether assessment processes exert any influence on conceptual change-, we should take into account the following points. Knowledge can be considered an instrument or a tool that is useful in different contexts, such as taking an exam, solving a practical problem, persuading someone, etc. As human conceptual knowledge is “situated” (Caravita & Halldén, 1994), the nature of the context in which knowledge is expected to be used is likely to affect activities students perform to construct such knowledge. Thus, for example, if students expect to take a multiple-choice exam requiring recall of facts and information, they are likely to study in a way different from the way they would study if they expected to solve open-ended questions (Alonso-Tapia, 1999; AlonsoTapia & López, 1999). Assessment tasks and design will affect the degree of commitment and thus of conceptual understanding. What kinds of assessment process characteristics are most likely to promote conceptual understanding? In our view, the following characteristics, that will be discussed next, should be considered: Most suitable tasks: those demanding the application and use of knowledge for solving problems implying some degree of novelty (analogous and transfer tasks). Teachers make explicit for what goals understanding of particular content is relevant. Tasks designed to allow teachers to identify specific factors in students that hinder conceptual change. The assessment process covers the different nodes and links of the conceptual network students are supposed to construct. Teachers give specific help based on assessment, whether this takes place before, during or after instruction. Teachers avoid messages and classroom practices stressing the relevance of assessment for goals extrinsic to understanding. 3.1.

Types of Assessment Task to Promote Conceptual Understanding

With regard to assessment tasks, existing evidence suggest the use of open tasks demanding the application and use of knowledge for solving problems involving some degree of novelty (analogous and transfer tasks), as these problems require the use of knowledge schemata for the construction and even reconstruction of mental models to guide the solution process (Alonso-Tapia, 1997; Schnotz & 1997). The need to build such models may help the student to detect knowledge gaps and may stimulate his/her subsequent efforts to overcome them. Most importantly, however, if students know beforehand that they must solve certain types of problem, they may attempt to confront with these in advance. Nevertheless, the use of open tasks may not be sufficient for producing such outcomes, as they seem to depend on

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the interaction between personal characteristics, knowledge, thinking skills and motivation. What kinds of tasks are we referring to? It depends, among other things, on the subject matter being assessed, as it defines the kind of knowledge representations e.g. schemata, scripts, mental models- that students are expected to construct and the particular situations to which these representations are expected to be applied. Nevertheless, Baxter and Glaser (1998) have developed a working analytic framework for organising assessment tasks in two dimensions on which expert competence depends. The first one defines the subject-matter knowledge necessary for carrying out the task. According to it, assessment tasks can demand rich, integrated and usable knowledge or can be “lean” with respect to knowledge. The second dimension defines the process skills underlying performance. According to this dimension, assessment tasks can be open or constrained. Thus, tasks can be divided into four categories: 1) content rich-process constrained, 2) content richprocess open, 3) content lean-process constrained, and 4) content lean-process open. According to Baxter and Glaser, tasks of the first category emphasise knowledge generation and recall, such as “Describe the main causes of political revolutions, such as the French, and explain how they are related” or “Describe the process of erosion and explain the physical and chemical sub-processes that produce it”. They are unlikely to stimulate the use of study strategies promoting conceptual understanding. It also may occur with tasks of the third category, content leanprocess constrained, such as doing an exercise following very specific instructions. When assessment tasks are open, as it is the case of second and fourth categories, the need to reconstruct knowledge they demand can facilitate conceptual change. Though this beneficial effect may depend on the interaction between prior knowledge needed to accomplish the task and other variables such as motivation to gather, activate and transform knowledge. An example of this kind of task taken from our own research on understanding causality in history will be given below (see Figure 1). Other examples regarding science can be found in Alonso-Tapia and Pérez (1997), Pérez and Moreno (1999), Baxter and Glaser (1998) and Duschl and Gitomer (1997), among others. In history, students have to learn not only what happened in the past and why, but also how different categories of facts tend to affect historical changes when certain conditions are met (Alonso-Tapia et al. 1997; Alonso-Tapia & Villa, 1999). This learning implies the construction of conceptual representations dealing with multicausality. The understanding of causal relations can be assessed if we ask students what is likely to happen in hypothetical or real situations. These situations are more or less analogous to that found when students study a particular historical change. To answer this kind of questions involves the use and transfer of previous representations to solving problems analogous to those on which conceptual models have already been built. As an example, Figure 1 shows “a simplified model” of the main factors that caused the French Revolution. It is not “the model” explaining the French Revolution, but only a tentative one that usually guides instruction in

