Instructional psychology: past, present, and future trends: Sixteen essays in honour of Erik de Corte (Advances in Learning and Instruction)

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INSTRUCTIONAL PSYCHOLOGY: PAST, PRESENT, AND FUTURE TRENDS SIXTEEN ESSAYS IN HONOUR OF ERIK DE CORTE

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ADVANCES IN LEARNING AND INSTRUCTION SERIES Series Editors: K. Littleton, C. P. Constantinou, L. Mason, W.-M. Roth and R. Wegerif Further details: www.elseviersocialsciences.com Published VAN SOMEREN, REIMANN, BOSHUIZEN & DE JONG Learning with Multiple Representations DILLENBOURG Collaborative Learning: Cognitive and Computational Approaches BLISS, SÄLJÖ & LIGHT Learning Sites: Social and Technological Resources for Learning BROMME & STAHL Writing Hypertext and Learning: Conceptual and Empirical Approaches KAYSER & VOSNIADOU Modelling Changes in Understanding SCHNOTZ, VOSNIADOU & CARRETERO New Perspectives on Conceptual Change SMITH Reasoning by Mathematical Induction in Children’s Arithmetic KOZULIN & RAND Experience of Mediated Learning ROUET, LEVONEN & BIARDEAU Multimedia Learning: Cognitive and Instructional Issues GARRISON & ARCHER A Transactional Perspective on Teaching and Learning COWIE & AALSVOORT Social Interaction in Learning and Instruction VOLET & JÄRVELÄ Motivation in Learning Contexts TERTTU TUOMI-GRÖHN & YRJÖ ENGESTRÖM Between School and Work – New Perspectives on Transfer and Boundary-Crossing DE CORTE, VERSCHAFFEL, ENTWISTLE & MERRIËNBOER Powerful Learning Environments: Unravelling Basic Components and Dimensions HAKKARAINEN, PALONEN, PAAVOLA & LEHTINEN Communities of Networked Expertise: Professional and Educational Perspectives Related journals — sample copies available online from: http://www.elsevier.com Learning and Instruction International Journal of Educational Research Computers and Education The Internet and Higher Education Early Childhood Research Quarterly

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INSTRUCTIONAL PSYCHOLOGY: PAST, PRESENT, AND FUTURE TRENDS SIXTEEN ESSAYS IN HONOUR OF ERIK DE CORTE EDITED BY

LIEVEN VERSCHAFFEL FILIP DOCHY MONIQUE BOEKAERTS STELLA VOSNIADOU

Published in Association with the European Association for Learning and Instruction

Amsterdam ● Boston ● Heidelberg ● London ● New York ● Oxford Paris ● San Diego ● San Francisco ● Singapore ● Sydney ● Tokyo

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Elsevier The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands First edition 2006 Copyright © 2006 Elsevier Ltd. All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN-13: ISBN-10:

978-0-08-045021-6 0-08-045021-0

For information on all Elsevier publications visit our website at books.elsevier.com

Printed and bound in The Netherlands 06 07 08 09 10 10 9 8 7 6 5 4 3 2 1

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Editor-in-Chief K. Littleton, Centre for Childhood Development and Learning, Open University, MK7 6AA, UK. E-mail: [email protected]

Editorial Board P. Boscolo, University of Padova, Italy. E. De Corte, University of Leuven, Belgium. W-M Roth, University of Victoria, British Columbia, Canada. Publisher’s Liaison R. Wegerif, Open University, UK.

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Contents

Preface

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Prof. dr. dr. h. c. Erik De Corte: A Biographical Sketch

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Introduction Filip Dochy, Lieven Verschaffel, Monique Boekaerts, and Stella Vosniadou

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Part I: Learning and Development 1. Curriculum, Pedagogy, and Learning in Early Childhood: Sites for Struggle — Sites for Progress Elizabeth Wood and Neville Bennett

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2. Mathematics in the Mind: Architecture, Development, and Educational Implications Andreas Demetriou and Areti Panaoura

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3. Attentional Processes, Abstraction, and Transfer in Early Mathematical Development Erno Lehtinen and Minna M. Hannula

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4. Examining Mathematics Learning From a Conceptual Change Point of View: Implications for the Design of Learning Environments Stella Vosniadou and Xenia Vamvakoussi

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Part II: Learning, Reasoning, and Problem Solving 5. Reasoning with Mental Tools and Physical Artefacts in Everyday Problem-Solving Roger Säljö, Ann-Charlotte Eklund, and Åsa Mäkitalo

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6. Modelling for Life: Developing Adaptive Expertise in Mathematical Modelling From an Early Age Wim Van Dooren, Lieven Verschaffel, Brian Greer, and Dirk De Bock

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PART III: Motivational and Emotional Aspects of Learning 7. Motivated Learning: What Is it and How Can it Be Enhanced? Monique Boekaerts and Rob Martens

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8. Student Learning in Context: Understanding the Phenomenon and the Person Noel Entwistle, Velda McCune, and Max Scheja

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9. The ‘Unhappy Moralist’ Effect: Emotional Conflicts between Being Good and Being Successful Fritz Oser, Evi Schmid, and Lisa Hattersley

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Part IV: Learning and Assessment 10. Educational Assessment: Towards Better Alignment Between Theory and Practice James W. Pellegrino and Daniel T. Hickey 11. Learning and the Emerging New Assessment Culture Filip Dochy, David Gijbels, and Mien Segers

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Part V: Learning and Technology 12. The Difficult Marriage Between Education and Technology: Is the Marriage Doomed? Gavriel Salomon and Dani Ben-Zvi

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13. Computer Support for Collaborative Learning Environments Heinz Mandl, Bernhard Ertl, and Birgitta Kopp

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14. E-pedagogies for Networked Learning Robert-Jan Simons and Maarten de Laat

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Part VI: Instructional and Organizational Designs for Learning 15. From Individual Learning to Organizational Designs for Learning Lauren B. Resnick and James P. Spillane

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16. From Plato to Brown and Beyond: Theory, Practice, and the Promise of Design Experiments Denis C. Phillips and Jonathan R. Dolle

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Contributors

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Author Index

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Subject Index

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Preface

In 2006 Erik De Corte reached the age of 65 and, consequently, officially retired as a professor in educational psychology of the K.U. Leuven. Because the official retirement of a scholar of the prestige of Erik deserves special and international attention, we have taken the initiative to produce an international scholarly book titled “Sixteen Essays in Honour of Erik De Corte” to celebrate this important event. We invited all other presidents of the European Association for Research on Learning and Instruction (EARLI) — Neville Bennett, Monique Boekaerts, Filip Dochy, Noel Entwistle, Erno Lehtinen, Heinz Mandl, Roger Säljö, Robert-Jan Simons, and Stella Vosniadou — to contribute to this book, together with a number of other famous scholars with whom Erik had a long and strong scientific and personal liaison, namely Andreas Demetriou, Fritz Oser, Jim Pellegrino, Denis Phillips, Lauren Resnick, and Gabi Salomon. Finally, we also inserted in the book a contribution from Erik’s own Center for Instructional Psychology and Technology (CIP&T). Each of these 16 authors was invited to involve (at least) one promising young scholar as co-author, so that the book did not only have well-established senior researchers as authors, but also some of the most talented junior scholars in our research field. Furthermore, the authors were asked to write a review of “the past, present, and future” of the subdomain of instructional psychology of their particular interest and expertise, knowing that the combination of all these contributions would provide quite a good coverage of the research field of educational psychology. The authors were given the chance to focus on their own research (program), as long as it was used as an illustration of or a commentary on the more general theoretical and/or methodological developments within the subdomain being covered. We would like to thank the authors for accepting our invitation so enthusiastically to contribute to this book, for the exceptionally smooth cooperation during all stages of the production process, and for the high quality of their final products. We are quite confident that the book will not only please Erik, to whom this book is dedicated, but will also find its way to a large number of scholars throughout the world, and, in doing so, will help further shaping the field of research on learning and instruction. We also express our thanks to the editor-in-chief and the members of the editorial board of the EARLI Series “Advances in Learning and Instruction” for accepting this book for publication in this Series and for their encouragement and support during the whole production process.

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Furthermore, we thank Mrs. Karine Dens and Mrs. Betty Vanden Bavière, for their immense editorial assistance in the preparation of the final book manuscript and with respect to the correction of the galley proofs. Finally, we are also indebted to the European Association for Research on Learning and Instruction, to the Scientific Network on “Powerful learning environments” of the Fund for Scientific Research–Flanders, to the Center for Instructional Psychology and Technology of the K.U. Leuven, and to Elsevier, for their financial support that allowed us to organize a small-scale scientific meeting around this book on the occasion of Erik’s official retirement, in the ‘Huis of Chièvres’ of the University of Leuven, the location where, about twenty years ago, the first EARLI conference took place. Lieven Verschaffel Filip Dochy Monique Boekaerts Stella Vosniadou September 2006

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Prof. dr. dr. h. c. Erik De Corte: A Biographical Sketch Lieven Verschaffel and Filip Dochy

Although there is not yet the slightest indication that there will come a drop in his scientific and professional activities once he reaches the official age of retirement, i.e., 65, at the end of the academic year 2005–2006, there are many good reasons to use that milestone in the life of Erik De Corte as an opportunity to take a pause and to look back at his career. When reading the 16 chapters of this book on the past, the present, and the future of the research field of instructional psychology, which ‘his’ European Association for Research on Learning and Instruction (EARLI) dedicated to him on the occasion of his official retirement as a professor of the University of Leuven, it will become clear in how many subdomains of this scientific field Erik De Corte has played an active and influential role. The goal of this introductory chapter is to situate his most important scientific contributions in a short biographical sketch that deals with the major steps in his academic career and with his most important contributions to educational sciences and to educational policy and practice.1 1 Evidently, this short biographical sketch can address only the major highlights in the academic career of Erik De Corte and his major scientific and professional accomplishments on the international scene. A more detailed curriculum vitae and a list of publications since 1990 can be found on http://perswww.kuleuven.be/~u0004455/

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Erik was born on June 15, 1941 in Blankenberge, Belgium. He obtained his certificate as a primary school teacher in 1960, but before he got the chance to start this profession, he was strongly encouraged by one of his former teacher trainers to start university studies in educational sciences at the University of Leuven. Four years later, he obtained his master’s degree in educational sciences from the same university. After his military service, he got a five-year full-time junior fellowship of the Belgian National Fund for Scientific Research, which allowed him to obtain, in 1970, his doctor’s degree in educational sciences at the University of Leuven. His doctor’s thesis was a report of his main research during the preceding years, namely a theoretical and empirical study on the determination, classification, and evaluation of the cognitive objectives of mathematics education at the primary school level. Based on a systematic and critical review of the available taxonomies of educational objectives on the one hand, and a series of empirical investigations on the other, he proposed an alternative classification of cognitive objectives that became quite influential in the Dutch-speaking educational (research) community during the 1970s and 1980s. This early work brought him already some international recognition, especially through the translations in German (1975) and French (1979) of a handbook on instructional sciences entitled Beknopte didaxologie that he coauthored with some other young Belgian and Dutch educational researchers of that time and wherein his doctoral research occupied a prominent position (De Corte, Geerligs, Lagerweij, Peters, & Vandenberghe, 1974, 1975, 1979). A recent description in English of Erik De Corte’s classification of educational objectives and a comparison with a revised version of Bloom’s taxonomy of educational objectives can be found in Anderson and Krathwohl (2001). Very shortly after he got his Ph.D., he was appointed as lecturer, in 1972 associate professor, and in 1976 professor of educational psychology, in the Faculty of Psychology and Educational Sciences of the University of Leuven. From 1971 until his retirement in 2006, he was mainly in charge of the courses in educational psychology for the students in educational sciences and psychology as well as for students in the teacher-training programs of other faculties. During the 1970s, his research interest shifted from the determination, classification, and evaluation of educational objectives to the study of the cognitive processes and structures underlying cognitive objectives, and to the learning and teaching processes that are necessary to attain those objectives (De Corte, 1980). This new interest led to the foundation, around 1980, of the Center of Instructional Psychology that, after a fusion with Joost Lowyck’s Center of Instructional Technology in 1990, became the Center for Instructional Psychology and Technology (CIP&T). Initially, his research and teaching in this domain were heavily influenced by the work of West-European and Russian (educational) psychologists such as Vygotsky, Davydov, Gal’perin, Selz, Kohnstam, and Van Parreren. However, as a result of several visits in the late 1970s to leading research centers in the U.S. (such as the Learning Research and Development Center (LRDC) in Pittsburgh directed by Robert Glaser and Lauren Resnick, and the School of Education of Stanford University where he met with other leading scholars like the late Richard Snow, Nate Gage, and Elliot Eisner), the dominant theoretical framework underlying both his research and teaching gradually became more and more influenced by other theories, especially the information-processing approach and, later,

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socio-constructivism. Rather than identifying himself with one single theoretical approach, Erik has always shown an openness to, and a penchant for, comparing and synthesising different theoretical perspectives. From such a theoretical framework, he has been working — and is still working — on numerous research projects, the most extensive one being the analysis and improvement of mathematical problem solving in elementary school children. Having started with symbolically presented addition and subtraction problems (e.g. De Corte & Verschaffel, 1981), his research interest moved towards elementary addition and subtraction word problems (e.g. De Corte & Verschaffel, 1985, 1987; De Corte, Verschaffel, & De Win, 1985) and, later on, to word problems about multiplication and division (e.g. De Corte, Verschaffel, & Van Coillie, 1988; De Corte & Verschaffel, 1996). In line with his broad-spectrum view on research methodology, these studies used a wide variety of data-gathering and data-analysis techniques, ranging from achievement tests over detailed quantitative analyses of children’s eye movements while reading and solving word problems (e.g. De Corte, Verschaffel, & Pauwels, 1990; Verschaffel, De Corte, & Pauwels, 1992) to semi-structured individual interviews with children (e.g. De Corte & Verschaffel, 1985, 1987) and design experiments in ecologically valid settings (e.g. Verschaffel & De Corte, 1997; Verschaffel, De Corte, Lasure, Van Vaerenbergh, Bogaerts, & Ratinckx, 1999). Whereas initially the research focus was on the roles of cognitive variables and mechanisms in children’s word problem solving, later studies took more and more into account the influence of the affective and socio-cultural context, as evidenced, e.g. in the influence of emotions, attitudes, and beliefs on children’s solution processes (e.g. De Corte, Op ’t Eynde, & Verschaffel, 2002; Op ’t Eynde, De Corte, & Verschaffel, 2001, 2002) and the impact of the mathematics classroom culture and practice (e.g. Depaepe, De Corte, & Verschaffel, 2006; Verschaffel, De Corte, & Borghart, 1997; Verschaffel, De Corte, & Lasure, 1994; Verschaffel, Greer, & De Corte, 2000) on children’s word problem-solving endeavors. Besides this major line of research, Erik was also involved in many other projects dealing with math-related topics such as computer simulation as a tool in studying teachers’ cognitive activities during error diagnosis in arithmetic (e.g. De Corte, Verschaffel, & Schrooten, 1991), cognitive effects of programming in Logo (e.g. De Corte, Verschaffel, & Schrooten, 1992; De Corte, Verschaffel, Schrooten, Olivié, & Vansina, 1993), strategic aspects of children’s numerosity judgement (Luwel, Verschaffel, Onghena, & De Corte, 2001, 2003), assessment instruments for the large-scale evaluation of new standards for mathematics education in the elementary school (e.g. Janssens, De Corte, Verschaffel, Knoors, & Colémont, 2002), and comparing mathematics education practices and cultures in several European countries (e.g. Depaepe, De Corte, Op ’t Eynde, & Verschaffel, 2005). Moreover, he acted as the (co-)supervisor of several other projects that were not (directly) related to mathematics education, such as analysis of cognitive processes in teaching behaviour (e.g. De Corte & Lowyck, 1983), the role of test expectations on study time and test performance (e.g. d’Ydewalle, Degryse, & De Corte, 1981; d’Ydewalle, Swerts, & De Corte, 1983), the role of test item format on students’ problem-solving strategies and performances (e.g. Dochy, Moerkerke, De Corte, & Segers, 2001), analysing and improving text comprehension strategies in upper elementary school children (e.g. De Corte, Verschaffel, & Van de Ven, 2001), and designing and assessing a powerful learning environment for self-regulated learning among university students (e.g. Masui & De Corte, 1999, 2005).

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Besides this involvement in a large number of particular research projects, Erik has, from the very beginning of his career, been very active in publication activities of a more general nature, wherein he has striven to synthesise, review, and critically discuss the developments in the research fields of educational psychology and mathematics education as a whole. He has pursued this integrative activity as author of state-of-the-art papers in leading international journals (e.g. De Corte, 1990, 1995, 2000, 2004; De Corte, Verschaffel, & Masui, 2004), as (co-)author of chapters in prestigious international handbooks (e.g. De Corte, 1996; De Corte, Greer, & Verschaffel, 1996; De Corte & Verschaffel, 2006; De Corte, Verschaffel, & Lowyck, 1996; Verschaffel & De Corte, 1996; Verschaffel, Greer, & De Corte, in press; Weinert & De Corte, 1996, 2001), as editor of special issues (e.g. De Corte, 1987, 1999), and of edited books (e.g. De Corte, 2003; De Corte, Linn, Mandl, & Verschaffel, 1992; De Corte, Lodewijks, Parmentier, & Span, 1987; De Corte, Verschaffel, Entwistle, & Van Merriënboer, 2003; Mandl, De Corte, Bennett, & Friederich, 1990; Verschaffel, De Corte, Kanselaar, & Valcke, 2005; Vosniadou, De Corte, & Mandl, 1994; Vosniadou, De Corte, Mandl, & Glaser, 1996). In this respect, we especially mention that he was the editor for the section “Instructional Psychology” of the International Encyclopedia of Education, second edition (Husén & Postlethwaite, 1994) and that he coedited (with the late Franz Weinert) the International Encyclopedia of Developmental and Instructional Psychology (De Corte & Weinert, 1996). Besides the above-mentioned research and publication activities, he has also been very active in joint research and development projects with scholars in Central and South America, Africa, and Asia. Since 1997, he has coordinated several projects relating to the innovation of mathematics education in Chilean elementary schools. Within the framework of the cooperation between the Republic of South Africa and the Flemish Ministry of Education, he acted from 1997 to 2003 as a promoter of seven consecutive research projects relating to different aspects of educational innovation in the new South Africa. Since 2003 he is the Flemish project leader of a research program on “Addressing the direct and indirect impact of HIV/AIDS on pre- and school-going children in South Africa”, which is part of a comprehensive, joint cooperative research program of the Flemish Interuniversity Council (VLIR) and the University of the Western Cape, South Africa. From 1995 to 2003, he coordinated a joint Ph.D. program in educational sciences of the Assumption University (Bangkok, Thailand) and the Faculty of Psychology and Educational Sciences of the University of Leuven. Erik De Corte has not only played a leading role in the research community through his quantitatively and qualitatively impressive list of scientific publications and research and development projects. He is equally and maybe even better known for his numerous and decisive contributions to the development, the organisation, and the professionalisation of the national, the European, and the worldwide community of researchers in the domain of learning and instruction, as evidenced in the following selective list of professional responsibilities. He was one of the founders — if not the founding father — of the European Association for Research on Learning and Instruction (EARLI), of which he was the first President (1985–1989). He was also the founding editor of the EARLI journal Learning and Instruction (1990–1993), and since 1997 he has been one of the associate editors of the EARLI book series ‘Advances in Learning and Instruction’. From 1994 until 1998 he was

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President of the Division on Educational, Instructional, and School Psychology of the International Association of Applied Psychology. He is a Fellow of the International Academy of Education (IAE) since 1997, and was elected in 1998 as President of this Academy for a three-year period, and subsequently reelected for the period 2001–2006. In an attempt to contribute to closing the gap between educational research and practice — another great concern of Erik throughout his whole career (e.g. De Corte, 2000; Weinert & De Corte, 1996, 2001) — he took, in his capacity of President of that Academy, the initiative, together with Herbert Walberg, to launch the IAE “Educational Practices Series”, a series of booklets, written by internationally wellknown experts and published and distributed by the International Bureau of Education (Geneva); the pocket format booklets provide for a broad audience of educational professionals timely syntheses of research on educational practices that generally improve learning and that are of wide international importance (see http://www.ibe.unesco.org). Recently, he initiated, together with Neville Postlethwaite, a parallel IAE “Educational Policy Series”, published and disseminated by the International Institute for Educational Planning (Paris) (see http://www.unesco.org/iiep/). In 1995 he was elected as a member of the Academia Europaea. He also is a member of the Royal Norwegian Society of Sciences and Letters, Class of Humanities. In 1998, Erik De Corte was nominated as a member of the “College of Fellows” of the International Bureau of Education (Geneva), an integral part of UNESCO, and in 2002 he was elected as Foreign Member of the National Academy of Education of the United States. In the academic year 1998–1999, he was invited as a Visiting Scholar at the School of Education of Stanford University. And, finally, he was elected for a Fellowship at the Center for Advanced Study in the Behavioral Sciences at Stanford during the last year of his academic career (2005–2006). For his numerous and varied contributions to the field, he received many awards. He was awarded (with Lieven Verschaffel) the 1987 Research Award of the National Council of Teachers of Mathematics in the U.S.A. for an article on his research on young children’s mathematics problem solving, published in the November 1987 issue of the Journal for Research in Mathematics Education, entitled “The effect of semantic structure on first graders’ strategies for solving addition and subtraction word problems”. At the 7th European Conference for Research on Learning and Instruction, held in Athens in August 1997, he received, together with the late Richard Snow, the first “EARLI Oeuvre Award for Outstanding Contributions to the Science of Learning and Instruction”. In March 2000, he was awarded a doctorate honoris causa of the Rand Afrikaans University, Johannesburg, South Africa and, in March 2003, a doctorate honoris causa of the University of the Free State, Bloemfontein, South Africa. At the 25th International Congress of Applied Psychology, held in Singapore in July 2002, he received the “Award for Outstanding Career Contribution to Educational Psychology” of Division 5 (Educational, Instructional, and School Psychology) of the International Association of Applied Psychology. In all these scientific and professional activities Erik has acted, above all, as a bridgebuilder. His broad theoretical and methodological training, his indefatigable energy, his open and jovial personality, his synthetic and organisational talents, his good mastery of many languages, his incomparably large network of professional and personal contacts

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with people all over the world, and, last but not the least, the unqualified support of his wife Rita, have allowed him to build bridges between diverse groups of people: between researchers of different theoretical backgrounds and methodological traditions; between scholars from different regions, countries, and continents; between scientific researchers, policy makers and practitioners; and between established experts and talented newcomers in our research field.

References Anderson, L. W., & Krathwohl, D. R. (Eds). (2001). A taxonomy for learning, teaching, and assessing. A revision of Bloom’s taxonomy of educational objectives. New York: Addison-Wesley. De Corte, E. (1980). Processes of problem solving: Comparison of an American and a European view. Instructional Science, 9, 1–13. De Corte, E. (Ed.). (1987). Acquisition and transfer of knowledge and cognitive skills. International Journal of Educational Research, 11, 601–712. De Corte, E. (1990). Toward powerful learning environments for the acquisition of problem-solving skills. European Journal of Psychology of Education, 5, 5–19. De Corte, E. (1995). Fostering cognitive growth: A perspective from research on mathematics learning and instruction. Educational Psychologist, 30, 37–46. De Corte, E. (1996). Instructional psychology. In: E. De Corte, & F. E. Weinert (Eds), International encyclopedia of developmental and instructional psychology (pp. 33–42). Oxford, UK: Elsevier. De Corte, E. (Ed.). (1999). On the road to transfer: New perspectives on an enduring issue in educational research and practice. International Journal of Educational Research, 31, 555–654. De Corte, E. (2000). Marrying theory building and the improvement of school practice: A permanent challenge for instructional psychology. Learning and Instruction, 10, 249–266. De Corte, E. (Ed.). (2003). Excellence in higher education. London, UK: Portland Press. De Corte, E. (2004). Mainstreams and perspectives in research on learning (mathematics) and instruction. Applied Psychology: An International Review, 53, 279–310. De Corte, E., Geerligs, C. T., Lagerweij, N. A. J., Peters, J. J., & Vandenberghe, R. (1974). Beknopte didaxologie (3rd rev. ed.). Groningen: Tjeenk Willink. De Corte, E., Geerligs, C. T., Lagerweij, N. A. J., Peters, J. J., & Vandenberghe, R. (1979). Les fondements de l’action didactique. De la didactique à la didaxologie. Bruxelles: Éditions De Boeck. De Corte, E., Geerligs, C. T., Peters, J. J., Lagerweij, N., & Vandenberghe, R. (1975). Grundlagen didaktischen Handelns. Von der Didaktik zur Didaxologie (Beltz Studienbuch, 81). Weinheim/Basel: Beltz Verlag. De Corte, E., Greer, B., & Verschaffel, L. (1996). Learning and teaching mathematics. In: D. Berliner, & R. Calfee (Eds), Handbook of educational psychology (pp. 491–549). New York: Macmillan. De Corte, E., Linn, M., Mandl, H., & Verschaffel, L. (Eds). (1992). Computer-based learning environments and problem solving (NATO ASI Series F: Computer and Systems Sciences). Berlin: Springer, pp. XV–484. De Corte, E., Lodewijks, H. G. L. C., Parmentier, R., & Span, P. (Eds). (1987). Learning and instruction. European research in an international context (Vol. 1). Leuven: Leuven University Press. De Corte, E., & Lowyck, J. (1983). Heroriëntatie in het onderzoek van het onderwijzen [Reorientation in research on teaching]. Tijdschrift voor Onderwijsresearch, 8, 242–260. De Corte, E., Op ’t Eynde, P., & Verschaffel, L. (2002). Knowing what to believe: The relevance of mathematical beliefs for mathematics education. In: B. K. Hofer, & P. R. Pintrich (Eds), Personal

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epistemology: The psychology of beliefs about knowledge and knowing (pp. 297–320). Mahwah, NJ: Lawrence Erlbaum Associates. De Corte, E., & Verschaffel, L. (1981). Children’s solution processes in elementary arithmetic problems: Analysis and improvement. Journal of Educational Psychology, 58, 765–779. De Corte, E., & Verschaffel, L. (1985). Beginning first graders’ initial representation of arithmetic word problems. Journal of Mathematical Behavior, 4, 3–21. De Corte, E., & Verschaffel, L. (1987). The effect of semantic structure on first graders’ solution strategies of elementary addition and subtraction word problems. Journal for Research in Mathematics Education, 18, 363–381. De Corte, E., & Verschaffel, L. (1996). An empirical test of the impact of primitive intuitive models of operations on solving word problems with a multiplicative structure. Learning and Instruction, 6, 219–243. De Corte, E., & Verschaffel, L. (2006). Mathematical thinking and learning: Bridging research and practice. In: I. Sigel, & A. Renninger (Eds), Handbook of child psychology: Vol. 4. Child psychology and practice (pp.103–152). New York: Wiley. De Corte, E., Verschaffel, L., & De Win, L. (1985). The influence of rewording verbal problems on children’s problem representations and solutions. Journal of Educational Psychology, 77, 460–470. De Corte, E., Verschaffel, L., Entwistle, N., & Van Merriënboer, J. (Eds). (2003). Powerful learning environments: Unravelling basic components and dimensions. Oxford: Pergamon Press. De Corte, E., Verschaffel, L., & Lowyck, J. (1996). Computers, media, and learning. In: E. De Corte, & F. E. Weinert (Eds), International encyclopedia of developmental and instructional psychology (pp. 695–700). Oxford, UK: Elsevier. De Corte, E., Verschaffel, L., & Masui, C. (2004). The CLIA-model: A framework for designing powerful learning environments for thinking and problem solving. European Journal for Psychology of Education, 19, 365–384. De Corte, E., Verschaffel, L., & Pauwels, A. (1990). Influence of the semantic structure of word problems on second graders’ eye movements. Journal of Educational Psychology, 82, 359–365. De Corte, E., Verschaffel, L., & Schrooten, H. (1991). Computer simulation as a tool in studying teacher’s cognitive activities during error diagnosis in arithmetic. In: P. Goodyear (Ed.), Teaching knowledge and intelligent tutoring (pp. 367–378). Norwood, NJ: Ablex. De Corte, E., Verschaffel, L., & Schrooten, H. (1992). Cognitive effects of learning to program in Logo: A one-year study with sixth-graders. In: E. De Corte, M. Linn, H. Mandl, & L. Verschaffel (Eds), Computer-based learning environments and problem solving (NATO/ASI Series F: Computer and Systems Sciences, pp. 207–228). Berlin: Springer. De Corte, E., Verschaffel, L., Schrooten, H., Olivié, H., & Vansina, A. (1993). A logo-based tool-kit and computer coach to support the development of general thinking skills. In: T. M. Duffy, J. Lowyck, & D. H. Jonassen (Eds), Designing environments for constructive learning (NATO/ASI Series F: Computer and Systems Sciences, Vol. 105, pp. 109–124). Berlin: Springer. De Corte, E., Verschaffel, L., & Van Coillie, V. (1988). The effect of type of number, problem structure, and mode of response on children’s solutions of multiplication word problems. Journal for Mathematical Behavior, 7, 197–216. De Corte, E., Verschaffel, L., & Van de Ven, A. (2001). Improving text comprehension strategies in upper primary school children: A design experiment. British Journal of Educational Psychology, 71, 531–559. De Corte, E., & Weinert, F. E. (Eds). (1996). International encyclopedia of developmental and instructional psychology. Oxford, UK: Elsevier. Depaepe, F., De Corte, E., Op ’t Eynde, P., & Verschaffel, L. (2005). Teaching percentages in the primary school: A four country comparative study. In: L. Verschaffel, E. De Corte, G. Kanselaar, & M. Valcke (Eds), Powerful environments for promoting deep conceptual and strategic learning (pp. 147–171). Leuven: Leuven University Press.

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Depaepe, F., De Corte, E., & Verschaffel, L. (2006). The culture of the mathematics classroom: A complex determinant in students’ learning: Theory and research. In: J. Elen & D. Clark (Eds), Dealing with complexity in learning environments (pp. 89–106). (Advances in Learning and Instruction Series). Amsterdam: Elsevier. Dochy, F., Moerkerke, G., De Corte, E., & Segers, M. (2001). The assessment of quantitative problem-solving skills with “non of the above” items (NOTA items). European Journal of Psychology of Education, 16, 163–177. d’Ydewalle, G., Degryse, M., & De Corte, E. (1981). Expected time of test and the acquisition of knowledge. British Journal of Educational Psychology, 51, 23–31. d’Ydewalle, G., Swerts, A., & De Corte, E. (1983). Study time and test performance as a function of test expectations. Contemporary Educational Psychology, 8, 55–67. Husén, T., & Postlethwaite, T. N. (Eds). (1994). International encyclopedia of education. Oxford, UK: Pergamon Press. Janssens, R., De Corte, E., Verschaffel, L., Knoors, E., & Colémont, A. (2002). National assessment of new standards for mathematics in elementary education in Flanders. Educational Research and Evaluation, 8, 197–225. Luwel, K., Verschaffel, L., Onghena, P., & De Corte, E. (2001). Strategic aspects of children’s numerosity judgement. European Journal of Psychology of Education, 16, 233–255. Luwel, K., Verschaffel, L., Onghena, P., & De Corte, E. (2003). Strategic aspects of numerosity judgement: The effect of task characteristics. Experimental Psychology, 50, 63–75. Mandl, H., De Corte, E., Bennett, S. N., & Friederich, H. F. (Eds). (1990). Learning and instruction. European research in an international context: Volume 2.1. Social and cognitive aspects. Oxford: Pergamon Press. Masui, C., & De Corte, E. (1999). Enhancing learning and problem solving skills: Orienting and self-judging, two powerful and trainable learning tools. Learning and Instruction, 9, 517–542. Masui, C., & De Corte, E. (2005). Learning to reflect and to attribute constructively as basic components of self-regulated learning. British Journal of Educational Psychology, 75, 351–372. Op ’t Eynde, P., De Corte, E., & Verschaffel, L. (2001). “What to learn from what we feel?”: The role of students’ emotions in the mathematics classroom. In: S. Volet, & S. Järvelä (Eds), Motivation in learning contexts: Theoretical and methodological implications (pp. 149–170). Oxford: Pergamon Press. Op ’t Eynde, P., De Corte, E., & Verschaffel, L. (2002). Framing students’ mathematics-related beliefs: A quest for conceptual clarity and a comprehensive categorization. In: G. C. Leder, E. Pekhonen, & G. Torner (Eds), Beliefs: The hidden variable in mathematics education (pp. 13–38). Dordrecht: Kluwer. Verschaffel, L., & De Corte, E. (1996). Number and arithmetic. In: A. Bishop, K. Clements, C. Keitel, & C. Laborde (Eds), International handbook of mathematics education (Part I, pp. 99–138). Dordrecht: Kluwer. Verschaffel, L., & De Corte, E. (1997). Teaching realistic mathematical modeling in the elementary school. A teaching experiment with fifth graders. Journal of Research in Mathematics Education, 28, 577–601. Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge in mathematical modeling of school word problems. Learning and Instruction, 7, 339–360. Verschaffel, L., De Corte, E., Kanselaar, G., & Valcke, M. (Eds). (2005). Powerful learning environments for promoting deep conceptual and strategic learning (Studia Paedagogica). Leuven: Leuven University Press. Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4, 273–294.

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Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H., & Ratinckx, E. (1999). Learning to solve mathematical application problems: A design experiment with fifth graders. Mathematical Thinking and Learning, 1, 195–230. Verschaffel, L., De Corte, E., & Pauwels, A. (1992). Solving compare problems: An eye-movement test of Lewis and Mayer’s consistency hypothesis. Journal of Educational Psychology, 84, 85–94. Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems (pp. xvii-203). Lisse, The Netherlands: Swets & Zeitlinger. Verschaffel, L., Greer, B., & De Corte, E. (in press). Whole-number arithmetic. In: F. Lester (Ed.), Handbook of research in mathematics education. New York: Macmillan. Vosniadou, S., De Corte, E., & Mandl, H. (Eds). (1994). Technology-based learning environments: Psychological and educational foundations (NATO/ASI Series F: Computer and Systems Sciences, Vol. 137). Berlin: Springer. Vosniadou, S., De Corte, E., Mandl, H., & Glaser, R. (Eds). (1996). International perspectives on the design of technology-supported learning environments. Mahwah, NJ: Lawrence Erlbaum Associates. Weinert, F. E., & De Corte, E. (1996). Translating research into practice. In: E. De Corte, & F. E. Weinert (Eds), International encyclopedia of developmental and instructional psychology (pp. 43–50). Oxford, UK: Elsevier. Weinert, F. E., & De Corte, E. (2001). Educational research for educational practice. In: N. J. Smelser, & P. B. Baltes (Eds), International encyclopedia of the social and the behavioral sciences (pp. 4316–4326). Oxford, UK: Elsevier.

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Introduction Filip Dochy, Lieven Verschaffel, Monique Boekaerts, and Stella Vosniadou

While learning and instruction have occurred in all centuries, the amount of research investigating these processes has accumulated enormously during the past decades. Moreover, several societal and scientific developments have quite dramatically changed our ways of thinking about learning and instruction. These developments have resulted in new models and theories of competence, learning, instruction, and assessment, which have, in turn, affected, at least to some extent, the actual ways of learning and teaching in classrooms, in corporate training, and in other forms of formal or informal education. All contributions to this book, written in honour of Erik De Corte, testify of, but at the same time reflect upon, these developments in the (research) field of learning and instruction, to which Erik De Corte contributed significantly, as will be illustrated by numerous references to various aspects of his work in the different chapters of this book. The theoretical frameworks and methodological approaches presented in the different chapters reflect these societal and scientific developments and how they have been addressed in research on learning and instruction. Hereafter, we briefly list some of these major and most remarkable developments. The information age. As far back as in classical Greece, scientists were considered experts in all sciences and areas of knowledge. Until recently, some scientists could claim a more or less full grasp of all knowledge within a certain discipline. However, information is now being exchanged rapidly and knowledge is growing at an exponential rate. Scientists need to master the basic knowledge of their field and the competences necessary to navigate around their discipline. This shift is also true for teachers, who have traditionally been accepted as the sources of all knowledge and experience within educational contexts. Today, teachers are more correctly conceived as keys to open the doors to different domains of knowledge and experience. The information age is characterized by an infinite and permanently changing mass of information. Successful functioning in this era involves many new cognitive, metacognitive, social, and affective competences, such as critical thinking, problem solving, searching for relevant information, efficient use of data, working in teams efficiently, reflection and self-evaluation, self-efficacy, flexibility, etc. The use of Internet and educational technology. Education has started using the electronic possibilities in all its forms. The use of e-mail, local-area networks, shared communication systems, the Internet, shared electronic databases, video conferencing facilities, electronic

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self-study materials, study support and guidance through networks, assessment systems, intake and monitoring systems, and so on, lead to the development and implementation of new teaching and learning strategies. Video can be used when surrogate experiences must be presented (e.g., exotic rituals, dangerous physical phenomena, animations of invisible phenomena), or when dynamic processes or phenomena cannot be adequately presented in printed material (e.g., plasma currents). The computer has become indispensable not only for testing and calculating, but also for simulating complex processes and systems (e.g., economic or physical models) and for practicing specific skills (e.g., in elementary arithmetic or foreign language learning) or more complex competences. Integrated learning and assessment systems are developed to support students during learning. The changing labour market. The labour market is rapidly changing and demands a more flexible labour force with increased short-term, part-time, and casual working. There is increased pressure from industry for education to deliver graduates who are immediately employable and effective in business and industry. Employer organizations have pointed to an insufficient match between the outcomes of study programmes and labour market needs. If vocational and academic education systems are required to supply graduates who can function immediately within the labour force, this implies a growing need for instructional techniques and assessment procedures for relevant competences. Institutes for vocational training are developing learning and assessment systems for vocational qualifications which encompass learning outside formal education and training. Lifelong learning. Economic pressures requiring also major restructuring in the labour market were crucial factors that led governments and employers to emphasize the importance of flexibility or adaptivity within the labour force and the ability of employees to transfer previously learnt skills and acquire new competences throughout their working lives. Also, the rapid turnover and the increasing amount of information, on the one hand, and the use of technology, on the other, increase the need for learning constantly. It is widely accepted that the need for lifelong learning will increase even more rapidly in the near future. Changing students. Free market ideology and strategies have recently entered the world of education and more and more initiatives are being taken at government levels to promote a more demand-driven approach towards education. As a consequence, students are progressively more seen as ‘clients’ or ‘consumers’. Besides, children and youngsters themselves do change in their preferential and usual ways of learning. They learn more from technological sources than anything else and learn in new ways by means of manipulating variables in simulated worlds, by means of multitasking, by means of communicating through video conferencing and chatting, by experiencing with new software (and certainly not by reading the manual), by means of solving virtual problems, by playing real-time games such as the o-game, etc. With these developments within broader society as a background, the present book aims at reviewing and discussing research about what it means to acquire and demonstrate competence and how to conceive, design, implement, and evaluate powerful learning arrangements aimed at the acquisition of this competence. This book is divided into six major parts. Part I presents chapters that deal with learning and development. The second part focuses on learning, reasoning, and problem solving. Several chapters from these first two parts focus exemplarily on mathematics

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education, Erik De Corte’s major research field. Part III concerns motivational and emotional aspects of learning. In Part IV, developments in research on learning and assessment are addressed, while the fifth part contains chapters on the relationship between learning and technology. The sixth and last part of this book consists of a chapter that critically reflects on spreading scientific knowledge and developing competences through redesigning organizations in order to optimise professional learning, and the last chapter critically reviews designing educational research. Each of the 16 chapters is self-contained. They are all structured in terms of the past, the present, and the future of a particular subdomain of the research field of educational psychology. They all include a critical analysis of existing research and theory; sometimes the authors’ own research is used to illustrate main points. Most chapters end by proposing a research agenda for the future and by discussing educational implications. The international composition and orientation of the author teams guarantee a worldwide perspective on the past, the present, and the future of educational psychology as a field of research and as an important player on the educational scene. In the remainder of this introduction, we will briefly highlight the content of each chapter.

Part I: Learning and Development Early childhood education occupies a significant place in international research, theoretical developments, and policy reform agendas. Current international trends in structuring curricula reveal different orientations towards principles, aims, content, and goals, with different implications for pedagogy, learning, and assessment practices. The first chapter by Elizabeth Wood and Neville Bennett takes a comparative, analytical perspective on these developments, focusing on the Foundation Stage in England, Te Whaariki in Aotearoa, New Zealand, and the Reggio Emilia approach in Northern Italy. It is argued that early childhood education can be conceptualized, as a site for struggle and progress in the key areas of curriculum, pedagogy, and learning. In the second chapter, Andreas Demetriou and Areti Panaoura first summarize their comprehensive theory of the architecture and development of the human mind. This theory postulates that the mind is organized in three layers, namely (a) processing potentials, (b) a knowing layer addressed to the environment involving several domain-specific systems, including mathematical thought, and (c) a self-oriented knowing layer including self-awareness and self-control. The composition, interrelations, and development of these systems are briefly described. The chapter then focuses on mathematical thought: it outlines its composition and development, and summarizes several studies showing how school performance in mathematics is related with processing efficiency, IQ, reasoning, self-awareness, and personality factors. Finally, the implications for educational practice are discussed. In the field of education, questions of transfer and generalization of knowledge and skills are of great importance. In their chapter, Erno Lehtinen and Minna M. Hannula first summarize different, contradictory approaches to transfer, and, second, show how transfer and the abstract nature of mathematical concepts are linked. Third, it is suggested that, in early mathematical development, domain-specific attentional processes of focusing on mathematical aspects in everyday surroundings are crucial for the development of an

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abstract number concept and the transfer of numerical skills. The transfer of numerical skills is neither an automatic feature of the human mind nor a direct result of teaching, but is produced by a complex development of abstract mathematical knowledge and attentional processes. In Chapter 4, Stella Vosniadou and Xenia Vamvakoussi examine mathematics learning and teaching from a conceptual change perspective. It is argued that the conceptual change theoretical framework, originally developed to explain students’ difficulties in learning science, can be fruitfully applied to mathematics. This claim is supported with empirical evidence from recent experimental studies. It is argued that the conceptual change theoretical framework can be used as a guide in identifying mathematical concepts that are going to be difficult for students, in predicting students’ systematic errors, and in constructing student-centred explanations of counter-intuitive math concepts. The implications for the design of mathematics learning environments are discussed.