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Spanish schools. Understanding of this model implies not only being able to say that this or that factor contributed to the revolution. It also implies realising that the historical events included in Figure 1 belong to different categories: natural, technical, economic, social, political, military, personal and ideological, to mention only a few. Furthermore, it implies realising that, if similar conditions were met, they would usually contribute to historical change in the same way. For example, demand being constant, scarcity increases prices; war causes the state to run up debts. Thus, in relation to the study of the French Revolution, what kinds of task may be used to assess whether students’ conceptual understanding has evolved in the expected direction? Table 1 shows some of the hypothetical situations designed to assess conceptual understanding of some causal relations included in Figure 1. Each situation is followed by questions asking for inferences about what might happen in relation to prices, impoverishment of peasants, problems of city dwellers, etc. Students have to justify their answers, so that the mental representations underlying them can be detected. The way students perform the tasks described provides information about the conceptual representations related to causal understanding in history, and about the way they reason according to such representations. These tasks constitute good criteria of attainment of learning goals. However, in our research it emerged that most secondary school students are not used to this kind of task since most assessment tasks are constrained (Villa & Alonso-Tapia, 1996), their performance reflects a very poor and fragmented conceptual structure (Alonso-Tapia & Villa, 1999; Alonso-Tapia, Asensio, & López, 2000a). However, if students know in advance that they have to carry out tasks such as these described, and if they have been introduced to the kind of thinking and study strategies suitable for coping with the difficulties of such tasks, the likelihood of using such strategies and thus of changing their mental representations increases. 3.2. Making Explicit the Relevance of Learning Goals The nature of assessment tasks is a key factor in fostering conceptual change. However, in our view, this factor is unlikely to be sufficient in real situations. As educational psychology has shown (Olson & Zanna, 1993; Schiefele, 1991), students do not usually strive to understand unless they perceive that the tasks to be accomplished are relevant for assessment. Only if teachers help students to perceive the relevance of understanding concepts and procedures involved in classroom tasks, in spite of the actual usefulness of such knowledge, students are likely to make the effort needed to learn them and, eventually, to change their mental representations. How, then can teachers make relevance more salient? Teachers can make salient the relevance of knowledge to be constructed and assessed through assessment task design and contextualisation that meet two conditions: a) they challenge students with authentic problems (Duschl & Gitomer, 1997), and b) the solution of these problems allows the acquisition of some competence whose value students are able to appreciate (Alonso-Tapia, 1997). An example will illustrate this point.

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Consider, for instance, the task in Table 2 taken from our research on human geography understanding. The answer to each question depends on at least three kinds of factors: a) student’s mental representation of phenomena to which simple concepts such as infrastructure, capital, advanced technology refer; b) student’s mental representation of causal processes to which each question refers (e.g. a student may think that “giving grants to the best students to go abroad to prepare and specialise is generally negative for the progress of a country because all students should be given the same opportunities”); and c) the particular conditions of the country or the way the measure stated in the question should be applied –what may be good for one country, may not be good for another. Due to this last factor and to the hypothetical and open nature of the questions, there are not right or wrong direct answers. Thus, students must make an effort to imagine different scenarios in order to decide when the causal relation between the action considered and economic development would apply, and when it would not. However, the specific tasks designed for assessment are “situated” in the context of a more general and authentic problem: the need to be aware of the implications of our decisions when we vote in a general election. The perceived relevance of this problem may contribute to increasing students’ efforts to understand, and thus increasing the likelihood of conceptual change. 3.3.

Designing Tasks to Identify Knowledge Gaps and Misconceptions

Understanding and conceptual change may not occur even if students perceive the relevance of acquiring knowledge needed for solving assessment tasks. Often, understanding cannot take place without help. Sometimes students lack some conditions that seem to be necessary for conceptual change to occur. For example, when they have well rooted pre-existing alternative conceptions, that are very incoherent, and the commitment to them is very strong. To deal with this problem effectively, teachers should be able to diagnose when there is a lack of such conditions and why, and to identify the specific factors that hinder students’ understanding and conceptual change. Assessment strategies to manage these problems may be to ask students for an explanation of their answers, as shown in Table 2, or to design hypothetical situations that may allow teachers to explore the causes of students’ difficulties, as exemplified by the tasks included in Table 1. These strategies can allow teachers to identify different kinds of knowledge characteristics that may constitute an obstacle to understanding (Alexander et al., 1991). Furthermore, conceptual maps can be used to identify the strength and coherence of previous knowledge (Jonassen, Beissner, & Yacci, 1993). For these assessment strategies to be efficient, that is, to facilitate conceptual understanding, they have to be used continuously, not only occasionally. Moreover, it should be pointed out that knowledge revision often appears to take place through a gradual transformation of mental representations. This seems to be especially true when students have to learn complex conceptual models after examining different sources of information. It occurs, for example, when students

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try to understand the causes of historical changes, they have to make sense of data from experiments in order to understand scientific concepts, or they have to make sense of data that are anomalous with regard to their existing conceptions (Limón & Carretero, 1997; Chinn & Brewer, 1993).

As far as the set of tasks used throughout the assessment process covers the different nodes and links of the conceptual network students are supposed to construct, teachers will be able to help in the building of such a network through aids specifically needed, such as pointing out information not considered or contradictions implied by anomalous data.