Part II: Learning, Reasoning, and Problem Solving In their chapter on “Reasoning with mental tools and physical artefacts in everyday problem-solving” Roger Säljö, Ann-Charlotte Eklund, and Åsa Mäkitalo argue that throughout history people have created cultural tools to support thinking. In the context of mathematics, this intimate interdependence between human sense-making and artefacts is obvious, and there are many different tools that serve as prosthetic devices for thinking, calculating, and problem solving. Later, an empirical study is reported of how people handle a currency conversion problem when solving it through mental arithmetic, with paper and pencil, or with a mini-calculator. The analytical focus is on the modelling/conceptual dimension as well as on the algorithmic part. It is argued that the current externalization of cognitive functions into digital tools has profound implications for teaching and learning. In Chapter 6, Wim Van Dooren, Lieven Verschaffel, Brian Greer, and Dirk De Bock provide a review of the research on mathematical modelling and applied problem solving. Following introductory remarks on the nature of mathematical modelling, the role of traditional word problems as a vehicle for teaching genuine mathematical modelling at the elementary and lower secondary school level is described. It is explained in detail what is meant by superficial mathematical modelling, by contrasting it with genuine modelling behaviour. Then, elements in the traditional school practice and culture that help to explain why many students do not develop a genuine modelling disposition are reviewed. It is argued why and how the modelling perspective can be taken seriously at the elementary level. Finally, some promising directions and pitfalls for further research are given.

Part III: Motivational and Emotional Aspects of Learning The seventh chapter by Monique Boekaerts and Rob Martens addresses the impact of motivational processes. It has become clear that these processes play a crucial role in educational innovations, and that neglecting these processes is an important cause of failed educational innovations. New learner and teacher roles in (socio-constructivist) learning

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environments are reviewed. Components involved in learning are discussed and motivation and volition as parts of self-regulation and motivational conditions for meaningful learning and for psychological needs fulfilment are introduced. The chapter also deals with questions such as: What is the impact of tempting alternatives and at what price comes the effort needed to resist such temptations? Finally, this chapter also deals with possible interventions aiming at enhancing specific teacher skills. The chapter by Noel Entwistle, Velda McCune, and Max Scheja describes research into student learning at university in relation to the specific contexts experienced. The differing types and levels of data collection and analysis used in the research are explained. This is illustrated by three studies, looking first at an investigation where the focus is on groups of students, and then at two differing approaches to focusing on the study behaviour of individual students. The implications of contrasting research designs on the ways in which the relationships between teaching–learning environments and learning processes and outcomes come to be understood are considered, and the differing messages these findings convey to academic staff in higher education are discussed. The next chapter by Fritz Oser, Evi Schmid, and Lisa Hattersley is about emotional conflicts between being good and being successful. On the basis of De Corte and Op ’t Eynde’s reflection on cognitively influenced emotions, the so-called ‘unhappy moralist’ effect is described; it states that doing the right thing is often followed by feelings of not being successful in life and vice versa. This effect is akin to the effect of the ‘happy victimizer’ which states that children attribute to the wrongdoer only positive feelings. In a couple of older studies, the phenomenon of the ‘unhappy moralist’ is localized; in a couple of newer studies it is tried to provide empirical evidence for this effect. The authors also discuss educational implications. Since the unhappy moralist effect has a high emotional loading, one important educational goal would be to teach students that morality is only morality if it is in conflict with personal needs/gains that would precisely hurt this morality. This conflict, thus, is the core of any moral emotion and moral education.

Part IV: Learning and Assessment In their chapter called “Educational assessment: Towards better alignment between theory and practice” James Pellegrino and Daniel Hickey discuss the importance of assessment in the educational process and the confusion that often surrounds its use, differentiating between levels and functions. The level at which an assessment is intended to operate involves varying distance in ‘space and time’ from the enactment of instruction and learning and has implications for how well it can fulfill the formative, summative, or programme evaluation functions of assessment. Different levels and functions of assessment also have varying degrees of match with theoretical stances about the nature of knowing and learning. This issue is explored, and it is discussed how broader views of knowing and learning can aid efforts to balance assessment functions and better align assessment, instruction, and the curriculum. Whereas the previous chapter addresses the issue of assessment and its relation to ‘instruction and curriculum’ mostly from a US perspective, Filip Dochy, David Gijbels,

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and Mien Segers look at the emergence of innovations in assessment and its relation to learning from a EU perspective. The authors start by highlighting the most relevant developments in this area as seen in many European countries and underpin these with recent research into, as De Corte called it, ‘powerful learning environments’. Then, important issues in the so-called new ‘assessment culture’ are discussed. Next, different effects of assessment practices on students’ learning are explained. In addition, recent studies on the relation between assessment, on the one hand, and motivation and study approaches, on the other, are described. Furthermore, empirical evidence for the role of students’ assessment preferences and their perceptions of the learning environment is presented. Finally, three new developments are discussed, namely blended assessment, advances in edumetrics, and assessment engineering. Concluding recommendations are given for teachers and researchers.

Part V: Learning and Technology In their chapter entitled “The difficult marriage between education and technology: Is the marriage doomed?” Gavriel Salomon and Dani Ben-Zvi argue that the overall marriage between education and technology is still a far way from delivering its promises. A critical reflection on the current state of the complex relation between education and technology is given. It is asked why the wide-spreading access to new technologies in schools did not yield the expected changes and under what conditions it could bring about the desired improvements in teaching and learning. First, a series of reasons for the marital difficulties encountered between education and technology are explored. Then examples of innovative and successful projects are provided as well as some guidelines for good research that addresses the complex relationship between education and technology, yielding a happy and innovative marriage between the two partners. Chapter 13, by Heinz Mandl, Bernhard Ertl, and Birgitta Kopp, deals with computer support for collaborative learning environments. The analysis given is based on a moderate constructivist view on learning, which emphasizes the need to support learners instructionally in their collaborative knowledge construction. First, the extent to which the computer can provide tools for supporting collaborative knowledge construction is illustrated. Second, a focus on instruction itself is set and the kinds of advanced instructional methods that computer tools may provide for the learners are shown. Furthermore, the learners’ prerequisites and how they must be considered when constructing learning environments are discussed. In “E-pedagogies for networked learning” Robert-Jan Simons and Maarten de Laat describe how pedagogies in networked learning have developed. First, an analytical scheme of five learning metaphors is presented that is used in the next paragraphs to analyse connections between technical approaches to networked learning and pedagogical approaches. Then the history of the use of computers in education is sketched from the point of view of learning and instruction. Finally, two stages of networked learning are discerned: teacher-centred approaches and community-centred approaches. In each stage, prototypical examples of pedagogical models of networked learning are described as well as the associated learning metaphors.

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Part VI: Instructional and Organizational Designs for Learning According to Lauren Resnick and James Spillane, disseminating instructional psychology so that it makes a difference in the world of practice is difficult. Their chapter examines four approaches to distributing scientific knowledge so that it enables change in the thinking and practice of individuals and organizations — telling people, developing study tools that support particular learning, designing protocols of practice, and redesigning organizations to optimise professional learning. Exploring the redesign of organizations, the authors argue that other social sciences need to be mobilized with psychology in order to address the organizational as well as individual dimensions of the challenge in applying instructional psychology. In the final chapter of the book, Denis Phillips and Jonathan Dolle examine the history of ideas underpinning design experiments, as a distinct orientation towards both research and programme development, from Plato to Brown, Collins, and De Corte. The authors argue that the various methods design experiments employ are still underdeveloped, and their maturation has been stunted because of inherent tensions between two goals: scientific rigour and practical application. Justifying claims scientifically requires careful control of many variables, while successful classroom application requires designs that are continually adapted and redesigned. To advance, researchers using design experiments must prioritise these goals and situate findings within a more complete research programme. In the final part of this introduction, we will pinpoint at some major recurrent themes and overarching ideas that emerge throughout the 16 chapters and that probably will (continue to) dominate the research field of instructional psychology in the coming years. We will structure these themes and ideas around the four components of De Corte’s CLIA (Competence, Learning, Intervention, Assessment) model for the design of powerful learning environments (see De Corte, Verschaffel, & Masui, 2004). While this model has been primarily developed for and applied to regular classroom settings, it also seems relevant for the urging developments in lifelong learning, which gained considerable importance in recent years (as argued in the first part of this introduction; see also Dochy, 2005). Since this model tries to synthesize the recent inquiry-based knowledge on learning and instruction, it is not surprising that many topics and ideas discussed in the different chapters fit within this framework; but at the same time, these chapters raise many new important issues and insights that will stimulate and help researchers to design, implement, and evaluate novel environments that are conducive to fostering in all students self-regulatory and collaborative learning skills, productive and transferable knowledge, and a disposition towards competent thinking and problem solving. Competence in a domain, the first component of De Corte’s model, involves the following components: a well-organized and flexibly accessible domain-specific knowledge base, heuristic search methods for problem analysis and transformation, metaknowledge, self-regulatory skills, and positive affects (i.e. beliefs, attitudes, and emotions) about the domain. According to De Corte et al. (2004), it is the integrated mastery of these components that constitutes genuine competence, which is nicely expressed in the term ‘disposition’. Several contributions to this book comprise attempts to further explore the complex

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interplay between the different components, with a special attention for the role of the latter components. Demetriou and Panaoura’s model of ‘the architecture of the mind’, for instance, tries to provide a detailed account of how different self-regulatory functions intervene in understanding and problem solving. Moreover, metaknowledge and awareness of others’ mental functions and states are essential parts of this architecture. Both the chapter of Lehtinen and Hannula, and of Van Dooren et al. support, albeit for different levels of mathematical expertise, the ‘dispositional’ nature of mathematical competence by emphasizing, respectively, the regulation of attentional processes in mathematical learning and problem-solving situations, and, the important interaction between cognitive, metacognitive, and affective components in the solution of mathematical application problems. Vosniadou and Vamvakoussi’s analysis highlights the importance of metaknowledge and self-regulatory skills to overcome the barriers imposed by misconceptions in learners’ prior knowledge base. A largely neglected aspect of competence is addressed in the chapter by Oser et al., wherein the tension between being successful and being good (in the moral sense of the word) is analysed. Learning. According to De Corte et al.’s (2004) model, the following characteristics of productive learning are well documented by a substantial amount of research: it is an active/constructive, cumulative, goal-directed, self-regulated, situated, collaborative, and individually different process of constructing meaning and knowledge. The view of learning as an active, cumulative, and constructive activity has nowadays become common ground among educational psychologists. These features of learning reveal themselves in most, if not all, contributions, but especially in Vosniadou and Vamvakoussi’s analysis from a conceptual change perspective of how mathematical conceptions are formed and changed. Learning will be most productive when students can choose and determine their own objectives and regulate their own learning activities. Metaconceptual awareness seems to ease learning processes. Several chapters document not only how important it is that learners set appropriate goals and are metacognitively, motivationally, and behaviourally regulating their own learning process, but also how difficult it is for many students to do so. Boekaerts and Martens’ research, for instance, documents how students enrolled in higher education may fail to direct their attention to important learning tasks, to invest effort in applying deep-level learning strategies, and to persist in the face of diversion, difficulty, and failure. The idea that learning and cognition are situated activities was strongly put forward in the late 1980s, in reaction to the then dominant cognitivistic view of learning and thinking as highly individual and purely mentalistic processes occurring in the brain, and resulting in encapsulated mental representations (Collins, Brown, & Newman, 1989). Nowadays, learning is conceived as an interactive activity between the individual and the physical, social, and cultural context and artefacts, and especially through participation in cultural activities and contexts (Sfard, 1998). The dependency of human reasoning on the use of cultural tools is a recurrent theme in many chapters, but particularly in the chapter by Säljö et al., which shows how reasoning takes place in symbiosis with cultural tools and how our thinking has to be attuned to the ways in which such external resources operate. The basic idea that learning is not a purely ‘solo’ activity, but a distributed one implies that the learning effort is shared by the individual student and his partners in the learning

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environment. The social nature of learning is addressed in many chapters, but receives special attention in the chapters of Mandl et al. and Simons and De Laat, wherein collaborative learning and networked learning are the main topics. A different perspective with roots in organizational psychology and corporate training research is presented in Resnick and Spillane’s chapter, wherein individual learning is analysed in relation to organizational learning. According to these authors, one cannot arrive at understanding of the whole — the group or the organization — by aggregating from individuals. Approaches from each level have to be combined, informing each other to allow for a synthesis of the two. (Instructional) psychologists have had considerable influence on recent theories of organizational change, but we will need to create new routines and procedures in order to build organizations that are better suited to using effectively what is known about human learning. Finally, De Corte et al. (2004) emphasize that the processes and outcomes of learning vary among students due to individual differences in a diversity of aptitudes that affect learning, such as prior knowledge, conceptions of learning, learning strategies, interest, motivation, self-efficacy, beliefs, and emotions. This individual perspective is again represented in several chapters, but especially in Demetriou and Panaoura’s theory of the human mind, which specifies the factors that are responsible for inter-individual differences in mental functioning and development, and in the chapter by Entwistle et al., who show how differently high-school students react and adjust themselves to new learning environments. Instruction. Taking into account the well-known cognitive apprenticeship model of learning and teaching of Collins et al. (1989) but also later research-based attempts at changing the classroom environment in line with De Corte’s model, such as the “Fostering Communities of Learners” (FCL) project of Brown and Campione (1994, 1996), and the Jasper-project of the Cognition and Technology Group at Vanderbilt (CTGV, 1997, 2000), De Corte et al. (2004) have outlined a series of instructional principles for the design of powerful learning environments, which are in line with the above-defined ‘disposition’, on the one hand, and the characteristics of constructive learning, on the other. 1. Initiate and support active, constructive acquisition processes in all students. 2. Foster the development of self-regulation strategies in students. 3. Embed students’ constructive acquisition activities preferably in real-life situations, that offer ample opportunities for social interaction, and that are representative of the tasks and problems to which students will have to apply their knowledge and skills in the future. 4. Create opportunities to acquire general learning and thinking skills embedded in the subject-matter fields. 5. Create a classroom culture that induces in students explicitation of and reflection on their learning activities and problem-solving strategies. 6. Allow for the flexible adaptation of the instructional support in order to take into account the individual differences in aptitudes among learners. These principles are echoed in many chapters of this book. While explicitly endorsing these principles, Vosniadou and Vamvakoussi, starting from a conceptual change perspective, further elaborate on certain guidelines and add a few others, such as the address-

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ing students’ initial theories and their entrenched presuppositions, increasing their metaconceptual awareness, and stimulating the use of external representations and cultural artefacts. However, as argued and documented in different chapters, an increasing number of researchers signal that educational innovations based on the above-mentioned design principles for learning environments are by no means a guarantee for success. Bringing the entire ‘real’ and ‘authentic’ world into the classroom is, for example, not always the best solution. Context-independent problems do have a role in education too. If there is no decontextualization, learning remains bounded to a specific context, practice, or framework. So, a good balance between contextualisation and decontextualization is needed. Other reasons why powerful learning environments may not yield the expected learning effects are: building in too many ‘pedagogical agents’ which distract students; teachers lacking insight into how motivational processes operate in learning environments and/or giving these processes insufficient attention in their teaching; handing over the responsibility for learning to students who are not yet well prepared for independent studying and not yet willing to take up this increased autonomy; teachers’ neglect of students’ perceptions of the new learning environment …. For these reasons, Entwistle et al. recommend that research on the effectiveness of these new ways of learning produces not only group-level analyses, but also ones at sub-group and individual levels to indicate how differing sub-groups and individuals are adjusting to these environments. Making teachers aware of how motivation processes operate in learning environments may be another useful approach (see the chapter by Boekaerts and Martens). In the two examples of recent design studies explicitly discussed by De Corte et al. (2004) — namely the “Fostering Communities of Learners” project and the Jasper-project — instructional technology has been called on to increase the power of the learning environment. As argued convincingly in the chapters by Mandl et al., by Salomon and Ben-Zvi, and by Simons and De Laat, it is clear that in such advanced computer-based environments, the computer can be a powerful tool for providing communication, advanced instructional methods, and also an array of valuable and authentic resources for collaborative and individual learning. On a broader scale, however, information and communication technology in education has yet to prove its unique and worthwhile contributions to learning and instruction. According to Salomon and Ben-Zvi, such contributions of technology to education will be realized to the extent that it comes to serve truly new learning environments, based on novel principles of teaching and learning, and also on new goals, such as the skills of team work, conflict resolution, accessing information and integrating it, designing criteria for information selection, and ways of solving new problems. These are not the kinds of commonly aimed at and measured learning outcomes. If we want to assess the contribution of ICT and the learning environments in which it is embedded, we need to assess such achievements rather than the standard ones. The latter recommendation of Salomon and Ben-Zvi brings us to the last component of the CLIA framework, namely assessment. Assessment. According to De Corte et al. (2004), forms and methods of assessment should be aligned and integrated with the preceding components of their model. This implies that classroom assessments should meet the following conditions.

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1. Assessment instruments should address and monitor students’ progress towards the acquisition of the full range of disposition. 2. Assessment instruments should provide diagnostic feedback about students’ deep understanding of content and their mastery and productive use of learning and thinking skills. In that perspective assessment tools should not only address learning outcomes but also trace students’ learning processes and strategies. 3. Assessment forms should contain assignments that are meaningful for the learners, and that offer opportunities for self-regulated and collaborative — besides individual — approaches to tasks and problems. 4. Assessment practices should help students develop skills in self-, peer-, and co-assessment. The chapters by Pellegrino and Hickey and Dochy et al. recall (some of) these principles, but add several new elements by stressing that fostering learning and instruction through assessment is strongly influenced by the following additional factors: recognizing the negative influence of traditional testing on students’ motivation and wellbeing, and, thus, also on the learning process itself; providing effective ‘assessment for learning’ to students; focusing at immediate- and close-level assessment; and providing a better alignment of learning and instruction with assessment in appropriate learning environments. Finally, we want to add a few concluding words concerning the future of the relationship between educational research and educational practice. At several places, this book also pinpoints towards the fact that special attention should be paid to “marrying theory building and the improvement of school practice” — to use the title of one of Erik De Corte’s (2000) articles about this issue. This book shows multiple roads towards possible key educational issues for making this marriage successful: the integration of knowledge, skills, and attitudes in authentic professional situations; teachers as coaches that are fully feedback-oriented towards individuals rather than designers of fixed learning tracks for groups; the use of more teamwork, team teaching, and learning across disciplines and subjects; a transparent assessment policy within each training programme aiming at balanced assessment in blended learning environments; students’ perceptions of heavy study load, of stress, of lack of clarity of goals, and lack of feedback as determining variables in creating powerful learning environments; and creating technology-based networked learning situations that enhance students’ motivation, etc. Resnick and Spillane argue that we have to be more aware of the difficulties of disseminating instructional psychology, so that it makes a difference in the world of practice; and that we have to invest more resources and energy into the development of new approaches to distributing scientific knowledge, so that it enables change in the thinking and practice of individuals and organizations. The issue of bridging educational research, policy, and practice is also a major theme of Bennett and Wood’s chapter, which illustrates, for the domain of preschool education, how broad-scale reform movements based on innovative views on learning and instruction are mediated by teachers’ theories and experiences, leading to multiple interpretations and re-contextualizations that are situated in local cultures and contexts. The tension between theory and practice is also the starting point of the closing chapter by Phillips and Dolle, which comprises a historical and philosophical analysis of one

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of the dominant research methodologies in our field of research (and also in this book), namely design experiments. The underlying idea of this methodology is that an effective way to better understanding the processes of learning — and, thus, advancing theory — consists in designing and realizing innovative learning environments that are powerful for eliciting in students the intended processes of knowledge and skill acquisition. But, although such design experiments may also contribute to the elaboration of a theory of learning from instruction, one should also be aware of its limitations. The authors warn that it is time to abandon the idea that design experiments can fulfill both functions simultaneously and the notion that design experiments can serve as a self-contained research programme. They strongly endorse the sentiment expressed by De Corte and Verschaffel (2002, p. 529), that design experiments “[can] be beneficially complemented by more analytic research, such as studies in which different versions of complex learning environments are systematically contrasted and compared with a view to the identification of those aspects which contribute especially to their high power and success”.

References Brown, A. L., & Campione, J. C. (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: The MIT Press. Brown, A. L., & Campione, J. C. (1996). Psychological theory and the design of innovative learning environments: On procedures, principles, and systems. In: L. Schauble, & R. Glaser (Eds), Innovations in learning: New environments for education (pp. 289–325). Mahwah, NJ: Lawrence Erlbaum Associates. Cognition and Technology Group at Vanderbilt. (1997). The Jasper Project: Lessons in curriculum, instruction, assessment, and professional development. Mahwah, NJ: Lawrence Erlbaum Associates. Cognition and Technology Group at Vanderbilt. (2000). Adventures in anchored instruction: Lessons from beyond the ivory tower. In: R. Glaser (Ed.), Advances in instructional psychology: Vol. 5. Educational design and cognitive science (pp. 35–99). Mahwah, NJ: Lawrence Erlbaum Associates. Collins, A., Brown, J. S., & Newman, S. E. (1989). Cognitive apprenticeship: Teaching the crafts of reading, writing, and mathematics. In: L. Resnick (Ed.), Knowing, learning, and instruction: Essays in honor of Robert Glaser (pp. 453–494). Hillsdale, NJ: Lawrence Erlbaum Associates. De Corte, E. (2000). Marrying theory building and the improvement of school practice: A permanent challenge for instructional psychology. Learning and Instruction, 10, 249–266. De Corte, E., & Verschaffel, L. (2002). High-powered learning communities: Design experiments as a lever to bridge the theory/practice divide. Prospects, 32, 517–531. De Corte, E., Verschaffel, L., & Masui, C. (2004). The CLIA-model: A framework for designing powerful learning environments for thinking and problem solving. European Journal for Psychology of Education, 19, 365–384. Dochy, F. (2005). Learning lasting for life and assessment: How far did we progress. Presidential address at the 11th Biennial Conference of the European Association for Research on Learning and Instruction, Nicosia, Cyprus. Retrieved on 14 March 2006 from http://www.earli.org/conferences/previous_conferences/earli_2005/presidential_address. Sfard, A. (1998). Two metaphors for learning mathematics: Acquisition metaphor and participation metaphor. Educational Researcher, 27(2), 4–13.

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Curriculum, Pedagogy, and Learning in Early Childhood: Sites for Struggle — Sites for Progress Elizabeth Wood and Neville Bennett

Introduction Early childhood education occupies a significant place in international research and policy reform agendas, as reflected in global discourses and trends (Olmsted, 2000; Penn, 2004). These developments have been influenced by wider global agendas which link high-quality preschool education with improved educational performance and achievement for children, positive impacts on children’s transition to statutory schooling, and subsequent benefits for society. Research agendas are being influenced by policy reforms in identifying the structural factors that determine high-quality provision, specifically effective teaching and learning, and appropriate curriculum frameworks (Moyles, Adams, & Musgrove, 2002; Siraj-Blatchford, Sylva, Muttock, Gilden, & Bell, 2002). In many countries, policy reforms have led to increased funding, and unprecedented levels of government intervention in pedagogy, curriculum, and assessment practices. While the overall direction of policy reforms has been broadly welcomed, there remain a number of problems and challenges, which are situated in the dialectical relationship between theory, policy, and practice (Wood, 2004a). The aim of this chapter is to review past, present, and future trends in curriculum, pedagogy, and learning, in the context of rapidly changing policy and theoretical contexts. Drawing on international research, we will argue that these three areas can be conceptualised as sites for struggle (Soler & Miller, 2003) and sites for progress (Schoenfeld, 1999), and reflect differential power relations between key stakeholders. As a site for struggle, early childhood education has been underpinned by an eclectic theoretical and ideological base, which has traditionally been strong on ideals and aspirations, but weaker on empirical evidence about pedagogy and curriculum. Psychological theories of learning have had a dominant influence, but have not provided a coherent underpinning for pedagogy and curriculum development. This has created conceptual gaps which, in some countries, have

Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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been filled by government-led change programmes. In contrast, Schoenfeld (1999) identifies ‘sites for progress’, e.g. curriculum, pedagogy, assessment, change, where there are significant practical challenges which can be conceptualised in ways that can advance theory. For Schoenfeld, research on teaching-in-context bridges theory and practice, by developing rigorous characterisations of how and why teachers do what they do, and what models can be developed to guide or improve practice. There remain significant challenges to the early childhood community which can be solved in the contexts of practice. Because of the nature and extent of government reform programmes, teachers have a central role in mediating, adapting, and resisting the impact of national policies (Wood, 2004a; Wood & Bennett, 2000, 2001). So, what funds of knowledge are available, and what are the key sites for struggle and progress? This chapter provides a critical overview of contemporary theory and research in curriculum, pedagogy, and learning, in order to address these questions. The first section describes international policy trends in curriculum development, with a particular focus on the Foundation Stage in England, Te Whaariki in Aotearoa New Zealand, and the Reggio Emilia approach in northern Italy. The following two sections focus on pedagogy and learning, and indicate specific sites for struggle and progress, drawing on theory, research, and policy developments. The concluding section identifies a future research agenda which aims towards developing a rigorous theoretical underpinning in each area that can both challenge and inform policy and practice.

Curriculum Development: Struggle and Progress The early childhood curriculum remains a site for struggle because there are multiple ways in which the construct of curriculum has been interpreted, i.e. different curriculum models and multiple conceptualisations of the child as learner (Soler & Miller, 2003). There are longstanding beliefs that the activities in which the children engage (play-based, child-initiated, teacher-directed) constitute the curriculum. The established progressive child-centred ideology reinforced the focus on activities rather than outcomes, and less attention was paid to specifying desirable knowledge, skills, understanding, dispositions, and outcomes, within a clearly articulated curriculum framework. As early childhood education has become a site for significant development and policy activity, many of these assumptions have been contested from different theoretical positions (Dahlberg, Moss, & Pence, 1999; Olmsted, 2000). There is consistent evidence that high-quality provision has positive effects on children’s learning and development and their subsequent learning careers, and results in positive social and economic outcomes for society (Sylva & Pugh, 2005). This evidence has informed international trends towards structuring curricula and improving provision and services for children and their families, particularly those experiencing social and economic disadvantages (Anning, Cullen, & Fleer, 2004; Olmsted, 2000). These developments are taking place at a regional level (e.g., the Reggio Emilia approach in northern Italy) at state level in the United States and Australia, and at national level, e.g. in England, New Zealand, Norway, Sweden, Spain, and Denmark. As this chapter will reveal, some curriculum models are transcending national boundaries, and are impacting on international developments. A wide range of policy players and stakeholders is involved, and the extent to which different voices are

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represented varies widely, thus creating similar sites for struggle and progress across international contexts (Dahlberg et al., 1999; Nuttall, 2003; Penn, 2004). What constitutes an appropriate curriculum raises fundamental epistemological issues about curriculum goals and content, whose knowledge is prioritised, what knowledge is selected, and how that is represented by young children, and with young children. Such levels of policy-making activity can be seen as a mixed blessing: increased funding and support have developed alongside demands for quality and accountability, with varying levels of influence on curriculum, pedagogy, and assessment. Considerable effort has been focused on linking theoretical principles with curriculum frameworks, and recent trends towards sociocultural and postmodern orientations are challenging established developmental orientations (Hedges & Cullen, 2005; MacNaughton, 2000). In contrast, the educational pragmatism of some contemporary policy frameworks has the potential to impact on practice in much more direct and instrumental ways (Broström, 2003; Wood, 2004a). These trends can be exemplified by examining the policy frameworks for England, alongside contrasting international perspectives. The Policy Context in England In 1988, the National Curriculum was introduced for children aged 5–16, with national testing at ages 7, 11, 14, and 16. Test results for 7 year olds revealed the differential preschool experiences and achievements of 4–5 year old children on entry to primary school. Although the statutory age of starting school is 5 years, in practice the majority of 4 year olds enter primary school in the reception class, which is now known as Year R. The reception year falls within the policy framework for preschool education, and has always occupied a difficult structural position between the informal approaches in preschool settings, and the more formal approaches in the primary school (Wood, 2004b). The need to measure children’s progress from the end of Year R into Key Stage 1 of the National Curriculum (age 5–7) was a key driver in extending policy reforms to the preschool sector. The first national curriculum framework for 4–5 year olds was introduced in 1996, but was poorly conceptualised, and was substantially revised in response to feedback and pressure from the early childhood community. The Foundation Stage was introduced from 2000 onwards, and applies to all 3–5 year old children in private and public (government-funded) settings. The Curriculum Guidance for the Foundation Stage (CGFS) (DfEE/QCA, 2000) sets out learning outcomes in six areas which reflect the subject orientation of the English National Curriculum: literacy and language, mathematical development, knowledge and understanding of the world, physical development, creative development, and personal, social and emotional education. Within each area, learning goals are definitive and ‘stepping stones’ or competence indicators identify developmental pathways towards the goals. These define the expectations for what most children will attain by the end of Year R. The Foundation Stage Profile (DfES/QCA, 2003) is a centralised, statutory baseline assessment which is designed to enable practitioners to track children’s progress, and identify their achievement in relation to the goals. In 2002, the government introduced Birth to Three Matters (DfES, 2002) for 0–3 year old children in private and public group settings. This framework is organised around four key aspects: a strong child, a skilful communicator, a competent learner, and a healthy child, and emphasises the importance of reciprocity in relationships

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and interactions between children and their parents and caregivers. Both the CGFS and Birth To Three Matters frameworks are intended to provide ‘seamless’ progression and continuity with the National Curriculum. The term ‘practitioner’ is now commonly used to encompass all adults who work in preschool settings, regardless of their qualifications. However, government-funded settings, including all Year R classes, are typically led by qualified teachers with graduate or postgraduate level qualifications. The CGFS describes the principles that underpin good and effective practice (DfEE/QCA, 2000, pp. 11–12), with a focus on the practitioner’s role, specifically with regard to teaching, planning, and assessing. Well-planned and purposeful play is valued, and can be both childand adult-initiated. The guidance exemplifies learning opportunities that are appropriate for young children and help them to achieve the goals. Although teachers have broadly welcomed the CGFS (Aubrey, 2004), it has been criticised for encouraging ‘water-tight planning for highly specific and standardised outcomes’ (Adams, Alexander, Drummond, & Moyles, 2004). A report by the national inspection agency, the Office for Standards in Education (OfStEd, 2004), also identified a number of problems with the implementation of the Foundation Stage, the assessment demands of the Profile, and the extent to which Year 1 teachers made effective use of assessment information from Year R teachers. The reform agenda includes raising standards in literacy and numeracy based on recommendations from school effectiveness research, international comparisons of educational performance, variations in the quality of teaching and learning in these subjects, and differential rates of progression, especially for children in inner city schools (Hurry, Sylva, & Riley, 1999). The National Literacy Strategy (DfEE, 1998) and National Numeracy Strategy (DfEE, 1999) developed Frameworks for Teaching across the 4–11 Primary age range. Whilst the strategies claim to be based on empirical research, the evidence on which they drew was selective, and served a policy remit for developing direct instructional strategies which would (theoretically) be effective for all teachers in all schools. The evidence base on how young children learn and develop was not used systematically (Wyse, 2004) with the result that instructional strategies, which were effective with older children, were inadequately differentiated for younger children. The policy agenda focused on school and teacher effectiveness, which created a dominant discourse and system of ideas that emphasised a technical/rational model of curriculum, pedagogy, and assessment. These developments have created new sites for struggle in early childhood education (Wood, 2004a). The curriculum frameworks for literacy and numeracy adopt a linear, sequential, and hierarchical curriculum model, with implicit assumptions about learners and learning. While these frameworks embody culturally valued knowledge, they do not consistently embody theoretical principles and practices that are empirically derived from within the early childhood community. There remain problems in adopting competencybased and outcomes-led curriculum frameworks. Highly specified outcomes-led curricula lead to outcomes-led assessment criteria, so that assessment practices may focus more on tracking content coverage, than on providing deep understanding of children’s learning (Wood & Bennett, 2001). The focus on subject-based content knowledge has led to an erosion of practical first-hand experiences, play-based activities, spontaneity, and independence in children’s learning (Adams et al., 2004; Moyles et al., 2002). However, the extent to which such flexible curriculum and pedagogical approaches can be achieved in practice has always been a contentious area (Bennett, Wood, & Rogers, 1997). There is an assumption

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that when children make their own choices, and follow their own interests, learning becomes a much more powerful activity. However, this is dependent on the range of choices available, the amount of interaction with more, or differently, knowledgeable others (including peers and adults), the provision of supportive resources, and the potential for children’s activities to be connected to worthwhile learning (knowledge, skills, attitudes, and dispositions) (Bennett et al., 1997). As developments in other countries indicate, the flexibility and spontaneity implied within a learner-centred, play-based curriculum and pedagogy creates many challenges. Contrasting Perspectives: Te Whaariki and Reggio Emilia In Aotearoa New Zealand, the early childhood curriculum framework, Te Whaariki (Ministry of Education, 1996), was designed to be culturally relevant to the Pakeha (white European) and the minority Ma¯ori cultures. The curriculum and its related assessment framework (Ministry of Education, 2004) enjoyed a long period of consultation, development, and trialling, with the involvement of the academic and practitioner communities. The curriculum framework is organised around age-related concepts of infants, toddlers, and young children, and the goals reflect the more traditional terminology of developmental domains (Cullen, 1996). The definition of curriculum is ‘the sum total of the experiences, activities, and events, whether direct or indirect, which occur within an environment designed to foster children’s learning and development’ (Ministry of Education, 1996, p. 10). The curriculum has been envisaged as a whaariki, or mat, which is woven from principles, strands, goals, and learning outcomes. The goals relate to the overall learning environment, what the children learn and experience within that environment, and the ways in which practitioners make links between the home, community, the setting, and other early childhood services. This flexible framework requires practitioners to develop their own programme perspectives, depending on the age and interests of the children, the cultural, structural, or philosophical context of the particular service and the interests of the parents and staff (May, 2001). There are significant differences between the English and New Zealand frameworks. The learning outcomes in Te Whaariki are descriptive rather than definitive; they are holistic in the sense that they transcend subject boundaries, and are not hierarchically organised. Te Whaariki focuses on children and their learning: curriculum planning is based on responding to children’s interests and fostering learning dispositions. Learning outcomes (skills, knowledge, and understanding) are embedded in activities and experiences that reflect those interests. Te Whaariki has moved gradually from a developmental towards a sociocultural theoretical underpinning. The early childhood centre or classroom is conceptualised as a community of learners, where learning is a co-constructive process which involves the child acting in context, with increasingly competent forms of participation (Cowie & Carr, 2004). Narrative approaches to assessment reflect contemporary sociocultural orientations. The practitioners focus on what children are learning, how learning happens, and the role that other adults play in their learning. Family involvement is encouraged through shared assessments across home and the setting, with family members contributing to children’s documented learning stories. Fleer (2002) argues that developing a sociocultural perspective for assessment is one of the greatest challenges facing educationalists, because practices that

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follow this perspective must be framed to map the transformation of knowledge and understanding, and how those transformations occur through participation in communities of practice. Te Whaariki shares many similarities with the Reggio Emilia approach in northern Italy (Edwards, Gandini, & Forman, 1993) because key principles about how children learn drive curriculum design. There is no established or approved curriculum, and the content is shaped by the child’s interests and ideas. Children are seen as competent learners and communicators who express their progress and achievement through multi-modal representations. The teaching–learning dynamic is seen as co-constructive: children and adults work collaboratively on short- and long-term projects, which may be adult- or child-initiated. Each Reggio Emilia centre has a specialist art teacher (atelierista) who works alongside teachers and children. Pedagogy and assessment are responsive to the child, based on listening, observing, and interacting. Pedagogical documentation is a form of communication with adults who are involved with the child at home and in the setting. The processes of documentation and discussion constitute professional development, in which teachers generate their own theories and solve problems in the contexts of practice. These contrasting orientations reflect fundamental theoretical, social, and political assumptions about children and childhood, and about the purposes of early childhood education. In England, the emphasis on transforming curriculum and pedagogy is a direct challenge to play-based orientations, which often promoted a facilitating pedagogical model. The literacy and numeracy frameworks have been influenced by direct instructional strategies, with an emphasis on school readiness, and ‘curriculum coverage’. The sociocultural and holistic underpinning of Reggio Emilia and Te Whaariki is equally challenging. The focus on building a curriculum around children’s ideas, dispositions, interests, strengths, needs, and behaviours has created tensions between developmental and sociocultural orientations (Broström, 2003; Cullen, 1996; Fleer, 2002; Hedges & Cullen, 2005; Nuttall, 2003). The Piagetian orientation of ‘development leading learning’ has been interpreted as a ‘watching and waiting’ approach in which practitioners respond to children’s readiness to show interest and become involved in activities. In contrast, sociocultural theories imply a proactive role for practitioners through their pedagogical framing and strategies: they can actively stimulate children’s interests with worthwhile content, based on the Vygotskian orientation of ‘learning leading development’ (Wood & Attfield, 2005). As De Vries (1997) argues, these orientations are not polarised. In developmentally based curricula, teachers should actively help children to find their purposes, and challenge children to pursue a specific purpose within their self-chosen activities. Thus, it can be argued that reconciling developmental and sociocultural orientations remains a key site for progress. The Reggio Emilia and Te Whaariki approaches emphasise that children learn by participating in repertoires of practice. However, participation in itself may not provide sufficient focus on learning repertoires of skills and knowledge. The early childhood field appears polarised on beliefs about subject knowledge: for some, this approach is contrary to how young children think and learn and, as argued previously, invites formal ‘top-down’ curriculum models. Broström (2003) argues that the content of Te Whaariki is diffuse, and that there is no explicit relationship between aims and content. Hedges and Cullen (2005) make a strong case for strengthening the place of subject content knowledge in Te Whaariki in order to provide ‘deep’ and meaningful learning experiences. There is consistent evidence

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to support the view that children’s engagement with the subject disciplines creates strong foundations for their subsequent learning, particularly in literacy and numeracy (Roskos & Christie, 2000; Wood & Attfield, 2005), because these embody powerful cultural tools and symbol systems. Therefore it can be argued that placing responsibility on practitioners to formulate their own content is a potentially risky endeavour in preschool settings, because of the different levels of training, knowledge, and understanding across the sector. As the following section argues, there remain tensions between learner- and curriculum-centred approaches in these contrasting models. Juxtaposing Curriculum- and Learner-Centred Models All curricula reflect systems of ideas and effects of power (Popkewitz, 2000) regarding the knowledge that is considered valuable in a society, both in the immediate and longer terms. The reification of any system of ideas has strengths and weaknesses. In early childhood, a key site for struggle centres on defining the organising principles for curriculum content and design, and reconciling the tensions between curriculum- and learner-centred approaches (Wood & Bennett, 2001), both of which have different implications for practice. The English system reifies a curriculum-centred approach because it is organised around definitive learning outcomes in the subject domains, which influence progression and continuity across phases. In contrast, Te Whaariki and Reggio Emilia reify learnercentred approaches within combined developmental and sociocultural orientations. Sites for progress in curriculum theory and research suggest that teachers and learners can coconstruct the curriculum, based on adult-directed and child-initiated activities, including play (Anning et al., 2004; Johnson, Christie, & Wardle, 2005). Such an orientation demands sophisticated approaches to curriculum design, planning, and assessment, sound understanding of subject matter knowledge and of the ways in which this can be presented to young learners. Theoretically it is inevitable that curriculum models should combine some developmental elements (building on children’s existing knowledge and interests) and instrumental elements (preparing children for the next steps in learning, or the next stage in education). It is also desirable that curriculum models should aim towards specifying what forms of knowledge are appropriate for young children, and how they engage with the subject disciplines in their early learning careers. However, whether one model is more optimal, or more effective, than another remains contentious, and will always be influenced by culturally situated systems of ideas that shape curriculum design and content (cf. Anning et al., 2004; Nuttall, 2003). As the following section shows, there are similar challenges in conceptualising appropriate pedagogical strategies in relation to curriculum- and learner-centred orientations.