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For example, Duschl and Gitomer (1997) have developed a set of tasks and suggested a set of criteria in the form of questions to be used in science classrooms through which teachers can assess and scaffold students’ thinking, which must be based on valid reasoning inferences, in order to improve their conceptual understanding. For instance, these questions are aimed at: a) Helping them to establish relationships (What goes together? Is there anything that does not belong? Why? How are things alike?). b) Improving clarity (Does it say what you want it to say? Will it be clear to someone else?). c) Inducing the student to examine the consistency between inferences and evidence (Is the statement supported by observations? If so, which ones? Is it supported by the observations of others? If so, which ones?). d) Helping the student to back up their representations with the use of examples (Can you give an example? Is it a good example for this purpose? Can you think of an original example?). e) Helping them to make sense of the information available (Is this what you expected? Is there anything that does not fit? Can you predict the outcome?, etc.). f) Encouraging the consideration of alternative explanations (Is there another way to explain it? Is your explanation plausible? What does this explanation say that the other doesn’t? etc.). g) Favouring elaboration of the theme (Is this term related to something we did before? Is it related to something you did in another class?, etc.). h) Improving accuracy (Is the statement consistent with other information on the same topic? How does the model compare with other models? How does it compare with other representations?). Similar sets of questions can be developed in relation to the process of analysing and integrating information in social sciences. These questions can favour understanding, as they encourage students to process their knowledge more deeply (questions a, b, d, g and h), focus their attention on data not considered and on contradictions (questions a, c, e), and draw attention to the possibility of and need to look for alternative explanations (question f). The assessment conditions described up to this point may contribute directly or indirectly to conceptual change. I say “may” because, the assessment context created by teachers not always makes salient to students that understanding is the goal at stake. The nature of the assessment task, the way assessment outcomes are provided to students, the amount of stress put on grades can make goals other than understanding more salient. When this occurs, such as when a teacher stresses the importance of assessment scores for goals extrinsic to understanding and significant learning -grades, competition among peers, etc.-, students tend to avoid the use of study strategies favouring conceptual elaboration and understanding, as many studies have shown (e.g. Alonso-Tapia & López, 1999; Blumenfeld, Puro & Mergendoller, 1992; Covington, 2000; Garner, 1990). As a consequence, in order for assessment to contribute to conceptual change, teachers should avoid messages and classroom practices stressing the relevance of assessment for goals extrinsic to learning and understanding (see Linnenbrink & Pintrich, this volume).

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PORTFOLIO ASSESSMENT AS AN INTEGRATED FRAMEWORK TO PROMOTE CONCEPTUAL UNDERSTANDING

The assessment conditions favouring conceptual understanding are most effective if they take place in the context of an assessment process that integrates assessment and instruction, such as portfolio assessment in the context of project-oriented instruction (Duschl & Gitomer, 1997; Tierney, Carter, & Desai, 1991). This context increases the possibility of helping students to become aware of the relevance and benefits of trying to understand and of using learning strategies that favour conceptual change. However, the term portfolio has been referred to as a “chameleon”, as there are different ideas of how portfolio assessment should be contextualised and carried out (e.g. Calfee & Perfumo, 1996; Underwood, 1998). An example, taken from one of our most recent works (Alonso-Tapia, Asensio, & López, 2000b), that illustrates our conception is introduced in the Appendix. As can be seen in this example, portfolio assessment in the context of project-oriented instruction has several characteristics that increase the likelihood of conceptual change. First, the project itself that constitutes the context for assessment derives from the need to solve a problem through the active construction of a mental representation that must be firmly based on reasons linking available information to conclusions. There is no single answer to the problem. Thus, the need to “build a case” acts as a driving force for understanding and conceptual change. Second, the discussion of initial representations creates the context for a “cognitive conflict” that forces the student’s initial self-assessment of his/her own ideas against the pattern provided by the explanations of his/her classmates. Third, the projects are not carried out without instructions. On one hand, students have a guide (as shown in the Appendix) designed to promote reflection and self-regulation. On the other, instructions and tasks provide a structure that allows teachers to assess more or less “on-line” students’ work and to give them accurate feedback. This can be carried out in a quite systematic way following guidelines similar to those developed by Duschl and Gitomer (1997) for the assessment conversation in science classrooms. These guidelines state the type of question appropriate to ask at different points throughout the project, according to students’ specific difficulties. These questions help them to consider aspects of the problem that have been neglected or misinterpreted, and thus to improve their conceptual understanding. Fourth, the structure of the portfolio, the stress put on self-assessment and feedback from peers, as well as on retaining original pieces of work and those improved through reflection (see Appendix, step 4, points 1 and 2) help to make students aware of the way they represent reality and how these representations change. This contributes to wide and deepen their conceptual understanding.

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Fifth, even if students have to be graded, several aspects make salient the progressive nature of conceptual development. These aspects are: 1) the need to include in the showcase portfolio examples of the different tasks carried out in the course of the project; 2) the fact that students have to consider why such pieces of work best reflect the correct conceptualisation of causality in relation to the problem stated; 3) the fact that students are graded in relation to a progressive profile of skills (e.g. drawing inferences from texts, tables or graphs and establishing causal explanations), and 4) the fact that students discuss with the teacher the objectives on which they should concentrate in future project work. 5.