Pedagogy: Struggle and Progress Until recent years, pedagogical theory received little attention in early childhood. Trends towards transforming pedagogy have been based on critiques of Developmentally Appropriate Practice (DAP), developing sociocultural orientations, and challenging established discourses and practices. Both Reggio Emilia and Te Whaariki espouse a pedagogy of listening and

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observing as the basis for informed interactions with children. However, the quality and educational potential of those interactions will depend on the knowledge bases of the practitioners, their ability to connect children with worthwhile content, and to provoke transformational learning. Such flexible pedagogical approaches also require practitioners to meet the needs of individuals and groups of children. The policy context in England exemplifies trends towards transforming pedagogical strategies and routines, and exerting more control over teachers. The CGFS also specifies pedagogical routines and strategies (Siraj-Blatchford, 2004), including proactive roles for teachers in designing learning environments, planning teacher-directed activities, following child-initiated activities, and assessing children’s progress and achievements. This guidance validates mixed pedagogies, by acknowledging the importance of planned and purposeful play, which can be both child-initiated and adult-directed. However, as Wood (2004b) argues, these constructs are problematic in theory as well as in practice. It is not clear whose plans and purposes take precedence (the teacher’s or the child’s), and practitioners have to develop their own interpretations of these guidelines. As noted previously, the prescribed pedagogy in the English literacy and numeracy strategies validates teacher-directed activities, direct instruction, and whole class teaching. Research evidence indicates that teachers experience considerable challenges in matching the linear, hierarchical structure of the strategies, with the more flexible pedagogy in the Foundation Stage, and the less predictable patterns of young children’s learning (Adams et al., 2004; OfStEd, 2004; Wood & Bennett, 2001). Contemporary research is creating sites for progress by addressing these tensions, and conceptualising effective pedagogical approaches in early childhood. Conceptualising Effective Pedagogy in Early Childhood Education The international research agenda has been increasingly focused on the ‘effectiveness’ of different early childhood settings in relation to pupil learning outcomes and subsequent learning careers (Sylva & Pugh, 2005). The study on Effective Provision of Preschool Education (EPPE), and its linked projects in the UK, are an outcome of this agenda. The EPPE project is a large-scale, mixed-method, longitudinal study tracking the progress and development of 3000 children over an eight year period (aged 3–11) who have attended different types of preschool provision (Sylva, Sammons, Melhuish, Siraj-Blatchford, & Taggart, 1999). Using an educational effectiveness design employing multi-level modelling techniques, the study has identified the impact of a range of child, parent, home, and preschool influences on children’s attainment and social outcomes. The results of the quantitative analyses of effective settings were used to select a small number of case studies for more detailed qualitative investigation of effective practice. Outcomes from the study on Researching Effective Pedagogy in the Early Years (REPEY) (Siraj-Blatchford et al., 2002) have identified a wide range of pedagogical strategies and techniques that affect child outcomes. The authors distinguish between pedagogical interactions (specific behaviour on the part of adults) and pedagogical framing (the behind-the-scenes aspects of pedagogy which include planning, resources, and routines). The main findings validate mixed pedagogies, alongside proactive roles for practitioners. The most effective pedagogues model appropriate language, values and practice; encourage sociodramatic play; praise, encourage, ask questions and interact verbally with children. Effective pedagogy

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includes ‘teaching’ and the provision of instructive learning and play environments and routines. The most effective settings provide both teacher-initiated group work and freely chosen yet potentially instructive play activities. Excellent settings tend to achieve an equal balance between adult-led and child-initiated interactions, play, and activities. The most highly qualified staff provide the most direct teaching alongside the kind of interactions which guide but do not dominate children’s thinking (Siraj-Blatchford et al., 2002). These findings do not endorse the direct instructional strategies embedded in the English literacy and numeracy strategies: the emphasis is rather on developing opportunities for ‘sustained shared thinking’ which are responsive to children’s interests, but at the same time connect them with subject knowledge, and tools for thinking and learning. A study on the Pedagogical Effectiveness in Early Learning (SPEEL) (Moyles et al., 2002), which is also linked to EPPE and REPEY, focused on the theories and practices of teachers and preschool practitioners, specifically in relation to the impact of their decisions and actions on children’s learning. Although the participants endorsed the educational potential of play, they often had difficulties with understanding their role, and assessing the outcomes of play. Thus although the Foundation Stage guidance incorporates a pedagogy of play, achieving this in practice remains a considerable challenge (Wood & Attfield, 2005). Conceptualising a Proactive Pedagogical Model The concept of direct, intentional teaching has been anathema to curriculum models that are informed by developmental theory. However, the findings discussed in the previous section challenge teachers to move towards proactive, mixed pedagogical approaches, which reflect sociocultural conceptions of learning leading development (Wood, 2004b). The findings are relevant to conceptualising a play-based pedagogy because the environments in which play occurs and the interactions between adults and children constitute indicators of high-quality provision. These recommendations are consistent with international research: contemporary theoretical perspectives indicate that learning through play should not be left to chance, but can be channelled through co-constructed activities in which adults and children share goals, intentions, and meanings (Johnson et al., 2005; Wood & Attfield, 2005). In summary, findings from contemporary research studies reflect the complexity of teaching and learning in the early years, in the context of diverse forms of provision. There is consistent evidence to support the view that effective pedagogy is not characterised by adherence to a particular method or theoretical orientation but involves a mix of strategies and techniques which rely on the professional judgement of teachers and other practitioners in the setting. Pedagogical approaches that combine adult-directed and children’s selfinitiated activities require high levels of professional knowledge and expertise. This is equally relevant in the prescriptive approaches in the English Foundation Stage, and the more flexible, descriptive approaches in Te Whaariki and Reggio Emilia. Therefore, a site for progress across international contexts is better understanding teachers’ pedagogical framing and strategies, specifically in combining child-initiated and teacher-directed activities, and the interactive and co-constructive nature of those activities (Wood, 2004b). Further understanding is needed of how teachers combine strategies for nurturing and inspiring children’s interests, recognising and responding to their interests, fostering

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positive dispositions towards learning, and connecting children with subject knowledge in order to enrich and extend deep learning. Contemporary directions in pedagogical theory confirm the view that teaching is a knowledge-based activity, which is highly interactive and contingent on dynamically changing goals (Schoenfeld, 1999). Teachers’ pedagogical decisions and actions are situated in complex structures and realities; they are not passive implementers of externally driven change (Wood & Bennett, 2000, 2001). Rather they draw on complex pedagogical epistemologies in order to adapt, mediate, and contest national policies, based on their personal theories, knowledge, values, and beliefs (Wood, 2004a). Curriculum and pedagogical theory and practice can thus be conceptualised as sites for progress. However, as the next section argues, progress is linked to contemporary advances in learning theory.

Learning: Struggle and Progress Early childhood education draws on an eclectic ideological and theoretical underpinning which has not provided an agreed or consistent basis for practice. The charge that developmental theory has not served early childhood education well is based on critical and postmodern perspectives, regarding the efficacy of the links between developmental psychology and curriculum models (Cullen, 1996; Wasik, Bond, & Hindman, 2002). In a critique of DAP, MacNaughton (2000) draws on feminist and poststructuralist perspectives, and challenges established knowledge-power regimes. MacNaughton argues that DAP has contributed to social inequality and injustice because the traditional child development and empirical knowledge on which it is based is ethnocentric. In addition DAP processes and principles contribute to discriminatory practices in terms of gender, ethnicity, and disability because children are positioned in relation to developmental norms. Combining Individual and Situated Perspectives Contemporary learning theories have moved away from a predominantly developmental/individual orientation towards a social and cultural orientation, and aim to integrate the individual/cognitive and social/situated perspectives (Schoenfeld, 1999). Anderson, Greeno, Reder, and Simon (2000) have identified points of agreement between these perspectives, and argue that both can provide accounts of learning that occur in groups and in solitary activity. While there are different emphases within each orientation, both provide ways of paying respect to the importance of human individuality, the importance of social practice, and the importance of education to the development of individual identity (Anderson et al., 2000). The international trends described in this chapter represent a sustained endeavour to link social-cultural theories with guidance for curriculum, pedagogy, and assessment. Contemporary interpretations have contested the certainties of developmental theory, and have generated contrasting discourses about learning which are applicable across the life span, rather than specifically to early childhood. A key tenet of sociocultural theory is that learning is situated in social practices, and is dependent on the extent to which experts enable novices to participate effectively in practices that are typical in their home, community, and

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workplace. Learners are social actors who draw on, and contribute to, the resources of the settings and practices in which they participate (Wenger, 1998). Studies that adopt a situated perspective typically analyse relationships and interactions between individuals and other people, with the tools, symbol systems and technologies of the culture, and with the learning environment (Engeström, Miettinen, & Punamaki, 1999). However, the emphasis on contextually situated support for learning may have been over-stated at the expense of the processes of internalisation. As Shayer (2003) argues, in Vygotskian theory, co-operative interactions with peers and adults awaken internal developmental processes, which are internalised and become part of the child’s independent developmental achievement. Combining individual and situated perspectives is a site for theoretical progress, as discussed in the following section. Contemporary Sociocultural Orientations Exponents of sociocultural theories highlight four key areas in understanding learning which combine individual and situated perspectives (Schoenfeld, 1999; Sfard, 1998). First, at an individual level, learning is interpretive, recursive, and incremental, based on learners constructing new knowledge and capacities on existing foundations. Learning involves progress along trajectories or repertoires of participation, with increasing competence in different practices. A second key area is that learning is socially centred and involves dynamic inter-relationships between teachers and learners. Rather than ‘watching and waiting’ on development, teaching becomes a decisive force because teachers and learners coconstruct knowledge, which builds new cognitive structures and ‘higher mental processes’. Vygotsky (1978) proposed that effective teaching and learning occur in the ‘zone of proximal development’ (ZPD) where the more (or differently) knowledgeable other leads the novice just ahead of their current level of knowledge and understanding through scaffolded interactions. The concepts of co-construction, scaffolding, and the ZPD are used frequently in international discourses in early childhood education. However, they are often used uncritically and selectively, and this theoretical shift is not without its critics. Philosophically, the concept of the ZPD has been interpreted in different ways (Lambert & Clyde, 2003; Ortega, 2003; Shayer, 2003), based on an autocratic/transmissive model, and a democratic/participative model. In the autocratic/transmissive model the ZPD is a controlling structure, where responsibility for learning is dependent on a transmission process from the teacher or expert to the learner or novice. The ZPD can be conceptualised as an instructional or training model because the locus of control is with the teacher rather than the learner, and the teacher defines the end point, or learning objective. This model is represented in the English literacy and numeracy frameworks for teaching, because the prescribed teaching objectives define the choice, pacing, and sequencing of the curriculum content. The range of work to be covered is identified for each age group, and is organised into termly objectives, which give focus and direction to the teaching. The frameworks recommend a wide range of effective instructional strategies including direct teaching, demonstrating, modelling, questioning and discussing, investigating and responding to children’s ideas, and evaluating children’s responses. However, the efficacy of these frameworks in early childhood remains contentious, because the teacher orchestrates learning, with less focus on the learner’s intentions and motivations. In a study of progression and

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continuity, Wood and Bennett (2001) noted that the pacing and sequencing of teaching in Year R and Year 1 classrooms were not always consistent with children’s learning journeys in literacy and numeracy, because teachers had to move on to the next teaching objectives regardless of the children’s achievements and levels of understanding. In the democratic/participative model, the ZPD is conceptualised as an enabling structure which allows differently knowledgeable others to participate in joint activities, in which the teacher’s strategies are finely tuned to the learner’s observed intentions, motivations, behaviour, language, knowledge, and activity. The teacher aims to identify a ‘problem space’, or gap between current and potential levels of learning and development. Active participation by the learner is encouraged and valued. Learners are encouraged towards independent thought and action, using metacognitive skills and strategies, which support the transformation of participation. As argued previously, this model requires intimate interactions between learners and teachers in order to develop the ‘sustained shared thinking’ that characterises effective pedagogy. Pedagogically, this orientation is challenging: approaches that allow children high curricular self-choice (such as Reggio Emilia and Te Whaariki) do not guarantee that they will learn the necessary skills, knowledge, and understanding that are essential in the immediate term, and serve as a foundation for subsequent learning. Even where play and self-initiated activities result in ‘unintended learning outcomes’ (Bennett et al., 1997) teachers need the knowledge and expertise to recognise these outcomes, and guide the child towards further related learning. The third key area in contemporary sociocultural theory is that learning is contextually situated because knowledge is embedded in social settings and practices (Wenger, 1998). Participation in social practices influences cognitive and motivational change: learning is synonymous with changes in the ways that individuals participate in social practices. As Sfard (1998) argues, the metaphor of learning as participation should not be taken to imply that there is no individual acquisition: rather the distinction between internal cognitive processes and external, interpersonal contexts is less clear-cut than in the metaphor of learning as acquisition. Participation is gradually transformed through joint enterprise, mutual engagement, and shared repertoires within communities of practice. Progression, therefore, is conceptualised as the transition from the periphery to the centre of a social practice, and from novice to expert, or at least to gradually more competent forms of practice which are increasingly self-regulated (Wenger, 1998). The fourth key area is that learning is distributed across a range of contexts and coparticipants, and is influenced by cultural tools, symbol systems, and technologies. Learning is facilitated by the learner’s engagement with authentic practices that are situated in everyday contexts, including foundational knowledge in the subject disciplines. Learning as an outcome of activity and social participation involves transformational processes within the individual, and the social context. However, the actions of individuals within an activity system involve learning transformations which can be unique and individual, and may not always be predictable (Engeström, 1999). Sociocultural theories provide an explanatory framework for progression in the subject disciplines from the ‘emergent’ rather than the ‘ages and stages’ perspective. Children’s conceptual frameworks gradually become more integrated and more automatic: the integration of procedural skills and conceptual knowledge leads to greater flexibility, application, transfer, and metacognition.

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Sociocultural orientations thus have significant implications for conceptualising learning, curriculum, pedagogy, and assessment. However, where these theories are used as systems of ideas to underpin curriculum models, some caution must be exercised, because practitioners may misinterpret, or pay lip service to the principles, without clear understanding of their meaning, the ways in which they are expressed in classrooms, and their impact on children’s learning. Sociocultural theories are being used and interpreted selectively. Conceptualising learning as the transformation of participation, as in Te Whaariki, is theoretically complex, and raises further epistemological issues about where and how those transformational processes occur (in the individual, in the social context), what repertoires of participation are created in preschool settings, and what repertoires of skills and knowledge children need in order to engage successfully, and with increasing levels of competence. Similarly, the Reggio Emilia approach raises critical questions about knowledge–power relationships, and the extent to which children may be fulfilling their own, or adults’ purposes and goals. Theoretically, synthesising fundamentally individual and social accounts of learning remains a significant site for progress. As Schoenfeld (1999) recommends, the implications of this endeavour for pedagogical and curriculum development need to be worked out in the contexts of practice.

Conclusion This chapter has provided insights into international policy reforms and developments in early childhood education, focusing on varying emphases and orientations, and the implications for practice. Reform agendas are also linked to ongoing debates about what constitutes good quality provision for young children, and are linked to a global agenda for improving children’s experiences and life chances. Alongside reform agendas there are significant theoretical developments which are acting as further catalysts for change. On the basis of the foregoing analysis, curriculum, pedagogy, and learning constitute sites for struggle as well as sites for progress. But to what extent are these sites for progress located in reform agendas, or in the contexts of research and practice? Government-led change programmes in early childhood education have posed problems and challenges to early childhood teachers and other practitioners that need to be solved in the context of practice. The evidence presented in this chapter shows how such reforms are mediated by teachers’ theories and experiences, leading to multiple interpretations and recontextualisations that are situated in local cultures and contexts. Furthermore, policy documents may be reified at a specific point in time, but are continuously modified in and through practice, leading to further changes at policy level. These processes can be seen in England, where policy documents have been contested from within the educational community, and have been withdrawn or redesigned, or have produced further clarification and exemplification (Wood, 2004a). In Aotearoa New Zealand, Te Whaariki continues to evolve through recontextualising the original aims in relation to contemporary sociocultural theories, and by articulating the curriculum with wider educational policy developments, specifically in addressing continuity with primary education (Nuttall, 2003). The Reggio Emilia approach has provoked wide interest, to the extent that it has created an international industry in disseminating its principles and practices, even though there is no established curriculum.

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Thus it can be argued that the policy–practice dialectic is closely related to the theory– practice dialectic. Given the complexity and significance of international trends in early childhood, a key site for progress is improving the knowledge bases of teachers and other practitioners in the sector. The challenges for a future research agenda are essentially practical, but, as Schoenfeld (1999) has argued, can also be conceptualised in ways that advance theory, and provide models that can guide or improve pedagogy, curriculum, and assessment practices. In the early childhood community, there are funds of culturally situated knowledge, as well as professional values and beliefs, which reflect the complex dynamics of practice. Further theoretical advances can be derived from developing rigorous characterisations of what teachers do, in relation to their pedagogical epistemologies, within differing social, cultural, and political frameworks. The inclusion of different voices and perspectives in contemporary research agendas constitutes sites for progress, by opening up possibilities for new and different readings of learning, pedagogy and curriculum, play, and assessment. A future research agenda in early childhood education should aim towards generating new understandings about the complex dynamics which are situated in the dialectical relationships between policy and practice, research and practice, and theory and practice. The challenges to the research and practitioner communities include creating sites for progress in which theoretical developments can be generated through practice, and can inform debates and developments across national and international contexts.

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Popkewitz, T. S. (2000). The denial of educational change: Systems of ideas in the construction of national policy and evaluation. Educational Researcher, 29(2), 17–29. Roskos, K., & Christie, J. (Eds). (2000). Play and literacy in early childhood: Research from multiple perspectives. Mahwah, NJ: Erlbaum. Schoenfeld, A. H. (1999). Looking toward the 21st century: Challenges of educational theory and practice. Educational Researcher, 28(7), 4–14. Sfard, A. (1998). On two metaphors for learning and the dangers of just choosing one. Educational Researcher, 27(2), 4–13. Shayer, M. (2003). Not just Piaget; not just Vygotsky, and certainly not Vygotsky as alternative to Piaget. Learning and Instruction, 13, 465–485. Siraj-Blatchford, I. (2004). Quality teaching in the early years. In: A. Anning, J. Cullen, & M. Fleer (Eds), Early childhood education: Society and culture (pp. 137–148). London: Sage. Siraj-Blatchford, I., Sylva, K., Muttock, S., Gilden, R., & Bell, D. (2002). Researching effective pedagogy in the early years (REPEY). Research report no 356, Department for Education and Skills. London: Her Majesty’s Stationery Office. Soler, J., & Miller, L. (2003). The struggle for early childhood curricula: A comparison of the English Foundation Stage Curriculum, Te Wha 苶riki and Reggio Emilia. International Journal of Early Years Education, 11(1), 57–67. Sylva, K., & Pugh, G. (2005). Transforming the early years in England. Oxford Review of Education, 31(1), 11–27. Sylva, K., Sammons, P., Mehuish, E., Siraj-Blatchford, I., & Taggart, B. (1999). Technical paper 1: An introduction to the Effective Provision of Pre-school Education Project (EPPE). London: Institute of Education, Department for Education and Employment. Vygotsky, L. (1978). In: Mind in society. M. Cole., V. John-Steiner., S. Scribner, & E. Souberman (Trans. & Eds). Cambridge, MA: Harvard University Press. Wasik, B. A., Bond, M.A., & Hindman, A. (2002). Effective early childhood curriculum for children at risk. In: O. Saracho, & B. Spodek (Eds), Contemporary perspectives on early childhood curriculum (pp. 63–89). Greenwich, CT: Information Age Publishing. Wenger, E. (1998). Communities of practice: Learning meaning and identity. Cambridge: Cambridge University Press. Wood, E. (2004a). A new paradigm war? The impact of national curriculum policies on early childhood teachers’ thinking and classroom practice. Teaching and Teacher Education, 20, 361–374. Wood, E. (2004b). Developing a pedagogy of play for the 21st century. In: A. Anning, J. Cullen, & M. Fleer (Eds), Early childhood education: Society and culture (pp. 17–30). London: Sage. Wood, E. A., & Attfield, J. (2005). Play, learning, and the early childhood curriculum (2nd ed.). London: Paul Chapman. Wood, E., & Bennett, N. (2000). Changing theories, changing practice: Early childhood teachers’ professional learning. Teaching and Teacher Education, 16, 635–647. Wood, E., & Bennett, N. (2001). Early childhood teachers’ theories of progression and continuity. International Journal of Early Years Education, 9, 229–243. Wyse, D. (2004). The National Literacy Strategy: A critical review of empirical evidence. British Educational Research Journal, 29, 903–916.

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Chapter 2

Mathematics in the Mind: Architecture, Development, and Educational Implications Andreas Demetriou and Areti Panaoura

Introduction For many, mathematics is a very special kind of activity of the human mind that enables some privileged persons to conceive of very abstract and bizarre concepts and solve very cumbersome, obscure, and impenetrable problems. For others, there is nothing special in mathematics. It is just one of many activities of the human mind which, when pulled to the extreme, requires a special talent to grasp the concepts involved and use them in original ways for the solution of important problems. We ally with this second interpretation. That is, we believe that mathematics does involve some special mechanisms of representation and mental processing which are appropriate for the representation and processing of quantitative relations. At the same time, we also believe that these mechanisms are constrained by the organization and the possibilities of one kind of brain, the human brain, and, at present, they are learned and practiced in one particular kind of culture, the human culture. Thus, any theory about the nature, the architecture, and the development of mathematics will have to specify the domain-specific processes and functions that it involves, the general potentials and processes of the human mind that sustain and frame its functioning, and their dynamic relations both in real time during problem solving and in ontogenetic time. In this chapter we will attempt to satisfy these requirements in the context of a theory of cognitive organization and growth that is experimentally based and that integrates three traditions in psychology, namely the experimental, the differential, and the developmental tradition. Specifically, this theory models, first, the more dynamic, real-time, aspects of mental functioning to explain how information from the environment is recorded, represented, stored, and processed for the purpose of understanding and problem solving. Second, the theory also specifies the factors that are responsible for intra- and inter-individual differences in mental functioning and development. Thus, it can be used to describe and explain why persons do not perform equally well across different domains of cognitive abilities or Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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why persons differ between each other in reference to this or that ability. Finally, the theory models the development of mental functions in order to specify both their state and form at different phases of life and the causes and mechanisms underlying their transformation with growth. In the pages following we will first summarize the general postulates of this theory and then focus on mathematical thinking, in order to highlight its place in the architecture of the human mind, its inter-dependencies with the other components of the human mind, and its development. At the end of the chapter we will summarize a series of studies that were designed to show how the various dimensions of the human mind specified by the theory are related to school performance in mathematics and draw the implications of these findings for education.

The Architecture of the Human Mind The human mind is a hierarchical and multidimensional edifice that involves both generalpurpose and specialized processes and abilities (Carroll, 1993; Gustafsson & Undheim, 1996; Jensen, 1998). Figure 1 illustrates our general representation of the processes and functions involved in the developing mind (Demetriou, 2004; Demetriou, Christou, Spanoudis, & Platsidou, 2002; Demetriou, Efklides, & Platsidou, 1993; Demetriou & Kazi, 2001, 2006). Understanding, learning, or performing on any task, at a particular point in time, is a mixture of all of these processes. General Processes The general processes revolve around a strong directive–executive function (DEF) that is responsible for setting and pursuing mental and behavioral goals until they are attained. The constructs serving DEF may be specified from three different perspectives, that is, their (i) efficiency, (ii) their capacity, and (iii) the fundamental operations that they involve. Processing efficiency refers to how well the person executes the processes activated in the service of DEF at a given moment. Technically speaking, processing efficiency refers to the ability to focus on, encode, and operate on goal-relevant information and inhibit or resist to goal-irrelevant information until the current mental or behavioral goal is attained. Thus, selective attention is the functional manifestation of processing efficiency. Ideally, processing is considered to be efficient when it is completed without mistakes and unnecessary mental operations that would result in excessive mental effort or waste of cognitive resources. A common measure of efficiency is speed of processing. Traditionally, the faster an individual can recognize a stimulus or execute a mental act, ignoring irrelevant information, if required, the more mentally efficient he or she is thought to be. Processing capacity is the maximum amount of information and mental acts that the mind can efficiently activate simultaneously under the direction of DEF. In the current psychological literature, working memory is regarded as the functional manifestation of processing capacity. It is generally accepted that working memory involves both central executive processes and modality-specific storage that specializes in the representation of different types of information. Baddeley’s (1993) model is exemplary for this type of architecture of working memory. According to this model, working memory involves two

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DEF Selective attention Control of Inference Performance evaluation Theory of mind Theory of intelligence Cognitive self-concept

Domain specific thought systems

speed

Spatial Social Categorical Quantitative Verbal Causal

Working memory Specialized storage Visual Phonological Other

Figure 1: The general model of the domain-general and domain-specific systems of the human mind. general systems, the central executive system (which is the locus of the executive operations involved in DEF) and the episodic buffer (everything that is active at a particular moment), and two specialized storage buffers, one specializing for the storage of phonological and the other specializing for the storage of visuo/spatial information. Directive-executive control processes involve five basic components: (i) a directive function that sets the mind’s current goals; (ii) a planning function that proactively constructs a road map of the steps to be made in the sake of the goal; (iii) a comparator or regulatory function that regularly effects comparisons between the present state of the system and the goal; (iv) a negative feedback control function that registers discrepancies between the present state and the goal and suggests corrective actions; (v) an evaluation function that enables the system to evaluate each step’s processing demands vis-à-vis the available structural possibilities and necessary skills and strategies of the system so as to make decisions about the value of continuing or terminating the endeavor and evaluate the final outcome achieved. These regulatory functions operate under the current structural constraints of the system that define the system’s current maximum potentials discussed above (Demetriou, 2000; Demetriou & Kazi, 2001). Moreover, consciousness is an integral part of DEF. That is, the very process of setting mental goals, planning their attainment, monitoring action vis-à-vis both the goals and the plans, and regulating real or mental action requires a system that can remember and review and therefore know itself. Therefore, a self-concept and a theory of mind (i.e., awareness of others’ mental functions and states) are part of the very construction of the system (Demetriou, 2004; Demetriou & Kazi, 2001). Domains of Thought and Specialized Processes Specialized processes refer to mental operations and problem-solving skills that are suitable for the handling (i.e., the comparison, the combination, and the transformation) of different types of information, relations, and problems. We propose that to qualify for the status of a

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domain of thought, a block of mental operations must satisfy the following criteria. First, it must serve an identifiable special function or purpose vis-à-vis the organism’s adaptational needs. Second, it must be responsible for the representation and processing of a particular type of relations between environmental entities. In fact, the special function of the system is to enable the organism to deal with a particular type of environmental relations. Third, it must involve specialized operations and processes that are appropriate for the representation and processing of the type of relations concerned. In a sense, the operations and processes of a domain of thought are the mental analogs of the type of relations concerned. Fourth, it must be biased to a particular symbol system that is better appropriate than other symbol systems to represent the type of relations concerned and facilitate the execution of the operations concerned. Our research has uncovered the following six domains of thought that satisfy these criteria: categorical, quantitative, spatial, causal, verbal, and social thought (Demetriou, 2004; Demetriou et al., 1993, 2002; Demetriou & Kazi, 2001). In the pages below we will focus on the domain of quantitative reasoning, which is the main object of this chapter. Each of the domains is itself a very complex system that is organized in different layers and that it involves multiple components at each layer. Specifically, each domain involves (i) core processes, (ii) rules, mental operations, and processing skills, (iii) and knowledge and beliefs. Core processes ground each of the domains into its respective environmental realm. If a minimum set of conditions is present in the input, they are activated and automatically provide an interpretation of the input, which is consistent with their organization (Demetriou, 2004). The operations, rules, and principles of the second level refer to systems of mental (or, frequently, real) actions that are used to intentionally deal with information and relations in each of the domains. From the point of view of development, core processes constitute the starting points for the construction of operations, rules, and knowledge included in each of the domains. That is, at the initial phases of development, operations, rules, and knowledge arise through interactions between the core processes and the corresponding domain of the environment. Then they are differentiated and reconstructed as a result of their own interaction with the environment and with each other. Finally, each system involves knowledge of the reality domain with which it is affiliated. Conceptual and belief systems pertaining to the physical, the biological, psychological, and the social world are found at this level of the organization of the various systems. Figure 1 illustrates our conception of the on-line relations between the representation of information in short-term storage, its control by DEF and more long-term knowledge and beliefs about it and about the person’s relevant abilities, preferences, etc., and the domain(s) activated. In brain-relevant terms, this conception is consistent with the assumption that the brain involves circuits specializing in the representation of environmentrelevant information (such as the parietal lobe for quantitative information or the occipital lobe for visuo-spatial information) and circuits (such as the frontal lobe) specializing in the surveillance, coordination, and regulation of these environment-relevant circuits (Dehaene, 1997). Efficiency as such refers to the communication between circuits as much as with the condition and functioning of particular circuits (Case, 1992; Thatcher, 1992). Thus, development and individual differences in understanding and problem solving across domains may be caused by systematic variation in any of these systems or in their communication. We hope that this claim will become clearer in the pages following.

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Development Processing efficiency There is ample evidence that processing speed changes uniformly with age, in an exponential fashion, across a wide variety of different types of information and task complexities, such as mental rotation, memory search, visual search, mental addition, and geometric analyses. That is, change of speed of processing is fast at the beginning (i.e. from early to middle childhood) and it decelerates systematically (from early adolescence onwards) until it attains its maximum in early adulthood (Demetriou et al. 2000, 2002; Kail, 1991). This pattern of change, which is illustrated in Figure 2, reflects the fact that, with age, the time taken by the brain to complete an operation becomes smaller due to improvements in the interconnectivity of the neural circuits in the brain and the improvements in the myelinization of neuronal axons that insulate the communication between neurons. As a result, the representation and manipulation of information in the brain becomes faster and more efficient (Case, 1992; Thatcher, 1992). Working memory There is general agreement that the capacity of all components of working memory (i.e. executive processes, phonological, and visual storage) increases systematically with age. In fact, the development of all three components seems to follow the same pattern of change and to be able to be described by a logistic curve, which is very similar to

High

Processing efficiency High Low Cognitive level Low Low Working memory

High

Figure 2: The idealized model of the relations between changes in processing efficiency, working memory, and thought.

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the exponential curve that describes the change of processing efficiency (Demetriou et al., 2002). This pattern of changes in working memory is illustrated in Figure 2. Executive function, self-awareness, and self-representation Zelazo and his colleagues (Frye, Zelazo, & Burack, 1998; Zelazo & Frye, 1998) have recently generated solid empirical evidence about the development of executive control. According to this evidence, children up to the age of 3 years can represent only a single goal and they cannot shift from one goal to another according to a certain rule. This becomes possible at about the age of 5, when children are able to integrate the rules into a higher order rule that specifies when each of the two lower order rules is to be used. According to Zelazo and Frye (1998), the rules that specify the goal for a particular sequence of actual or mental actions aimed to solve a problem is a conscious process where there is awareness of the rules as plans for action. In line with these findings, Band, van der Molen, Overtoom, and Verbaten (2000) showed that a global response control mechanism enabling children to inhibit all bending responses, if needed, is established by the age of 5 years. However, selective inhibition, that is, the ability to selectively inhibit different responses according to differentiated goals continues to develop until adolescence. Thus, during the primary school years executive control becomes differentiated and planful, thereby making action plans available to the thinker. That is, planfulness integrates under an overarching plan the main goals and objectives, the subgoals, and the strategies and actions needed to attain goals and subgoals, and a time plan that specifies when strategies and actions are to be applied. So defined, planfulness is present before the age of about 9–10 years. In fact, practically all of the mathematical tasks addressed to children of this age at school require this kind of planfulness, in addition to mathematical knowledge and skills, because they require actions according to a preconceived complex and hierarchical action plan (Vurpillot, 1998). The proper operation of DEF depends on the evaluative functions that provide on-line and final information about the success or failure of the action plan applied. Without this function, DEF may be less accurate than needed or it may misdirect the thinker relative to the problem at hand. In our laboratory, we study self-evaluation of cognitive performance from the age of 3 years to maturity (Demetriou & Kazi, 2001). The general pattern of development is rather easily described. Specifically, it seems that self-evaluation develops in a recycling fashion, which involves three major cycles: 3–7, 8–12, and 13–18 years of age. That is, within each phase of development, self-evaluation and self-awareness about the relevant mental operations is very low and inaccurate at the beginning and it tends increasing and becoming more accurate with development until the end of the phase. Entering the next phase resets self-evaluation of cognitive outcomes and self-awareness about the cognitive processes involved to zero, from where it gradually takes off again with the development of the new phase-specific problem-solving operations and skills. This pattern of change in selfawareness indicates that the thinker needs time and experience to acquire knowledge and sensitivity to the condition of the operations and processes of the new phase. It must be noted, however, that these developmental trends in self-evaluation and self-awareness coexist with large individual differences in the accuracy of self-evaluations and self-awareness. These differences are related to the development of the specialized domains of thought. Having sketched the general architecture of the human mind and the development of its domain-general functions, we will now turn to quantitative thinking.

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The Domain of Quantitative Thought The Architecture of Quantitative Thought All elements of reality can potentially undergo quantitative transformations. Things aggregate or separate so that they increase, decrease, split, or multiply in space or time for many different reasons. Obviously, perception, representation, and some kind of processing of quantitative information are important for adaptation for most living organisms. As a result, these processes are present in many other animals but humans (Dehaene, 1997). In humans, quantitative thought starts as a very simple perception of small quantities and ends up, under appropriate conditions, in understanding calculus and differential equations. What are the core processes, the basic operations and rules, and the knowledge involved in quantitative thought? Subitization is an example of the core processes involved in this system. Subitization refers to our ability to specify the numerosity of small sets (smaller than three or four elements) by simply looking at them. The basics of a mental number line, which is used to represent, intuitively at the beginning, the quantitative relations between sets seems also to be a core process in this system. The mental number line may be conceived as the mental analog of an actual line where each number occupies a particular place. This mental lining up of numbers enables the thinker to mentally inspect the line at particular regions of it so that a target number can be compared to other numbers, which are smaller (on the left) or bigger (on the right) than it. Its neurological analog involves several areas of the brain, such as the inferior parietal lobe, which are activated and orchestrated in the sake of representing the quantitative information abstracted by the eyes (or other senses as a matter of fact) from the environment (Dehaene, 1997). At the second layer of organization, quantitative reasoning involves actions enabling the thinker to deal mentally with the various quantitative transformations mentioned above. Prominent among these actions is counting, which enables one to specify the quantity of things that exceed the subitization limits. Piaget (Piaget & Scheminsca, 1952) was the first to clearly spell out how the internalization of actions on objects results in the construction of mental operations, their inter-coordination into structures, and their systematic development with experience. The third level of the organization involves all kinds of factual knowledge about the quantitative aspects of the world. Examples include knowledge about time reading, money values, and rules underlying everyday transactions, and numerical knowledge, such as, the multiplication tables. The Development of Mathematical Thought Obviously, there is both an evolutionary and a developmental relation between the three layers in the organization of a specialized domain of thought. Specifically, more basic layers are biologically more constrained, they appeared earlier in evolution, they are more important in functioning in the early stages of development, and their early functioning generates the basic material for the construction of processes, skills, and concepts at the higher levels. This developmental linkage between functional levels in the organization of quantitative thought will become apparent in the outline of the development of mathematical thought to be given below (Demetriou, Pachaury, Metallidou, & Kazi, 1996; Demetriou, Platsidou, Efklides, Metallidou, & Shayer, 1991).

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Infant core mathematics A few weeks old infants can subitize the numerosity of sets including up to three elements and they are capable of distinguishing between different numbers of objects. Xu and Spelke (2000) argue that number representation in infants depends on a mechanism for representing approximate rather than exact numerosity. This mechanism represents information iconically (Wiese, 2003). Moreover, young infants are capable for performing simple arithmetic operations within the subitization limits. For instance, Wynn (1992) found that 4- to 5-month-old infants are capable of calculating the exact result of simple arithmetic operations, such as 1 ⫹ 1 ⫽ 2 (Wynn, Bloom, & Chiang, 2002). These findings suggest that there is an unlearned core of numerical competence that precedes language or any kind of domain-specific formal training (Starkey, 1992). This core seems to lead to a global mental number line, which involves very few numbers at the beginning that are iconically encoded, they are approximately related, and they form the foundations for the proto-quantitative schemes that emerge with the advent of language. Proto-quantitative schemes At the age of 2–3 years, children handle representations that are taken as single undifferentiated blocks that stand for familiar objects or concepts and have a transparent relation to them. As a result, relations at this early phase of development are not constructed as such but are intuitively “read out,” so to speak from the representational block. Thus, in regards to number, at the age of 2 years, children begin to use the sequence of number names. For example, in their daily experience they can imitate the number sequence in rhymes song (Fuson, Richards, & Moser, 1982). Moreover, they possess “proto-quantitative schemes” (Resnick, Bill, & Lesgold, 1992) that enable them to solve simple mathematical tasks that require judgment on the basis of absolute criteria (e.g., “few,” “many,” and “a lot”) or to make comparisons on the basis of a single dimension (e.g., “less,” “more,” etc.) (see Gelman & Gallistel, 1978). Coordination of proto-quantitative schemes At about the age of 3–4, children start to differentiate representations and thus to operate on two of them at the same time. Thus, at this level, coordination of proto-quantitative schemes becomes possible. For example, the “increase–decrease scheme,” which is geared on the representation of the number line, is coordinated with the basic principles of counting. This coordination enables children to specify quantities and numbers with certain accuracy and to grasp some aspects of cardinal and ordinal numbers. The steps in the development of cardinality are instructive in this regard. Specifically, according to Fuson and Hall (1983), at the beginning, when counting, children recite the last number with no clear idea that it relates to quantity, but because they realize it is a response an adult would expect. Later on, they start to understand that the last number of the count relates to the quantity. That is, they start to realize that the last number in the series of numbers spelled out indicates a quantity. Finally, they come to realize that if they are stopped in the middle of a count they can say how many objects they have counted so far and then carry on, which indicates the beginning of integration of order with numerosity. Interestingly, at this stage, children can use pictorial representations of their counting. That is, they can translate their counts into accurate pictures. Dimensionalization of quantitative schemes At about the age of 5–6 years, representations or operations on representations are integrated with each other. The result is that

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proto-concepts evolve into dimensions and operations become ensembles that can be planned in advance. Thus, in the domain of quantitative thinking, the coordination of proto-quantitative schemes leads to actual quantitative judgments and estimations. For example, they coordinate the “increase–decrease scheme” mentioned above with basic counting skills and the ensuing concepts of cardinality and ordinality, thereby acquiring a first understanding of number conservation. Moreover, by the end of this phase, cardinality and ordinality are well integrated with each other, so that children can translate order into numerosity and vice versa. Numerical operations in action can also be applied and tagged to symbols (Griffin, 2004). As a result, children at this age show some understanding of the relations between operations, such as the inverse relationship between addition and subtraction or division and multiplication. Finally, children start to be able to use iconic representations, such as simple marks, to represent objects. This implies a grasp of the relations between multiple aspects of numbers and operations on them, as well as the relations between them and their representations. That is, children carry out procedures in the mind in just the same way as they would operate with tangible objects. Integration of quantitative dimensions In the next phase, at the age of 7–9 years, the representations and the mental operations constructed above are integrated into systems that can be revised at will. As a result, thinking becomes analytical and fluid. In the domain of quantitative reasoning proper, mathematical concepts, such as cardinal and ordinal number, can be used as means for the representation and processing of different aspects of reality. This opens the way for the dimensionalization of reality. Thus, at this phase, the child can conceive of properties, such as, length, weight, or area, and operate on their relations. Moreover, simple formal mathematical relations can be processed (e.g., equations, such as 8 ? 3 ⫽ 5 and a ⫹ 5 ⫽ 8, can be solved) (Demetriou et al., 1996). This integration of concepts and operations into systems enables children to shift to more elaborate strategies in numerical problem solving. For example, they become able to abandon the “counting-all” strategy in favor of the “counting on.” That is, in problems such as 8 ⫹ 5 ⫽ ?, they take 8 as their starting point and they go on from there counting another 5 units, instead of counting separately all of the objects to be counted (Krebs, Squire, & Bryant, 2003). Moreover, there is evidence that 8-year olds have some implicit knowledge of negative numbers (Borba & Nunes, 2000), implying the emergence of an abstract, potentially variable-like, conception of number. Emergence of overarching mathematical constructs Representations at the age of about 10–12 years are quite complex relative to the representations of the previous phase, because they can integrate multiple dimensions. That is, in all domains, two dimensions with at least two levels each can be represented and operated on. In the domain of quantitative reasoning, proportionality becomes possible initially as an ability to grasp proportional relations that appear obvious (e.g., problems involving numbers that are multiples of one another, such as 2/4 and 4/8). Simple symbolic representations can, moreover, be coordinated in order to specify a general quantity (e.g., equations, such as x ⫽ y⫹3, can be solved when y is specified) (Demetriou et al., 1996; Demetriou & Kyriakides, in press). As a result, children start to be able to advance proofs of mathematical relations, such as “the sum of two odd numbers is an even number” by developing the proper arguments (Healy & Hoyles, 2000).

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Bridging of overarching mathematical constructs At the next level, at about 13–14 years of age, thinking starts to become emancipated from intuitive supports, thereby becoming able to operate strategically on complex problems that require systematic differentiation of relevant from irrelevant information and integration of relevant information according to the current goal. This indicates an explicit understanding that the solution resides in the relations between the components of the problem. As such, this understanding provides a wholistic approach to problems, which enables the thinker to conceive of and explore alternative possible solutions and test them against each other until the best one is selected. This approach to problems enables the thinker to reduce the problem load when complexity is the major obstacle to solution by appropriately partitioning the goal and operational complexity in manageable subgoal traps and fill in gaps in information through inter-relating other well-defined information. Thus, at this level, quantitative thinking can grasp counterintuitive proportional relations (e.g., the child can specify which of the two ratios, 4/5 or 7/8, is bigger) and solve algebraic problems where the unknown can be specified in reference to another, separately specified, construct (specify m given that m ⫽ 3n ⫹ 1 and n ⫽ 4) (Demetriou et al., 1996; Demetriou & Kyriakides, in press). Moreover, at this age, visual proof becomes possible in geometry, indicating that adolescents become able to imagine how the triangles can be moved around from one configuration to another (Tall, 1995). Grids of relational and generalized mathematical concepts At the next level, at about the age of 15–16 years, the limitation that the components to be integrated are well defined is removed. As a result, adolescents become able to integrate implicitly related structures. For example, they can now specify the value of x when it is known that x ⫽ y ⫹ z and x ⫹ y ⫹ z ⫽ 20 (i.e., 10) or when the equation L ⫹ M ⫹ N ⫽ L ⫹ P ⫹ N is valid (i.e., when M ⫽ P). These problems require an abstract conception of number such that it leads to the understanding that any number can be expressed by alternative symbols and that symbols can be reciprocally defined in reference to each other, depending upon the particular relation that connects them. Thus, at this level, number is understood as a variable (Demetriou et al., 1996; Demetriou & Kyriakides, in press). Principled mathematics At the next level, at the age of 16–17, adolescents start to be able to integrate relations at multiple levels and conceive of the underlying principles that interconnect them. Thus, systems of mathematics can be grasped at this level. The formal geometrical concept is constructed from the formal definition, and the properties of the formal object are only those that can be deduced from the definition (Tall, 1995). At this stage, students are able to develop logical arguments by themselves and they appreciate the necessity for such arguments. They also understand the difference between definitions, axioms, and theorems. Relations Between Mathematical Thought, Processing Efficiency, and Self-Awareness The outline of development of the various processes given above suggests that there is development everywhere. Speed of processing increases, control of processing becomes more efficient and fast, working memory expands, self-awareness becomes more accurate, refined,

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and focused, and mathematical thought becomes increasingly more complex, versatile, abstract, and ingenious. How are all of these courses of development interrelated? A series of studies in our laboratory tried to answer this question (Demetriou et al., 1993, 2002). One of these studies focused on the inter-relations between the three dimensions of processing efficiency, that is, speed and control of processing and working memory, and three domains of reasoning, namely, mathematical thought, which is of our concern here, and verbal and spatial reasoning (Demetriou et al., 2002). In this study, four groups of children and adolescents were involved in a longitudinal design. Specifically, 8-, 10-, 12-, and 14year-old participants at the first testing were examined in three consecutive years in all of these domains. To have indices of processing efficiency in these domains, we measured the time needed to read a single familiar word, recognize a numerical digit, or a geometrical figure either under conditions of maximum facilitation, which represents speed of processing, or under conditions of interference, which represents control of processing. Working memory was measured by tasks addressed to phonological and visuo/spatial short-term storage space (STS) and the central executive. The phonological STS was addressed by verbal and numerical tasks. Participants were presented with series of words or numbers (two to seven) and they were asked to recall them in the order of their presentation. The visuo/spatial STS (Short-term storage space) was addressed by a task requiring to store and recall shape, position, and orientation of geometric figures. The central executive was addressed by a set of tasks requiring one to combine either verbal with numerical or verbal with visual information at presentation and then recall the one or the other type, according to the instructions. The reasoning tasks addressed quantitative, verbal, and spatial reasoning. Quantitative reasoning was addressed by two types of tasks. That is, numerical analogies of varying difficulty (e.g., 6 : 12 : 8 : ?, 6 : 4 : 9 : ?) and simple algebraic equations requiring to specify the arithmetic operations missing from them (e.g., (2 # 4) @ 2 ⫽ 6). Verbal reasoning was addressed by verbal analogies and syllogistic reasoning tasks. Spatial reasoning was addressed by mental rotation and coordination of perspectives tasks. This is a very complex study that generated a wealth of data presented in detail in a long monograph (Demetriou et al., 2002). Here we will only focus on the relations between mathematical reasoning and the various dimensions of processing efficiency and working memory addressed by the study. Reference to verbal and spatial reasoning will only be made for comparative purposes. To specify these relations, a structural equation model was built where each of the three reasoning domains was regressed on all of these processes. The model was tested separately on the performance attained at each of the three measurement waves both before and after controlling for the effect of age. Figure 3 shows the part of the model that is concerned with mathematical reasoning. It can be seen that a very large part of the variance of performance on the mathematical reasoning tasks was accounted for by the condition of speed of processing (55%, 51%, and 37% at each of the three successive testing waves, respectively) and the central executive of working memory (17%, 49%, and 53% at the three testing waves, respectively). Therefore two aspects of processing and representational efficiency, speed of processing and executive control in working memory, enable one to predict with astonishing accuracy the condition of mathematical reasoning during a very crucial period of development, that is, from middle childhood to middle adolescence.