A WORD ON TEACHERS’ ASSESSMENT

A final, but not less important question is: how do teachers actually assess their students’ knowledge? Results from three recent studies (Villa & Alonso-Tapia, 1996; Alonso-Tapia & López, 1999; Alonso-Tapia, 1999) have shown that secondary, high school and university teachers employed assessment procedures far from adequate for fostering understanding, conceptual change and self-regulation. Especially throughout secondary education assessment tasks do not have the above mentioned characteristics. For example, 68% of assessment tasks in social sciences imply rote learning. In other cases, such as those of math and physics, more than 70% of the tasks and questions students have to deal with are “exercises”, which are not the same as “problems”. Exercises require algorithmic knowledge, whereas problem-solving implies using knowledge for constructing a representation of the problem and planning the solution process (Villa & Alonso-Tapia, 1996). Even more importantly, many teachers believe that their tasks assess conceptual understanding, when in fact such questions assess knowledge learned by rote (Alonso-Tapia, Asensio, & López, 2000c). In other cases, the problem stems from the remaining assessment conditions: the extent to which assessment goals are made salient by teachers, the frequency and distribution of assessment tasks, the amount of time available for performing them, and the frequency and kind of feedback given to students. To sum up, if we wish to improve conceptual understanding and to foster conceptual change, we should concentrate on changing the whole assessment practices instead of simply focusing our attention only on single particular aspects. 6.

IMPLICATIONS FOR FUTURE RESEARCH

As already said, there are many aspects of the assessment process that may directly or indirectly influence conceptual development. However, empirical research aimed at identifying the specific effects of assessment tasks and contexts on learning and understanding is scarce. As Calfee (1999-2000) has pointed out, assessment has undergone enormous development during the last decade. However, though this development includes many of the characteristics that, according to the ideas described above, can improve motivation, self-regulation, understanding and

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conceptual change, there is almost no empirical research devoted to identifying the conditions under which real assessment practices have the expected positive effects. Thus, let us point some problems to consider in the future research agenda. First, some difficulties for such studies derive from a lack of clarification of the task characteristics that may contribute to identify students’ sources of misunderstanding. Information conveying the meaning of concepts and theories is included in texts, graphs, tables, maps, diagrams, objects, drawings, etc., but understanding the information from these sources implies particular processes that pose specific problems for students. However, assessment design seems not to take into account this fact. It makes difficult to identify whether students’ answers show a lack of conceptual understanding or a lack of the required skills to process and integrate information from such sources (Alonso-Tapia, 1997). Second, in the case of portfolio assessment, teachers should ensure that the set of learning tasks covers the whole conceptual networks to be learned. Thus, it is possible to identify the type and coverage of students’ representations. However, and despite some exceptions (Marshall, 1993), there is a lack of systematic research on the structure of the set of tasks on which teachers base their assessment decisions, and on the effects of using these sets with regard to students’ understanding. Third, in order to identify the effects of portfolio assessment in the context of project-oriented learning, it is necessary to collect information on how the teaching process has been carried out. As Underwood (1998) has shown, portfolio assessment is not what it was intended to be, but what it really has been done. If teachers have in mind not the portfolio assessment system but traditional assessment tasks and procedures, then their teaching practices and assessment criteria will not lead students to understanding, but to performing in a predetermined way, regardless of whether they really understand or not. This last point is reinforced when the standard-setting assessment methods used by educational authorities correspond to the testing culture (Dochy, 2001), as these methods constitute a contextual factor that teachers and students have in mind while working. Thus, in order to determine the effects of portfolio assessment on understanding, researchers should also take into account the kind of context defined by standardsetting assessment practices. Finally, we should point out that research on the effects of assessment on understanding and conceptual change is important not only for practical purposes, but also for theoretical reasons. Studies on conceptual understanding and change often produce results that lack of ecological validity and that are not efficient to obtain students’ change. This is because research is often carried out in experimental, artificial contexts, but also because even if experimental tasks are ecologically valid, students face them with strategies and attitudes shaped by teaching and assessment practices that do not develop their appropriate motivational patterns. Thus, it is necessary to investigate the effects of real assessment practices in order to clarify what factors and conditions affect knowledge construction and revision.

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APPENDIX Example of portfolio assessment design in the context of project oriented instruction in the social sciences (Alonso-Tapia, Asensio, & López, 2000b).

STEPS First step: Activation of learning motivation by means of problems than can be solved following different paths. At the beginning of the term, the teacher explains the meaning of the work to be carried out and shows how this work can help students’ personal development. To achieve this purpose, he/she introduces a problem that can help to arouse pupils’ curiosity and to show the relevance of achieving the learning objectives. “Before we start work, let me tell you the story of Alan, Eve, Barbara and Paul. They are more or less the same age as you. They are worried because their families are poor, they come from poor towns, and they would like to be better off. One day they get together and discuss why things are the way they are and what can be done to improve them. Alan thinks the problem is that those in charge are unfair, that they burden people with taxes and don’t try to help them. He thinks new people should be in power. Eve thinks differently. She thinks the problem is that there are no industries in the town; if there were, things would be different. So she asks herself what could be done to create industry in the town. Barbara has a still different view. She says that there are too many people in the town. There are not enough resources for everyone, and if some people left and went to other places, there would be more opportunities. She wonders what could be done to encourage emigration. Paul, meanwhile, thinks the problem is that the poor are not united, and that if they were they could change a lot of things. He asks himself how they could be brought together. What do you think? Which of the four is right, and why?”

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The teacher leaves the pupils some time to express and discuss their opinions in order to discover the mental representations underlying them. Then he goes on: “The problem of Alan, Eve, Barbara and Paul could be your problem. Whether we are rich or poor, we all want to improve. But to do so, we have to know which is the best way. Would you like to know who’s right and why? Well, if you really want to, you can, but you ’II have to do some investigation. Where? In the past. How? By looking for information that allows you to answer the questions included in each one of the following projects. You can carry out the projects in whatever order you like. I will provide different cues to guide you in your work”. Second step: Presentation of alternative work projects. Project 1. Sometimes, in the past, there have been periods in which many people emigrated from one place to another. It happened, for example, when America was discovered and colonised or later, when the American west and Australia were also colonised. What motivated these people to emigrate? What conditions facilitated emigration? Who emigrated? What consequences did emigration have? Did emigration improve the way people lived, or not? Why? What lessons can we learn from what happened then? Would emigration have the same consequences today as in that era, or not? Why? Project 2. Throughout the and centuries some countries, the first of which was Great Britain, industrialized rapidly. What caused such rapid industrialization? Did industrialization improve the way people lived, or not? Why? What lessons can we learn from what happened then? Would the industrialization of a country or region have the same consequences today as it had in the past or not? Why? Project 3. Sometimes in the course of History –for example, at the times of the American, the French or the Russian Revolution- the political system of a country changed drastically for the better: the new system was fairer, at least in theory. What factors caused such changes? Did those political transformations improve the way people lived, or not? Why? What lessons can we learn from what happened then? Would a political revolution have the same consequences today as it had in the past, or not? Why? Project 4. In the course of History poor people, especially those belonging to the working class, have united to defend their rights and to try to free themselves from poverty. This happened, for example, when the Trades Union Movement developed in the century. What factors gave rise to this movement? ? Did the movement improve the way people lived, or not? Why? What lessons can we learn from what happened then? Would a social movement like that have the same consequences today as it had in the past or not? Why? “The idea is that each one of you (the task could also be assigned to small groups of students) starts one of the previous projects, explaining and justifying his/her conclusions as the work progresses. Why? What are you going to learn and achieve through this? What will it be useful for? And how are we going to organise the work?” Third step: Clarifying objectives and procedures for carrying out the projects. “This project work has several objectives. First, it will help you to answer the questions included in each project and, therefore, to solve the initial problem. Second, it will also help you to think for yourselves, to improve the quality of your reasoning and to learn criteria that will allow you to decide in an informed way”.

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“Your work on the projects will involve obtaining, analysing and organising information about the problem from different sources -texts, graphs, tables, pictures, maps, objects, and so on. And you ’ll have to do this properly so that you don’t make mistakes in your inferences or reach the wrong conclusions. You ’ll have to take into account important factors, such as the historical moment and conditions, how long things took to develop, to change or to happen, and so on”. “How am Igoing to help you? First, I'll give you a work-guide". (Included below). “ And, more importantly, I'm going to teach you how to look for information and how to analyse and organise it properly. Together, we'll analyse the way you reason and argue in favour of or against different hypotheses to see whether they can be backed up or not”.

Forth step: Assessment. First of all, the teacher explains how to organise the portfolio that will constitute the information base for assessing the students' work. “As you know, your work will be assessed. But, the most important point while you're working is to do “your” project, to work “for your own benefit”. So, if this is the aim of the task why assessment? How is the work going to be assessed? Assessment will be, in first place, selfassessment aimed at monitoring and self-regulating your work. Every day you will have to put your work, correctly dated and classified, in a folder: copies of texts, graphs, tables and other documents examined and analysed, with your interpretations and comments attached, as well as your classmates’ comments or those that you have received from me. This will be your portfolio. You will also have to include a weekly summary, including the answers you can give so far to the questions stated”. Second, the teacher introduces the idea and the context for self-assessment and explains its meaning and the criteria for carrying it out “We are going to see, in the course of our classes, how to interpret different kinds of document. will give you procedures and criteria for analysis and interpretation, and, you will have to make regular self-assessments of your work using these criteria. These selfassessments will also have to be included in the portfolio, but without taking out the original piece of work. This will help you to check your progress, to know what you have had to change and to understand why”.

Third, the teacher explains the process of assessment for grading. “When it comes to assessment for giving grades, you will choose from your portfolio the pieces of your work - always correctly dated- that, from your point of view, best reflect your progress. When you make this selection , though, you must include pieces that represent each one of the kinds of element necessary to give a representation of your progress. For example, essays with your answer to the problems supported by arguments; tables, graphs, historical maps and other documents analysed and interpreted; reasoned answers to the hypothetical problems posed in the course of the work, and so on. You will have to say why you consider them appropriate and I will tell you the aspects that should be reconsidered and why. Then we will discuss the goals for the next project”.