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Note: The three coefficients in each set stand for testing the model on each successive wave. Coefficients in roman letters come from testing the model on row correlations. Coefficients in italics come from testing the model after partialling out the effect of age.

Figure 3: The structural equation model of the relations between processing efficiency (PE), central executive of working memory (ExWM), phonological short term memory (STMph), and quantitative thought at the three testing waves. Does the effect of these two dimensions vary with the development? It does in a very interesting way. It can be seen that the effect of speed of processing decreases from the one testing wave to the next (55%, 51%, and 37% of the variance at each of the three successive testing waves, respectively) whereas the effect of the central executive is not systematically related to age (17%, 49%, and 29% of the variance at the three testing waves, respectively). It is clear that these two factors are differentially associated with the development and functioning of mathematical thinking. This assumption is supported by some further findings concerning their effects on mathematical reasoning. Specifically, attention is drawn to the fact that the relation between speed of processing and mathematical reasoning decreased enormously at all three testing waves (4%, 14%, and 13% of the variance at each of the three successive testing waves, respectively) when this relation was purified from the effect of age. The relation of working memory with mathematical reasoning was much less affected and, in fact, it increased in the second testing wave (10%, 81%, and 23% of the variance at each of the three successive testing waves, respectively) as a result of this manipulation. This pattern of relations suggests that processing speed is the developmental factor in regard to the development of both working memory and mathematical thought. That is, changes in processing speed with age open the way for expansion in working memory capacity and the advance of mathematical reasoning to higher levels of functioning. Working memory is the individual differences factor. That is, for each level of processing efficiency, variations in the executive processes of working memory are associated with individual differences in the actual attainment of mathematical reasoning. In other words, the actual state of working memory conditions how much of the available processing potential, as specified by processing speed, is to be actualized into real skills and concepts in mathematical thinking. Moreover, the decrease of the role of speed of processing with

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age signifies that, with development, other factors come onto the stage, such as interests, motivation, special experiences, etc. We will focus on this part of the picture later on. Are the relations described above unique to mathematical thought or are they also present in other domains? Extending the model to include spatial and verbal reasoning suggested that some relations are unique to mathematical thought and some are general. Specifically, the very strong effect of processing efficiency and executive control on working memory is present in all three domains. However, dependence on specialized storage varied across domains. It was high in spatial reasoning and weak in verbal and mathematical reasoning. These differences suggest that the development and functioning of reasoning in different domains is differentially related to the condition of general processing functions and abilities. Mathematical Thought, Self-Awareness, and Self-Representation Are people aware of cognitive processes when they do mathematics? Are they accurate in their self-representations of strengths and weaknesses in mathematics? How self-awareness and self-representation in this domain compare to self-representations in other domains of thought? A series of studies in our laboratory (Demetriou & Kazi, 2001, 2006) were designed to answer these questions. The studies presented in Demetriou and Kazi (2006) show that self-awareness of cognitive processes appears very early in age, they are concerned with all types of cognitive processes, and that, by the age of 7 years, they are already refined enough to be able to compare specialized processes, such as counting and arithmetic operations in mathematics. On the basis of these findings, we suggested that self-awareness is actually one of the main constellations of processes that constitute general intelligence or g, the other two main constellations being general processing efficiency and general inferential processes. Moreover, these studies showed that at different phases of development, self-awareness reflects the state, form, and dynamics of the processes that are attainable within each phase, weakly and imprecisely at the beginning of the phase and strongly and precisely at the end. Moreover, within each developmental phase, awareness moves from the surface or content-based characteristics of the abilities to be attained in a phase, such as the objects or object characteristics involved, to their procedural and functional characteristics as such. In other words, the development of self-awareness seems to be a recycling process such that within each developmental phase it is weak and imprecise and contentcentered at the beginning and stronger, more precise, and process centered at the end. This pattern of changes provides a developmental role to self-awareness. That is, the grasp of awareness at each cycle of development becomes part and parcel of the mental material that will be reorganized into the new inferential structures of the next cycle. That is, reasoning develops as a result of a formalization process that constantly maps onto each other inferential patterns and action schemes within and across domains, thereby generating new management, validation, and reasoning patterns. The grasp of awareness of the processes characteristic of each cycle is a sine qua non condition for the transition to the next cycle because it enables the thinker to redescribe the processes and schemes of the present level into a higher, more efficient and flexible level of representation (Karmiloff-Smith, 1992). How does mathematical thought fare in this system of self-awareness and selfrepresentation? Research strongly suggests (Demetriou & Kazi, 2001, 2006) that this is

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probably the domain that is transparent to awareness more than any other domain of thought. Specifically, structural equation modeling suggests that self-evaluation of the performance attained on mathematical tests closely covaries with the actual performance as evaluated by the researcher. In one such study, which involved participants from 11 to 16 years of age, 46% of the variance in self-evaluation of performance on the mathematical tasks addressed to our participants was accounted for by the condition of the actual performance in the domain. Moreover, another respectable 16% was accounted for by general cognitive ability. The corresponding values for the domain of causal, social, and spatial thought were very close to 0% and 9%, respectively (Demetriou & Kazi, 2001). This privileged position of mathematics in the system of self-awareness reflects, on the one hand, that learning mathematics is an effortful, largely domain-free, enterprise that activates general cognitive ability, it allows self-observation, and it is guided by clear criteria for what is right and wrong. On the other hand, it may be the basis of the fact that people have rather clear attitudes to mathematics. They like them, when they know that they are successful on them, and they dislike them when they know that they are not (Schoenfeld, 1992). Processing Efficiency, Intelligence, and School Performance in Mathematics A series of studies in our laboratory focused on the relations between actual school performance in mathematics and the various aspects of the architecture of the mind discussed here. In one of these studies, which involved participants from the age of 12 to 18, we showed that as much as 71% of the variance of school performance in mathematics (72% in science and 27% in Greek) was accounted for by general cognitive ability. In another study, we were able to decompose this effect into the components of general cognitive ability. Specifically, this study included classical measures of intelligence (i.e. the WISC-R3) and measures of processing efficiency (i.e. speed and control of processing) in addition to cognitive development measures of the five domains of thought mentioned above. This study showed that a large part of the variance of school performance in mathematics was accounted for by these three components of general cognitive ability. That is 25%, 23%, and 6% of this variance was accounted for by processing efficiency, general IQ, and reasoning in the five domains, respectively (Demetriou, 2005). Figure 4 shows the model that decomposed performance in three school subjects into these three components. Several other studies (Demetriou, 2005) attempted to specify these relations for primary school children. These studies show that the relations outlined above generally hold, although they are generally weaker and differently distributed over the various dimensions. One of these studies showed that the variance of performance on school mathematics is accounted for by processing efficiency (4%), working memory (24%), and reasoning in the various domains (10%). Moreover, self-concept about mathematical ability, in primary school, is mainly dependent on school performance in mathematics (6% of the variance) rather than on more general cognitive processes (practically nil effects). Another study showed that the self-concept about mathematical ability depends to a certain extent on the condition of processing capacity (6% of the variance), although changes in it depend more on actual performance in mathematics (11% of the variance). However, the self-concept about mathematical thinking does not affect actual school performance in mathematics.

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Figure 4: The structural model of the relations between the dimensions of mind and school performance in science, mathematics, and language.

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Finally, some other studies showed that noncognitive factors, such as openness to experience (4%) and strength of will (9%), account for an additional significant part of the individual differences in school mathematics (Demetriou, 2005).

Educational Implications This chapter outlined the general architecture of the human mind and specified the place of mathematical thought in this architecture. The general postulate is that the human mind involves both general processes and constraints and specialized domains of reasoning and understanding. Mathematics is one of these specialized domains. Each of these domains is present from birth and its functioning begins with a limited set of core abilities and processes that enable the newborn to abstract simple domain-specific information quickly and accurately. Subitization and the mental number line are two of the core processes in the domain of mathematical thought. The domain-specific systems then take off and develop as a result of continuous differentiation, reorganization and recombination, and coupling and integration with domain-specific cultural productions and symbol systems. In the domain of mathematics, oral and written numerals, for instance, come to express and eventually mold the core number line. Algebra expresses the relations between multiple representations of the number line. We have seen that development in the domain of mathematics from birth through the end of adolescence generates increasingly more complex, abstract, and rule-governed concepts, and more versatile, flexible, and planfull problem-solving skills. We have also seen that there is a very close relation between the development of mathematical thought and the development of processing efficiency and executive control processes in working memory. In fact, the relation was so strong that a very large part of the variance in mathematical thought is accounted for by the condition of these two indices of domain-free processes. The implication of this finding is very clear: The constructions in mathematics at a particular age reflect the available processing and representational resources of the human mind to a large extent. The reader is also reminded that working memory explains individual differences in mathematical reasoning, for each level of processing efficiency at successive ages. In educationally relevant terms, this statement implies that having accurate information about these dimensions of domain-free processes would greatly help teachers decide what is learnable, at the ages concerned, of the various concepts and skills they want to transmit and how individual children will respond to them. Practically speaking, teachers must have access to measures of processing efficiency and representational capacity of their students. Modern technology makes these examinations a rather easy business, although special training is needed to address and interpret these examinations. It is also notable that there is a close relation between self-awareness and self-evaluation, on the one hand, and the development of mathematical thought on the other. This set of domain-general processes complements processing efficiency and working memory as forces shaping the construction of domain-specific concepts and skills. That is, these processes actually enable the thinker to reflect on the relations between

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concepts and actions, thereby reducing or projecting them into another more abstract and integrative system of actions and concepts. In other words, these processes provide the frame for shaping the potentialities afforded by processing and representational efficiency into real mathematical concepts. Therefore, processing efficiency sets the frame for what mental constructions are possible; domains, such as quantitative reasoning, provide the primary material for these potentialities to be materialized; and self-awareness abstracts general reasoning patterns by organizing and tagging domainspecific realizations into supra-domain inference patterns. This analysis gives a new meaning to the Piagetian (Piaget, 2001) mechanism of reflective abstraction as the main driver of cognitive development. If obtaining measures of processing efficiency and capacity is important for the teacher in order to make decisions as to what is appropriate for each individual student at a particular phase in the student’s life, the systematic manipulation of self-awareness and self-regulation processes by the teacher is important for the scaffolding of the learning process. That is, addressing these processes would have to lead the student to see relations between objects, actions, or concepts that are not so apparent, construct new concepts or operations that would integrate these objects, actions, or concepts at higher levels, and tag these new concepts or operations with symbols that would give them an autonomous mental existence, make them manageable and integratable with other concepts, and even reveal their own weaknesses and demands. In short, the teacher would have to be able to lead the student in the process of reflecting upon mental self-modification process in an accurate concept-specific way (Demetriou & Raftopoulos, 1999). Finally, it is highly interesting that the measures of general cognitive processes and abilities were able to account for such a large part of variance in school mathematics. This suggests strongly that our measures of these processes (i.e., speed of processing and executive control in working memory) have captured the backbone of school mathematics, because they constrain the kind of constructions that are possible at successive age phases. Therefore, it is to be concluded that using the measures both for diagnostic and remedial purposes would enable teachers of mathematics in the real classroom to plan their activities and interventions in ways that would maximize their efficiency. Specifically, the pattern of relations between mathematics and the various dimensions of the architecture and development of the mind summarized above suggest strongly that teachers must have access to information about their students’ processing efficiency as such, general intelligence, and the developmental condition of reasoning. At the same time, the teacher must be able to decide what kinds of concepts can be taught to individuals of different intellectual and developmental profiles vis-à-vis these dimensions. Obviously, these requirements presuppose that appropriate tests, such as those presented here, are available to the school as well as the appropriate maps that connect accurately and systematically different cognitive and developmental profiles to the mathematical curriculum throughout primary and secondary schools. Unfortunately, we are a long way from this ideal state of affairs. We urge the field to start moving in this direction, if the level of education is to be raised from an amateurish and artistic state to a professional and scientific state, in line with other domains, such as public health, transportation, and communication.

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References Baddeley, A. D. (1993). Working memory or working attention? In: A. D. Baddeley, & L. Weiskrantz (Eds), Attention, selection, awareness, and control. A tribute to Donald Broadbent (pp. 152–170). Oxford: Clarendon Press. Band, G. P. H., van der Molen, M. W., Overtoom, C. C. E., & Verbaten, M. N. (2000). The ability to activate and inhibit speeded responses: Separate developmental trends. Journal of Experimental Child Psychology, 75, 263–290. Borba, R., & Nunes, T. (2000). Are young primary school pupils able to manipulate representations of negative numbers? In: H. Fujita, Y. Hashimoto, B. Hodgson, P. Lee, S. Lerman, & T. Sawada (Eds), Proceedings of the 9th International Congress on Mathematical Education (pp. 171–178). Tokyo: Japan Society of Mathematical Education. Carroll, J. B. (1993). Human cognitive abilities: A survey of factor-analytic studies. New York: Cambridge University Press. Case, R. (1992). The role of the frontal lobes in the regulation of cognitive development. Brain and Cognition, 20, 51–73. Dehaene, S. (1997). The number sense: How the mind creates mathematics. Oxford: Oxford University Press. Demetriou, A. (2000). Organization and development of self-understanding and self-regulation: Toward a general theory. In: M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds), Handbook of selfregulation (pp. 209–251). San Diego, CA: Academic Press. Demetriou, A. (2004). Mind, intelligence, and development: A general cognitive, differential, and developmental theory of the mind. In: A. Demetriou, & A. Raftopoulos (Eds), Developmental Change: Theories, models and measurement (pp. 21–73). Cambridge: Cambridge University Press. Demetriou, A. (2005). The development of mathematical reasoning: Its interplay with processing efficiency, self-awareness, and self-regulation. Paper presented at the 11th Conference of the European Association for Research on Learning and Instruction, Nicosia. Demetriou, A., Christou, C., Spanoudis, G., & Platsidou, M. (2002). The development of mental processing: Efficiency, working memory, and thinking. Monographs of the Society of Research in Child Development, 67(Serial No. 268). Demetriou, A., Efklides, A., & Platsidou, M. (1993) The architecture and dynamics of developing mind: Experiential structuralism as a frame for unifying cognitive developmental theories. Monographs of the Society for Research in Child Development, 58(5–6, Serial No. 234). Demetriou, A., & Kazi, S. (2001). Unity and modularity in the mind and the self: Studies on the relationships between self-awareness, personality, and intellectual development from childhood to adolescence. London: Routledge. Demetriou, A., & Kazi, S. (2006). Self-awareness in g (with processing efficiency and reasoning). Intelligence, 34, 297–317. Demetriou, A., & Kyriakides, L. (in press). A Rasch-measurement model analysis of cognitive developmental sequences: Validating a comprehensive theory of cognitive development. British Journal of Educational Psychology. Demetriou, A., Pachaury, A., Metallidou, Y., & Kazi, S. (1996). Universal and specificities in the structure and development of quantitative-relational thought: A cross-cultural study in Greece and India. International Journal of Behavioral Development, 19, 255–290. Demetriou, A., Platsidou, M., Efklides A., Metallidou, Y., & Shayer, M. (1991). Structure and sequence of the quantitative-relational abilities and processing potential from childhood and adolescence. Learning and Instruction, 1, 19–44.

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Demetriou, A., & Raftopoulos, A. (1999). Modeling the developing mind: From structure to change. Developmental Review, 19, 319–368. Frye, D., Zelazo, P. D., & Burack, J. A. (1998). Cognitive complexity and control: I. Theory of mind in typical and atypical development. Current Directions in Psychological Science, 7, 116–121. Fuson, K. C., Richards, J., & Moser, J. M. (1982). The acquisition and elaboration of the number word sequence. In: C. Brainerd (Ed.), Progress in cognitive development: Children’s logical and mathematical cognition (Vol. 1, pp. 33–92). New York: Springer. Fuson, K. C., & Hall, J. W. (1983). The acquisition of early number word meanings. A conceptual analysis and review. In: H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 49–107). New York: Academic Press. Gelman, R., & Gallistel, R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press. Griffin, S. (2004). Contributions of central conceptual structure theory to education. In: A. Demetriou, & A. Raftopoulou (Eds), Cognitive developmental change (Cambridge Studies in Cognitive and Perceptual Development) (pp. 264–296). Cambridge: Cambridge University Press. Gustafsson, J. E., & Undheim, J. O. (1996). Individual differences in cognitive functions. In: D. C. Berliner, & R. C. Calfee (Eds), Handbook of educational psychology (pp. 186–242). New York: Macmillan. Healy, L., & Hoyles, C. (2000). From explaining to proving: A study of proof conception in algebra. Journal for Research on Mathematics Education, 31, 396–428. Jensen, A. R. (1998). The G factor: The science of mental ability. New York: Praeger. Kail, R. (1991). Developmental functions for speed of processing during childhood and adolescence. Psychological Bulletin, 109, 490–501. Karmiloff-Smith, A. (1992). Beyond modularity: A developmental perspective on cognitive science. Cambridge, MA: The MIT Press. Krebs, G., Squire, S., & Bryant, P. (2003). Children’s understanding of the additive composition of number and of the decimal structure: What is the relationship? International Journal of Educational Research, 39, 677–694. Piaget, J., & Scheminsca, A. (1952). The child’s conception of number. London: Routlege. Piaget, J. (2001). Studies in reflecting abstraction. London: Psychology Press. Resnick, L. B., Bill, V., & Lesgold, S. (1992). Developing thinking abilities in arithmetic class. In: A. Demetriou, M. Shayer, & A. Efklides (Eds), Neo-Piagetian theories of cognitive development (pp. 210–230). London: Routledge. Schoenfeld, H. (1992). Learning to think mathematically: Problem solving, metacognition and sense making in mathematics. In: D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–368). New York: MacMillan. Starkey, P. (1992). The early development of numerical reasoning. Cognition, 43(2), 93–126. Tall, D. (1995). Mathematical growth in elementary and advanced mathematical thinking. In: L. Meira, & D. Carraher (Eds), Proceedings of the 19th Conference of the International Group for the Psychology of Mathematics Education, Recife, Brazil, July 22–27 1995 (Vol. 1, pp. 61–75). Recife, Brazil: Universidade Federal de Pernambuco, Graduate Program in Cognitive Psychology. Thatcher, R. W. (1992). Cyclical cortical reorganization during early childhood. Brain and Cognition, 20, 24–50. Vurpillot, E. (1998). The development of scanning strategies and their relation to visual differentiation. Journal of Experimental Child Psychology, 6, 632–650. Wiese, H. (2003). Iconic and non-iconic stages in number development: The role of language. Trends in Cognitive Sciences, 7, 385–390.

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Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358, 749–750. Wynn, K., Bloom, P., & Chiang, W. (2002). Enumeration of collective entities by 5-month-old infants. Cognition, 83, B55–B62. Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74, B1–B11. Zelazo, P. D., & Frye, D. (1998). Cognitive complexity and control: II. The development of executive function in childhood. Current Directions in Psychological Science, 7, 121–126.

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Chapter 3

Attentional Processes, Abstraction, and Transfer in Early Mathematical Development Erno Lehtinen and Minna M. Hannula

Introduction Imagine a group of young children observing a complex situation without any precise instructions except being told to look carefully at what happens. Afterwards, they are asked to do something which requires exact recognition of the number of objects or events included in the observed situation. Some children are able to give correct answers, whereas others fail in the task. How can we explain these inter-individual differences? There are at least two types of explanations. It is possible that some children do not have the basic number skills needed in the task. The other explanation is that children may have learned the skills in other situations but some of them are not able or willing to use this prior knowledge in the new situation. The former explanation refers to general competency without paying any attention to the situational variation, whereas, the latter explanation makes a distinction between the initial learning situation and the new application situation. The latter type of explanation raises the question of transfer and the idiosyncrasy of the relation between the individual and the situation as important factors determining an individual’s activity in new situations. The transfer issue is normally discussed in the context of school learning, but more often we can observe the development of generalized knowledge and skills and varying attempts to apply prior knowledge in different everyday situations out of school. In this chapter, we aim to show that the development of early number skills and children’s ability to use them in novel situations opens up a new insight into the transfer question. Firstly, it raises the question of the existence and role of abstract knowledge. Secondly, it highlights the role of children’s own activity and especially their differing tendencies in focusing attention on numerosities in their everyday environments. Thirdly, it questions the immediate and correct application of previous knowledge as the only criterion for transfer.

Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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Different Approaches to Transfer Before looking deeply into the research on early number skills from the point of view of transfer, we briefly review the general discussion on transfer and abstraction. According to De Corte (1999), the problem of transfer and general applicability of knowledge and skills has been on the agenda of research in educational psychology throughout the previous century, and the interest in the issue has increased during last 10–15 years. In their review article on transfer, Bransford and Schwartz (1999) emphasize the fundamental importance of the transfer issue by referring to the fact that most educators want learning activities to have positive effects that extend beyond the exact conditions of initial learning. They are hopeful that students will show evidence of (positive) transfer in various situations. However, the issue of transfer is very controversial and has been the subject of many critical debates among researchers (see Anderson, Reder, & Simon, 1996; De Corte, 1999, 2003; Detterman, 1993; Lave, 1988; Ohlsson & Lehtinen, 1997). The critical discussion is partly based on experimental empirical findings, often showing failures of transfer (e.g., Detterman, 1993), and on theoretical analyses emphasizing the situated nature of activity and cognition (e.g., Lave, 1988). In their frequently cited analysis of the types of transfer, Salomon and Perkins (1989) distinguished between a low and a high road to transfer. The ‘low road’ transfer takes place when conditions in the transfer context are sufficiently similar to those in a prior context of learning. These can more or less automatically trigger responses similar to the learned processes in the initial situation. This type of transfer can be explained in Thorndike’s traditional terms of identical elements between initial and target situations or tasks. Singley and Anderson (1989) have reinterpreted Thorndike’s behaviouristic view into cognitive language in the frames of their ACT* theory, and defined transfer in terms of identical cognitive productions. The traditional Thorndikean view and its modern cognitivistic version highlight the objective similarity of the situations, and pays less attention to the subjective interpretations of the learners. Greeno and his collaborators (Greeno, Smith, & Moore, 1993) have proposed an approach, which deals with the similarity of the situations from the point of view of the learner’s activity in these situations. The activity in the learning situation takes place under certain affordances and constraints. Transfer is possible, if the new situation contains sufficiently similar constraints and affordances to the initial context, or if the learners interpret them similar. This view also highlights the similarity of the situations but not so much as an objective condition than as a set of features of the situation interpreted from the point of view of the learner’s intentional activity. The second road to transfer in the model of Salomon and Perkins (1989), namely the ‘high road’, depends on abstraction from the context of learning or application and a more or less conscious attempt to find general patterns and principles. This type of transfer is not immediate but demands time for exploration and mental effort. It is not the similarity in any superficial feature of the initial and target problems or situations that characterizes transfer but the identity that mediates transfer can sit at a very high level of abstraction. Bransford and Schwartz (1999) argue very similarly that effective transfer requires a sufficient degree of original learning, which leads to relevant abstractions. For Bransford and Schwartz, meaningful transfer is not only the immediate application of previously learned

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knowledge in new situations, they broaden the conception of transfer by emphasizing people’s ‘preparation for future learning’. Here, the focus shifts to assessments of people’s abilities to learn according to the future demands and opportunities of new situations. In addition they point out that an important aspect of active transfer involves people’s willingness to deal with the tasks in social interaction situations and to understand others’ ideas and perspectives. The meaning of social interaction for the development of abstract ideas was also emphasized by Ohlsson and Lehtinen (1997). Although traditional education on all levels is aimed at teaching knowledge and skills that are widely applicable, the ‘Zeitgeist’ of cognitive and educational sciences has taken another direction (Ohlsson & Lehtinen, 1997). Dominating theories of childhood learning (Rogoff, Mistry, Goncu, & Mosier, 1993), development of expertise (e.g., Ericsson, Krampe, & TeschRömer, 1993; Lave, 1988; Lave & Wenger, 1991), and laboratory experiments on transfer (e.g., Detterman & Sternberg, 1993) all seem to agree that cognition depends on knowledge that is domain specific and highly particular. The ability to perform a given task resides primarily in how much one knows about that particular task in a certain context, not in general principles or in any capacity for abstract thinking (Lenat & Feigenbaum, 1991). These ideas emphasize the use of concrete, episodic, and socioculturally embedded information seemingly without remarkable involvement of the general principles and abstract knowledge that have traditionally been connected to higher-order thinking. Situated cognition and sociocultural approaches have made a major contribution to the theoretical advancement and practical applicability of learning research. The domain specificity of expertise, the sociocultural context, the power of analogical reasoning, and the weak transfer faced in many educational situations are real phenomena and they have to be taken into account for any theory of higher-order cognition. However, we believe that this view is limited and does not cover all relevant aspects of human learning and cognition because the role of abstract knowledge and transfer is neglected or systematically underestimated (see Bransford & Schwartz, 1999; Salomon & Perkins, 1989). We agree with Hershkowitz, Schwarz, and Dreyfus (2001) who have proposed that the situated and sociocultural view of knowledge and the approaches emphasizing abstract views of knowledge and skills are not incompatible and could be included in the same framework. This is in line with the suggestion of Lobato and Siebert (2002), who argue that transfer should be reconceived along individual and cognitive dimensions, while also examining how transfer is situated in group practices and in sociocultural aspects of the environment. In order to understand learning and transfer in natural and complex situations it would be important to examine how people construe situations as similar, regardless of whether or not the generalizations that people make across situations lead to ‘correct’ or normative performance (Lobato, 2003). Lobato’s (2003; Lobato, Ellis, & Muñoz, 2003) ‘actororiented transfer’ perspective examines the processes by which actors form personal relations of similarity across situations. The actor-oriented transfer perspective argues that the basis for transfer is the learner’s often idiosyncratic construal of similarity rather than objectively given similar ‘elements’ in the environment. This approach highlights the crucial question which distinguishes the different theories of transfer: is the transfer defined in terms of the qualities of initial versus target situations and tasks, or is it mainly interpreted in terms of the immediate or long-term mental activities carried out by the learner in these situations?

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Erno Lehtinen and Minna M. Hannula The ‘applying knowledge’ metaphor of the traditional transfer paradigm suggests that the tasks across which transfer occurs remain unchanged during transfer, and that the “transferor” reproduces existing relations between fixed tasks (Beach, 1999; Sfard, 1998). In contrast, in actor-oriented transfer, the metaphor of construction replaces that of application. Relations of similarity are constructed or produced, not simply perceived or encoded. As a result, transfer situations are no longer viewed as static and unchanging but rather are dynamic sites for invention and reorganization. (Lobato & Siebert, 2002, p. 90)

In the new approaches to transfer, it is important how one recognizes the familiarity or similarity when entering new situations. If we shift our focus from very explicit experimental situations of typical transfer studies towards normal everyday situations or longterm learning of complex scientific or mathematical tasks, it is far from trivial how people interpret the situations and recognize new phenomena with the help of their previously constructed mental concepts. In their article about learning of abstract ideas, Ohlsson and Lehtinen (1997) claimed that in order to recognize an object as an instance of an abstraction, the person must already possess that abstraction. This is especially obvious in complex scientific theories like Darwinian evolution or Newtonian mechanics as well as in many mathematical concepts. Adopting the terminology of Hayek (1972), the abstract has primacy over the concrete. The primacy of abstraction turns the relation between similarity and generality on its head. In the classical view, similarity is an epistemologically primitive category. The similarities between two particulars are the basis for creating a generalization. In contrast, Ohlsson and Lehtinen (1997) suggest that people experience particulars as similar to the extent that, and because, those particulars are recognized as instances of the same abstraction. Abstraction engenders similarity rather than vice versa.

Mathematics Learning: Transferable or Situated Knowledge In the learning of mathematics, the questions of transfer and generalization are of great importance, and no form of mathematics education can avoid dealing with the transfer problem (De Corte, 2003). Current studies on mathematics learning have shown that in the traditional ‘decontextualized’ mathematics education, students often fail to learn the intended mathematical skills, which they could adequately apply in varying situations outside school. Instead, they often learn strategies and skills that help them to cope with typical school test situations without sufficient transfer to other situations. The studies also show that students’ attempts to apply these school-specific skills to so-called realistic problems frequently result in mindless solutions (Verschaffel et al., 1999). All these observations show that the generality and wide transfer of mathematical skills is not as obvious as has been traditionally assumed. On the contrary, mathematics learning seems to be subject to same kinds of problems of transfer that have been reported in other academic disciplines (Detterman, 1993). In her influential book Lave (1988) provides numerous examples of learning as a situated phenomenon in problem situations, which are basically mathematical. For example, she describes a member of a Weight Watchers’ programme solving a quantity determination

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problem: the participants were asked to prepare their lunch to meet the specifications laid out by the observer. They were to fix a serving of cottage cheese, supposing that the amount allotted for the meal was three-quarters of the two-thirds cup the programme allowed. The problem solver filled a measuring cup two-thirds full of cottage cheese, dumped it out on a cutting board, patted it into a circle, marked a cross on it, scooped away one quadrant, and served the rest (Lave, 1988). According to Lave (1988), the people participating in Weight Watchers’ courses never solved this kind of task by using standard procedures based on formal mathematics (e.g., 3/4 ⫻ 2/3 ⫽ 1/2), but used situated strategies embedded in the culturally formed activities. So-called ‘street mathematics’ is another example that has been used to demonstrate the situated nature of mathematical knowledge and learning. Carraher, Carraher, and Schliemann (1985) observed Brazilian children solving simple mathematical problems as they sold products on the street. The children were able to deal with multiplicative tasks by using situated strategies, while the same children failed to solve the same problems when they were presented in conventional mathematical form without the activity context at school. Lave (1988) criticizes the traditional belief that mathematics is a general tool, which can be transferred into new situations and applied to novel problems from different domains. Many researchers have accepted her idea, and the theories emphasizing the situated nature of learning and knowing have been very influential in general learning research and research on mathematics learning during the last decade. This approach to mathematics learning emphasizes that mathematical skills are learned as a by-product of different practical activities. These activities (individual or collaborative), not the cognitive characteristics of the mathematical concepts, are emphasized in this approach. The situated cognition view has inspired a whole new genre of studies on mathematics education mainly focusing on the discourses of the maths classrooms (e.g., Brown & Renshaw, 2000; Kumpulainen & Mutanen, 1999; Yackel & Cobb, 1996). We agree that situated approaches have been beneficial for a better understanding of typical mathematical reasoning in everyday situations, and for the development of a mathematics education that students experience as more authentic and useful. In our own studies during the last 2 decades (for a summary, see Lehtinen, Vauras, Salonen, Olkinuora, & Kinnunen, 1995), we have concluded that in typical mathematics learning and assessment situations, students can form interpretations and goals that are situated in nature, and far away from the ‘objective’ demands of the mathematical tasks they are dealing with. The above examples certainly show that subjects do not always use the correct mathematical operations in transfer tasks that are expected by the external observer. This means that, according to the criteria of the traditional transfer research, these subjects do not show any transfer. However, a deeper analysis of the tasks from the actor-oriented transfer perspective (Lobato, 2003) shows that, for example, in the Weight Watcher example, the subjects transfer a great deal of previously learned mathematical knowledge to the new situations, though they are not applying the full formula that would be the most elegant mathematical way to solve the problem. In other words, the strategies used by the subjects in typical examples of the situated cognition view are in fact a mixture of abstract mathematical knowledge and situational practices developed in the sociocultural context at hand. On the other hand, there are many motivational and social psychological explanations for why children coming from disadvantaged backgrounds, such as in the Carraher et al.

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(1985) study, often fail to demonstrate their existing knowledge and skills in formal school situations (see, Lehtinen et al., 1995). This means that the evidence presented by Lave (1988) and many others (e.g., Detterman, 1993) only shows that people are seldom able to exactly apply the expected full mathematical procedure in all situations, but it would be erroneous to interpret these findings as evidence that people do not have any abstract mathematical concepts that would be transferable into new situations. Even though we want to emphasize the important contribution of the situated paradigm, we argue that a merely situated approach to learning loses some fundamental aspect of mathematical knowledge, and can trivialize our conceptions about the processes related to the learning of mathematics. The situated approach tends to emphasize an inductive (and even empiristic) nature of the development of mathematical knowledge as well as a merely discursive and linguistic encoding of mathematical concepts. This approach, however, fails to explain the development of many characteristic features of mathematical knowledge such as the flexible system of natural numbers or the sense of necessity of arithmetic operations with small digits (e.g., Lehtinen, 1986), which are the basis for an exceptionally powerful transfer of mathematical knowledge. On the other hand, a deep analysis of the at least partly highly abstract ideas about numbers seems to be necessary for understanding, for example, the special conceptual change problems students face when learning the extensions of number concept (Lehtinen, Merenluoto, & Kasanen, 1997; Merenluoto & Lehtinen, 2004). There are reasons for arguing that the abstract nature of many mathematical concepts is the key feature for understanding the potential, although not always immediately evident, applicability of these concepts. The abstract nature of mathematical concepts also results in special forms of learning higher mathematical ideas on the basis of previous ones. This is self-evident in advanced mathematics, but is also typical of more elementary concepts of mathematics (Romberg, 1994). For example, many mathematical algorithms can easily be learned as mechanical operation sequences, but in order to be useful in various situations they should be consciously constructed on the basis of underlying abstract concepts. Staub and Stern (1997) describe mathematics as a particularly abstract domain because the affordances and constraints underlying the use of mathematical constructs may be different from the affordances and constraints in real-world situations.

On the Abstract Nature of Early Number Skills In her article about core knowledge, Spelke (2000) argues that the studies on how humans develop and deploy complex, species-specific, and culture-specific cognitive skills such as reading and mathematics, are normally focused on expert adults or children deliberately learning them in an educational context. She suggests that we should: broaden our search for insights into complex cognitive skills by considering the findings of research on two additional populations: very young children, who have not yet begun the process of skill acquisition, and nonhuman animals, who are destined never to acquire them. My reasoning is simple: When children and adults construct new cognitive abilities, they build on component

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cognitive systems with a long ontogenetic and phylogenetic history. Studies of infants and of nonhuman primates can shed light on these core knowledge systems. (Spelke, 2000, p. 1233) Hereafter, we summarize studies showing that abstract concepts are not only typical of advanced mathematical knowledge, but that already the very first ‘concepts’ young children use in quantitative thinking are abstract in nature. The analysis of early development of number skills is important because this initial knowledge will serve a fundamental element in the later construction of the system of natural numbers and arithmetic operations (Feigenson, Dehaene, & Spelke, 2004). According to classical theories in developmental psychology, human cognition develops on the basis of concrete elements linked to perception. Current advances in experimental developmental psychology and neuropsychology, however, open a different view to the early development of human cognition. New empirical results contrast with theories of conceptual development that assume that categorization on the basis of similarity of perceptual features is primary, and that only later do children learn to categorize on the basis of conceptual characteristics (Nelson, 2004). On the basis of the research on concept formation among infants and young children, Mandler (2004) proposes that the initial conceptual categories infants used in concept formation are abstract and global. These categories are formed in the effort to establish meaning for actions and events. The early concepts infants used in classifying things are not based on static perceptual features, but on the abstract categories of the roles that objects play in events. For example, Gleissner, Meltzoff, and Bekkering (2000) have shown that 3-year-old children code human behaviour and imitate it on the basis of hierarchically organized goals, which give them the opportunity to focus on relevant and more abstract aspects of the actions observed. Very similarly, Karmiloff-Smith (1995) argues that very young children are capable of using theory-like concepts, and the early theory building takes place without linguistic encoding and direct sociocultural influence. Many developmental psychologists have proposed that a possible explanation for infants’ ability to deal with complex principles of the physical, biological, and social environment is that they have innate domain-specific predispositions (Karmiloff-Smith, 1995; Spelke, 2000). Domain specificity means that dispositions are constrained to function in specific domains. However, within the frames of these domains, they afford the very early development of abstract and flexible ‘concepts’, which are not limited to any particular situation or specific stimulus but are transferable to novel tasks and situations. The innovative advancement of research methods of developmental psychology has afforded a new insight into the cognitive skills of infants. Feigenson et al. (2004) summarize studies dealing with the early development of numbers and conclude that there are two core systems that might contribute to the development of later forms of the number concept: (1) a fast but relative, imprecise discrimination of larger numerical magnitudes, and (2) an exact object tracking system operating in the small number range. These early systems for representing objects and approximate quantities are not unique to human beings, but can also be found in other animal species (for reviews, see e.g., Dehaene, 1997).

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These findings indicate, firstly, that infants, children, and adults share a common system of approximate quantification. This system results in representation of approximate number of items, and enables the comparison of the inter-relations between numerically different sets of items. The system provides infants with abstract representations of magnitudes, which are robust across modalities. Infants’ approximate number representations are not limited to visual arrays, but when tested with sequences of temporally distinct events such as sounds, 6- and 9-month-old infants show the same results as in visual test situations. These abstract representations support number-relevant computations. Infants’ numerical discriminations based on this system are imprecise and subject to a ratio limit: 6-month-old infants successfully discriminate 8 versus 16 and 16 versus 32 dots, but fail with 8 versus 12 and 16 versus 24 under the same conditions (Feigenson et al., 2004). During later development, the discrimination becomes more accurate, and experienced adults are able to make very precise approximate comparisons between large magnitudes. Although the idiosyncrasy of an individual’s experience may result in different situated features of this skill, the core process remains abstract and independent of any particular situation or experience. This means that the ability to make approximate comparisons is a powerful transferable skill but details (like the level of accuracy in a certain context) may depend on the specific situational experience. In addition to the approximate system, infants and adults have a second system relevant for quantification. This system enables individuating and precisely keeping track of small number of objects. Infants’ success in these tasks is not dependent on numerical ratio, but on the absolute number of items presented. The system of precise individuation enables infants to recognize ordinal relationships between numerosities and to form expectations about the numerical outcome of the increasing or decreasing of 1 or 2 items. In infants, this capacity is limited to numbers up to 2 or 3, meaning that the exact recognition fails for larger quantities. Like the first core system, the system for exactly representing small number of distinct objects is based on abstract representations in terms of modal independency: the system functions equally well with visual information and sounds. However, this system is limited to recognizing clearly separate objects only. Streams of continuous substances or objects that come into and go out of existence are not successfully recognized by infants (Feigenson et al., 2004). The latter limitation is important from the point of view of transfer. In some activities and environments the child can keep track and enumerate clearly separate objects, and the system for small number recognition is easy to activate. However, this is not the case in all natural situations. Normally the child has a great number of alternatives to interpret in the situation and there is seldom one clear set of separate objects attracting the child’s attention. Although a young child may have an abstract and thus, in principle, powerful transferable skill to recognize small numerosities, this skill may not necessarily become activated in all situations that, from the adult’s perspective, include obvious opportunities for numeric operations. How could these attentional processes needed for the utilizing of early number skills be characterized? According to Gibson and Spelke (1983) and Gibson and Pick (2000), one of the basic processes of perceptual learning is differentiation, which can be described as a narrowing down from a vast body of information to the optimal information that specifies the affordance of an event, object or layout. Gibson and Pick (2000) state:

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An active perceiver has the tasks of extracting the information that specifies relevant events and especially, of detecting information that specifies an affordance of the environment relevant to the perceiver’s species, needs, and powers. Learning to detect the information that specifies such a relationship is perceptual learning. Attempts at acting on such information contribute further information, serving to increase the specificity of what is detected. Information about the world is obtained in a continuous flow by an active perceiver. Cycles of perceiving follow one another, often in an exploratory fashion. Invariance over transformations can only be detected over time. (p. 149) The utilizing of numbers in one’s action requires that the number is abstracted over colour, size, and spatial configuration of the set of objects (Gibson & Spelke, 1983). A single object (as well a set of objects) can be analysed in such a way that its universal structure (its numerosity) becomes a figure, while its accidental detail fades into the background. As stated earlier, abstraction engenders similarity rather than vice versa (Olsson & Lehtinen, 1997). Recognition of the cardinality of a set could be conceptualized as the utilization of abstract knowledge about numerosity in a concrete situation. According to Olsson and Lehtinen, the cognitive purpose of abstraction is to facilitate the growth of larger and more complex structures. The function of abstraction is not only to provide generality but also to facilitate the assembly process and to provide a different categorization of the world than the one suggested by perceptual similarities. This means that the early knowledge of numerosity in an abstract form is a necessary element in later more complex mathematical constructs, such as the formal arithmetic procedures learned in school or the informal practices of quantitative reasoning typical of different cultural activities. Specifically, acquiring the knowledge of what specifies the affordance can be a longterm process in which the child’s developing perceptual systems provide information that is increasingly accessible for new purposes (Gibson & Spelke, 1983). Children’s ability to select and adjust strategies according to the requirements of different tasks increases with age, so that they learn to adjust their action according to the task-relevant features of the tasks (Pick & Frankel, 1974), and they become increasingly capable of inhibiting and controlling their actions during preschool years (Backen Jones, Rothbart, & Posner, 2003). Children’s learning to focus attention on the different aspects of the tasks is fundamental for understanding the learner’s own active role in transfer (Lobato, 2003). On the basis of their qualitative study, Lindahl and Samuelsson (2002) argue that when children’s intention is focused on specific phenomena, they seem to look for a variety of situations where they can practise and explore the phenomenon they want to master. Ericsson and Lehman (1996) show that experts seem to be capable of ‘seeing’ multiple possibilities to practise their skills in everyday situations, and this kind of active, explorative behaviour has been an essential part of their development from a very early age. Mathematical thinking in everyday life means focusing on mathematically meaningful features of the environment and action. It is a way of perceiving the world in a structured, mathematically affordable way. We build our physical surroundings according to geometric rules, use

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symmetric forms and structures, focus on number of items, and utilize numerical skills almost continuously. Learning the usefulness of number recognition skills in children’s own activities from early on facilitates the construction of a crystallised, abstract concept of natural numbers.

Attentional Processes and Transfer of Emerging Number Skills Most research on preschool children either focuses on core capacities that are present since infancy, or on developmental changes in task-related behaviour, typically on symbolic number tasks appropriate for school-aged children (for a review, see Mix, Huttenlocher, & Levine, 2002). Thus, nearly all our knowledge of young children’s numerical skills is based on studies that explicitly direct children’s attention to the aspect of number. Such studies fail to capture in method or theory the process by which children spontaneously focus on numerosity, and individual differences in this process that may be important for the development of more complex number skills. This attentional process is of great importance because recognition of the exact number when the number is utilized in action is not an automatic process, but an intentional act (Hannula, 2005). This proposal is based on the notion that number is not a property of the physical world itself, but is rather determined as a result of how we choose to carve up the physical world into individual elements (Piaget & Szeminska, 1952; Wynn, 1998). In natural surroundings, one has to focus one’s attention on the aspect of number in the set of items in question, and the set of items has to be defined before one can determine the exact number of items in a set. The concept ‘set of individuals’ is central to counting, simple addition and subtraction, and all natural number concepts (Spelke, 2003). The development of this concept is crucial for a young child’s piecemeal growth in understanding what oneness, twoness, and threeness mean (Spelke, 2003). It is also essential for focusing on the aspect of numerosity, because numerosity is, in particular, the quality of a set requiring focusing on the set of individuals, not only on the individuals. On the basis of our studies (Hannula, 2005; Hannula & Lehtinen, 2005; Hannula, Mattinen, & Lehtinen, 2005; Hannula, Räsänen, & Lehtinen, 2005), we argue that research focused on young children’s tendencies to spontaneously attend to numerical information that children are in principle capable of processing, can broaden our knowledge of developmentally significant numerical activities taking place in young children’s everyday surroundings, as well as the transfer of number skills into new situations. In these studies, we developed methods to separate the process of focusing on the aspect of numerosity from enumeration skills in 3–7-year-old children, which allowed us to study individual differences in children’s Spontaneous Focusing on Numerosity (SFON). In a typical task we asked a child to do exactly the same activity that was modelled by the experimenter. Activities consisted of sequences of repeated activities (e.g., feeding an animal figure on berries). The results showed not only remarkable individual differences in children’s selfinitiated focusing on number in certain tasks but also that there was stability in children’s SFON tendency across different tasks presented during the period from 3 to 6 years (Hannula & Lehtinen, 2005; Hannula et al., 2005). More importantly, SFON tendency was positively related to the development of numerical skills from the age of 3.5 to 6 years. The

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results also indicate that conceptual and procedural advances in enumeration enable and facilitate the child’s tendency to focus on numerosity. With more crystallised abstraction of the aspect of number, utilizing numerical skills in a variety of everyday situations becomes easier. More frequent focusing on numerosity, in turn, produces lots of practice in enumeration and thus develops enumeration skills further. The covariance of mathematical skills and SFON tendency was not explained by individual differences in non-verbal IQ or comprehension of verbal instructions (Hannula & Lehtinen, 2005). By using guided focusing tasks in one of our studies, it was shown that the children’s failure in SFON tasks was not caused by their inability to deal with the cognitive requirements of these tasks, but by the lack of focusing on numerosity in the tasks (Hannula & Lehtinen, 2005). In sum, SFON seems to be an important factor in the acquisition of cultural tools of numeracy, and it is by no means self-evident that, in natural social situations, all children notice the number of objects, and utilize them in action. This opens up a new approach to understanding children’s failures to transfer their mathematical skills into new situations. Successful transfer of previous mathematical knowledge into a new situation requires that the child focuses on the numerical aspects of the situation. The findings of the SFON studies show that this does not always happen although the children possess the number skills needed. Our hypothesis is that children’s learning experiences in their sociocultural context together with situation-specific features strongly afford and constrain their tendency to focus on numerosity. Improving Transfer through SFON Goldin-Meadow, Alibali, and Church (1993) have proposed that children’s first counting attempts are one of the first significant, easily noticed signals for adults to start providing guidance in quantitative skills. Social interaction and the aid of more experienced members of society are crucial for the development of higher-order processes and selfregulation, especially the controlling of attention (Gauvain, 2001). The social context affords children structured opportunities to practise, refine, and extend their cognitive skills (Gauvain, 2001). Participation in shared activities requires and also develops understanding of the intentions of others, cultural learning, motivation to share psychological states with others, and specific forms of cognitive representations for shared actions (Tomasello, Carpenter, Call, Behne, & Moll, 2005). The goals of socially defined activity determine which features of situations are important and, therefore, play a significant role in determining which features people will pay attention to in their interaction with objects and information (Greeno et al., 1993). The joint processes of children and adults direct children’s attention to relevant aspects of tasks, and help children acquire the culturally based numerical tools necessary for living in a society. These joint processes also help children understand the purposes of the tasks and certain cognitive strategies embedded in a variety of everyday activities (Gauvain, 2001; Gibson & Spelke, 1983). With studies of older students, Lobato and colleagues have shown that the social and physical aspects of a certain situation can support students’ attention towards particular mathematical properties rather than others in mathematics lessons (Lobato, 2003; Lobato et al., 2003).

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Our experimental study on SFON (Hannula et al., 2005) was aimed at encouraging daycare personnel to support children’s numerical focusing and deliberately direct children’s attention towards variation in small number of objects. The idea of making children more aware of the aspect of number by using deliberate variation was based on the proposal of Marton and Booth (1997). To learn something means to become capable of experiencing various aspects of the set of items in a certain, specific way. Thus, ‘threeness’ is experienced against the background of a potential variation in the aspect of number, against ‘twoness’ and ‘fourness’, for instance (Marton & Booth, 1997). In this way, children’s implicit knowledge about small numbers can become a more explicit target of intentional focusing, and children could learn the affordances of numerical aspects in a variety of everyday activities. The results of Hannula et al. show that it is possible to enhance children’s SFON tendency by means of social interaction. There was an experimental longterm effect on SFON tendency and subsequent development in cardinality-related skills from pretest to delayed post-test in the children with some initial SFON tendency in the experimental group. Hence, it is possible to increase children’s tendency to transfer their existing number skills in new situations. Focusing attention on the aspect of numerosity, ‘mathematical lenses’, and the abstract idea of numerosity seem to be important factors producing the transferable number skills. Learning to focus on numerosity may be one of the significant steps for young children on their way to learning to adopt mathematically meaningful perspectives on perceiving the world around them.

Conclusions and Discussion The frequently observed situations in which children (or later adults) are not able to transfer their mathematical knowledge into new situations do not mean that the very nature of mathematical knowledge is situation-specific; there are several other reasons why people do not apply their (abstract) mathematical knowledge in these situations. The main argument presented in this chapter highlights the importance of domainspecific attentional processes. It is obvious in the cases of transfer failures that the situations are not necessarily interpreted as mathematical by the child. This means that the child does not pay attention to the mathematically relevant aspects of the situation, and is thus not able to carry out the expected operations. It is the mediating role of attentional processes that makes it possible to integrate the cognitive and situated views of transfer. The mathematical core knowledge is abstract and not limited to any specific situation. However, the focusing of attention on numerosity, which fundamentally determines the utilization of mathematical knowledge, does depend on the situational features. The existence of relevant mathematical knowledge is a necessary but not sufficient precondition for transfer. The development of number skills shows that young children have abstract mathematical concepts that are, in principle, transferable to different novel situations. The actual application very much depends on the child’s spontaneous focusing on the quantitative aspect of the situation, which, in turn, is multifariously dependent on the features of the situation and the child’s experiences in the sociocultural environment. In other words, the world could appear to some children to be full of opportunities for practising early number

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skills, while others may not regard numerosities as relevant factors and consequently may not apply their emerging skills as frequently. In other situations, the application of general mathematical principles fails because the child has not yet adequately learned the abstract principles needed in these tasks. The research on the development of the number concept shows that the process of building more advanced concepts on the basis of the initial predispositions is a slow process (e.g., Fuson, 1988), and the child’s ability to repeat the socially mediated linguistic expressions (counting words) easily leads to overestimation of the level of the child’s actual mathematical concepts (Baroody, Lai, & Mix, 2006). Similarly, older children or adults can learn to imitate complex algorithms in a familiar learning situation but have not yet constructed the abstractions needed in applying these operations in new situations. The third possible way in which the immediate transfer of number knowledge may fail, is that the tasks in question require a great deal of knowledge about the content- and situation-specific practices and needed to apply the abstract mathematical principles. In this kind of situation, immediate transfer is not possible, even in principle, but the learner has to apply his or her abstract mathematical knowledge in order to carry out a long-lasting learning and problem-solving process. The problem of limited transfer of mathematical skills is a serious pedagogical problem, which should be carefully studied both in a school context and in different everyday situations. In future research on mathematics learning it is important to analyse how early domain-specific predispositions afford and constrain the later construction of increasingly complex concepts and the assembly of new abstractions on the basis of previous ones. Parallel with this cognitively oriented research, we need more detailed analyses of both the situational development of specific aspects of mathematical knowledge and the regulation of attentional processes in mathematical learning and problem-solving situations. Ten years ago, Ohlsson and Lehtinen (1997) argued that the very nature of scientific and mathematical knowledge is that they include abstract ideas, which are not simple generalizations of the concrete perceptual experiences, but are at least partly generated on the basis of prior abstract ideas. Ideas consist of other ideas, which consist of yet other ideas, and so on. They pointed out that this regress must be broken by postulating some starting point, some initial abstractions that can serve as the input to the very first applications of the assembly process. They discussed several possible solutions to this problem. The first was the long-standing one of postulating innate abstractions. However, they argued that historically, nativist theories have had little success and, thus, they were reluctant to embrace this solution. According to their opinion, there were not enough well-grounded suggestions as to what those primordial abstractions might be, and so they preferred other explanations. On the basis of the increasing amount of evidence produced by developmental psychology and brain research (Feigenson et al., 2004; Hirschfeld & Gelman, 1994; Karmiloff-Smith, 1995), at least the second author of the Ohlsson and Lehtinen (1997) paper is gradually changing his mind, and in the present chapter, we propose an alternative hypothesis: predispositions with long ontogenetic histories may have an important role in the cognitive development in certain domains and they may serve as starting points for constructing abstract mathematical concepts. Infants and young children apply their numerical core systems in a variety of situations. These activities are constrained by the abstract rules based on domain-specific predispositions. In the

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later development these early abstractions will be assembled into larger and more complex mathematical concepts.

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Gibson, E. J., & Spelke, E. (1983). The development of perception. In: J. H. Flavell, & E. M. Markman (Eds), Handbook of child psychology: Vol 3. Cognitive development (pp. 1–76). New York: Wiley. Gleissner, B., Meltzoff, A. N., & Bekkering, H. (2000). Children’s coding of human action: Cognitive factors influencing imitation in 3-year-olds. Developmental Science, 3, 405–414. 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. Greeno, J. G., Smith, D. R., & Moore, J. L. (1993). Transfer of situated learning. In: D. K. Detterman, & R. J. Sternberg (Eds), Transfer on trial: Intelligence, cognition, and instruction (pp. 99–167). Norwood, NJ: Ablex Publishing Corporation. Hannula, M. M. (2005). Spontaneous focusing on numerosity in the development of early mathematical skills. Annales Universitatis Turkuensis, ser B, tom. 282. Hannula, M. M., & Lehtinen, E. (2005). Spontaneous focusing on numerosity and mathematical skills of young children. Learning and Instruction, 15, 237–256. Hannula, M. M., Mattinen, A., & Lehtinen, E. (2005). Does social interaction influence 3-year-old children’s tendency to focus on numerosity? A quasi-experimental study in day care. In: L. Verschaffel, E. De Corte, G. Kanselaar, & M. Valcke (Eds), Powerful environments for promoting deep conceptual and strategic learning (pp. 63–80). Leuven: Leuven University Press. Hannula, M. M., Räsänen, P., & Lehtinen, E. (2005). Development of counting skills: Role of spontaneous focusing on numerosity and subitizing-based enumeration. Manuscript submitted for publication. Hayek, F. A. (1972). The primacy of the abstract. In: A. Koestler, & J. R. Smythies (Eds), Beyond reductionism (pp. 309–333). London: Hutchinson. Hershkowitz, R. Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32, 195–222. Hirschfeld, L.A., & Gelman, S.A. (Eds.) (1994), Mapping the mind: Domain specificity in cognition and culture. Cambridge: Cambridge University Press. Karmiloff-Smith, A. (1995). Beyond modularity. A developmental perspective on cognitive science (2nd ed.). London: The MIT Press. Kumpulainen, K., & Mutanen, M. (1999). The situated dynamics of peer group interaction: An introduction to an analytic framework. Learning and Instruction, 9, 449–473. Lave, J. (1988). Cognition in practice: Mind, mathematics, and culture in everyday life. New York: Cambridge University Press. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press. Lehtinen, E. (1986). Laskentoa ilman matematiikkaa [Counting skill without mathematics]. In: E. Lehtinen (Ed.), Tieto, tunne ja matematiikan opetus (pp. 45–74). University of Turku, Faculty of Education, Publications B:20. Lehtinen, E., Merenluoto, K., & Kasanen, E. (1997). Conceptual change from rational to (un)real numbers. European Journal of Psychology of Education, 12, 131–145. Lehtinen, E., Vauras, M., Salonen, P., Olkinuora, E., & Kinnunen, R. (1995). Long term development of learning activity: Motivational, cognitive and social interaction. Educational Psychologist, 30, 21–35. Lenat, D. B., & Feigenbaum, E. A. (1991). On the thresholds of knowledge. Artificial Intelligence, 47, 185–250. Lindahl, M., & Samuelsson, I. P. (2002). Imitation and variation: Reflections on toddlers’ strategies for learning. Scandinavian Journal of Educational Research, 46, 25–45. Lobato, J. (2003). How design experiments can inform a rethinking of transfer and vice versa. Educational Researcher, 32(1), 17–20. Lobato, J., Ellis, A. B., & Muñoz, R. (2003). How “focusing phenomena” in the instructional environment afford students’ generalizations. Mathematical Thinking and Learning, 5, 1–36.

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Lobato, J., & Siebert, D. (2002). Quantitative reasoning in a reconceived view of transfer. Journal of Mathematical Behavior, 21, 87–116. Mandler, J. M. (2004). The foundations of mind: Origins of conceptual thought. New York: Oxford University Press. Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah, NJ: Erlbaum. Merenluoto, K., & Lehtinen, E. (2004). Number concept and conceptual change: Towards a systemic model of the processes of change. Learning and Instruction, 14, 519–534. Mix, K. S., Huttenlocher, J., & Levine, S. C. (2002). Math without words: Quantitative development in infancy and early childhood. New York: Oxford University Press. Nelson, K. (2004). A welcome turn to meaning in infant development: Commentary on Mandler’s The foundations of mind: Origins of conceptual thought. Developmental Science, 7, 506–507. Ohlsson, S., & Lehtinen, E. (1997). Abstraction and the acquisition of complex ideas. International Journal of Educational Research, 27, 37– 48. Piaget, J., & Szeminska, A. (1952). The child’s conception of number. London: Routledge & Kegan Paul. Pick, A. D., & Frankel, G. W. (1974). A developmental study of strategies of visual selectivity. Child Development, 45, 1162–1165. Rogoff, B., Mistry, J., Goncu, A., & Mosier, C. (1993). Guided participation in cultural activity by toddlers and caregivers. Monographs of the Society for Research in Child Development, 58 (8, Serial No. 236), 1–179. Romberg, T. A. (1994). Classroom instruction that foster mathematical thinking and problem solving: Connection between theory and practice. In: A. H. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 287–304). Hillsdale, NJ: Erlbaum. Salomon, G., & Perkins, D. N. (1989). Rocky roads to transfer: Rethinking mechanisms of a neglected phenomenon. Educational Psychologist, 24, 113–142. Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27(2), 4–13. Singley, M. K., & Anderson, J. R. (1989). The transfer of cognitive skill. Cambridge, MA: Harvard University Press. Spelke, E. S. (2000). Core knowledge. American Psychologist, 55, 1233–1243. Spelke, E. (2003). What makes us smart? Core knowledge and natural language. In: D. Gentner, & S. Goldin-Meadow (Eds), Language in mind (pp. 277–311). Cambridge, MA: MIT Press. Staub, F., & Stern, E. (1997). Abstract reasoning with mathematical constructs. International Journal of Educational Research, 27, 63–75. Tomasello, M., Carpenter, M., Call, J., Behne, T., & Moll, H. (2005). Understanding and sharing intentions: The origins of cultural cognition. Behavioral and Brain Sciences, 28, 675–691. Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H., & Ratinckx, E. (1999). Learning to solve mathematical application problems: A design experiment with fifth graders. Mathematical Thinking and Learning, 1, 195–229. Wynn, K. (1998). Numerical competence in infants. In: C. Donlan (Ed.), The development of mathematical skills (pp. 3–25). East Sussex, UK: Psychology Press. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.

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Chapter 4

Examining Mathematics Learning From a Conceptual Change Point of View: Implications for the Design of Learning Environments Stella Vosniadou and Xenia Vamvakoussi1

The Problem of Knowledge in the Design of Learning Environments Most educational researchers seem to agree that mathematics learning does not consist of the passive absorption of certain abstract, de-contextualized concepts and procedural skills to be acquired by individuals through transmission teaching methods. Rather, researchers talk about the development of a mathematical disposition involving not only domain-specific knowledge and problem-solving skills, but also meta-knowledge, self-regulatory skills, motivational factors, and epistemological beliefs about mathematics (e.g., De Corte, Greer, & Verschaffel, 1996; Schoenfeld, 1992, 2002). Nevertheless, the discussion about the design of powerful learning environments that can foster the development of a mathematical disposition is not yet settled, often reflecting the controversy between cognitive and situated approaches to learning and teaching. The situated approach movement has drawn the attention of the mathematics education community to certain aspects of learning that were not considered important in the context of cognitive approaches, such as the relevance of the social and cultural context and the role of artefacts in learning (Anderson, Reder, & Simon, 1996; De Corte, 2004; Sfard, 1998). The situated approach has also been useful in pointing out the mismatch between the way mathematics is taught in the schools and the way it is used in real-life situations. It is argued that many school activities may be meaningless for students and this may be a source of creating inert knowledge that cannot be transferred to out-of-school situations 1

The present study was funded through the program EPEAEK II in the framework of the project "Pythagoras Support of University Research Groups" with 75% from European Social Funds and 25% from National Funds.

Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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(Brown, Collins, & Duguid, 1989). Thus, it has been suggested that training by abstraction is of little use, that instruction needs to be integrated in complex, social environments, and that learning should take place in authentic contexts. Although the situated approach has served an important role in de-emphasizing individual, cognitive — ‘in the head’ — internal processes and stressing instead the social, collaborative, and realistic aspects of learning that were previously neglected, it has also led to some misguided claims and inappropriate educational suggestions, as pointed out by Anderson et al. (1996). For instance, the claims that learning is always grounded in concrete situations, that knowledge does not transfer between tasks, and that training by abstraction is of little use, seem to draw only on limited empirical data and to neglect findings that this approach cannot predict. Another important limitation of the situated approach is that it has downgraded the problem of knowledge (Bereiter, 1997; Vosniadou, 2005). This is the case, because according to situativity theory, knowledge is not a thing to be acquired but a process in which one participates — the well-known debate between the ‘acquisition’ and ‘participation’ metaphors on knowing and learning. If we see knowledge as a process, then the emphasis on teaching shifts from teaching subject-matter content to teaching thinking and learning skills. Indeed, the main metaphor developed within the situated cognition approach has been the cognitive apprenticeship metaphor (Collins, Brown, & Newman, 1989). The problem with the cognitive apprenticeship metaphor is that it has not solved sufficiently the problem of finding an authentic culture for students to participate in expert practice. As argued in Vosniadou (2005), we can neither expect to enculturate primary and secondary school students in the cultures of the mathematicians, physicists, historians, etc., nor expect to produce ‘intelligent novices’ who are trained in expert practices ignoring the bodies of knowledge and systems of beliefs that go together with developing expertise in a given domain of knowledge. Cognitive apprenticeship becomes empty when its purpose is to practice cognitive skills in the absence of substantial knowledge building and where the domain knowledge is secondary to the learning skills that are to be acquired. According to Bereiter (1997), situativity theory has failed to provide a cogent idea of schooling and a new educational vision exactly because it has not been able to adequately address the problem of knowledge. Science and mathematics are not only processes in which one participates, but also the knowledge products of a complex social interaction. Although they are produced through the situated practices of scientists, they nevertheless have an objective non-situated reality, which is divorced from the processes that produced them. Just like paint is produced through a situated manufacturing process but as a product it can be used in many different situations, and thus it is not in itself situated (see Bereiter, 1997; Vosniadou, 2005), so is the case with scientific and mathematical knowledge. It can be used by engineers and architects, by computer scientists and artists, in situations very different from those that produced it, to create new knowledge and artefacts that may change the very culture in which we live. This point does not weaken the situated cognition approach thesis. Rather, it calls for an integrated approach to the design of learning environments, striving not only for the acquisition of mathematical skills through cognitive apprenticeship but also for deep, conceptual, subject-matter knowledge. The conceptual change approach, which will be described in detail below, addresses aspects of the problem of knowledge in the design of

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learning environments for the purpose of developing deep understanding of subject-matter knowledge.

The Conceptual Change Approach The conceptual change approach to learning and teaching has its roots in Thomas Kuhn’s revolutionary account of theory change in the history of science. In ‘The structure of scientific revolutions’ (Kuhn, 1970), Kuhn argued that scientific theories develop in the context of paradigms — i.e., webs of shared concepts, beliefs, practices — and shared commitments that students of science learn when they become scientists, and that theory change is not a cumulative but a revolutionary process during which the old paradigm is rejected and replaced with a new one. This account of theory change has served as a source of hypotheses about how concepts change not only in the philosophy and history of science but also in the process of learning science (Posner, Strike, Hewson, & Gertzog, 1982). The basis for the analogy between scientific theory change and the learning of science became the realization that students bring to the science learning task ‘preconceptions’, ‘misconceptions’, or ‘alternative conceptions’ (Driver & Easley, 1978; Novak, 1977; Viennot, 1979) that stand in the way of learning science. Posner et al. (1982) and also McCloskey (1983) argued that these alternative conceptions can be seen as theories that need to be replaced by the currently accepted, correct, scientific views through a process of conceptual change. For this conceptual change to be achieved, students need to experience dissatisfaction with their existing ideas, a dissatisfaction usually produced in instructional settings through cognitive conflict, and must understand the fruitfulness of the new, scientific explanations. The conceptual change approach was the leading paradigm in science education until it became subject to several criticisms, regarding both its epistemological assumptions and its instructional practices. Among other things, it has been pointed out that this theoretical framework provides a rather simplistic view of misconceptions, as being unitary, faulty conceptions, and that it ignores their interrelations with other concepts, as well their interaction with the situational context in which they are invoked (Caravita & Halldén, 1994; Smith, diSessa, & Rochelle, 1993). This view of misconceptions underlies the instructional practice of cognitive conflict that emerged from this theoretical framework, which aims at replacing students’ misconceptions with correct ideas. This practice has been criticized as not having a sound constructivist basis, as ignoring students’ productive ideas, and therefore, as being misguided and inefficient (Smith et al., 1993). In addition, Caravita and Halldén (1994) pointed out that conceptual change happens in a larger situational, educational, and socio/cultural context; that it is affected by motivational and affective variables; and that one cannot ignore the fact that science is socially constructed and validated (see also Driver, Asoko, Leach, Mortimer, & Scott, 1994; Pintrich, 1999). In the meantime, cognitive-developmental psychologists have also started investigating the conceptual change framework as a source of ideas to explain how concepts develop in the growing child (Carey, 1985; Vosniadou & Brewer, 1987). Research with infants has shown that children interpret their everyday experience in order to form broad explanatory

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frameworks that commit them to an ontology and a causality that distinguishes physical from psychological objects and which forms the basis for the knowledge acquisition process. For example, infants soon after birth seem to adhere to certain principles regarding the behaviour of physical objects (such as that they are solid and stable; that they do not move by themselves; that they fall ‘down’ when unsupported, etc.) that make it possible for them to function in the physical world (i.e., Baillargeon, 1994; Spelke, 1991). This initial naïve physics usually facilitates the learning of science through a process of continuous enrichment, as new information is added to the existing conceptual structures. However, when the new information to be acquired is radically different than what is already known (i.e., different in its structure, in the phenomena it explains, as well as in the very concepts that comprise it), prior knowledge may hinder the acquisition of the new, intended knowledge and the process of enrichment can result in the production of misconceptions (Gelman & Meck, 1992; Vosniadou & Verschaffel, 2004). Vosniadou and her colleagues have attempted to provide detailed descriptions of the development of knowledge in several areas of the natural sciences, such as observational astronomy (Vosniadou, 1994, 2003; Vosniadou & Brewer, 1992, 1994), mechanics (Ioannides & Vosniadou, 2001; Megalakaki, Ioannides, Vosniadou, & Tiberghien, 1997), geophysics (Ioannidou & Vosniadou, 2001), chemistry (Kouka, Vosniadou, & Tsaparlis, 2001), and biology (Kyrkos & Vosniadou, 1997). The results of these studies have shown that young children answer questions about force, matter, the earth in space, or about the composition of earth, mostly in an internally consistent way, revealing the existence of narrow but coherent initial explanatory frameworks. In the process of learning science, children usually add the new, scientific, information to their initial explanatory frameworks. The framework theory approach to conceptual change predicts that new information which is incompatible with what is already known is more difficult and time consuming to be learned than new information that can enrich existing structures. Moreover, given that learners are usually not aware of the ontological and epistemological commitments of their initial framework theory, they are most likely to use the same additive mechanisms with all forms of new knowledge making likely the formation of misconceptions. Many misconceptions can be explained as synthetic models reflecting students’ attempts to assimilate new information in their existing but incompatible knowledge structures. In the case of observational astronomy, examples of such synthetic models are the model of the dual sphere, the hollow sphere, or the flattened sphere; the model of the sun and the moon revolving around a spherical earth in a geocentric solar system, etc. (see Vosniadou & Brewer, 1992, 1994). The framework theory approach to conceptual change that we adopt meets all the criticisms of Caravita and Halldén (1994) and Smith et al. (1993). First, misconceptions are not considered as unitary, faulty conceptions. Rather, we describe a knowledge system consisting of many different elements organized in complex ways. Second, we make a distinction between the learner’s initial explanatory framework, prior to systematic instruction, and misconceptions that are produced after instruction. We explain the formation of the initial framework theories taking into consideration evolutionary factors, as well as young children’s interaction with their physical and social environment and the cultural tools which they have available. Third, our theoretical position is a constructivist one. Not only it assumes that new information is built on existing knowledge structures, it also uses

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constructivism to explain students’ misconceptions and to provide a comprehensive framework for making meaningful and detailed predictions about the knowledge acquisition process. More specifically, according to the conceptual change point of view that we propose, many misconceptions are formed precisely because learners have the tendency to enrich their prior knowledge with new information even when this information is totally incompatible with what they already know. Finally, while our approach investigates mainly the cognitive facets of conceptual change, it is complementary and not contradictory to other approaches that deal with motivational/affective and socio/cultural factors (Anderson, Greeno, Reder, & Simon, 2000).

The Framework Theory Approach to Conceptual Change and the Acquisition of Mathematical Knowledge It has been argued that the framework theory approach to conceptual change can be fruitfully applied in the case of mathematics learning (Vosniadou & Verschaffel, 2004). As it is the case that students develop an initial framework theory about physics on the basis of everyday experience, they also develop an initial framework theory about number, organized on the basis of certain core principles or presuppositions. Indeed, there is growing evidence that, even before any instruction, children form an initial understanding of number, based on their experience with natural numbers. According to Gelman (2000), children construct a ‘principled understanding’ of numbers on the basis of the act of counting. In science learning, students’ framework theories facilitate some kinds of learning but inhibit others. There is evidence that this also happens in the case of mathematics learning. For example, an early understanding of natural number and its properties supports children’s understanding of notions such as potential infinity (Hartnett & Gelman, 1998), while at the same time it stands in the way of students’ understanding of the properties and operations of rational numbers (Carpenter, Fennema, & Romberg, 1993; Moskal & Magone, 2000; Resnick et al., 1989; Yujing & Yong-Di, 2005). These findings support the argument that science and mathematics learning share certain similarities in terms of the significance of students’ initial explanatory frameworks for the acquisition of new, intended knowledge. A number of empirical studies conducted within the conceptual change theoretical framework have been presented in a special issue of Learning and Instruction (Verschaffel & Vosniadou, 2004). The research presented in this special issue has shown that the framework theory approach to conceptual change can be fruitfully applied to predict and explain students’ difficulties with fractions (Stafylidou & Vosniadou, 2004), the use of the negative sign in algebra (Vlassis, 2004), the number concept (Merenluonto & Lehtinen, 2004; Vamvakoussi & Vosniadou, 2004b), as well as students’ tendency to apply linear models in cases where they are not applicable (Van Dooren, De Bock, Hessels, Janssens, & Verschaffel, 2004). In the following section, we will present in greater detail two studies conducted in our lab which apply the framework theory approach to conceptual change to explain students’ difficulties with rational numbers.

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Developing the Concept of Rational Number As we have already mentioned, even before instruction, children construct a framework theory of number on the basis of the principles of counting. This foundational theory basically treats all numbers as natural numbers. Analysing the differences between the set of natural and the set of rational numbers, we point out two major differences: First, the set of natural numbers is discrete, whereas the set of rational numbers is dense. In the set of natural numbers, there is a finite number of numbers between any two numbers, whereas in the set of rational numbers there are infinitely many numbers between any two, non-equal, numbers. Second, any number within the set of natural numbers has a unique symbolic representation, whereas any number in the set of rational numbers has multiple symbolic representations; e.g., the symbols 4/2, 32/16, 2.0, etc., are different representations of the same numerical value 2. These particular differences between the set of natural and the set of rational numbers suggest that understanding about the structure of the set of rational numbers may be difficult for students. Indeed, there is evidence that the idea of discreteness is a barrier to understanding about density for students (Malara, 2001; Merenluoto & Lehtinen, 2002, 2004; Neumann, 1998), as well as for elementary school prospective teachers (Tirosh, Fischbein, Graeber, & Wilson, 1999). There is also evidence that the symbolic representation of the numbers involved may be a factor that interferes with students’ understanding about the structure of rational numbers intervals. For instance, Neumann (1998) reports that 7th graders had difficulties accepting that there could be a fraction between 0.3 and 0.6, probably because they thought of decimals and fractions as different, unrelated sorts of numbers. There is yet another way through which symbolic notation may affect students’ thinking about numbers: Students may consider decimals, as well as fractions, as different, unrelated subsets of the set of rational numbers. This assumption is supported by research showing that novices in a domain tend to group objects on the basis of superficial characteristics (e.g. Chi, Feltovich, & Glaser, 1981). This disposition may be enhanced by the fact that the operations as well as the ordering of fractions are considerably different than those of decimals. We claim that understanding about the dense structure of the rational numbers set requires conceptual change. On the basis of the framework theory approach to conceptual change described by Vosniadou (1994, 2001, 2003), we assume that the development of the concept of rational number is a slow and gradual process, constrained by the presupposition of discreteness as well as by the presupposition that any number has a distinct symbolic representation. Therefore, we expect that there will be intermediate levels of understanding of the concept of rational number and that students will generate synthetic models, reflecting the idea of discreteness and the belief that different symbolic representations refer to different numbers. These hypotheses were tested in two studies. In the first (Vamvakoussi & Vosniadou, 2004b), 16 9th graders participated in a 45-min individual interview during which they were asked to indicate how many numbers there are between two rational numbers: A pair of decimals with the same number of decimal digits, a pair of decimals with different number of decimal digits, a pair of similar fractions, a pair of dissimilar fractions, a fraction and a decimal. We found that the majority of our participants (11 out of 16) answered

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that there is finite number of numbers in all questions, describing intervals that preserve the discrete structure of natural numbers. Only 1 out of 16 students answered that there are infinitely many numbers both in the case of decimals and in the case of fractions. Even this student was reluctant to answer that there are infinitely many numbers between a decimal and a fraction, although he was informed that the particular numbers were not equal; instead, he explicitly said that he needed to turn the fraction into a decimal first, indicating that the symbolic notation of numbers constrained his understanding of density. The same constraint appeared in the responses of the remaining five students, who answered that there are infinitely many numbers in some but not in all questions. Two of these students changed their answer according to the symbolic representation of the numbers involved. For example, one of them answered that there is a finite number of numbers between decimals, but there are infinitely many numbers between fractions. He also explained that if one turns the decimals into fractions, one can find infinitely many numbers in between, indicating his belief that the structure of the interval differs, according to the symbolic representation of the first and the last number, even when the corresponding numerical values do not change. In addition, two of the participants explicitly expressed the belief that different symbolic representations refer to different numbers. For example, one of them answered that there is finite number of numbers in all questions, but she answered that there are infinitely many numbers between 3/8 and 5/8, mentioning several different symbolic representations of the fraction 4/8. As it is apparent, the above results support our hypotheses (a) that students find it difficult to understand the concept of rational number, (b) that the areas of difficulty are exactly those aspects of rational numbers that are inconsistent with the presuppositions of natural numbers (discreteness and unique symbolic representation), and (c) that students create intermediate conceptions (misconceptions, errors, synthetic models) that reveal their tendency to assimilate aspects of the new concept to their incompatible knowledge base. A second study (Vamvakoussi & Vosniadou, 2004a, in press) followed, with the purpose of further investigating the effect of the idea of discreteness and of the symbolic notation of numbers on children’s understanding of the structure of the rational numbers set. We were also interested to test the effect of an external representation, namely the number line, on children’s responses to tasks regarding density. Following an ongoing discussion in the conceptual change literature about the effect of external representations on students’ reasoning and understanding (Vosniadou, Skopeliti, & Ikospentaki, 2005), we hyphothesized that the effect of the number line would be rather limited and that it may disappear when the number line is withdrawn. The participants of the second study were 301 students, 164 9th and 137 11th graders. We designed two types of questionnaires, one open-ended and one forced-choice questionnaire, which consisted of questions regarding how many numbers there are between two rational numbers, as well as their symbolic representation. The number line was present in half of the items. The numbers 0 and 1 as well as the first number of each given interval were already placed on the number line. Our participants completed the questionnaires in two phases: Half of them received the questions with the number line at the first phase, whereas the other half received the questions with the number line at the second phase. In both cases, the first part of the questionnaire was withdrawn before the second part was handed out.

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Here we will refer only to the results obtained in the forced-choice condition. An example of the items without and with the number line is shown in Table 1. In this example, the answers are ordered from the more naïve to the more sophisticated (i–iv). Students received the answers in random order. The results showed that the presupposition of discreteness was still strong in the 11th grade, although the performance of the 11th graders was significantly better than the performance of the 9th graders. Indeed, about one third of the 11th graders answered that there is finite number of numbers in all the questions. On the basis of the participants’ responses in all the items, we categorized them in five categories. Table 2 presents the categorization and the corresponding percentages. With the exception of those placed in the ‘Density’ category, the students gave alternative accounts of the structure of the rational numbers intervals, reflecting the presupposition of discreteness and the effect of the symbolic notation of numbers. Students in the ‘Discreteness’ category treated all given numbers as if they were successive — e.g., they answered that there are no numbers between 0.005 and 0.006. Students in the ‘Refined Discreteness’ category did not consider the given numbers to be successive but still answered that there is finite number of numbers between the given numbers — for instance, Table 1: Second study: Examples of the items in the forced-choice questionnaires (Vamvakoussi & Vosniadou, 2004a, in press). Without the number line ●

How many numbers are there that are greater than 0.005 and, at the same time, less than 0.006? i. There is no such number. ii. There are the following numbers: 0.0051, 0.0052, 0.0053, 0.0054, 0.0055, 0.0056, 0.0057, 0.0058, 0.0059. iii. There are infinitely many decimals. iv. There are infinitely many numbers: simple decimals, decimals with infinitely many decimal digits, fractions, square roots. v. None of the above. I believe that …. With the number line

●

Place 0.2 on the number line. How many numbers are there that are greater than 0.1 and, at the same time, less than 0.2? i. There is no such number. ii. There are the following numbers: 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19. iii. There are infinitely many decimals. iv. There are infinitely many numbers: simple decimals, decimals with infinitely many decimal digits, fractions, square roots. v. None of the above. I believe that ….

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Table 2: Second study: Categorization of the participants (Vamvakoussi & Vosniadou, 2004a, in press). Forced-choice questionnaires Category Discreteness Refined discreteness Mixed Constrained density Density

9th graders (N=81)

11th graders (N=71)

4.9% 30.9% 40.7% 12.3% 11.1%

4.2% 16.9% 42.3% 15.5% 21.1%

that between 0.005 and 0.006 there are only the numbers 0.0051, 0.0052, … , 0.0059. Students in the ‘Mixed’ category answered that there are infinitely many numbers in some, but not all questions. More than half of the students in this category responded differently to intervals with different structures, according to the symbolic representation of the first and the last number. These students answered differently when the first and last numbers of the interval were decimals, as compared to when these numbers were fractions. Students in the ‘Constrained Density’ category answered that there are infinitely many numbers of the same symbolic representation in the given interval for at least one out of the six questions. These students were reluctant to accept that there may be, for instance, fractions between two decimals. Finally, students in the ‘Density’ category answered that there are infinitely many numbers, regardless of their symbolic representation, in all the questions. In addition, 15% of the 11th graders and 19.70% of the 9th graders answered that there are infinitely many fractions between 3/8 and 5/8, all equivalent to 4/8, indicating their belief that different symbolic representations of the number 4/8 count as different numbers. The effect of the number line on students’ performance was quite limited. There was no significant difference in the 11th graders’ performance in the questions with and without the number line. The number line improved 9th graders’ performance only in one specific case, which involved a shift from hundredths to thousandths. In addition, there was no significant difference in the performance of those who answered the questions with the number line in the first phase compared to those who answered the same questions in the second phase, indicating that the effect of the number line disappeared when the number line was not present. We should also note that it is not the case that the presence of the number line always had a positive effect — in fact, some students performed worse in the questions with the number line. The results of the second study further strengthened our previous results in showing (a) that the idea of discreteness is strong, both in the case of 9th and 11th graders, (b) that there are intermediate levels of understanding of the concept of density, and (c) that the symbolic representation of the numbers affects students’ thinking about the rational numbers’ intervals. It seems that students tend to think of fractions and decimals as unrelated

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mathematical objects, even though they have been explicitly taught how to turn decimals into fractions and vice versa. The above results are compatible with the predictions coming from the framework theory approach to conceptual change, and therefore support our hypothesis that new information about rational numbers cannot be simply added to what students already know, but requires a radical re-organization of the concept of number. How is such re-organization accomplished and what does it imply for the design of learning environments for teaching and learning mathematics?

Implications for the Design of Learning Environments in Mathematics De Corte (2004) has outlined certain principles that can be used as a guide for the design of powerful environments for learning mathematics, such as that learning environments should: – initiate and support active, constructive knowledge acquisition processes in all students; – allow for students to acquire control over their own learning; – provide students with the opportunity to elaborate mathematical knowledge in contexts that are meaningful for them; – create a classroom culture that supports collaboration among students and allows for students to reflect on their learning activities and their epistemological beliefs about mathematics and mathematics learning; – provide students with the opportunity to build substantial domain-specific knowledge and, at the same time, develop general learning and thinking skills embedded in the subject-matter knowledge. We fully agree with the above principles, which take into consideration cognitive, metacognitive, affective, and contextual aspects of learning. Focusing on the issue of conceptual change, we will further elaborate on certain guidelines which could be useful for curricula designers, teachers, and researchers who are interested in implementing powerful learning environments for mathematics learning. Breadth of Coverage of the Curriculum-time Considerations Conceptual change research shows that, similar to the case of science, the understanding of certain mathematical concepts is a difficult and time-consuming process. This finding calls for a reconsideration of decisions regarding the breadth of coverage of the curricula in mathematics education. It may be more profitable to design curricula that focus on the deep exploration and understanding of certain key concepts and their association with other concepts, both within and outside mathematics, instead of covering a great deal of material in a superficial way, which is likely to lead students to logical incoherence and the creation of misconceptions. In addition, teachers should be aware of the fact that even the most carefully designed learning environment should not be expected to produce results if they do not invest a considerable amount of time in the implementation (see e.g. Van Dooren et al., 2004).