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SPECIFIC WORK-GUIDE FOR DEVELOPING THE PORTFOLIO

General rules Include all your documents and comments always correctly dated and identified with your name. If you modify your point of view about a document, do not throw your initial comment away: comparison of the two comments will help you to be aware of your progress. A) Texts If you include a text in your portfolio, it would be appropriate to ask yourself the following questions and to include your reflections when trying to answer them: Do I understand all the words and concepts in the text? What is the main idea the author is trying to convey? Why do I think so? What was the author’s purpose when writing the text? Why do I think so? What has the information in the text to do with the questions I am trying to answer? Why do I think so? What kinds of comment have I received from my classmates about my point of view? Do I agree with them or not? Why? B) Graphs, tables and maps If you include a graph, a table or a map in your portfolio, it would be appropriate to ask yourself the following questions and to include your reflections when trying to answer them: Do I understand all data included in this document? What is the main information the author is trying to convey? Why do I think so? What was the author’s purpose when developing the document? Why do I think so? What has the information in the document to do with the questions I am trying to answer? Why do I think so? What kinds of comment have I received from my classmates about my point of view? Do I agree with them or not? Why? C) Non-written documents If you include references to non-written documents that were produced without the intention of communicating any information, it would be appropriate to ask yourself the following questions and to include your reflections when trying to answer them: What questions have I asked myself in order to identify the information they can potentially reveal about the socio-economic context in which they were produced? Have I missed anything important? What is the most important information this document is conveying in relation to the problem I am trying to solve? Why do I think so? What kinds of comment have I received from my classmates about my point of view? Do I agree with them or not? Why?

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D) Comparison and integration of information coming from different sources In order to solve the problem you are dealing with, you will probably have to relate different kinds of documents and try to integrate different pieces of information. If you have established such relationships, it would be convenient to ask yourself the following questions and to include your reflections when trying to answer them: Before integrating the documents, have I asked myself the following questions on each one of them considered in isolation? Do I understand all the data included in this document? What is the main information the author is trying to convey? Why do I think so? What was the author’s purpose when developing the document? Why do I think so? What has the information in the document to do with the questions I am trying to answer? Why do I think so? When integrating the information: Do the documents I am comparing have anything in common? Why do I think so? Do the kinds of information included in them coincide with, complement or contradict one another? Why do I think so? What kinds of comment have I received from my classmates about my point of view? Do I agree with them or not? Why? E) Solving prediction problems presented by the teacher (see Table 1) Have I considered all possibilities before choosing my answer? What kinds of comment have I received from my classmates about the way I have justified my point of view? Do I agree with them or not? Why? F) Essay showing your point of view on the problem From time to time throughout the project you will have to summarise your point of view on the problem you are trying to solve. In doing so, you will have to point out which factors can be considered as causes –direct or indirect- of phenomena like the one you have studied, what were the immediate and remote consequences, and whether it would be sensible for people to act in the same way today. In relation to these summaries, it would be appropriate to ask yourself the following questions and to include your reflections when trying to answer them: Questions referring to the writing process: What strategies have I used to decide what to say? Does my portfolio include drafts, schemes or products deriving from “brainstorms”? What questions have I asked myself to organise the text? Have I considered the purpose of my essay and the readers’ needs? How have I organised the argument –what are the premises and the conclusion? Have I made my point of view and my premises explicit enough? What have I done to lead my teacher and classmates to my own conclusions? Have I considered potential arguments against my point of view and accepted them (as far as possible)? Have I revised the written text? What criteria have I used? Questions referring to content: Have I articulated my point of view well enough? Why do I think so? What kinds of comment have I received from my classmates about my point of view? Do I agree with them or not? Why?

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GUIDE FOR PREPARING THE SHOW-CASE PORTFOLIO You have to prepare your show-case portfolio including the elements from your folder which, in your view, best show what you have understood and the abilities you have acquired. You should choose at least one element for each entry in the following assessment profile. Think about them before coming to the assessment session. Then we will discuss each element and set objectives for the future.

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CHANGE AS A PROCESS AND A DISPOSITION: A COMMENTARY

PIETRO BOSCOLO University of Padova, Italy

Abstract. The chapters of the section are considered and grouped according to two perspectives or dimensions: the object of change and the types of instructional interventions adopted or proposed. A dual view of change emerges; change as a process (conceptual change stricto sensu) and as a disposition (conceptual understanding). The instructional strategies aimed at facilitating change are viewed according to this dual perspective.

1. INTRODUCTION In any section of an edited book, strong similarities are usually expected between chapters, in that the various contributions should deal with a specific problem viewed from different but complementary perspectives. Thus, the relationship between similarities and differences is a matter of complementarity, something like a variation on a theme. If similarities are too pronounced – for instance, if all the chapters present a problem from the same perspective – the result risks boring the reader. If, instead, the differences are too pronounced – that is, if the common theme of the chapters provides only a weak connection between quite different perspectives and objectives – the result may be somewhat disappointing. This section exemplifies a third alternative. After reading the chapters of this section, it seems to me that two main underlying dimensions emerge. The first regards the object of change, the second the type of instructional intervention aimed at stimulating or facilitating it. Similarities and differences between the chapters lie along these two dimensions. Similarities – obviously excluding the common focus on instructional aspects – are not common to all the chapters, which, according to the first dimension, could be grouped into two sub-chapters: one regarding conceptual change (Wiser and Amin, and Mikkilä-Erdmann), and the other regarding conceptual understanding (Alonso-Tapia and Mason). This quite unusual (or less usual) relationship between similarity and difference in the section is welcome to a commenter, who does not feel constrained by too strong a framework, nor, alternatively, frustrated by lack of one. The clustering of the chapters has a stimulating effect, in that it may facilitate a different way of analysing the problem of conceptual change, or at least some aspects of it. The present commentary has two objectives. The first is to analyse the distinction conceptual change/conceptual understanding. The second is to discuss the instructional strategies adopted or proposed in the chapters to promote change. M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change. Issues in Theory and Practice, 415-419. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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Wiser and Amin’s study describes and explains how some students were taught some elements of thermal physics. The authors call their approach “twolanguage/integration”, in that conceptual change in a domain (in this case, thermal physics) involves a change in the relationship between the everyday concept and the scientific concept of a phenomenon (in this case, heat and heating). From this perspective, successful learning depends on the integration, not replacement, of the two conceptualisations, that is, the “naïve” with the scientific. As the authors point out, “the everyday conceptualisation continues to be held alongside the scientific one, with a restructured content”. Correct learning is obtained by use of computer models and metaconceptual teaching, aimed at making the students aware of the multiplicity of meanings of a word, and the differences between perception-based and scientific explanations. This study, focusing on the progressive restructuring of a physics concept misinterpreted in everyday experience, can be viewed as a prototypical example of the studies on conceptual change. Mikkilä-Erdmann’s study is somewhat less prototypical. It analyses the role of text in elementary school students’ learning of photosynthesis. In this study there is also an example of metaconceptual teaching, which is not based on the guided observation of a phenomenon or performed by a teacher’s scaffolding, as in Wiser and Amin’s study, but on the information conveyed by a written text plus “text units” (questions and statements) inserted in it. This study does not focus on the leaning of a scientific concept, but on the building of a mental model. This distinction is not only a matter of the different use of terminology, justified by different theoretical frameworks (mainly literature on conceptual change in the former chapter, and learning from text in the latter). It also implies a different methodological approach. Whereas Wiser and Amin adopt a microgenetic method, in Mikkilä-Erdmann’s chapter change is inferred from pre- and post-test differences in participants’ performance in text comprehension and generative questions. Analysis of data is quantitative, and the author is aware (see discussion in her chapter) that a qualitative one focusing on the process(es) of change, would also be necessary. Before considering the other two chapters, I wish to make some bibliographical comments on those just considered. In Wiser’s and Amin’s study, Vygotsky’s influence is evident although none of his works appear in the references. The authors use a microgenetic method, and the examples of teacher-learner interactions they report clearly exemplify scaffolding, which perhaps is not a Vygotskian metaphor, but certainly expresses a basic aspect of the Vygotskian approach to learning. This absence is surprising if we consider that in Thinking and speech (1934/1987) Vygotsky wrote masterly pages on the relationship between spontaneous and scientific concepts. About 40 years later, Nelson (1977) criticized the “historical” theories of cognitive development – the Piagetian and the Vygotskian – tending towards conceptualising cognitive development as the progressive disappearance of experiential knowledge, related to personal experience in specific domains, and replaced by categorical, formal knowledge acquired through schooling. Nelson (1977) argued that in an adult’s knowledge experience and formal knowledge co-

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exist; she gave the example of the concept of bear, conceptualised as a zoo animal by a child, and as a plantigrad with defined characteristics by an adult. The basic difference between the child and adult’s concepts of bear is that an adult – at least, a schooled one – possesses both types of knowledge. Nelson’s criticism was only partially legitimate, at least regarding Vygotsky. Of course, Vygotsky’s concern was not with conceptual change, but with the teaching/learning of “scientific” concepts, that is the concepts children learn in school, not only in the scientific domain. Perhaps, in his enthusiastic enterprise of renewing instructional methods for a new society, he could not admit the existence of “incorrect” school learning and was optimistically convinced that instruction would give the “best” concepts in the various subjects. However, his long discussion on how spontaneous (everyday) concepts prepare “from the bottom” the ground for the learning of the scientific concepts, and how this learning helps students organise the spontaneous ones better, was, and still is illuminating. In Mikkilä-Erdmann’s chapter, the missing reference is pre-vygotskian. The use of metaconceptual text units reminds the mathemagenic function of adjunct questions, that is questions included in instructional texts to stimulate the reader’s review or inspection behaviour (e.g., Rothkopf, 1966). The fortune of this instructional strategy as a research topic has decreased in recent years, also due to the contradictory results of empirical studies, although questions are always being extensively used in instructional practice. Mikkilä-Erdmann’s study proposes written questions as a tool for promoting conceptual change: a tool whose validity, in my opinion, deserves to be analysed through a design in which the effects of text structure and metaconceptual questions are kept distinct. Coming to the second sub-section, in Alonso-Tapia’s and Mason’s chapters the expression “conceptual change” seems to be used in a general meaning, as a synonym for conceptual understanding, and the authors’ concern is with the instructional conditions which may facilitate or hinder it. Mikkilä-Erdmann also assimilates change to “deep understanding” in the discussion of her chapter, but her focus is definitely on the change of specific misconceptions. Alonso-Tapia’s explicit focus is on conceptual understanding, and in his view assessment is a teacher’s major tool for favouring it. His examples of assessment, aimed at positively affecting student understanding (analogous and transfer tasks, explicit goals, use of portfolio, etc.) show that assessment is given the function of “organiser” rather than “synthesizer” of knowledge acquisition. Its objective is essentially to prepare the ground for active, reflective, and participative learning, rather than to check its amount and/or quality. The overlapping of conceptual change and understanding is less explicit in Mason’s chapter. Her main concern is with epistemological beliefs, the representations students construct on the nature and acquisition of knowledge. She argues that epistemological beliefs may be either a resource for learning, if a student views knowledge as a dynamic organisation, or an obstacle, if his/her view of knowledge is rigid. In Mason’s view, beliefs act as thinking dispositions, which may contribute, according to their levels of rigidity/flexibility, to developing or hindering students’ awareness of the need to revise their own knowledge. Thus, the author assumes that changing a rigid disposition should have a facilitating effect on