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Order of Acquisition of the Concepts Involved Usually the concepts that comprise a subject-matter area have a relational structure that influences their order of acquisition. In mathematics education it is often the case that the subject matter is assumed to have a hierarchical structure, in which new concepts follow logically from prior ones. For instance, Grossman and Stodolsky (1995) found that mathematics educators, compared with those of other studies, such as sciences and social studies, consider their subject to be highly sequential. This view of mathematics is compatible with the belief that learning is additive and may hinder mathematics teachers, as well as designers of mathematics curricula, from recognizing that the conceptual change issue is relevant in mathematics learning. Usually, this results in teaching ‘simple’ concepts first and then introducing the more ‘complex’ concepts, which are often presented either as being logical implications of what is already taught or as expansions of prior concepts. For instance, fractions are introduced much later than natural numbers and their operations; algebraic concepts, such as the concept of variable, are taught in secondary education or at the end of elementary school; the set of rational numbers is presented as an expansion of the set of natural numbers; the set of real numbers is similarly introduced as an expansion of the set of rational numbers. It is important to note that the concepts that are considered to be ‘simpler’ are usually the ones closer to children’s intuitive theories. Thus, children’s initial theories are confirmed and strengthened through instruction, resulting in cognitive inflexibility that hinders further understanding. Furthermore, introducing new concepts as expansions of prior ones is ineffective when what is needed is the restructuring of prior knowledge. There are two suggestions that should be taken into consideration: First, we should consider whether curricula should support the introduction of certain concepts at an earlier stage in mathematics education. For example, there is evidence to support that elaborating notions relative to fractions at an earlier stage in instruction may weaken the effect of early understandings about natural numbers (Yujing & Yong-Di, 2005). There is also an attempt to introduce algebraic thinking in elementary school (Carraher, Schliemann, & Brizuela, 2001). Of course, detailed empirical research is needed before we can introduce such innovations in schools. Second, we should take into consideration that an expansion of a concept from a mathematical point of view may not correspond to an enrichment of prior conceptual structures. To use an example from our study about the set of rational numbers, students cannot develop their understanding of the set of rational numbers if they do not abandon the presupposition of discreteness, if they do not realize that different symbolic representations may refer to the same mathematical object, and if they do not realize the relation between the ‘set’ of fractions and the ‘set’ of decimals. We suggest that the design of curricula needs to be based on the results of detailed empirical investigations that provide information about the way students develop understanding in a given domain and the order of acquisition of the concepts involved. The conceptual change theoretical framework can be used as a guide for researchers to identify mathematical concepts that are going to cause students difficulty. Addressing Students’ Initial Theories and Their Entrenched Presuppositions Special attention must be paid so that the information included in the curricula, books, and that communicated by the teachers does not foster students’ misconceptions and that it

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addresses students’ entrenched presuppositions on the basis of their initial number theory. To state an example from the current Greek 7th grade mathematics book, the rational numbers set is introduced in the following way: ‘All the numbers that we know, namely the natural numbers, decimals and fractions, together with the respective negative numbers, constitute the set of rational numbers’. This ‘definition’ certainly builds on students’ prior knowledge about numbers, but at the same time, enhances students’ initial tendency to group numbers on the basis of their symbolic representations. In order to avoid the creation of misconceptions, it is essential that designers of curricula and teachers be informed about the issue of conceptual change, as well as about the learning difficulties that this theoretical framework predicts. Towards this direction, a detailed description of the development of certain key concepts should be provided by researchers. Increasing Students’ Metaconceptual Awareness: Opportunities to Express and Elaborate Opinions Students are usually not aware of their explanatory frameworks and of the presuppositions that constrain them. This lack of metaconceptual awareness prevents students from questioning their prior knowledge and allows for the assimilation of new information into existing conceptual structures. This kind of learning by assimilation seems to form the basis for the creation of misconceptions and lies at the root of the inconsistency so commonly observed in students’ reasoning. A powerful learning environment should aim at increasing students’ metaconceptual awareness by providing the opportunity for them to externalize their beliefs and make them subject to evaluation by themselves, their fellow students, and their teachers. This can be done in environments that facilitate group discussion and the verbal expression and elaboration of ideas. Use of External Representations and Cultural Artefacts The use of manipulatives, models, and cultural artefacts is considered a significant component of powerful learning environments. However, it should be taken into consideration that the mere presence of such tools is not enough to mediate effective learning. Research in mathematics education suggests that the meaning of a mathematical idea is not necessarily carried by a more concrete representation (Clements & McMillen, 1996). It has also been observed that certain components of a manipulative aid or a representation may constrain children’s thinking about the concepts involved (see, e.g. Behr & Post, 1981). Moreover, findings from the conceptual change research suggest that an external representation is itself interpreted on the basis of students’ prior knowledge (Vosniadou et al., 2005). Our finding that the number line has limited effect on students’ performance in questions regarding density can be explained by the suggestion that the metaphor ‘numbers are points on a line’ is not necessarily easy to comprehend (Lakoff & Nunez, 2000; Nunez & Lakoff, 1998). It may also be the case that students’ responses in the questions with the number line reflect their ‘theories’ about numbers. But it is also possible that the number line, as a representational tool, may pose its own constraints to students’ understanding about numbers and, more specifically, about density. For instance, it is possible that some students consider the number line to be subject to constraints pertaining to a

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real-world object. Or, that the number line itself is interpreted on the basis of the fundamental presupposition of discreteness, as consisting of discrete points. So, barriers in the effectiveness of the number line could arise from students’ ‘theories’ about numbers and/or their initial ideas about the number line itself. Whatever the case, it should be taken into consideration that the use of external representations and artefacts should be supported by explicit teaching and explanations. Teachers should also be aware of the advantages and limitations of the tools they chose to use. To summarize, the conceptual change theoretical framework may be used as a guide to identify concepts in mathematics that are going to cause students great difficulty, to predict and explain students’ systematic errors and misconceptions, to provide student-centred explanations of counter-intuitive math concepts, to alert students against the use of additive mechanisms in these cases, to find the appropriate bridging analogies, etc. In a more general fashion, it highlights the importance of developing students who are intentional learners and have developed the metacognitive skills required to overcome the barriers imposed by their prior knowledge (Schoenfeld, 1987; Vosniadou, 2003).

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Chapter 5

Reasoning with Mental Tools and Physical Artefacts in Everyday Problem-Solving1 Roger Säljö, Ann-Charlotte Eklund, and Åsa Mäkitalo

Introduction Reasoning and problem-solving in the context of mathematics learning has been one of the research areas to which Erik De Corte and his colleagues (De Corte, Greer, & Verschaffel, 1996) have contributed successfully over the years. One of the topics the members of this team have addressed concerns how children learn to move between expressions formulated in everyday language, on the one hand, and in the symbolic resources of mathematics, on the other (for early work, see De Corte & Verschaffel, 1985, 1987). Put differently, this is an issue of how we learn to mathematize. Mathematizing implies being able to use the resources of mathematical notation and operations to model the world and to reach some kind of situationally relevant understanding and solution of a problem. An increasing ability to use mathematical tools for understanding and manipulating the world is a central sociocultural developmental process. Such skills cannot be reduced to an issue of doing mathematics in a narrow sense. When failing to mathematize in a productive manner, people are not just experiencing difficulties in academic exercises of mathematics. Rather, in the modern world insights into how numeric and non-numeric information is communicated and manipulated via symbolic notation and representational tools, such as diagrams, tables, and formulae, are essential for participating in many social practices. The problems explored in the work by De Corte and his colleagues concern to what extent teaching and learning of arithmetic is conducive to the development of such skills.

1

The research reported here has been funded by the Swedish Research Council.

Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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Sense-Making and Practices of Learning: Contextualizing Human Reasoning Solving so-called word problems is one setting in which children learn to mathematize and to go between the mediating resources of written language and mathematics, to use Vygotskian language. It is thus a matter of what O’Halloran (2004) refers to as inter-semiotic work. Word problems are a well-known component of elementary mathematics learning in which students encounter problems formulated in written language that they have to ‘translate’ into mathematical notation and operations. Quite often these problems are mininarratives of hypothetical situations in which, for instance, some economic transaction is described, or where a problem of dividing money, sweets, or something else in a specific manner is presented (cf. Verschaffel, Greer, & De Corte, 2000, p. ix). Inspired by the intriguing, to some extent even rather shocking, observations reported by scholars such as Baruk (1985) and Radatz (1983) on the apparent willingness of children to engage in rather absurd forms of reasoning in the context of doing word problems, De Corte, Verschaffel, and their team have explored fundamental features of human sense-making. The implications of these observations extend well beyond the mathematics classroom. In our opinion, the results of this research tell us something profound about the rationalities of human reasoning and its situatedness in institutional traditions of communication. One way to tell the story of the beginning of this work on sense-making in the context of word problems is to begin with the famous problem of the age of the captain explored by French scholars about 25 years ago (Baruk, 1985; cf. Verschaffel et al., 2000, p. 3). In one version, this problem has been formulated as: ‘There are 26 sheep and 10 goats on a ship. How old is the captain?’ When confronted with this problem, large groups of children — acting in the context of the mathematics classroom — were willing to engage in some kinds of calculations to arrive at an answer. In fact, a considerable proportion did not find anything extraordinary about this problem; it seemed to many pupils to conform to the expectations about what a word problem should look like. This general issue of sense-making in the context of word problems rose to more general public recognition through the study reported by Carpenter, Lindquist, Matthews, and Silver (1983) on the results of the Third National Assessment of Educational Progress in the United States. The problem that sparked the interest in this case was an equally famous one that involves division with remainders: ‘An army bus holds 36 soldiers. If 1128 soldiers are being bussed to their training site, how many buses are needed?’Although a majority (70%) carried out the expected division (arriving at the result of a quotient of 31 and a remainder of 12), only 23% in this original study concluded that one would need 32 buses. Almost the same proportion of students claimed that one would need 31 buses, and close to a third of the students did not connect their answer to the question asked but were content with ‘31 remainder 12’ (cf. Silver, Shapiro, & Deutsch, 1993), which cannot be seen as an answer to the question about how many buses would be needed. Since these early studies, these general problems of how children make sense of word problems have been explored in many studies (for a review, see Verschaffel et al., 2000). Various factors, such as the exact formulations of the problems, the details of the contexts in which students act, and many other features have been varied (cf. Reusser & Stebler, 1997; Säljö & Wyndhamn, 1988, 1993).

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What seems to be a core difficulty for the students with this kind of problem is to realize how the meaning expressed in the word problems is to be coordinated with the mathematical operations. From a cognitive point of view this concerns the issue of modelling, i.e. how one moves from one mediating tool (written language) to another one (mathematical notations and operations). The knowledge and skills students acquire, judging from the results of this work, are to a considerable extent dependent on whether this relationship is of a standard nature or not. Thus, the problem ‘A cow produces 18 litres of milk per 24 hours. How much milk does the cow produce during one week?’ is simple for fifth graders in the Swedish school, while the problem ‘Kalle goes to school and on average he has 7 lessons a day. How many lessons does he have per week?’ is considerably more difficult (Säljö & Wyndhamn, 1988). In the latter case, a considerable proportion of the students multiply 7 (number of lessons) by 7 (number of days). There are two observations that are interesting. The first one is that the students’ failure to solve the problem cannot be ascribed to ignorance in a general sense. They all know, when asked, that they go to school 5 days a week. The problem is one of realizing this when doing word problems, i.e. when acting in a textual reality. The second observation that is interesting is that mathematics teachers in many cases react negatively to problems of this kind. They often see this as a way of deceiving the children and making the task unnecessarily difficult. This is interesting, since it implies that learning how to model is not necessarily seen as an important element of learning mathematics at this stage. This also underscores the crucial remark made by Lave (1992) that the manners in which word problems are formulated can be seen as a reflection of a ‘microcosm’ of the theories of learning on which mathematics teaching rest. When the problems require that one has to pay extra attention to the issue of modelling, teachers consider them unnecessarily difficult, and the difficulties are often described as having to do with ‘language’ or ‘reading’ rather than with ‘mathematics’. De Corte, Verschaffel, Greer, and their colleagues systematized this research into modelling in the context of word problems by formulating problems that were identical from the mathematical point of view, but where the modelling was more or less conventional. In a series of studies they compared the performance on problems formulated as S(tandard)items and P(roblematic)-items, respectively (cf. Verschaffel et al., 2000, for an in-depth presentation). An S-item (‘A boat sails at a speed of 45 kilometres per hour. How long does it take this boat to sail 180 kilometres?’) is formulated according to the standard expectations and involves little or no problem for most children when it comes to modelling. A P-item (‘John’s best time to run 100 metres is 17 seconds. How long will it take him to run 1 kilometre?’), on the other hand, requires consideration of how it should be modelled, and if the information provided allows for a meaningful representation of the problem in mathematical form. The clear differences in performance on S- and P-items, and the clear indications that students very often do not attend to the problems of modelling, testify to something that is significant: the cognitive socialization that students are exposed to in schooling is quite specific. Their performance, and their difficulties, to a large extent seem to represent an adaptation to how schools ‘do business’, to put it in economic terms. What we see are adaptations to institutional modes of communicating and meaning-making. In this context it is also interesting to see that intercultural comparisons have been made with some very revealing results (Verschaffel, De Corte, & Lasure, 1994). The P-item above with John’s running, for instance, has been used in a number of countries in different parts of the

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world, and the results are thought-provoking: ‘the percentages of students in the various countries who gave the unqualified answer “170 seconds” ranged from 93% to 100%’ (Verschaffel et al., 2000, p. 44). Considering the cultural differences, and the differences in mathematics achievement on international comparisons between these countries, the results indicate that the institution of schooling socializes children to reason in particular manners. What elevates these findings to theoretical significance is that they in a rather dramatic manner illustrate the situatedness of human reasoning. And this is another, and complementary, perspective from which the story about sense-making in the context of doing calculations and mathematics can be told. In contrast to the difficulties children — acting as students in classroom contexts — have with word problems, studies performed by scholars such as Carraher, Carraher, and Schliemann (1985), Lave (1988), Saxe (1988), and others, have documented the apparent skill with which children (and adults) use mathematical operations in contexts of familiar everyday settings such as buying and selling. In comparative analyses, the performance differences between the context of paperand-pencil tasks in school settings and that of everyday transactions were substantial. When the reasoning involved transactions where money and familiar merchandise were involved, and when the arena for social action was buying and selling for the sake of making a living, the difficulties that were apparent in the formal learning context seemed to more or less disappear.

Artefacts and Reasoning In the present study, we want to continue exploring the situatedness of human reasoning, and its dependence on contextual and institutional resources for sense-making. This time we will not focus on the issue of the framing (Goffman, 1986) of a task, i.e. whether it appears in a school setting or in some other context, but rather explore the additional question of how material tools intervene into, transform, and support reasoning. One basic conclusion of the research summarized above is that the presence of material artefacts, such as money and goods to be sold or bought, facilitates the arithmetic operations. There are, of course, various reasons for this. Money, for instance, contributes to a certain kind of realism in the calculations, since making a mistake will be consequential in a very immediate sense. Also, counting and money go together in ontogenetic development in many societies. Children make experiences of counting and calculating in the context of using money, and the presence of money has been shown to make it easier to perform calculations (Lampert, 1986). At a more principled level, our mastery of intellectual tools, of which mathematical notations/operations and everyday language would be two very important types (Vygotsky, 1986), is intimately related to the development of material artefacts (Säljö, 1996). The conversion of intellectual insights and distinctions into material tools is one of the most important mechanisms through which cultures develop, and through which such development becomes cumulative. New tools emerge on the basis of collective experiences with old ones. In addition, the link between intellectual and physical tools is generally so intimate that it is more fruitful to think of objects such as compasses, computers, rulers, and so on, as simultaneously material and intellectual (or ideational), as Cole (1996) points out.

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In a sociocultural perspective, artefacts are not just dead objects. They are the products of meaning-making practices within a culture, and as cultural tools they invite and sustain specific kinds of practices and uses of symbol systems. In Donald’s (1991) terminology, they may be seen as externalizations of human cognitive and communicative practices. Learning to a large extent implies accommodating to such artefacts and tools. Since counting and doing arithmetic operations are parts of prominent cultural practices, this process of creating artefacts is visible in the development of tools that support, and transform, such actions (Säljö, 2005). Thus, in addition to doing mental arithmetic, counting can, and has, been done by means of paper and pencil (and material objects with similar functions such as clay tablets and wedges), abacus, addition machines, counting rods, slide rules, calculating machines, mini-calculators, and computer software. In passing, it could be mentioned that the human body sometimes is used as a mediating tool when counting and doing arithmetic. We use our fingers as external resources — or sign vehicles — when calculating, and body parts, thus, can be temporarily converted into semiotic tools. That these material artefacts will have profound implications for how we count and solve arithmetic tasks is evident. Dividing 44.87 ⫻ 16.33 takes considerable time to do as mental arithmetic, while it would be fairly easy for most of us to handle with a mini-calculator. The cultural, historical, and institutional situatedness of such tools is also obvious. Most people in the western world would not be helped if they were given an abacus to do a complex division of this kind, while many people in China, Japan, and other parts of Asia would be able to use such a tool productively. Some decades ago, skills in using slide rules were relatively widely spread in the population in many countries. Today, very few people learn to use this instrument. Each of these tools mediates mathematical operations in different manners. For instance, the slide rule has logarithmic scales as mediating inscriptions. The frequent user will get accustomed to thinking in terms of logarithms, and multiplications and divisions will be solved as additions and subtractions of logarithmic values. When using paper and pencil when multiplying, the calculations will be mediated by the fact that it is possible to ‘off-load’ the burden on the attention span by working systematically in a stepwise fashion, going back and forth between mental operations and inscriptions. Some very interesting studies of how abacus users accommodate to this particular technology have been carried out by Hatano and Stigler and their colleagues (Hatano, Miyake, & Binks, 1977; Miller & Stigler, 1991; Stigler, 1984). These empirical studies clearly illustrate several interesting features of the coordination between humans and artefacts, and how highly skilled reasoning is grounded in the uses of material artefacts. For instance, it is shown how experienced abacus users ‘internalize’, in the Vygotskian sense, a model of the abacus, and they report how they mentally ‘move’ the beads as they calculate. In sociocultural terminology this indicates how the ‘actions’ of moving the beads physically have been transformed into ‘operations’ that are performed automatically. Hatano et al. (1977) showed that, as this kind of ‘interiorization’ (p. 52) increased, the ‘mental operation came to involve only visual representation without relying on motor elements’ (p. 53) such as imitative finger movements. From a sociocultural perspective, this is a very important observation, since it supports the basic assumption that ‘intra-mental’ activity originates in cultural practices and in the coordination with cultural tools.

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In a similar vein, this research also illustrates how the mistakes made are contingent on the particular manner in which the abacus is organized and mediates calculations. Stigler (1984, p. 170) showed how certain errors are more frequent in relative terms among Chinese abacus users than they are among American students with no experience of the abacus. For instance, when doing mental calculations, students who were experienced abacus users more often made certain kinds of ‘carry-over mistakes’ that have to do with design of the abacus where you have to carry over at the number 5 (rather than 10). In the empirical study to be reported below we want to continue this line of research by studying how problem-solving and calculations in the context of a well-known type of everyday problem are mediated by intellectual tools and artefacts. Our point is one of illustrating how intimately tied to artefacts our cognitive skills are, or, to use Donald Norman’s (1993) words from the title of his famous book, to illustrate that it is to a considerable extent ‘things that make us smart’.

The Study In the empirical study, 60 participants (between 17 and 61 years of age) were asked to solve the following problem: How much is 1243,73 English Pounds in Swedish Kronor if one Pound is worth 13,88 Kronor? This is a word problem of a well-known kind. Most people in this age range have experiences of conversions between currencies. Even though they may not themselves be engaged in this kind of activity very often, most people are likely to have a fair understanding of what such a cognitive task of going from one currency to another implies.

Method and Participants The 60 participants, all adults, were randomly assigned to one of three groups with 20 persons in each. In the first group, the participants were asked to solve the problem through mental arithmetic (MA). If they asked during the session, they were told that they could not use paper and pencil. In the second group, the participants were given paper and pencil (P&P) to solve the problem. In the third group, finally, the participants were given a standard mini-calculator (CAL) to use when solving the problem. The data collection procedures were adapted to the respective conditions. In the MA condition, data were collected through audio recordings of the activities of the participants. For the two other groups, field notes were made, and the papers on which the participants in P&P group made their calculations were collected. The participants were given a written version of the problem to look at. The average age and some other information about the groups are given in Table 1. As can be seen, there is a certain difference in average age between the groups in spite of randomization. The group that did mental arithmetic is 3½ years younger than the group

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Table 1: Age characteristics of participants. Group

Mean age Variation Standard deviation

Mental arithmetic

Pencil & paper

Minicalculator

Total

32.7 17–61 11.0

36.2 21–57 9.9

35.7 22–56 10.36

34.8 17–61 10.4

in the paper and pencil condition, but the differences between the groups are not statistically significant (F ⫽ 0.660, df ⫽2, p ⬎ 0.05). Before continuing the presentation, it should be pointed out that the arithmetically correct answer when using four decimals is 17,262.9724 Swedish Kronor (SEK).

Results From an analytical point of view, solving a problem of this kind has two distinctive steps. The first implies mathematizing or modelling, i.e. transforming a sentence formulated in everyday language — a word problem — into relevant mathematical operations. If we look at the performance of the groups with respect to their ability to translate this statement into the expected multiplication 1243.73 ⫻ 13.88, we find that the three groups were quite similar. In all, 51 participants (85%) used multiplication in the expected manner as can be seen from Table 2. Some did this after some consideration, maybe even attempting other ways to solve it, but they ended up using multiplications. Nine participants used division or did not arrive at a clear conclusion about how to solve the problem. The proportions in the P&P and CAL groups that decided to multiply are identical, while in the MA group there is only one person who did not use multiplication. However, these differences between the groups must be seen as random variations. Thus, it can be concluded that the mathematizing aspect was not influenced by the presence or absence of artefacts. The interesting point, then, is how the second step — the performance of the multiplication — is managed by the members of the three groups. As expected, the differences here are quite dramatic. One problem in this context, of course, is what is to be considered a correct answer. Finding the exact arithmetic answer with four decimals is a very strict criterion. In Table 3, the answers have been ranked from those that were arithmetically exact (row 1) to those that approximated the correct answer more or less closely (rows 2 to 4). In the fifth row the rest of the answers are reported. As can be seen, none of the participants who used mental arithmetic arrived at the numerically exact answer, nor did they end up in the second category. Three participants came within ⫾100 SEK of the expected answer, and another three within the intervals between 100 and 500 SEK above or below the correct value. Fourteen were classified in category 5. In the group using paper and pencil, three participants produced an arithmetically

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Table 2: Proportion of participants who used multiplication or other procedures. Procedure chosen

Multiplication Division/other Total

Group Mental arithmetic

Pencil & paper

Minicalculator

Total

19 1 20

16 4 20

16 4 20

51 9 60

Table 3: Answers arrived at by participants. Answer

1. 2. 3. 4.

5.

Arithmetically exact answer Correct answer, rounding off to 17,262 or 17,263 Answer within ⫾100 SEK Answer, intervals between –100 & –500, and ⫹100 & ⫹500 SEK Other/no answer

Group Mental arithmetic

Pencil & paper

Minicalculator

Total

0

3

15

18

0

1

0

1

3

4

0

7

3 14

2 10

0 5

5 29

exact answer, and 10 ended up in category 5. In the group using a mini-calculator, 15 produced an arithmetically exact answer, and five were classified in category 5. An interesting initial observation is that the distribution in the CAL group is discrete; either the answer is exactly correct, or it falls completely outside the approximations that are indicated in rows 2 to 4. In statistical terms, and if one combines rows 1 and 2 to indicate a correct answer, rows 3 and 4 to indicate successful approximations, and row 5 to indicate failure to solve the problem, these observed differences in performance between groups are significant (
2 ⫽ 34.32, df ⫽ 4, p ⬍ 0.001). A clear outcome of this analysis is thus that if one is successful in the mathematizing, the use of a mini-calculator leads to correct answer with four decimals for 94% (15 of the 16) of the participants. With paper and pencil, the corresponding percentage is 19, and in the case of mental arithmetic no participant managed to arrive at an exact answer even though 19 of the 20 participants in this group modelled it correctly. What happened to the 16th person in the CAL group who identified the appropriate

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Table 4: Time used to solve the problem. Procedure chosen

Median time (in min) Mean time (in min) Variation width a

Group Mental arithmetic

Pencil & paper

Minicalculator

3.1 4.1 1.75–9

6.50 6.53 1.50–12

0.48 0.89 0.13–4

The time was measured until the person gave an answer or did not want to continue.

operation, but who did not arrive at the correct answer? In this case, the person made an error when entering one of the digits and did not repeat the multiplication to discover the mistake. This particular low-level mistake of pressing the wrong key in one sense is specific to this type of tool, but it seems to be infrequent judging from our data. The problem with this mistake is that the result produced may still appear approximately correct, which thus means that it may go unnoticed even if the person looks to see if the sum arrived at is reasonable. A similar mistake made when entering another digit might have resulted in a sum that would immediately be perceived as unrealistic. It should be pointed out that analogous mistakes involving low-level errors of misplacing numbers or the comma or writing the wrong numbers occurred in the other groups, too. In fact, they are more common in the latter groups. However, from a sociocultural perspective the differences in the processes of solving the problem are more interesting than the differences in outcomes. The Problem-Solving Process The differences in outcomes are symptomatic of variations in modes of reasoning. Let us illustrate this through some observations from the data in the groups. In Table 4, the time used in the various groups is presented. As can be seen, the mean time in the mental arithmetic group was slightly more than 4 min, in the paper and pencil group it was 6½ min, and in the group with the minicalculator it was 0.89 min (53 s, and the median less than half-a-minute). In the CAL group, some participants even managed to check their calculations within this short time-span. These are clear differences (in statistical terms, the F-value for the mean differences ⫽ 27.513, p ⬍ 0.001, and the
2 ⫽ 20.80, df ⫽ 2, p ⬍ 0.001, for a test of differences between medians). Let us illustrate these differences and comment on some of the implications. Reasoning while doing mental arithmetic As we have shown, 19 of the 20 participants in this group realized that they should solve the task by multiplying. Several of them struggled with the task for many minutes, but no one managed to arrive at the exact answer. The most common strategy was to use approximations at some stage.

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Roger Säljö et al. Excerpt 1, Participant MA6 (9 minutes)2 1.

Interviewer

2.

Participant

3. 4.

Interviewer Participant

5. 6. 7. 8. 9. 10. 11.

Interviewer Participant Interviewer Participant Interviewer Participant Interviewer

12. 13. 14. 15. 16.

Participant Interviewer Participant Interviewer Participant

… and then I’d like you to (.) do some calculations here on this problem how much is twelve hundred forty three point seventy three in English pounds ((inaudible)) one pound (.) is worth thirteen point eighty eight (5 secs) oh:: yes ((giggles)) well fourteen times twelve is my first thought then mm yep: about (.) which is hundred:: (.) sixty::six (.) that is sixteen thousand six hundred, sort of mm and then there’s a little more ((laughs)) mm so sixteen, and almost seventeen thousand kronor mm it should be mm (.) if I (.) should ask you to do more exact calculations well m: ((laughs)) no:: How would you do it then? If you could start and … oh; using my head, you mean? Oh mm (7 secs) Well, I would do it on paper then ((laughs)) (goes on to multiply for eight minutes)

Most participants directly or indirectly reacted to doing mental arithmetic on this kind of problem. There are frequent comments about the difficulties of solving such a problem and requests for paper and pencil. Excerpt 2, Participant MA1 (8½ minutes)

2

1.

Participant

2. 3. 4. 5.

Interviewer Participant Interviewer Participant

Can’t do that (16 secs) how much is English pounds in Swedish kronor if one pound is worth thirteen and eighty eight (.) and I sort of have to take (.) those pounds (points) mm times those Swedish kronor a can I write by hand?

Transcription conventions: (.) indicates short pause, (5 secs) indicates length of pause, No:, no:: indicates prolongation of sound, underlining indicates emphasis/stress, ‘-’ indicates cut-off.

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Interviewer Participant Interviewer Participant

83

no:: I’m not allowed to? I’d rather you … oh lord, my god (continues to calculate for eight minutes)

The transcripts contain many spontaneous comments signalling that the task was rather absurd, and some were even a bit annoyed. Seven of the participants worked on the multiplication for more than 5 min. These are interesting mental exercises where the participants attempt to move ahead, while at the same time repeating what they had done, until they eventually lose track of the numbers. Thus, there were many low-level mistakes having to do with the mechanics of the calculations. The participant who came closest to the expected value (17,288 SEK), took the problem as a real challenge, and he worked intensively at it for over 8 min with very little intervention by the interviewer. The complexity of attempting to do mental arithmetic on such a task is interesting to follow. Excerpt 3, Participant MA20 (8 minutes 10 seconds) 2.

Participant

3. 4.

Interviewer Participant

ok, ((clears throat)) (6 secs) m:: ((clears throat)), and then one can sort of think about what would be the easiest way to calculate this and that probably: is (.) one should perhaps do a little approximation (.) ah: ((clears throat)) then I:: will (4 secs) sort of oh:: sort of try to do (.) fifteen first and then take and (.) take: then I might take thirteen point nine instead and:: (.) so I’ll take times 15 first and then I’ll take minus one point one, which should be reasonably simple to calculate m ((clears throat)) then I’ll take that times ten then we’ll have ((inaudible)) six thousand two hundred: eh: six thousand two hundred: (2 secs) well what will that be (.) six thousand two hundred(.)nineteen let’s say ((clears throat)) (2 secs) six thousand two hundred:: (7 secs) six thousand two hundred (.) fifteen times (.) thirty seven can (inaudible) seventeen say eigh::teen we can say ((clears throat)) sixteen thousand two hundred eighteen uh ((clears throat)) sort of what do I get then, I get yes (5 secs) sixteen thousand two hundred eighteen I get (.) eigh- sixteen thousand two hundred eighteen about eighteen thousand (2 secs) six hundred fifty five (.) sixteen ((inaudible)) eighteen eighteen thousand six hundred: (4 secs) forty fiftyfive ha (.) ok so sixteen thousand (.) no eighteen thousand six hundred fifty five (2 secs) ((clears throat)) hm: and then I will take minus (2 secs) zero point one times that and

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5. 6.

Interviewer Participant

that should be about then sort of: (2 secs) one thousand two hundred: forty:: four times (.) pl- ((inaudible)) times ((inaudible)) plus one hundred twenty: (2 secs) five about ((clears throat)) (3 secs) one thousand two hundred forty three minus two hundred twenty four that’ll be sort of one thousand one hund:: (.) one hundred twenty four will be (4 secs) no plus that’s what we should have eh: then it’ll be one thousand (.) threehun:: (3 secs) sixty:: (.) four (.) thousand, did I think correctly now (5 secs) should be one thousand three hundred sixty: (.) seven one thousand three hundred sixty seven about (.) one thousand three hundred sixty seven one thousand three hundred sixty seven (5 secs) ok (.) and what am I supposed to deduct from that well from (5 secs) ((clears throat)) we should deduct we said (4 secs) from (.) eighteen thousand (2 secs) eh:: (7 secs) eighteen thousand:: (.) twelve that is six thousand (.) six thousand two hundred:: eighteen thousand six hundred fifty five I think sort of (2 secs) eighteen thousand six hundred fifty five eighteen thousand six hundred: (.) fifty five minus thirteen sixty seven (4 secs) six hundred fifty five ((clears throat)) minus then we’ll take away one, then we’ll have seventeen thousand six hundred fifty five (2 secs) hm:: six hundred fifty five minus three hundred that’ll be seventeen thousand (4 secs) seventeen thousand:: three hundred fifty five eh:: what did I have left fifty five:: seventeen thousand three hundred fifty five minus (2 secs) what did we say then (7 secs) eh: minus sixty seven that’ll be eighty eight then (.) mm (3 secs) seventeen thousand three hundred fifty five minus se::venteen thousand (.) eh: two hundred eighty eight(.) eight (9 secs) seventeen thousand two hundred eighty eight maybe should (.) be reasonable (5 secs) two hundred eighty eight ((clears throat)) I suppose I don’t have to check the calculations or may one do that if one wants to or? you can if you want to two hundred and eighty eight, I’ll surely forget it (.) seventeen thousand two hundred eighty eight (23 secs) ((clears throat)) eighteen (2 secs) ah it’ll be seventeen thousand two hundred eighty eight

This is, by any standard, a very impressive cognitive performance, which is not easy to follow in all its detail for an outsider. As the participant moves ahead, he dialogues with himself, constantly repeating the interim results so as not to forget them and simultaneously

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observing and correcting his own calculations. In Vygotskian parlance, his mode of talking/thinking can be understood as a mix of ‘inner speech’ (i.e. thinking) with abbreviations and idiosyncratic elements, and ‘outer speech’, i.e. he communicates with the interviewer. He does not attempt to multiply the numbers given as they are, but rather works in an iterative manner using the approximations 15 and 13.9 as a starting point. Then he multiplies and successively tries to adjust the multiplications by moving closer to the exact value. The duration of this concentrated cognitive (intra-mental) and communicative (inter-mental) work is 8 min. It should also be pointed out that none of the six participants who reached an approximately correct answer in this group (rows 3 and 4 in Table 3), tried to do a direct multiplication. Rather, they all worked with approximations which they tried to adjust in successive steps. Reasoning with paper and pencil The participants in this group used more time than did those in the previous group. This reflects that there were fewer people who gave up. The situation appeared more reasonable and realistic when there were external tools available for the operations. Still there are some who had various kinds of problems with the multiplication and with placing the comma in the right position. Thus, also in this case there were many low-level mistakes that concern the mechanics of calculating. There are only four participants who ended up in the two top rows in Table 3, and another six came within ⫾500 of the exact answer. In this condition, the strain on short term memory is of course considerably reduced. Also, here it is possible to check the calculations and to use double strategies as did P&P9, who made a multiplication with the approximate values of 1200 and 14, and then attempted to make the exact calculation (where he however misplaces the comma and ends up with a very large number. He reflects on this, but does not suggest any change but claims the number ‘looks very big’). Excerpt 4, participant P&P9

Figure 1: Calculation by P&P9 starting with an approximation (right hand calculation) and continuing with the exact multiplication.

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But, in general, with this technology there are many places where the calculations can go wrong. This implies that even if one is capable of handling the conceptual problem of deciding what kind of operation that is productive, there are many steps where there will be mistakes in the algorithmic part of the reasoning process. Reasoning with a mini-calculator For some of the participants in this group the problem obviously appears trivial. They immediately conclude that one ‘only’ has to multiply the numbers given, as participant CAL4 puts it. Excerpt 5, participant CAL4 (11 seconds) Participant

It is only to multiply. That’s one pound, that’s how many you should have (points)

However, even though 15 of the 20 participants in this group end up with the correct answer in a short time, their reasoning is not always as direct as this. In many cases there is some kind of hesitation or reflection on how to proceed. Three participants, among those fifteen who eventually ended up with the correct answer, began by dividing, and they carried out the division. When they saw the result of the division, they realized that it was not realistic given the relationship between the two currencies. They then reread the problem and thought it through. They thus actively used the external device in a reflective process in which they considered if the result was realistic or not. In fact, this kind of consideration of how reasonable the answer appeared was quite common in this group. One participant even explicitly made an approximation before using the calculator so as to be sure what to expect, and he manages to do this within 17 s. Excerpt 6, participant CAL8 (17 seconds) Participant

If you have 1200 pounds then you multiply that by 10 and then there’s a little bit more (goes on to make the correct calculation)

In all cases except one in this group, those who do not manage to arrive at the exact answer use division instead of multiplication. The only low-level mistake is by the person who accidentally pressed a wrong key. This implies that the problem for the four members who do not find the correct answer is with the mathematizing or modelling part of the problem.

Discussion: The Tool-Using Intellect and the Externalization of Cognitive Processes In a sociocultural perspective, human reasoning is dependent on the use of cultural tools. Such tools are viewed as externalizations of human insights and cultural practices. Even linguistic tools must be viewed in this perspective. When engaging in mental arithmetic in this study, participants are relying on cultural tools that are codified in a particular kind of language with

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certain distinctions and algorithmic procedures. However, humans have the added possibility of converting intellectual tools into artefacts that can be used as prosthetic devices that support reasoning and problem-solving. Luria (1981) expresses this peculiar position that humans have by pointing out that people live in a double reality, as it were; a reality that is simultaneously physical and linguistic/communicative (cf. Cole, 1996, for a further discussion). In this sense, artefacts are not dead or neutral objects, rather they embody distinctions and procedures that have emerged in cultural practices and that have been externalized into artefacts. This implies that when reasoning we have a particular kind of division of labour, where cognitive operations of the individual interact with artefacts that codify collective cultural experiences. The outcome thus follows from a joint effort between a cognising individual and a cultural tool in mediated action (Wertsch, 1991). The results clearly illustrate how the cognitive activities differ in the various conditions. When doing mental arithmetic, success in the mathematizing part of the problem will not lead to a correct result. Instead, the individual has to engage in laborious, and mostly unsuccessful, multiplications and attempt to memorize as the calculations progress. This turns out to be quite a challenge with space for lots of low-level errors. With the technology of paper and pencil, the success rate is much higher, since the strain on our limited attention span is considerably reduced. The technology of paper and pencil enters as a prosthetic device that contributes to the reasoning by supporting some of the remembering that has to be done. But still there is plenty of room for mistakes. Numbers and commas will be misplaced, additions will go wrong, and so on. This is shown by the fact that only about half of the members of this group eventually end up close to the expected answer. In both these conditions, the person, after finishing the mathematizing part of the problem-solving, has to use the algorithm to arrive at a correct answer. That is, the individual has to remember what the algorithm looks like, and (s)he has to organize the problem accordingly. Every step must be carried out, and the correct answer is supposed to follow. Empirically, though, this was far from always the case in this study. This is perhaps the biggest difference when using the mini-calculator. In the latter case, the concrete calculations go under ground, as it were. The various steps of the algorithm for doing a multiplication are no longer necessary to follow or, perhaps, even to know. The users enter numbers and press the keys for the functions that are required. This implies that the exact manner in which the calculations are made is no longer visible to the person engaging in the task. There is a new division of labour when reasoning between what we do in our head and what the physical artefact does. We put our trust in the machine for the algorithmic part of the work. The distance between understanding the nature of the problem and arriving at an exact answer is thus much smaller when using the calculator, and 94% of those who managed the mathematizing part arrived at the expected answer. Only one person made a mistake when entering the numbers, and he did not check by repeating the calculations; a procedure which was otherwise quite frequent. An interesting aspect of these observations is what happens to our competences in this field of mathematizing and performing calculations when we rely on various technologies. A reasonable guess is that our experiences of, and tolerance for, mental arithmetic in contexts such as this will be reduced. We will look for the calculator whenever we run into situations like this, and the comments and complaints we heard in this study testify to this. In a Platonic perspective this may be seen as

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a loss of some specific skills of calculating. Just as Plato in the dialogue Phaedrus (2002) worried about the text replacing the need for memorizing, a development which would make people dependent on external resources, the calculator may be seen as a threat to certain kinds of algorithmic skills. The alternative metaphor would be that the external tool in situations like this liberates our reasoning and makes it possible to focus on the more conceptual aspects. The impressions from our data are that with the mini-calculator the user has more time to interact with the task in a reflective manner. One can test one mode of doing the calculation, check the results, perhaps try another one, reread the task, and dialogue with the artefact. And all this can be done fairly quickly. However, what is really interesting about knowing and skills of this kind in a sociocultural perspective is the extent to which our intellectual activities become coordinated with cultural tools. Our reasoning takes place in symbiosis with tools, and our thinking has to be attuned to the manners in which such external resources operate. An interesting feature of the recent developments in digital technology, of which the mini-calculator is just one example, is that the externalization processes no longer concern just information, which was the case with texts and other static representations such as graphs, diagrams etc. As Shaffer and Kaput (1999) and Shaffer and Clinton (2005) point out, the externalizations now also extend to cognitive processes. Thus, in the mini-calculator, as in other digital resources, what was previously cognitive processing of individuals is now to a large extent carried out by external tools. What this implies for our knowing and for our skills is one of the most interesting, and challenging, questions for learning theory and for education. The new technologies are not neutral. Rather, they produce new habits and learning styles. People become accustomed to being able to make effortless calculations without going the traditional route via the stepwise procedures that are necessary with paper and pencil. Their problem-solving will rely on a more iterative process of going back and forth between the problem, the modelling, and the algorithmic calculations. It costs very little in terms of time and effort to do repeated calculations and to experiment with various solutions. This is not a small change, and the pedagogical challenges when the calculations go under ground into an artefact of this kind are interesting. Our traditional approaches to skill training that rely on learning to calculate by hand and by using paper and pencil are at stake, and so is the idea of progression that is built into this tradition of going from the simple to the complex. One may also consider in this context the consequences of the fact that doing calculations by means of paper and pencil may not be a common activity for children outside school in the future. And we can be sure about one thing: even when the externalizations of cognitive processes become more advanced, the conceptual interpretation, and the modelling will always depend on human knowing and local sense-making. In this sense, solving word problems — and realizing why John will not run 1 km in 170 s — typifies the difficulties that humans will continue to experience, and that we have to prepare ourselves for during our schooling. Sense-making is always relative to circumstance, and knowing depends on the particular questions we formulate in a complex and multifaceted reality. Thus, the attempts to understand how people learn to move between semiotic systems, such as spoken and written language and mathematical notations and operations, that Erik De Corte, Lieven Verschaffel, and their collaborators have contributed to, have significant implications for theories of learning and for educational practice.

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References Baruk, S. (1985). L’âge du capitaine. De l’erreur en mathématiques [The age of the captain. On error in mathematics]. Paris: Seuil. Carpenter, T. P., Lindquist, M. M., Matthews, W., & Silver, E. A. (1983). Results of the third NAEP mathematics assessment: Secondary school. Mathematics Teacher, 76, 652–659. Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in schools. British Journal of Developmental Psychology, 3, 21–29. Cole, M. (1996). Cultural psychology: A once and future discipline. Cambridge, MA: The Belknap Press. De Corte, E., Greer, B., & Verschaffel, L. (1996). Mathematics teaching and learning. In: D. C. Berliner, & R. C. Calfee (Eds), Handbook of educational psychology (pp. 491–549). New York, NY: Simon & Schuster Macmillan. De Corte, E., & Verschaffel, L. (1985). Beginning first graders’ initial representation of arithmetic word problems. Journal of Mathematical Behavior, 4, 3–21. De Corte, E., & Verschaffel, L. (1987). The effect of semantic structure on first graders’ strategies for solving addition and subtraction word problems. Journal for Research in Mathematics Education, 18, 363–381. Donald, M. (1991). Origins of the modern mind. Three stages in the evolution of culture and cognition. Cambridge, MA: Harvard University Press. Goffman, E. (1986). Frame analysis: An essay on the organization of experience. Boston, MA: Northeastern University Press. Hatano, G., Miyake, Y., & Binks, M. G. (1977). Performance of expert abacus operators. Cognition, 5, 47–55. Lampert, M. (1986). Knowing, doing, and teaching multiplication. Cognition and Instruction, 3, 305–342. Lave, J. (1988). Cognition in practice: Mind, mathematics, and culture in everyday life. Cambridge, MA: Cambridge University Press. Lave, J. (1992). Word problems: A microcosm of theories of learning. In: P. Light, & G. Butterworth (Eds), Context and cognition. Ways of learning and ways of knowing (pp. 74–92). New York, NY: Harvester/Wheatsheaf. Luria, A. (1981). Language and cognition. New York, NY: Wiley. Miller, K. F., & Stigler, J. W. (1991). Meanings of skill: Effects of abacus expertise on number representation. Cognition and Instruction, 8, 29–67. Norman, D. A. (1993). Things that make us smart: Defending human attributes in the age of the machine. Reading, England: Addison-Wesley. O’Halloran, K. L. (2004). Mathematical discourse: Language, symbolism, and visual images. London: Continuum. Plato. (2002). Phaedrus. Oxford, England: Oxford University Press. Radatz, H. (1983). Untersuchungen zum Lösen eingekleideter Aufgaben [Studies of problemsolving in the context of verbal (literally: dressed up) problems]. Zeitschrift für MathematikDidaktik, 4, 205–217. Reusser, K., & Stebler, R. (1997). Every problem has a solution: The suspension of reality and sense making in the culture of school mathematics. Learning and Instruction, 7, 309–328. Saxe, G. B. (1988). Candy selling and math learning. Educational Researcher, 17(6), 14–21. Shaffer, D. W., & Clinton, K. A. (2005). Why all CSCL is CL: Distributed mind and the future of computer supported collaborative learning. Retrieved February 10, 2005, from http://140.115.126.10/cms/uploads/CSCL05-FP-0206.doc Shaffer, D. W., & Kaput, J. J. (1999). Mathematics and virtual culture: An evolutionary perspective on technology and mathematics education. Educational Studies in Mathematics, 37, 97–119.