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promoting conceptual change. This assumption, supported by some examples from empirical research, seems to be plausible, although it has to be verified. Thus, both Alonso-Tapia and Mason seem to make, although to differing degrees, the meaning of conceptual change overlap with conceptual (deep) understanding not only in the scientific but also in other domains. Early studies on conceptual change flourished in the fields of research on cognitive development and science education, with an emphasis on how children’s “theories” change and are dismissed or integrated in their development (Dole & Sinatra, 1998). A shifting emphasis from conceptual change to understanding, that is, from a view of change as a process to change as a disposition, seems to bear important consequences for both educational practice, on the one hand, and research and theoretical reflection, on the other. From an educational perspective, which is the focus of this section, the problem of conceptual change is then not only how to help students modify their limited or incorrect knowledge and beliefs. The more general problem is how to help them deal with the multiple occasions on which instruction provides them with “difficult” explanations: difficult because they contrast with everyday experience, or superficial prior knowledge, or the effects of students’ inadequate “socialization to learn”. Regarding research, “understanding” is a “heavy” word, not as neutral as “change”, since its meaning does not only involve cognitive but also motivational components; not only ability, but also intentionality to learn. Investigating the ways students of different school levels approach learning is a major goal for educational research, as the recent focus on intentional and motivational aspects of conceptual change has already demonstrated (Linnenbrink & Pintrich, in press; Pintrich, Marx, & Boyle, 1993). Moreover, including the concept of change in the wider one of understanding means conceptualising a “discontinuous” model of learning, one in which the construction of knowledge implies recurrent restructuring. This would require a variety of instructional strategies, aimed not only at making students acquire new concepts, but also monitoring the quality of those they already possess. Regarding this aspect, I will now briefly consider the second dimension: the degree of structure in the instructional strategies adopted or suggested for promoting conceptual change and understanding. 3. INSTRUCTIONAL STRATEGIES TO PROMOTE CHANGE: A MATTER OF STRUCTURE? In Wiser and Amin’s study the change process is activated by computer models and stimulated by verbal interaction in which the teacher has a scaffolding role, whereas in Mikkilä-Erdmann’s study written questions and statements as well as the text content guide the learner to the “right” concept or theory. As Wiser and Amin’s chapter clearly shows, scaffolding is a very structured method, by which the learner is lead step by step towards recognising the limitations of his/her conceptualisation of a phenomenon and the correctness of an alternative explanation. MikkiläErdmann uses no scaffolding, but the objective of metaconceptual units is quite clear: guiding the reader to changing his/her knowledge about photosynthesis.

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In Alonso-Tapia and Mason’s chapters, several strategies are suggested, including authentic tasks, problem solving, collaborative discussion, portfolio, community of learners: in a word, a constructivist pedagogy. Thus, the two underlying dimensions considered in this commentary – the object of change and the type of instructional intervention – substantially converge towards a same grouping of the chapters: conceptual change is obtained by more structured strategies, whereas conceptual understanding seems to require a less directive instructional method. This distinction seems to suggest that to change a concept – making it a “scientific” one – scaffolding may be the most appropriate strategy if combined with guided observation or, at least, written description of the phenomenon. This means “pushing up” a learner’s zone of proximal development by helping him/her to reorganise the fuzzy boundaries of everyday knowledge and beliefs. Instead, to change more general beliefs, such as those many children and adults share on the nature of knowledge and knowing, the learners should be provided with the conditions for constructing – that is, assimilating, negotiating, and progressively tuning and reshaping - knowledge in individual and collaborative situations. Analysing through empirical studies how the two types of strategies interact, and with what instructional outcomes, could be an interesting agenda for future research on conceptual change and understanding. REFERENCES Dole, J. A., & Sinatra, G. M. (1998). Reconceptualizing change in the cognitive construction of knowledge. Educational Psychologist, 33, 109-128. Linnenbrink, E. A., & Pintrich, P. R. (in press). The role of motivation in intentional learning. In G. M. Sinatra, & P. R. Pintrich (Eds.), Intentional conceptual change. Mahwah, NJ: Lawrence Erlbaum Associates. Nelson, K. (1977). Cognitive development and the acquisition of concepts. In R. C. Anderson, R. J. Spiro, & W. E. Montague (Eds.), Schooling and the acquisition of knowledge. Hillsdale, NJ. Lawrence Erlbaum Associates. Pintrich, P. R., Mark, R. W., & Boyle, R. (1993). Beyond cold conceptual change: The role of motivational beliefs and classroom contextual factors in the process of conceptual change. Review of Educational Research, 63, 167-199. Rothkopf, E. Z. (1966). Learning from written materials: An exploration of the control of inspection behavior by test-like events. American Educational Research Journal, 3, 241-249. Vygotsky, L. S. (1987). Thinking and speech (N. Minick, Trans.). New York & London: Plenum Press. (Original work published 1934)