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Silver, E. A., Shapiro, L. J., & Deutsch, A. (1993). Sense making and the solution of division problems involving remainders: An examination of middle school students’ solution processes and their interpretations of solutions. Journal for Research in Mathematics Education, 24, 117–135. Stigler, J. W. (1984). “Mental abacus”: The effect of abacus training on Chinese children’s mental calculation. Cognitive Psychology, 16, 145–176. Säljö, R. (1996). Mental and physical artifacts in cognitive practices. In: P. Reimann, & H. Spada (Eds), Learning in humans and machines: Towards an interdisciplinary learning science (1st ed., pp. 83–96). Oxford, England: Pergamon. Säljö, R. (2005). Lärande och kulturella redskap. Om lärprocesser och det kollektiva minnet [Learning and cultural tools. On processes of learning and the collective memory]. Stockholm: Norstedts Akademiska Förlag. Säljö, R., & Wyndhamn, J. (1988). A week has seven days. Or does it? On bridging linguistic openness and mathematical precision. For the Learning of Mathematics, 8(3), 16–19. Säljö, R., & Wyndhamn, J. (1993). Solving everyday problems in the formal setting. An empirical study of the school as context for thought. In: S. Chaiklin, & J. Lave (Eds), Understanding practice. Perspectives on activity and context (pp. 327–342). Cambridge, MA: Cambridge University Press. Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling in the elementary school. Learning and Instruction, 4, 273–294. Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets & Zeitlinger. Vygotsky, L. S. (1986). Thought and language (A. Kozulin, Trans.). Cambridge, MA: MIT-Press. Wertsch, J. V. (1991). Voices of the mind: A sociocultural approach to mediated action. Cambridge, MA: Harvard University Press.

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Chapter 6

Modelling for Life: Developing Adaptive Expertise in Mathematical Modelling From an Early Age Wim Van Dooren, Lieven Verschaffel, Brian Greer, and Dirk De Bock

Introduction One of the major justifications for the important role of mathematics in the elementary and secondary school curricula is that it provides a set of tools for describing, analysing, and predicting the behaviour of systems in different domains of the real world (Blum & Niss, 1991). The development of students’ disposition1 to apply mathematics to make sense of everyday-life situations and to solve problem situations in the real world — otherwise termed ‘mathematical modelling’ — gets a central place in contemporary mathematics curricula and reform documents worldwide. For example, in the Principles and Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM, 2000, p. 3) in the United States, one can read that: Quantitative information available to limited numbers of people a few years ago is now widely disseminated through popular media outlets. The need to understand and be able to use mathematics in everyday life and in the workplace has never been greater and will continue to increase. Mathematical modelling can be thought of as a complex process involving a number of phases. Many authors have proposed descriptions of this process (e.g. Blum & Niss, 1991; Burkhardt, 1994; Mason, 2001; Verschaffel, Greer, & De Corte, 2000), but, essentially,

1

With the notion ‘disposition’, we refer both to students’ ability and their inclination towards modelling (see De Corte, Greer, & Verschaffel, 1996).

Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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they all bear a family resemblance to the modelling cycle schematically represented in Figure 1 (see Verschaffel et al., 2000): (1) Understanding the phenomenon under investigation, leading to a model of the relevant elements, relations and conditions that are embedded in the situation (situation model), (2) constructing a mathematical model of the relevant elements, relations, and conditions available in the situation model, (3) working through the mathematical model using disciplinary methods in order to derive some mathematical results, (4) interpreting the outcome of the computational work to arrive at a solution to the real-world problem situation that gave rise to the mathematical model, (5) evaluating the model by checking if the interpreted mathematical outcome is appropriate and reasonable for the original problem situation, and (6) communicating the solution of the original real-world problem. Consider, for example, the modelling process required in the following real-world situation: A travel leader plans to visit the 509-m-high Taipei 101 tower with a group of 289 people. He asks the janitor of the building if it is feasible to get everybody to the top floor in 45 min. The janitor knows that, due to technical problems with two other lifts, the tourists can only use one lift with a maximum capacity of 20 people, and that a trip with this lift takes (in either direction) 86 s. When thinking about this problem, a competent modeller first develops a situation model that consists of a so-called ‘quotitive’ model of division (‘how many groups of 20 people fit in the total group of people?’) and a proportional relationship between the number of lift trips and the time required (‘each trip requires the time to go up and down plus some time for embarking and disembarking’). A first part of the solution is to figure out how many lift trips are needed. The mathematical model derived from the quotitive model of division is 289/20, which in the derivation gives the result 14.45 or 14 remainder 9. Interpreting this result in terms of the original situation model would imply that the lift needs to go up 15 times, if all tourists have to be taken up. Then, the required time needs to be mathematised, as the product of the number of lift trips (15) and the time required for each lift trip (2 ⫻ 86 s ⫹ time for (dis)embarking), minus the duration of the last trip Phenomenon under investigation

Understanding

Situation model

Modelling

Communication

Interpreted results

Mathematical analysis

Evaluation

Report

Mathematical model

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Figure 1: Schematic diagram of the process of mathematical modelling (Verschaffel et al., 2000, p. xii).

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downwards (86 seconds). For the ease of calculating, one could estimate the total time required for each complete lift trip as 3.5 min and for a trip up or down as 1.5 min. The derived result from working through the mathematical model 15 ⫻ 3.5 ⫺ 1.5 is 51. This result again needs to be interpreted in terms of the original problem situation: about 51 min is required to get 289 people up, so the available time of 45 min will probably not be sufficient. When communicating that result to the travel leader, the janitor is implicitly required to do more than just saying ‘no, it is impossible’. He is expected to communicate that the available time is almost sufficient, and perhaps to suggest that the travel leader tries to save some minutes elsewhere in his travel plan or strives for efficient embarking and disembarking. Or he might ask whether there are (many) children in the group and, in that case, suggest exceeding the maximum of 20 persons per lift trip, and save a few trips. As a preliminary, we want to comment briefly on some important characteristics of the mathematical modelling process, and on the definition of the term as we use it in the current chapter. First, while modelling consists sometimes of mapping information available in a realworld situation (givens) onto a ‘ready-made’ mathematical model available in schematic form in the cognitive repertoire of the modeller2, this is certainly not always — and even not typically — the case. Often, the real-world situations urge problem solvers to (re)construct, refine or extend mathematical models. Examples can be found in the work by Lesh and Doerr (2003). Second, whereas these two variants of modelling require that students have already at their disposal at least some mathematical models and tools to mathematize, there is another kind of modelling wherein model-eliciting activities are used as a vehicle for the development of mathematical concepts. This type of modelling is often called ‘emergent modelling’ (Gravemeijer, 2004). Although it is sometimes difficult to make a clear distinction, emergent modelling is associated with different phases of the teaching/learning process and with different kinds of instructional activities. This chapter will focus more strongly on the two former variants of modelling than on emergent modelling. Third, although models are developed for specific purposes and/or originate in specific situations, the need to develop a mathematical model is often accompanied by an interest in its reusability and transferability (Lesh & Doerr, 2003). Especially when a mathematical modelling task is offered in a school or in a corporate training context, the goal generally is not that students or trainees learn to tackle only that particular task. Rather, students and trainees are expected to recognize classes of situations that can be modelled by means of a certain mathematical concept, relation or formula, and to develop some degree of routine and fluency in mapping problem data to the underlying mathematical model and in working through this model to obtain a solution. However, as will be argued throughout the chapter, one major problem with the traditional approach to modelling is that learners will start to apply certain familiar and well-trained mathematical models also in settings where they are neither relevant nor valid.

2

The use of the term ‘mapping’ does not imply any qualification of the complexity of the underlying thinking process, although some scholars would be reluctant to use ‘modelling’ in cases where the mapping between the situational and the mathematical model is completely straightforward.

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Fourth, while modelling is often performed to answer more or less well-defined questions (as in the example above), this is certainly not always the case. Modelling also occurs in situations where no well-defined question has been posed, but where one wants to make sense of, predict, or explain a phenomenon. Natural objects (like trees or shells), artwork or design products (like a traditional African carpet or a painting by Mondriaan) or social phenomena (like demographic growth or traffic jams) as such can, for example, also elicit mathematical modelling activities in some people. Note that the term ‘model’ is also used within purely abstract mathematical contexts. For example, mathematicians try to describe and generate fractals by means of iterations of functional relations. Although there exist in nature some patterns that can be seen as models of mathematical fractals (e.g. trees, rocky coastlines or snowflakes), the first goal here is to use mathematical models to describe new and purely mathematical objects (independent of the existence of a referent in nature). Fifth, modelling in real life occurs generally in socially and culturally rich environments. Modellers are not individuals working in isolation, but have access to other people and to graphical, computational, information storage and communication capabilities of modern information technology that will also shape behaviour. A sixth characteristic is that the modelling process is not a straightforwardly sequential activity consisting of several clearly distinguishable phases. Most typically, modellers do not move sequentially through the six different phases of the modelling process (see Figure 1), but rather run through several modelling cycles wherein they gradually refine, revise or even reject the original model. As pointed out by Ikeda and Stephens (2001), a major task for modellers is to seek a proper balance between oversimplification and overcomplexity — or, stated positively, between parsimony and precision — taking into account not only features and goals of the modelling task as such, but also personal and situational constraints, the sociocultural context and so on. Since there is no single, correct solution for finding this balance, modellers need to realise that their solutions are inherently provisional and debatable. In the above example, a precise numerical answer was not required, as the travel leader only wanted to know whether 45 min would be enough. On the other hand, given that the travel leader had to make a quick decision, the janitor had to respond quickly, starting from some (untested) assumptions and (rough) estimations. Further, as suggested above, the janitor might suggest some adjustments if the estimate is slightly higher than 45 min. The structure of the rest of this chapter is as follows. First, we problematise the educational role of traditional word problems as a vehicle for teaching genuine modelling at the elementary and lower secondary school levels, and we provide some research-based examples of how school word problems elicit in students a superficial version of the modelling cycle described in Figure 1. Then we explain in detail what we mean by a superficial approach to mathematical modelling, by contrasting it with genuine modelling. Afterwards we look for elements in traditional school practice and culture that help to explain why so many students do not develop a genuine modelling disposition. Next, we argue why, and demonstrate how, the modelling perspective can be taken seriously already at the elementary level. We close the chapter with a discussion of some promises and pitfalls that relate to this proposal.

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School Word Problems: A Vehicle for Acquiring an Authentic and Adaptive Mathematical Modelling Expertise? Historically, one major way of teaching the modelling process is through word problems, i.e. verbal descriptions of problem situations, typically presented in a school context, wherein a question is raised the answer to which can be found by performing one or more mathematical operations on the numbers in the problem (Verschaffel et al., 2000). An analysis of the long and worldwide history of word problems reveals that they have been included and are still being used, with the ostensible aim of accomplishing several goals (Blum & Niss, 1991; Verschaffel et al., 2000). Here, we will focus on their oldest, and probably most important goal, namely offering practice for the everyday-life situations in which learners will need to apply what they have learned in school. The (implicit) idea is to bring reality into the mathematics classroom, to create occasions for learning and practicing different aspects of applied problem solving, without the practical (organisational, financial … ) inconveniencies of direct contact with the real-world situation evoked by the problem statement. By means of such ‘best alternatives’ for the real-world situations outside the classroom, students become prepared for the mathematical requirements they will face in their (future) everyday lives. For a very long time, word problems have played this application function without much reflection and critical concern. Of course, there have always been individuals showing (some) awareness of the bridging problem between reality and mathematics, and the risks involved — Lewis Carroll (in Fisher, 1975) provides a marvellous example (summarized in Verschaffel et al., 2000, pp. 132–134) — but many teachers, textbook writers and researchers have been using, and still use nowadays, word problems as if there was no bridging problem at all. During the last 10–15 years, however, it has been argued by scholars from various disciplines like mathematics education, psychology, linguistics and anthropology (e.g. Boaler, 1994; Davis, 1989; Gerofsky, 1997; Jacob, 1997; Lave, 1992; Reusser & Stebler, 1997a) that the current practice of word problems in school mathematics does not at all foster in students a genuine disposition towards relating mathematics to reality. Hereafter, we present three research-based examples wherein students have constructed an approach to word problem solving that is reduced to the routinely execution of one or more arithmetic operations with the numbers in the problem, without any serious consideration of possible constraints of the reality of the problem context. The most spectacular, and probably also the most quoted case, is that of the French and German researchers (IREM de Grenoble, 1980; Radatz, 1983) who posed ‘nonsensical’ problems like ‘There are 26 sheep and 10 goats on the ship. How old is the captain?’ and found that many elementary school children were prepared to answer these problems by doing arithmetical operations on the given numbers, expressing no concern about the appropriateness or meaningfulness of their answers. Radatz (1983) found that the number of children trying to come to an answer to such problems increased with age (from 10% in kindergarten and first grade to 30% in second grade and almost 60% in third and fourth grades). Inspired by this striking example and several other from the literature, Greer (1993) and Verschaffel, De Corte, and Lasure (1994) carried out paper-and-pencil studies with upper

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primary and lower secondary school students, using a set of ‘tricky’ problems including the following: – 450 soldiers must be bussed to their training site. Each army bus can hold 36 soldiers. How many buses are needed? – Bruce and Alice go to the same school. Bruce lives at a distance of 17 km from the school and Alice at 8 km. How far do Bruce and Alice live from each other? – John’s best time to run 100 m is 17 s. How long will it take him to run 1 km? They termed these items ‘problematic’ in the sense that proper answers require (from their point of view) considerations based on real-world knowledge and assumptions rather than the routine application of some simple arithmetic operations. In both studies, students demonstrated a very strong tendency to exclude real-world considerations from their answers when confronted with such problematic items. For instance, in the study by Verschaffel et al. (1994), only 17% of all answers were considered as ‘realistic’ (i.e. taking into account considerations related to the real-world situation). A third category of examples comes from recent research on students’ tendency to routinely apply proportional solution methods in various kinds of mathematical problems, for which another solution method than the proportional one is appropriate. For instance, in a series of studies, De Bock et al. (e.g. De Bock, Van Dooren, Janssens, & Verschaffel, 2002) showed that more than 80% of 12- to 16-year-old students inappropriately answered word problems like: ‘Farmer Gus needs 8 h to fertilise a square pasture with sides of 200 m. How much time will he approximately need to fertilise a square pasture with sides of 600 m?’ (giving the answer ‘24 h’ in this case). A recent study assessed the development of students’ routine application of proportionality in solving word problems through elementary school (Van Dooren, De Bock, Hessels, Janssens, & Verschaffel, 2005a). Comparable to the findings of Radatz (1983) mentioned before, Van Dooren et al. discovered that for some word problems, the number of correct answers decreased with years of schooling, due to a dramatic increase in the tendency of students to overuse proportional solution methods. For example, for the problem ‘Ellen and Kim are running around a track. They run equally fast but Ellen started later. When Ellen has run 5 laps, Kim has run 15 laps. When Ellen has run 30 laps, how many laps has Kim run?’, the percentage of correct answers decreased from 56% in third grade to 29% in sixth grade, whereas the number of inappropriate proportional answers increased from 5% in third grade to 50% in sixth grade. Although there are clear differences between the various tasks described above as well as between the specific kinds of errors that students commit when solving them, there is a common link in that they all elicit some kind of superficial mathematical modelling behaviour in many students. In the next section, we will elaborate on some characteristics of such a superficial way of mathematical modelling, and contrast it with what we consider as a (more) genuine way.

Superficial Versus Genuine Approaches to Mathematical Modelling In the previous section, we already indicated that applying mathematical models to handle problem situations could be done superficially instead of in a genuine way. By a superficial way, we mean a modelling process as shown in Figure 2. A particular (well-trained)

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Superficial strategy choice

Phenomenon under investigation

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Situation model

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Communication

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Mathematical analysis

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Mathematical model

Interpretation

Derivations from model

Direct reporting of mathematical result

Figure 2: Superficial mathematical modelling process (Verschaffel et al., 2000, p. 13). mathematical model is triggered automatically by certain conspicuous elements in the problem situation — or even worse, merely by certain key words in the problem statement — and the result of the calculations is immediately communicated as the answer, without referring back to the original problem situation to verify that it is a meaningful response to the original question, or to check its reasonableness. Note that this is a prototypical description. Not all of these characteristics are (equally prominently) present in every superficial modelling process. Sometimes, as for the captain’s age problem mentioned in the previous section, the error lies in a mathematical model being applied to data that have no logico-mathematical relation whatsoever. In other cases, such as the buses problem used by Greer (1993) and Verschaffel et al. (1994), a correct model can be chosen and applied, but the evaluation or refinement phase may be neglected because some peculiarities of the real-world situation are overlooked. In still other cases, students may tend to apply a completely wrong mathematical model to the problem situation; for instance, when they apply a proportional strategy (5 ⫻ 3 ⫽ 15, 30 ⫻ 3 ⫽ 90) instead of the correct additive one (5 ⫹ 10 ⫽ 15, 30 ⫹ 10 ⫽ 40) in the runner problem used by Van Dooren et al. (2005a). In this last case, some well-practiced problem-solving schemes and conceptions that are deeply rooted in students’ prior knowledge may interfere with the application of the correct mathematical models and concepts.3 3

The interference of prior knowledge in the acquisition and application of new knowledge is often interpreted from a conceptual change framework (Vosniadou, 1999). Recently, this framework is also being applied to the investigation of teaching and learning processes in mathematics (see Vosniadou & Vamvakoussi, this volume; Verschaffel & Vosniadou, 2004).

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Contrary to the superficial way of doing school word problems, the genuine way refers to a process wherein no steps of the modelling cycle presented in Figure 1 are omitted and wherein most, if not all, of the above-mentioned characteristics of (authentic) mathematical modelling are found. Hereafter, we contrast the superficial and the genuine versions of modelling for the different phases of the modelling cycle, adapted to word problems and presented to students in a school context. The first phase of the mathematical modelling cycle involves understanding the situation described in the problem statement — what we have termed forming a situation model. In this phase, students have to consider and decide what elements are essential and what elements are less important to include in the situation model. In the case of genuine modelling, it is essential to have knowledge about the phenomenon under consideration and, even more importantly, to activate this knowledge rather than to suppress it (as in the superficial version of modelling). Moreover, this real-world knowledge base does not need to be considered as closed. In genuine modelling activities, students can extend it in the course of solving a problem by exploiting such resources as asking others, accessing information sources and carrying out physical or mental experiments. Thinking of a word problem version of the lift problem introduced at the beginning of this chapter, this open-endedness could, for instance, imply that students would make rough estimates of the number of adults, children or maybe people in wheelchairs in the group of tourists and incorporate this extra information in the situational model that they build of the problem. In the next phase, the situation model needs to be mathematised, i.e. translated into mathematical form by expressing mathematical equations involving the key quantities and relations. For this, students need to rely on another part of their knowledge base, namely mathematical concepts, formulas, techniques and heuristics. The production of a mathematical model is influenced heavily by the goals that are implicitly or explicitly present in the situation, imposed by the instructional context (e.g. a written assessment) or negotiated. For example, students have to consider whether a problem calls for a precise or approximate answer and whether and to what extent complications related to the realistic aspects of the situation should be accommodated. The outcome of these considerations can go in several directions, depending on the modeller’s personal interpretation. Another issue influencing the mathematisation process is the availability of resources. These include mathematical techniques known or potentially constructable by the modeller, the presence of representational resources (graphs, manipulatives, … ) and the availability of software modelling tools, calculators and so on. After the mathematical model is constructed and results are obtained by manipulating the model, the bald, numerical result needs to be interpreted in relation to the situation model. At this point, the result also needs to be evaluated against the situation model to check for reasonableness. Depending on the perceived fit between the result of the operations on the mathematical model and the situation model, students need to judge the appropriateness of revising or refining the model to take into account local or minor misfits, or even to abandon the model and look for another. If the lift problem were used as a genuine modelling task in a school context, students would have to consider the original problem situation again after having done the computational work, because the division 289/20 resulted in a non-integer outcome, and they would have to decide how they would deal

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with this outcome (use the non-integer number as such, the integer number with remainder, the rounded-down number or the rounded-up number) before they could proceed. As a final step, the interpreted and validated result needs to be communicated in a way that is consistent with the goal or the circumstances in which the problem arose. In typical school word problems, task requirements do not go beyond reporting the outcome of the calculational work. However, in genuine modelling situations, it can be appropriate or even necessary to report on the way the answer was obtained, to provide arguments in support of the model being used (and against alternative models), to critically compare different models or even to create an artefact. In all these cases, students also need to tailor their communication to their target audience. When the lift problem was used as a genuine modelling task, students would have to bear in mind the origin of the travel leader’s question when formulating their answer, because the travel leader would not be satisfied with a simple ‘no, this is impossible’. In Figure 3 we elaborate the earlier schematic diagram of mathematical modelling in Figure 1, by including the different complicating influences on the process of modelling that were discussed and illustrated in the above contrastive analysis. It is clear from this analysis that in each phase of a genuine modelling process, mindfulness, sense making, and flexibility are required of modellers. If they discard any of these three qualifications in any phase, the outcome of the modelling process may be flawed. As

Knowledge about phenomenon

Phenomenon under investigation

Understanding

Communication

Task requirements

Interpreted results

Modelling

Resources

Interpretation

Mathematical model

Mathematical analysis

Report

Situation model

Evaluation

Possible recycling

Modelling goals

Derivations from model

Comparison of alternative models

Figure 3: Elaborated view of the modelling process (Verschaffel et al., 2000, p. 168).

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such, genuine mathematical modelling seems to require what Hatano has called ‘adaptive’ — rather than ‘routine’ — expertise (Hatano, 2003).

Superficial Modelling Behaviour: In Search of Explanations In the previous sections, we showed and illustrated that genuine mathematical modelling seems to occur rather frequently and naturally in real-life situations (like the lift problem from the introductory section) while at the same time, current practices of teaching word problem solving generally do not develop in students a genuine disposition towards mathematical modelling, but rather a narrow routine expertise — to use Hatano’s (2003) terminology. Over the past few years, researchers have searched for elements in the traditional instructional environment that underlie the observed superficial modelling behaviour of so many students. In this section, we briefly review the results of this search. The development of students’ superficial tactics for doing word problems is assumed to occur implicitly, gradually and tacitly through being immersed in the culture of the mathematics classroom in which they engage. Putting it another way, students’ superficial approach develops from their perceptions and interpretations of the didactical contract (Brousseau, 1997) or the socio-mathematical norms (Yackel & Cobb, 1996) that determine — explicitly to some extent, but mainly implicitly — how to behave in a mathematics class, how to think, how to communicate with the teacher and so on. More specifically, this enculturation seems to be mainly caused by two aspects of instructional practice, namely (1) the nature of problems given and (2) the way in which these problems are conceived and treated by teachers. With respect to the characteristics of traditional word problems that appear in classrooms and textbooks, Reusser and Stebler (1997a, p. 323) concluded the following: Only a few problems that are employed in classrooms and textbooks invite or challenge students to activate and use their everyday knowledge and experience. Most word problems used in mathematics instruction are phrased as semantically impoverished, verbal vignettes. Students not only know from their school mathematical experience that all problems are undoubtedly solvable, but also that everything numerical included in a problem is relevant to its solution, and everything that is relevant is included in the problem text. One can add to Reusser and Stebler’s (1997a) critical analysis that, in traditional school word problem solving, the mathematical model that seems applicable at first sight is almost always also the correct one, that word problems often contain key words or other hints that help to identify the operations-to-perform routinely, they rarely require more than a couple of minutes to be solved and that they generally ask for a single, precise answer with only very little attention to explaining and justifying how that answer is obtained (e.g. De Corte & Verschaffel, 1985; Kilpatrick, 1985; Lave, 1992; Reusser & Stebler, 1997a). Cooper (1992) extended this criticism to assessment contexts, by analysing typical items from national assessment instruments in the UK. Owing to the circumstances of collective, written testing contexts, word problems in tests generally are to be treated as undoubtedly solvable, with all relevant data and only relevant data included, requiring a single, precise answer, and taking only a short time to be solved.

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Less research-based evidence exists on the second instructional factor, namely the way in which word problems are treated by teachers in mathematics lessons. One study that sheds some light on this factor is that by Verschaffel, De Corte, and Borghart (1997), in which future elementary school teachers solved the same items as in the earlier described study by Verschaffel et al. (1994), and afterwards they evaluated four alternative answers from (imaginary) pupils to those same items, including a typically ‘realistic’ and the nonrealistic answer based on the routine, straightforward application of the number sentence ‘hidden in the word problem’. Less than half of future teachers’ answers to the word problems were scored as ‘realistic’. Moreover, in their evaluations, they scored non-realistic answers higher than realistic answers. Several studies have convincingly shown that the classroom culture has indeed a decisive impact on students’ word problem solving behaviour. Students rather easily leave their routine modelling behaviour if they are taken outside the traditional classroom word problem solving context. Some studies show significant positive effects on students’ modelling processes and performances when students are put in more authentic settings with concrete materials and/or the request to perform a certain action instead of answering a written question (see e.g. DeFranco & Curcio, 1997; Reusser & Stebler, 1997b; Van Dooren, De Bock, Janssens, & Verschaffel, 2005b). Positive effects are even found when students are offered tasks in a social science class setting instead of the mathematics lesson (Säljö & Wyndhamn, 1993), or when the formulation and presentation of word problems is changed with a view to make the tasks more authentic (Palm, 2002). The study by Van Dooren et al. (2005b), however, suggests that the effect of an authentic task setting is rather limited. Although students in their study showed genuine modelling behaviour when solving an authentic task, they reverted to superficial modelling behaviour when — two days later — the same task was offered again as a traditional word problem. As will be elaborated upon in the next sections, the development of an adaptive mathematical modelling expertise cannot be achieved in a single intervention, but seems to require more radical changes in the kind of application problems that are offered to students throughout their mathematics curriculum, and in the way in which they are treated in the classroom.

Taking the Modelling Perspective Seriously Already at the Elementary Level On the basis of the above-mentioned reflections and empirical investigations, several suggestions can be put forward for improving the quality of teaching and learning mathematical modelling already at the elementary school level. A minimal and rather easily achievable goal — which has already been accomplished (at least to some extent) in many new textbook series worldwide — is improving the quality of word problems as applications in several ways, such as: – Break up the expectation that any word problem can be solved by adding, subtracting, multiplying or dividing, or by a simple combination thereof. – Eliminate flaws in textbooks that allow superficial solution strategies to be undeservedly successful. – Vary problems so that it cannot be assumed that all data included in the problem, and only those data, are required for solution.

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– Weed out word problems in which numbers do not correspond to real life. – Accept forms of answer other than exact numerical answers. However, on top of this list of recommendations, which constitute a minimal response to the identified flaws in traditional teaching of word problems, we propose a more radical solution, namely to reconceptualise word problems as exercises in genuine mathematical modelling and to design new curricula and teaching/learning materials built on this reconceptualisation. In recent years, several researchers have set up design studies in which they developed, implemented, and evaluated experimental programmes aimed at developing in elementary and middle school students such a genuine disposition towards mathematical modelling. Typical examples are: – Several developmental research projects from the Freudenthal Institute in The Netherlands (see e.g. Gravemeijer, 1997), – the Jasper studies of the Cognition and Technology Group at Vanderbilt (1997) wherein mathematical problem solving is anchored in realistic contexts using new information technologies, – Lehrer and Schauble’s (2000) experimental curriculum for mathematics and science teaching in young children built upon the modelling approach, – English and Lesh’s (2003) recent work around ‘ends-in-view’ problems wherein neither the givens, nor the goal or the necessary solution steps are specified clearly, and – the learning environment for mathematical modelling and word problem solving in upper elementary school children developed by Verschaffel, De Corte, Lasure, Van Vaerenbergh, Bogaerts, and Ratinckx (1999). The following characteristics are common to these experimental programmes: – The use of more realistic and challenging tasks, which do involve some, if not most, of the complexities of real modelling tasks (such as the necessity to formulate the problem, seek and apply aspects of the real context, select tools to be used, discuss alternative hypotheses and rival models, decide upon the level of precision, interpret and evaluate outcomes). – A variety of teaching methods and learner activities, including expert modelling of strategic aspects of the modelling process, small-group work and whole-class discussions. Typically the focus is not on presenting and rehearsing established mathematical models, but rather on demonstrating, experiencing, articulating and discussing what modelling is all about. – Creating a classroom climate that is conducive to the development of genuine mathematical modelling and of the accompanying beliefs. Generally, these studies have produced positive outcomes in terms of performance, underlying processes, and motivational and affective aspects of learning. After reviewing the available research evidence, Niss (2001, p. 8) concluded that ‘application and modelling capability can be learnt — and according to the above-mentioned findings has to be learnt — but at a cost, in terms of effort, complexity of task, time consumption and reduction of syllabus in the traditional sense’.

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To some extent, the above-mentioned characteristics of the modelling approach are beginning to be implemented in mathematical frameworks and tests in many countries. However, according to Niss (2001), in general international terms, genuine and extensive applications and modelling perspectives and activities continue to be scarce in everyday practices of mathematics education. Niss points to two important barriers, namely the difficulty of getting the modelling perspective into tests (in which it is easier to include tasks with a more closed character) and the extremely high demands that such a modelling approach puts on teachers (mathematically, pedagogically and personally).

Promises and Pitfalls of the Modelling Perspective Besides the two factors that jeopardize the implementation of the modelling perspective pointed out by Niss (2001), there are some other difficulties and challenges in putting the modelling perspective forward in the mathematics classroom. A first critical issue is: How far can and should we go in our efforts to make the modelling tasks that we present in the classroom more authentic or realistic? How much reference to the complexity of reality is possible and appropriate in the classroom context? Gravemeijer (1997) convincingly argued that there will always be an insurmountable difference between solving problems in out-of-school reality and solving word problems in mathematics lessons or tests (see also Sethole, 2005). But if we accept that there will always remain some gap, what can be an appropriate level of reference to the ‘real world’ that should be established in the classroom? And is encouraging students to use their real-world knowledge not opening a Pandora’s box? We want to argue that there is not just one appropriate level of realism, but we think that this does not necessarily pose an impassable didactical problem. The question about a model’s degree of abstraction and precision does not need to be regarded as a difficulty, but as part of what we want students to learn to make careful, deliberate judgements about, as one of the aspects of adaptivity in a mathematical modelling expertise. As we already explained above, difficulties with respect to the level of realism and precision are most serious when word problems are presented in contexts that preclude discussion, as when students are working alone on written tests. We can refer, for example, to Cooper’s (1992) critical discussion of test items from national assessment instruments in the UK. One item asked how many times a lift that can carry up to 14 people would have to go up to take 269 people. The marking scheme specifies that 19 or 19.2 are not acceptable answers. Cooper (1992, p. 235) commented on that marking scheme that ‘Some reference to the real must be made, but not too much’. Children indeed need to avoid merely reporting the result of 269 / 14, but at the same time they should also neglect such considerations as some people might use the stairs in the morning rush, a lift is not always full or some lift users may require more space because of a wheel chair. But within the context of a classroom, where discussion and collaboration are possible, the degree of precision, the reasonableness of certain assumptions, and so on, may be of course negotiated, and such activities can contribute to the development of students’ modelling expertise.

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A second, related issue is whether implementing a modelling perspective implies that traditional word problems need to be banned from the classroom. We think that such traditional word problems can still have their role, as students need to learn to apply powerful schemes for identifying, understanding and solving certain categories of problems. For example, the schemes of addition, multiplication or direct proportionality are very powerful and applicable in a wide variety of situations. So, it is important that students learn to master these schemes and to apply them in various contexts in a fast and correct way. However, the problem arises when students are given no training in discriminating between those cases where a scheme is appropriate and where it is not, so that superficial cues can automatically trigger these mathematical schemes (see e.g. the studies on the overuse of proportionality, De Bock et al., 2002; Van Dooren et al., 2005a). There should be room for different kinds of word problems with distinct instructional goals. At one time they may be used mainly to develop routine scheme application skills, i.e. to create strong links between mathematical operations and prototypically ‘clean’ model situations (with little room for timeless discussions about situational complexities that might jeopardize this link), whereas at other times, word problems may be used primarily to develop a genuine modelling approach, in which case they act as exercises in relating real-world situations to mathematical models and in reflecting on that complex relationship. Both activities seem important in the development of a genuine mathematical modelling expertise. In this respect, Galbraith and Stillman (2001, p. 301) propose an interesting problem classification that focuses on the differences in terms of the kind of thinking processes they are expected to elicit in students, as well as in terms of their underlying assumptions about the link between word problems and the real world: – Injudicious problems, wherein realistic constraints are seriously violated; – Context-separable problems, wherein the context plays no role in the solution and can be stripped away to expose a purely mathematical question; – Standard application problems, where the necessary mathematics is context-related and the situation is realistic, but where the procedure is still rather standard; – Genuine modelling problems, where no mathematics as such appears in the problem statement, and where the demarcation and formulation of the problem, in mathematical terms, must be at least partially supplied by the modeller. We agree with Galbraith and Stillman (2001) that injudicious problems are to be avoided because they strongly reinforce the belief that mathematics has nothing to do with the real world, which may lead to students deliberately excluding their knowledge about the phenomena under consideration. But we think that context-separable and standard application problems do have a meaningful role in mathematics education. However, when using them, one should be cautious about the risk that students start to apply to certain familiar and well-trained concepts routinely and transfer them also to settings where they are neither relevant nor valid (Niss, 2001). Moreover, we should not labour with the latter two types of problems under the illusion that they will foster the development of an adaptive mathematical modelling expertise. Only in the fourth category described by Galbraith and Stillman (2001) is genuine mathematical modelling as we described it in this contribution invoked.

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Another important issue is from what age one can start teaching mathematical modelling according to the above-mentioned perspective. Mathematical modelling is often considered as a topic that can only be introduced at the secondary and tertiary levels. However, by treating mathematical modelling as an advanced topic that only can and should be introduced at the secondary or tertiary level, a great number of students’ early experiences are ignored and missed. As Usiskin (2004) points out, already in the earliest years of primary school, children can have several experiences with mathematical modelling that require merely very basic arithmetical ideas. For instance, the four basic arithmetic operations (+, ⫺, ⫻, /) can be considered as mathematical models that are useful for understanding various situations in the real world. So, as pointed out by Usiskin (2004), much of what is done in standard mathematics curricula, even at the elementary stage, can be characterised as modelling even though it is not acknowledged as such by pupils (and teachers). Indeed, the core of the modelling process – comprised setting up a correspondence between some aspect of a real-world situation and a mathematical structure, carrying out appropriately motivated operations within that structure and interpreting the results of those operations back in the real-world context — is applicable, in principle, to the solution of the simplest of word problems like ‘John has 5 apples and Mary has 3 apples. How many do they have together?’ Even in such simple cases a judgment is required whether or not an operation provides an appropriate model for a situation described (see e.g. the ‘distance to school’ problem on p. 96). But this fundamental insight is masked, both for students and teachers, in typical traditional teaching, which omits instructive counterexamples where the superficially appropriate operation turns out to be inappropriate (e.g. see Usiskin, 2004; Verschaffel et al., 2000). Greer and Verschaffel (2006) proposed the term ‘implicit modelling’ for this initial level wherein the student (and, likewise, his/her teacher) is essentially modelling without being aware of it. In their framework, this initial level is followed by a second level, called ‘explicit modelling’ (in which attention is drawn to the modelling process), and a third level, called ‘critical modelling’ (whereby the roles of modelling within mathematics and science, and within society, are critically examined). An issue of emerging prominence that we want to address is whether teaching for adaptive modelling expertise is feasible for all students and why it is important. Over the past few years, several authors like Keitel (1989) and Mukhopadhyay and Greer (2001) have made strong pleas for engaging all students in the modelling perspective, both for the empowerment of the individual and for the betterment of society. For Mukhopadhyay and Greer (2001), this ‘political aspect’ can be considered as a third perspective — beyond the (purely) cognitive and the social/cultural perspectives — from which mathematics education in general, and teaching and learning mathematical modelling in particular, should be critically analysed. In relation to this political aspect, the most important reason for introducing the modelling perspective to all students is to help as many people as possible to ‘become critical thinkers who can use mathematics as a tool for analysing social and political issues, and can reflect on that tool use, including its limitations’ (Mukhopadhyay & Greer, 2001, p. 310). Evidently, once mathematics educators start applying this modelling perspective on a larger scale and allow students to bring in their personal experience when trying to make sense of all kinds of technical, social and cultural issues and phenomena, they will be confronted quickly and inevitably with the diversity of these experiences in

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terms of gender, social class and ethnic diversity (see e.g. Boaler, 1994; Tate, 1994). The best way to prevent students from becoming alienated by mathematics and its authority and to help students use mathematics as a powerful tool for analysing issues in their personal lives seems to be engaging them in such modelling activities, with careful attention to the relevance of the problem contexts and to the diversity in views and approaches that can arise (e.g. Gutstein & Peterson, 2005). Given the multiphased, multidimensional and highly adaptive nature of the process, mathematical modelling is often viewed as an activity that is within the reach of only older and/or more capable students. The intention of this chapter was to show that it is not only important, but also feasible, to develop an adaptive modelling expertise in all students and to start doing this already from a young age on.

Acknowledgements This research was supported by Grant GOA2006/01 ‘Developing adaptive expertise in mathematics education’ from the Research Fund K.U.Leuven, Belgium. The chapter is an elaborated synthesis of plenary lectures given by Brian Greer and Lieven Verschaffel at several international conferences over the past few years.

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Mukhopadhyay, S., & Greer, B. (2001). Modelling with purpose: Mathematics as a critical tool. In: B. Atweh, H. Forgasz, & B. Nebres (Eds), Socio-cultural aspects in mathematics education (pp. 295–311). Mahwah, NJ: Erlbaum. NCTM. (2000). Principles and standards for school mathematics. Reston, VA: Author. Niss, M. (2001). Issues and problems of research on the teaching and learning of applications and modelling. In: J. F. Matos, W. Blum, S. K. Houston, & S. P. Carreira (Eds), Modelling and mathematics education. ICTMA9: Applications in science and technology (pp. 72–89). Chichester, U.K.: Horwood. Palm, T. (2002). The realism of mathematical school tasks. Features and consequences. Doctoral thesis N° 24, Department of Mathematics, Umea University, Umea, Sweden. Radatz, H. (1983). Untersuchungen zum Lösen eingekleideter Aufgaben [Studies of problem-solving in the context of verbal (literally: dressed up) problems]. Zeitschrift für Mathematik-Didaktik, 4, 205–217. Reusser, K., & Stebler, R. (1997a). Every word problem has a solution: The suspension of reality and sense-making in the culture of school mathematics. Learning and Instruction, 7, 309–328. Reusser, K., & Stebler, R. (1997b). Realistic mathematical modeling through the solving of performance tasks. Paper presented at the seventh International Conference on Learning and Instruction, Athens, Greece. Säljö, R., & Wyndhamn, J. (1993). Solving everyday problems in the formal setting. An empirical study of the school as a context for thought. In: S. Chaiklin, & J. Lave (Eds), Understanding practice: Perspectives on activity and context (pp. 327–342). Cambrige: Cambridge University Press. Sethole, G. (2005). From the everyday, through the inauthentic, to mathematics: Reflection on the process of teaching from contexts. In: H. L. Chick, & J. L. Vincent (Eds), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics education. (Vol. 4, pp. 169–175). Melbourne, Australia: University of Melbourne. Tate, W. E. (1994). Race, retrenchment, and the reform of school mathematics. Phi Delta Kappan, 75, 477–485. Usiskin, Z. (2004). The arithmetic operations as mathematical models. In: H.-W. Henn, & W. Blum (Eds), ICMI Study 14: Applications and modelling in mathematics education (pp. 279–284). Dortmund, Germany: Department of Mathematics, University of Dortmund. Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005a). Not everything is proportional: Effects of age and problem type on propensities for overgeneralization. Cognition and Instruction, 23(1), 57–86. Van Dooren, W., De Bock, D., Janssens, D., & Verschaffel, L. (2005b). Students’ overreliance on linearity: An effect of school-like word problems? In: H. L. Chick, & J. L. Vincent (Eds), Proceedings of the 29th conference of the international group for the psychology of mathematics education (Vol. 4, pp. 265–272), Melbourne, Australia: University of Melbourne. Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems. Learning and Instruction, 4, 339–359. Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modelling of school arithmetic word problems. Learning and Instruction, 4, 273–294. Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H., & Ratinckx, E. (1999). Design and evaluation of a learning environment for mathematical modelling and problem solving in upper elementary school children. Mathematical Thinking and Learning, 1, 195–229. Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets & Zeitlinger.

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Verschaffel, L., & Vosniadou, S. (Eds). (2004). The conceptual change approach to mathematics teaching and learning. Learning and Instruction [Special issue], 14(5) 445–548. Vosniadou, S. (1999). Conceptual change research: State of the art and future directions. In: W. Schnotz, S. Vosniadou, & M. Carratero (Eds), New perspectives on conceptual change (pp. 3–13). Amsterdam: Pergamon. Yackel, E., & Cobb, P. (1996) Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.

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Chapter 7

Motivated Learning: What Is it and How Can it Be Enhanced? Monique Boekaerts and Rob Martens

Introduction In the last two decades, researchers in the field of educational psychology have studied motivated learning in real-life settings. New learning concepts have emerged, such as independent learning, informal learning, active learning, problem-based learning, and work-based learning. Studies conducted in such (socio)constructivist learning environments highlighted the different roles that students and teachers must adopt and it has become clear that motivation is a crucial aspect, not in the least because it is key in self-regulation, teamwork, deep level learning, and inquiry. Some investigators (e.g. Ryan & Deci, 2000) equated motivated learning in constructivist learning environments with intrinsic motivation, while others referred to a host of motivation components to describe motivated learning. In this chapter we seek to answer questions such as: Have we made progress towards the goal of understanding the effect of motivation on learning in real-life settings? What components are involved in motivated learning? Can we exert influence on students’ motivation? To answer these and related questions, this chapter will follow the distinction proposed by Pintrich (2000) between research that primarily aims at understanding motivation as a process (pure basic research) and research aimed at changing or manipulating students’ motivation (use-inspired research). We will present an eclectic overview of the research literature. For reasons of clarity, the focus of this chapter will be on studies in higher education. We want to avoid a problem that is often addressed in motivational research, namely, the interrelatedness of skill and will confuses the picture. Evidently, students enrolled in higher education have proven to be cognitively able to achieve academic goals but they may differ in their willingness to direct their attention to valued and nonvalued tasks, invest effort to apply a deep-level learning strategy, and persist in the face of diversion, difficulty, and failure. The chapter is organized into four main sections. First, we summarize the research literature on innovations in higher education that aimed at promoting deeper learning. Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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Second, we conceptualise motivation as a psychological construct that originates in a holistic experience that is characterized by beliefs about goal-directed behaviour and students’ perceptions of motivational conditions. In the third part of this chapter, we describe a conceptual framework that depicts motivation as an integral part of self-regulation. The final section presents some interventions to improve students’ motivation and volition in higher education and suggests directions for future research.

Innovation in Higher Education: Poor Results? New Learning Several researchers have combined social constructivism and information and communication technology (ICT) into what they call ‘new learning’ (Simons, van der Linden & Duffy, 2000). Essential components include collaborative learning, development of higher order skills, self-assessment, coaching, authentic tasks as point of departure for learning, individual responsibilities, and e-learning. Examples of this new learning are Web Quests, online courses, problem-based education, project-based education, competency-based education, virtual companies, management games, and simulations. Often direct instruction is replaced by ‘ill-structured tasks’ that resemble authentic problems. According to Järvelä and Volet (2004) in such learning environments motivation is a central concept: From a motivational point of view, the implication is that learners’ adaptation to complex social learning situations, such as sharing knowledge and maintaining coordinated activity, require cognitive, motivational, and socio-emotional skills that are different from, and often more challenging than, more conventional and well-structured learning situations. (p. 193). Poor Results? Although these new developments have inspired numerous innovations in higher education in recent years, many researchers and practitioners remain hesitant about their success. Evidence is building up that often new learning innovations do not live up to expectation. Lowyck, Lehtinen, and Elen (2004) even conclude that ‘new learning approaches often fail when applied in ecological settings’. They conclude that developers are overly optimistic and ignore the literature, which shows that students don’t use learning materials or use them in a very different manner than expected. For example, Vermetten, Vermunt, and Lodewijks (2002) showed that college students did not learn differently in a project-based, new learning environment. They investigated the effects of a large-scale curriculum reform, shifting from a ‘traditional’ approach to a powerful learning environment with project-based education. The reform failed to enhance deep-level learning and self-regulation. Gulikers, Bastiaens, and Martens (2005) also studied the effect of new learning environments in higher education. They studied a simulation that was developed by the Open University to stimulate active learning in social sciences. More concretely, ill-structured,

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authentic tasks were used to enhance students’ exploration and experimentation skills as well as their intrinsic motivation and their task performance. The simulation environment failed to change the students’ study approach compared to students who had worked in learning environments with less multimedia and ICT to simulate authentic contexts; it did not decrease surface-level processing, did not increase intrinsic motivation, and study results did not change. Lodewyk and Winne (2005) made a critical analysis of the ill-structured tasks that are used in higher education. They registered students’ self-efficacy for learning and performance while working on well- and ill-structured tasks. Students reported higher self-efficacy for learning and performance for a well-structured task. Moderate achievers reported significantly more difficulty with the ill-structured task. It seems that ill-structured tasks elicit a feeling of difficulty and may therefore decrease students’ self-efficacy and their interest in working on the task. Fortunately, not all innovations in higher education lead to disappointing results. Meta-analyses on problem-based learning (e.g., Dochy, Segers, Van den Bossche, & Gijbels, 2003) provided evidence that problem-based learning leads to better learning outcomes: students are less oriented toward memorization and tend to look for the underlying meaning in a text. Despite some interesting results, we have to raise the question: why are educational innovations in higher education less successful than originally expected? Why do students keep using surface-level learning strategies, and why are they inclined to minimize effort, exploration, and inquiry? It seems that we do not fully understand how motivation works in real-life settings. Vague theoretical assumptions underlie many educational innovations and better insights are needed into how students’ perceptions and motivation are linked to their behaviour in the college classroom. We will discuss each aspect in turn. Student perceptions and motivation are difficult to control Martens, Gulikers, and Bastiaens (2004) examined how college students experienced the ill-structured, authentic tasks that were used in a variety of courses of a distance learning university. Students’ perceptions in authentic learning environments were registered and contrasted to the expectations expressed by the designers. Marked differences were found. For instance, it was expected that the authentic context of the learning environment would stimulate explorative behaviour, but students’ score on this variable was lower than anticipated by the developers. However, students rated the ill-structured, authentic learning environment as less confusing than the developers had expected. Although the reported intrinsic motivation did not differ significantly from what the developers had expected, this study clearly illustrated the difficulties that developers have in making correct assumptions of how students actually perceive authentic learning environments. In general, it becomes more difficult to predict how undergraduates work in illstructured learning environments and how they perceive these environments when autonomy is handed over to the students, as is the case in most innovative learning environments in higher education. Researchers in the field of distance learning also concluded that selfstudy methods often lead to unexpected study outcomes, because no information is available on how students perceive the autonomy that has been created (Martens, Valcke, Poelmans, & Daal, 1996). Clearly, the enthusiasm that developers express about new learning technologies masks their view on the student perspective. It seems that what is

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currently delivered to students is driven by what is technologically possible rather than what is educationally desirable. Vague theoretical assumptions underlie educational innovation in higher education As argued previously, most new learning environments in higher education are based on the principles of social constructivism. Although most researchers acknowledge that motivation plays a major role in such environments, the precise mechanism that engenders intrinsic motivation in the college classroom is still obscure. One of the reasons for this lack of insight is that social constructivism is viewed as a philosophy of learning — or an ideology — based on the idea that knowledge is constructed by the learner at the time of learning, rather than as a model for systematic instructional design (Strijbos, Kirschner, & Martens, 2004; Van Merriënboer, Clark, & de Croock, 2002). The problem is that a philosophy or ideology is too vague to serve as a design model. For example, Martens et al. (2004) pointed to the poor underpinnings of the claim that working in new learning environments enhances students’ explorative behaviour as well as intrinsic motivation. Van Merriënboer and Martens (2002) also illustrated that the guidelines for the design of new learning environments in higher education are too vague. The new teacher and student roles are not specified well, and next to nothing is known about what happens to students’ motivation when teachers hand over autonomy and responsibility for learning in the college classroom. In-depth studies should be set up about students’ and teachers’ conceptions of what they have to do in the new learning environment. In this respect, Boekaerts and Simons (1995) explained that student and teacher roles should be complementary; defining one role automatically implies that the other role is specified as well. What do we know about teacher and student conceptions of their complementary roles in the new learning environments? We assume that the college teachers who adopted the new learning environments, had subscribed to the view that the quality of student learning depends on the type of experiences they have had within the teaching–learning environment that was provided to them. We also assume that they considered it their role to provide learning experiences that elicit intrinsic interest in the course content so as to engender deep-level processing. A further assumption is that these teachers expected from their students that they invest effort and take responsibility for learning. All these expectations about the student role presuppose that college students have realistic expectations of task demands and have easy access to the necessary self-regulation strategies to work their way through the course. Is this a realistic role expectation? We will address this question in the following sections. Students’ Conceptualisations of the New Learner Role Winne (1995) described the self-regulation strategies that undergraduates need to have access to in great detail. In his view, self-regulating college students are able to seek and retrieve information in the domain of the task. They set their own learning goals and monitor their task engagement. They are capable of fine-tuning, redrawing strategic plans, and identifying deviations from the path they had planned to follow. They are also capable of revising their domain knowledge and beliefs about competence as well as dealing with obstacles. In their commentary on Winne’s paper, both Boekaerts (1995) and Corno (1995) argued that not all college students display this rich repertoire of self-regulation strategies.

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Many college students still expect their teachers to specify the content of the curriculum, arrange learning units and activities in a sequential order, give assignments and assess them, and generally design the learning environment in such a way that they perceive the learning content as personally relevant and the context as supportive for the development of their knowledge and skills. Our argument here is that undergraduates bring epistemological beliefs to the classroom (e.g., about their own role and about the complementary teacher role) and that these beliefs about what learning at university entails affect their strategy use quasi-automatically. What does the literature say about this issue? Schommer (1990) studied college students’ epistemological beliefs and reported that the quality of undergraduates’ writing products was predicted by their belief about the ease and quickness of learning. Entwistle (2003) addressed the following two questions: ‘Why is it difficult for students to adopt a deep level approach to learning and why do college students revert to the use of shallow cognitive strategies after they have practiced the use of deep level processing strategies?’ Recall that we are talking about higher education students who have proven to be able to adopt deep-level learning strategies. On the basis of their results, these researchers argued that college teachers need to be aware that not all students want to achieve a deep understanding of the material. Students who do not value the material discussed in the lecture or in the textbook tend to process it in a superficial way, either adopting a surface-level approach (i.e., students tend to take minimal account of the course demands and they rely on syllabus-bound accretion of information, using routine memorization and procedural learning) or a strategic approach (i.e., students strive for high grades by organizing their study time with effective time management and monitoring). These two approaches stand in sharp contrast to the deep-level approach that Winne (1995) described, and as already indicated in the first section of this chapter, causing many disappointing results in (innovations of) higher education. Another reason why college students revert to surface-level processing strategies and to external forms of regulation is summarized in the statement: teachers only value the products of learning and not the learning process itself. Winne (1995) explained that many college students do not consistently use the newly acquired strategies because they consider them time consuming (these strategies do not run on autopilot yet) and because they are not convinced that these strategies will always work (the students have not built up the necessary selfconfidence). In short, most students produce the results that the teacher rewards and adapt their strategies to fit the teachers’ rewards. Hence, students’ perception of the assessment plays an important role and should be aligned with the behaviour that is required. For example, students might fall back on memorization when teachers set multiple-choice questions or questions that do not require insightful deliberation (Martens et al., 2004). It is essential that teachers in higher education who want to try out new teaching methods have insight into the reason why students might fall back on old habits. In the next section we will address the motivational components that might affect their conscious or unconscious choices.

Components Involved in Motivated Learning Many studies have examined how cognition and motivation work together to determine learning processes in higher education contexts such as the college classroom and preservice training. Some investigators focused primarily on deep-rooted motivational aptitudes

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that are activated in the learning situation (such as psychological needs, values, epistemological beliefs about a domain, future time perspective, personal goals, and individual interest). They argued that learning activities that go back on these deep-rooted aptitudes are pleasurable while activities that conflict with these needs, values, beliefs, interest, and goals are frustrating and uncomfortable. Other researchers have taken a different perspective. They focused on the motivational beliefs that impact on strategy use and still other researchers studied the actual perceptions or appraisals that students have of learning tasks and situations. Whatever perspective researchers take, motivation always influences upcoming and ongoing actions in three basic ways: it affects the direction of students’ actions or the choices they make (what events, situations, and facts do they opt to act on), the intensity of their actions (based on the value that they have attached to the learning activities), and the effort they are prepared to invest over time in the pursuit of their actions. In the next three sections we will address (1) the motivational beliefs that affect strategy use, (2) the motivational conditions for meaningful learning, and (3) fulfilment of psychological needs during the learning process. First, we will give a description of the motivated behaviour of two undergraduates, so that the reader will have a better understanding of the related concepts we will be dealing with. Glynnis and Tessa are two undergraduates in educational psychology, who enrolled in a new course. They both want to become school advisors and have developed an interest in children with learning problems. They are practically oriented and motivated to read books about how to help children learn more effectively. Glynnis and Tessa were surprised to hear during their first class meeting that students had to take on the responsibility for their own learning (i.e., the class was set up according to the principles of social constructivism and they were unfamiliar with this type of instruction). They had to read three scientific articles for next week’s class. After class, Glynnis told Tessa that she felt irritated when she heard that the class would be divided into groups in order to learn from and with each other. She teamed up with three girls she hardly knew and they had more or less forced her to agree to meet on Monday morning to discuss the content of the three articles. At the start of the second meeting, the teacher asked the students to write down in detail how they had prepared for class. This is what Glynnis wrote: “I first made a plan of action. I decided that I would read the longer article on Friday afternoon and the two shorter ones on Saturday morning. On Saturday afternoon I planned to make a summary of the three articles. However, on Friday afternoon I quickly discovered that the first article was very dense and that I could not grasp the meaning after first reading. I kept telling myself that I could do it, so I slowed down my pace and started highlighting the main points in the text. I felt more confident when I read my summary of the major points that I had extracted from the first part of the text. I also got more interested in what I read because I could now see that

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the information was relevant for helping problem students learn. On Saturday morning, I was quite happy when I discovered that the two shorter articles were more easy to read and that I had some time left to re-read the first article and link the practical ideas and suggestions made in the third article to the theoretical remarks made in the first one.” Tessa wrote: “The first article was very difficult. I was disappointed that the information was not readily applicable, even though the teacher had assured us that it was highly relevant for building up our professional competence. I fought my way through the first two pages. I felt that I did not understand half of the stuff and that I could not concentrate. I must admit that I was distracted by the travel magazines on my table and that thinking of holidays made me feel low on energy. I went downstairs to talk to my house mates. They asked me to go shopping with them. I denied the offer because I needed to work. I went back upstairs with a pot of coffee and I deliberately put the travel magazines out of sight. I half heartedly started reading but the feeling of difficulty popped up again as soon as I started reading the text. After half an hour reading I felt tense. I was thinking that the course was well above my limits and that I should consider switching courses. Then Robin rang me. He had had a similar experience but informed me that the two shorter articles were easier to read. He advised me to read them first and then go back to the longer article because it would make far more sense then. On Sunday morning I went back to the difficult text. I still found it hard to concentrate but I made reading more interesting by linking the theory to the practical examples in the second article. I managed to make the summary as I had promised my team mates. I did not want to let them down for I needed their help with my statistics exam.”

Motivation Components Associated With Effective Strategy Use Pintrich (2000, 2003) set out to identify the types of cognitive and self-regulation strategies that undergraduates use to comply with task demands such as the ones given in the two above vignettes. In order to understand a piece of text or a lecture, students make use of three types of strategies, namely rehearsal, elaboration, and organizational strategies. Use of the latter two strategies was associated with deeper understanding than use of rehearsal strategies alone. Pintrich’s research indicated that undergraduates’ use of the three types of strategies is influenced by the value they attach to the learning goals, their goal orientation, and the confidence they have that they can make progress under the current learning conditions. One of the most robust findings is the link between self-efficacy and the quality of strategy use (Pintrich, 2000). Undergraduates who build up confidence in their cognitive skills alongside the proceduralization of these skills express positive feelings about their ability to use these skills. Pintrich found that students who expressed that they would do well in the course (high self-efficacy) were more cognitively involved in trying to master the learning material, reported the use of

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all three types of cognitive strategies (rehearsal, elaboration, organization), engaged in planning, monitoring, and steering their own learning process, and obtained a higher overall final grade. Positive relations were also found between students’ perception of task value (i.e., how important they find a learning task, how interested they are in the material, how useful they think the learned skill is for future use) and their use of effective cognitive and self-regulation strategies. The relationships between task value and performance measures were also positive but they were not as strong as with self-efficacy. Pintrich and his colleagues also showed consistent positive relations between students’ goal orientation and their strategy use; college students who set themselves mastery goals – meaning that they strive for improvement and learning — were more likely to make use of their cognitive and self-regulation strategies than students who just wanted to get good grades. Admittedly, adopting grade goals might come at a cost in terms of anxiety and negative affect. Current findings suggest that undergraduates’ motivational beliefs and conceptualization of the new learner role — and the type of strategy use this implies — are crucial aspects of the new learning environments. This information is not new. What is new, though, is that student beliefs are considered to be domain-specific, changeable, and under the influence of the students’ perceptions of the quality of learning environment. Ever increasing evidence confirms that contextual factors determine to a large extent whether or not students are motivated to learn (i.e., form a learning intention) and also whether they are prepared to control and manage various aspects of the learning process and learning environment in order to achieve the learning goals (i.e., exercise volitional control). We will discuss the strategies that students use to self-regulate their motivation and effort later. Now, we will illustrate that environmental conditions exert an influence on students’ goaldirected behaviour. Motivational Conditions for Meaningful Learning Substantial evidence links characteristics of the social learning environment to learning outcomes and students’ well-being. Several researchers have shown that higher education students who do not feel well integrated into the social learning environment are at risk to obtain poor results and even drop out of the system (Beekhoven, 2002). It is important to realize that a social learning environment can be a virtual place, such as a virtual company, and may even refer to some students sharing ideas in computer supported collaborative learning (CSCL). Similar motivational processes are at work in diverse social contexts. For example, the CSCL process can be hindered by ineffective supervisors or suboptimal group processes (e.g. Strijbos et al., 2004). It seems that feedback designed to help college students acquire academic skills is important in all contexts. Kitsantas and Zimmerman (1999) showed that it increased the quality of the undergraduates’ writing skill as well as their self-efficacy beliefs and satisfaction with their performance. Several researchers described the instructional conditions and social practices that play an important role in fostering or undermining the effort that students are willing to invest. It has long been established that specific aspects of the teaching–learning environment,

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particularly the quality of instruction, have a direct positive or negative effect on learning outcomes. Clarity and pace of instruction and the type and amount of structure provided are prominent examples. Entwistle (2003) also found that teacher enthusiasm and empathy as well as a thorough explanation of the material that links directly to students’ current understanding affect the learning outcomes positively. Some teacher behaviour has been linked with suboptimal student performance, such as being humourless, unfair, expressing low expectations in students’ capacity, presenting them with irrelevant assignments, and being too controlling (Filak & Sheldon, 2003; Skinner & Belmont, 1993). The experiences that students have had with different instructional methods in the past trigger expectancies and affects in similar situations. These cognitions and affects might have a profound effect on students’ perceptions, the choices they make, the intensity of their actions, and the effort they are prepared to invest. Pekrun, Goetz, Titz, and Perry (2002) studied the emotions that are triggered in academic settings, such as joy, boredom, hopelessness, anxiety, anger, and feeling relaxed and relieved. They showed that arousal experienced in the classroom is labelled differently by different students and provides motivational and physiological energy by triggering action-related goals and intentions. Recall that in the above second vignette, Tessa felt relieved that she could keep a promise made to her teammates. When triggered, expectations and emotions serve the function of preparing and sustaining students’ reactions to important upcoming and ongoing activities, and directing their attention to salient cues in the learning environment (Boekaerts, 2003; in press). Fredrickson (2001) showed that some cues may raise the level of arousal in all students (e.g., speaking in public) but that it is the students’ interpretation of the arousal in terms of negative or positive emotions (e.g., anxiety, worry, anticipated pride) that affects the outcomes. The performance of individuals who tend to interpret felt arousal as negative, will be more impeded than the performance of students who experience both positive and negative emotions. Recall that Glynnis felt irritated by the teacher’s request to work in small groups. Apparently, she considered group work a suboptimal condition for learning in the college classroom and the mere mention of the event triggered negative affect. Glynnis found the first article difficult, but the feeling of difficulty did not trigger negative emotions. On the contrary, she made the choice to go slower and highlight the most important points in the text. The fact that she could generate a concrete action plan to deal with this taxing situation made her feel more confident. Glynnis also experienced positive emotions when she discovered that the information in the text had practical value for her. Tessa also made several choices; she declined an offer from her housemates to go shopping despite the fact that she felt fed up with reading the text. She as well experienced a feeling of difficulty but persisted for half an hour, at which time she felt tensed. Her anxiety triggered low expectations and she even considered giving up the course. Her appraisal of the learning situation was suboptimal at that point but a social event, namely Robin ringing her, changed her emotional state from negative to positive and provided new energy to continue with the assignment. She even developed an interest in the assignment when she discovered that Robin was right and that the two other articles were easier to read. On Sunday, Tessa persisted on the task because she did not want to lose her friends’

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social support. It is evident from these examples, that students make many choices during the learning process, and this is the topic of the next section. Fulfilment of Psychological Needs during the Learning Process Students who have developed an individual interest in a course are intrinsically motivated, meaning that they have identified their own learning goals in relation to the course and made these goals part of their long-term strivings. It is important to realize that adopting the learning goals of a course as one’s own necessarily implies that students have identified these goals as coherent with their values, interests, and psychological needs or with their current concept of ‘Self’. Deci and Ryan (1985) and Ryan and Deci (2000) placed the origin of students’ motivation in three basic psychological needs, namely, the need for competence, autonomy, and social relatedness. They found that learning conditions that satisfy these three basic psychological needs foster positive emotions and active, constructive task engagement whereas learning conditions that frustrate these needs trigger negative emotions and passive behaviour. The next sections will describe these basic needs. The impact of choice According to Levesque, Zuehlke, Stanek, and Ryan (2004) psychological needs are essential for psychological growth and well-being. Evidence suggests that students will naturally tend towards contexts, activities, and relationships that support the satisfaction of these needs (Ryan & Deci, 2000). Deci and Ryan (1985) showed that feeling to be an origin rather than a pawn is an important motivational condition for meaningful learning. Students must have opportunities to set themselves demanding but realistic tasks (tasks that are within their zone of proximal development) in order to experience personal causation, they need to experience firsthand what their own strengths (self efficacy) and weaknesses are and learn ways to handle these weaknesses. An important aspect of the life of college students involves completing coursework, being successful in their studies, and working towards a degree. Accordingly, it is assumed that satisfaction of the need for autonomy and competence are essential for college students’ growth and subjective well-being. Levesque et al. (2004) reported that contexts that support autonomy (e.g., absence of perceived pressure) and competence perception (e.g., through positive informational feedback) increased the well-being and intrinsic motivation of both German and American university students. Nichols (2004) also described the positive effect of perceived autonomy. Their conclusions all went in the same direction: the more autonomy students perceive, the higher their intrinsic motivation. Boekaerts and Minnaert (in press) studied undergraduates’ developing interest in a 14week-long introductory course in Education that was set up according to the principles of social constructivism. Students had to learn from and with each other while working in small groups on assignments designed to explore the resource material. The hypothesis was that students would develop an interest in the course over time and that their developing interest would be affected jointly by the beliefs they held about learning in small groups and their actual experiences in the college classroom, measured in terms of the fulfilment of their psychological needs. In accordance with Self-Determination theory, Boekaerts and Minnaert found that inclines and declines in student interest were indeed

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largely due to the interest they had generated in previous same-topic sessions as well as their perception of the local learning conditions in terms of the fulfilment of their psychological needs. Deci and Ryan (1985) gave the fulfilment of the need for autonomy a primary role in the self-regulation process. They showed that students are more motivated (i.e., spend more time, show greater concentration, and invest more effort) to complete a task if they have chosen the task themselves than when they feel forced to do it. These researchers made a distinction between different types of behaviour regulation, namely intrinsic regulation, identified regulation, introjected regulation, and external regulation. Students whose behaviour is guided by their personal values, needs, and interests report that they inherently enjoy doing the task. Their behaviour is guided by intrinsic interest (intrinsic regulation). In contrast, students who do their course work because they want to stay out of trouble and avoid negative consequences, such as failure, reprimands, dropping out of class, are externally regulating their behaviour. In between these two extremes, Deci and Ryan located various forms of self-control. For example, students may engage in a task because not engaging in it would make them feel guilty (introjected regulation), or because they think that their actions may be instrumental to getting good results (identified regulation). Being interested in the task or activity is the prototypical form of intrinsic regulation. Learners who express a high degree of interest in a task or activity will actively and constructively engage in learning when there is a chance to realize or to further develop at least one of their valued interests (Lewalter & Krapp, 2004). In a similar vein Kuhl (2000) argued that individuals feel satisfied when they consider the goals that they pursue as coherent with their psychological needs or with their conception of ‘self’. These theorists reserved the term ‘self-regulation’ to refer to behaviour that supports the pursuit of one’s own goals and contrasted it to self-control, which refers to actions aimed at coping with pressing or taxing environmental demands rather than satisfying personal needs. Kuhl explained that negative affect is often associated with the pursuit of the latter type of goals, implying that students primarily focus their attention on the reduction of these negative emotional states. These coping processes cost processing capacity and interfere with the pursuit of students’ own goals (e.g., belongingness goals). It is important to note that self-control may often be necessary to complete a task and may, as such, be beneficial to learning. We will come back to this issue when we discuss volitional strategies. The impact of social relatedness and support Remarkably, little is known about the impact of fulfilment of the need for social relatedness in higher education. A feeling of belonging is a basic human need and belongingness has multiple and strong effects on emotional patterns and on cognitive processes (Ryan & Deci, 2000). Lack of belonging is linked to a variety of negative effects on health, adjustment, and well-being. Feelings of pride and respect that flow from definition of the self as a member of a group or community appear to be translated into greater loyalty to the group or community and enhanced compliance with the group rules. In the last decade, many researchers have argued that focusing on an individual student to describe and explain motivation and self-regulation ignores the impact of the

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social context on learning (e.g., Yowell & Smylie, 1999). These researchers emphasized that the development of interest and self-regulatory skills occurs through reciprocal interactions among students and teachers as elements of the social context. McCaslin and Hickey (2001) described the reciprocity between teacher and student(s) in terms of ‘co-regulation’. This form of shared responsibility refers to the various ways that teacher and peers can provide scaffolding support when it is needed. Various forms have been identified, including scaffolding for understanding, autonomy, and positive classroom climate.

Motivation and Volition as Integral Parts of Self-Regulation Earlier we argued that teachers in higher education who try out new teaching methods need to have insight into the reasons why students might fall back on old habits. Teachers assume that students are agents who rely on their own learning history to guide their behaviour in the classroom. They also assume that students have access to a set of wellfunctioning strategies for learning. At this point we want to remark that both assumptions are questionable. Many teachers, educators, and researchers have confused students’ behavioral intentions (wishes, expectancies, goals) with their ability to translate intentions into actions. There is indeed a big difference between wanting to do something and actively pursuing that goal. For example, Tessa may intend to prepare well for a test or for class but refrain from doing so because competing goals prevent her from investing the required effort (e.g., her housemates ask her to go shopping). Also, students may be convinced that it is worthwhile to invest time and effort in learning but they may lack the self-regulatory strategies to implement their intention. We are alluding here to the difference between motivation and strategic behaviour to get the job done. Gollwitzer (1990) and his colleagues illustrated this distinction with the Rubicon metaphor. They described the link between motivation (the goal-setting) and volition (the goal-striving stage) as a path connecting two sides of a river representing commitment. Goal-setting processes are considered to precede commitment. These processes refer to the individuals’ conscious and preconscious attempts to transform a motivational state into an intention to act. When arriving at the other side of the river, implementation strategies are in order to carry out the intention. Students who intend to cross the Rubicon may be firmly committed to do so and may even have activated the necessary action plans. However, when they start crossing the river they might discover that these action plans are inappropriate or incomplete because the conditions or task characteristics they have anticipated are inaccurate. For example, a text may be more difficult or more boring to read than expected, or there is no Internet access. Another possibility is that the mental representation that the students made of the task when they were still on the other side of the river (motivation) may not have specified the possible distractions, obstacles, and breakdown of plans that could occur. This implies that the students should adapt their action plans, generating new scripts to deal adequately with the observed impediments. As previously argued, generating action plans ‘on the fly’ takes up processing capacity and interferes with the learning process per se. Boekaerts and Corno (in press) argued therefore that it is essential that students have easy

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access to volitional strategies before they start crossing the Rubicon. These strategies will be discussed next. Different Types of Volitional Strategies Corno (2004) described volitional strategies in terms of ‘good work habits’ and reported that weaker students find it hard to implement such strategies, particularly when difficult work must be completed. As mentioned previously, research exploring motivational beliefs found that students who have a strong focus on learning goals, have high levels of self-efficacy and attach value to the task are more likely to use effective cognitive and metacognitive strategies. A logical elaboration of these findings is that students who hold these favourable motivational beliefs automatically translate them into effective motivation strategies. Wolters and Rosenthal (2000) examined the relation between students’ motivational beliefs and their use of five specific motivational strategies, namely, environmental control (Tessa put the travel magazines out of sight), self-consequating (Tessa reminded herself that she needed to make a summary because she had promised her friends), interest-enhancement (Tessa made her reading more interesting by linking theory to practice), mastery self-talk (Glynnis: I kept telling myself that I could do it), and performance selftalk (e.g., making yourself work hard to outbest others). Wolters and Rosenthal showed that students who had a learning goal orientation were more likely to report using all five motivational self-regulation strategies. This finding suggests that students who engage in meaningful learning have the skill to scaffold their own motivation process (i.e., get on the growth pathway, that will be discussed below) and that they can overcome motivational problems (e.g., boredom, difficulty, distraction) when they occur. Boekaerts (in press) described the conditions that call for good work habits and she emphasized that teachers need (1) to scaffold their students’ skill to pick up the cues in the environment that signal distraction, obstacles, and taxing processing demands and may thus interfere with task completion, (2) to help their students design when–where plans that link these cues to effective volitional strategies, and (3) to provide sufficient practice to develop their students’ competence in using these plans. Where Are Motivation and Volition Strategies Located in the Self-Regulation System? Boekaerts’ dual processing self-regulation model (e.g., Boekaerts & Niemivirta, 2000) made a distinction between two parallel self-regulatory pathways, the mastery or growth pathway and the well-being pathway (see Figure 1). Students who have favourable appraisals about a task or assignment will start activity in the mastery or growth pathway. This implies that they perceive the task as congruent with their personal goals; the activity is then energized from top-down (i.e., from the students’ own values, needs, interests, and goals). When specific environmental or internal cues signal to students that there is a mismatch between the task and their personal goals, they start activity in the well-being pathway. What students think to do and what they actually do is then energized by bottom-up processing (i.e., by cue-driven processing with the purpose of preventing harm, threat, and loss). In later publications (Boekaerts, in press, and Boekaerts and Corno, in press), the model was elaborated with a pathway that connected the two original pathways. It was argued

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(Meta)cognitive strategy use

Learning intention

Motivational beliefs

Working Memory

Appraisal pp

Affect

Assessment

Growth pathway

Well-being pathway

Figure 1: Dual processing self-regulation model (Boekaerts, 2005). that students who have easy access to volitional strategies use these strategies to stay on the mastery pathway and to re-route activity from the well-being pathway to the growth pathway. Hence, volitional strategies or good work habits are conceptualised as a switching track between the growth pathway and the well-being pathway. Evidence is accumulating that students’ conscious and unconscious decisions to raise or to lower effort during the learning process are located in the self-regulation system at the level of volitional strategies. Several researchers (e.g., Corno, 2004; Wolters & Rosenthal, 2000) argued that volitional strategies to stay on the growth pathway or get off the well-being pathway, come at a cost. Using volitional strategies to support top-down self-regulation is considered to be effortful (recall Glynnis’ and Tessa’s example). Likewise, recovering from emotions and redirecting attention to the learning task is effortful. In this respect, Turner and Schallert (2001) showed that students who experience emotions and who are more concerned with restoring their well-being than with learning can move into the growth direction, provided they (re)appraise the goal as instrumental, and call upon volitional strategies to prevent unproductive rumination about the causes of the emotion. Baumeister and Eppes (2005) also showed that students who had to focus on their emotions and make an attempt to control them tended to give up faster on a successive task than those who did not have to control their emotions. These researchers suggested that the self-regulation strategies that are needed to control emotions interfere with active engagement and persistence on a task, unless the spent energy is restored. Students who had to resist to temptation (e.g., refrain from eating chocolates during the experiment) tended to give up faster on solving a difficult puzzle than either students who had not been tempted with chocolates or those who had been allowed to eat them. It seems that the effort needed to resist temptation interacted with the effort needed to persist on the task. This finding

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clearly points in the direction of possible intervention strategies, which will be addressed in the next section.

Interventions and Conclusions In the beginning of this chapter we referred to the ‘new learning’ or ‘competency-based’ reforms in higher education and we pointed to some disappointing results. Teachers and developers seem to lack insight in motivational processes or take these processes for granted. We will now touch on interventions, aimed at the student, learning environment, or teacher. In the first place we can change students’ motivational beliefs, strategies, and epistemological beliefs. Students can be trained to have better access to volitional strategies, and use these strategies to stay on the mastery pathway or re-route activity from the well-being pathway to the growth pathway. Rozendaal, Minnaert, and Boekaerts (2003) found that high anxiety and lack of confidence are associated with surface-level processing. Providing information to students about their mastery level and giving them clear guidelines, hints, and tips on how to proceed, might reduce anxiety. This may especially be the case in relation to ill-structured tasks. Another type of ‘motivational information’ that can be provided to students is information about the goals of a course (Husman, Derryberry, Crowson, & Lomax, 2004). Vansteenkiste, Simons, Lens, Sheldon, and Deci (2004) found that emphasizing intrinsic goals enhances intrinsic motivation and deep-level learning. In the second place, a learning environment should be designed more mindfully. Van Merriënboer and Martens (2002) stated that developers build in all kinds of multimedia in new learning environments in the hope to make these environments more stimulating. In fact, they only distract students from the learning content. Too many distracters come at a cost, for they require students to actively redirect their attention to the growth path. Wellstudied are changes in the learning environment that directly influence students’ perception of autonomy, relatedness, and competence. Many studies showed that handing over autonomy and control to students might have positive effects on effort and deep-level learning, provided students are able and willing to shoulder the responsibility for learning that comes with increased autonomy. In the third place, we need to look more closely at teacher skills. Filak and Sheldon (2003) found that teachers’ enthusiasm affects students’ interest in a subject matter: teachers with high intrinsic motivation have students with high intrinsic motivation. Interestingly, these teachers are not always the older or more experienced teachers. Filak and Sheldon found that teachers who are relatively unfamiliar with a course or a content domain are more intrinsically motivating to students. Teachers who had given the same course for many years suffer from what these researchers called the ‘course burn out effect’. Course rotation between teachers may be a good strategy to increase teachers’ and students’ motivation. This chapter provided ample examples of the fact that teachers and developers often lack insight into motivational processes. In line with Lowyck et al. (2004), we conclude that increasing number of researchers signal that educational innovations fail and that ‘new learning’ paradigms are by no means a guarantee for success. This chapter described what goes wrong when students’ motivation is neglected. Making teachers aware of how motivation processes operate in the college classroom or in virtual learning environments

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(e.g. by explaining to them the difference between motivation and volition) may be an effective way to scaffold the design of powerful learning environments. It is our hope that this chapter contributes to this important goal.

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Gulikers, J., Bastiaens, Th., & Martens, R. (2005). The surplus value of an authentic learning environment. Computers in Human Behaviour, 21, 509–521. Husman, J., Derryberry, W., Crowson, H., & Lomax, R. (2004). Instrumentality, task value, and intrinsic motivation: Making sense of their interdependence. Contemporary Educational Psychology, 29, 63–76. Järvelä, S., & Volet, S. (2004). Motivation in real-life, dynamic, and interactive learning environments: Stretching constructs and methodologies. European Psychologist, 9, 193–197. Kitsantas, A., & Zimmerman, B. J. (1999). Acquiring writing revision skill: Shifting from process to outcome self-regulatory goals. Journal of Educational Psychology, 91, 241–250. Kuhl, J. (2000). A functional design approach to motivation and self-regulation: The dynamics of personality systems and interactions. In: M. Boekaerts, P. Pintrich, & M. Zeidner (Eds), Handbook of self-regulation (pp. 111–163). San Diego, CA: Academic Press. Levesque, Ch., Zuehlke, A., Stanek, L., & Ryan, R. (2004). Autonomy and competence in German and American university students: A comparative study based on self-determination theory. Journal of Educational Psychology, 96, 68–84. Lewalter, D., & Krapp, A. (2004). The role of contextual conditions of vocational education for motivational orientations and emotional experiences. European Psychologist, 9, 210–221. Lodewyk, K. R., & Winne, Ph. H. (2005). Relations among the structure of learning tasks, achievement, and changes in self-efficacy in secondary students. Journal of Educational Psychology, 97, 3–12. Lowyck, J., Lehtinen, E., & Elen, J. (2004). Students’ perspectives on learning environments. International Journal of Educational Research, 41, 401–406. Martens, R., Gulikers. J., & Bastiaens, Th. (2004). The impact of intrinsic motivation on e-learning in authentic computer tasks. Journal of Computer Assisted Learning, 20, 368–376. Martens, R., Valcke, M., Poelmans, P., & Daal, M. (1996). Functions, use and effects of embedded support devices in printed distance learning materials. Learning and Instruction, 6, 77–93. McCaslin, M., & Hickey, D. T. (2001). Educational psychology, social constructivism, and educational practice. A case of emergent identity. Educational Psychologist, 36, 133–140. Nichols, J. D. (2004). Empowerment and relationships: A classroom model to enhance student motivation. Paper presented at the AERA 2004 conference, San Diego, CA. Pekrun, R., Goetz, Th., Titz, W., & Perry, R. P. (2002). Academic emotions in students’ self-regulated learning and achievement: A program of quantitative and qualitative research. Educational Psychologist, 37, 91–105. Pintrich, P. R. (2000). The role of goal orientation in self-regulated learning. In: M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds), Handbook of self-regulation (pp. 452–502). San Diego, CA: Academic Press. Pintrich, P. R. (2003). A motivational science perspective on the role of student motivation in learning and teaching contexts. Journal of Educational Psychology, 95, 667–686. Rozendaal, J. S., Minnaert, A., & Boekaerts, M. (2003). Motivation and self-regulated learning in secondary vocational education. Learning and Individual Differences, 13, 273–289. Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well being. American Psychologist, 55, 68–78. Schommer, M. (1990). Effects of belief about nature of knowledge on comprehension. Journal of Educational Psychology, 82, 489–504. Simons, R.-J., van der Linden, J., & Duffy, T. (2000). New learning. Dordrecht/Boston: Kluwer. Skinner, E. A., & Belmont, M. J. (1993). Motivation in the classroom: Reciprocal effects of teacher behavior and student engagement across the school year. Journal of Educational Psychology, 85, 571–581. Strijbos, J. W., Kirschner, P. A., & Martens, R. L. (Eds). (2004). What we know about CSCL in Higher Education. Dordrecht, NL: Kluwer.

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Turner, J. E., & Schallert, D. L. (2001) Expectancy-value relationships of shame reactions and shame resiliency. Journal of Educational Psychology, 93, 320–329. Van Merriënboer, J., Clark, R., & de Croock, M. (2002). Blueprints for complex learning: The 4C/ID-Model. Educational Technology, Research & Development, 50, 39–64. Van Merriënboer, J. J. G., & Martens, R. (2002). Computer-based tools for instructional design. Educational Technology, Research & Development, 50, 5–9. Vansteenkiste, M., Simons, J., Lens, W., Sheldon, K., & Deci, E. (2004). Motivating learning, performance, and persistence: The synergistic effects of intrinsic goal contents and autonomy-supportive contexts. Journal of Personality and Social Psychology, 87, 246–260. Vermetten, Y., Vermunt, J., & Lodewijks, J. (2002). Powerful learning environments? How university students differ in their response to instructional measures. Learning and Instruction, 12, 263–284. Winne, P. H. (1995). Inherent details in self-regulated learning. Educational Psychologist, 30, 173–187. Wolters, C. A., & Rosenthal, H. (2000). The relation between students’ motivational beliefs and their use of motivational regulation strategies. International Journal of Educational Research, 33, 801–820. Yowell, C.M., & Smylie, M.A. (1999). Self-regulation in democratic countries. Elementory School Journal, 99, 469– 490.

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Chapter 8

Student Learning in Context: Understanding the Phenomenon and the Person Noel Entwistle, Velda McCune, and Max Scheja

Introduction Many years ago, Cronbach (1975) described the gulf between psychologists who studied learning and those who studied individual differences. He urged psychologists to bridge that gulf, but the methodological divide is still affecting the direction of research on teaching and learning today, although there have been some studies that have brought together learning processes and individual differences (see, e.g., Lehtinen, Vauras, Salonen, Olkinuora, & Kinnunen, 1995). The two dominant strategies for investigating learning in the 1970s have been joined by others, with educational research moving away from its previous sole reliance on psychological theory and, methodologically, on experimental studies and large-scale surveys. Besides the introduction of sociocultural perspectives, theories of learning have been developed from naturalistic investigations within classrooms, and these have provided alternative conceptualisations which focus directly on the student’s perspective on learning, derived mainly from fine-grained analyses of interview data. The research on teaching and learning in higher education has used differing levels of conceptualisation, as well as contrasting methods of collecting and analysing data, all of which can lead to confusion in reporting research on student learning within university contexts. This chapter seeks to clarify these aspects and, in particular, to foreground the issue of levels of analysis in relation to the ways in which students perceive and conceptualise their experiences of teaching–learning environments, and how these perceptions affect their approaches to learning, study strategies, and learning processes. While drawing on the related literature, this chapter will focus on three specific studies, which will be used to illustrate more general trends in the research area.

Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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Differing Levels of Conceptualising Student Learning in Context At a broad level of conceptualisation, learning at university can be seen in terms of relatively stable conceptions of knowledge and learning that students develop and that influence their ways of studying. Perry’s (1970) work introduced a developmental scheme that suggested how students progress through a series of stages in their thinking about the nature of academic learning, moving from a belief that knowledge is fixed and certain to a recognition of relativism. Säljö (1982) described a similar progression in conceptions of learning as students move from seeing learning as building up knowledge incrementally, through a view of learning as acquiring meanings for themselves, to seeing learning in differentiated ways in relation to their purposes. This final stage involves a crucial transformation which makes students more alert to, and metacognitive about, their own ways of learning and studying (Entwistle, in press). Other work on student learning focused on the more specific ways in which students tackled a set task and led to the description of approaches to learning (see Marton & Säljö, 1997) with the distinction between a deep approach and a surface approach reflecting the transformation seen in conceptions of learning, but at a more specific level of analysis. The original studies by Marton and his colleagues not only drew attention to the importance of seeing learning from the student’s perspective, but also showed how the processes of learning depended on the student’s intention in approaching a task. Marton and his colleagues demonstrated convincingly that both context and content influenced the approach to learning (Fransson, 1977). However, subsequent research showed that approaches could be relatively stable, as students develop habitual ways of dealing with certain tasks (Entwistle & Ramsden, 1983). This relative stability allowed the development of questionnaire measures to operationalise the distinction between deep and surface approaches to learning through the use of Likert-type inventories, which were then extended to cover aspects of organising and monitoring study activities (Biggs, 1987; Entwistle & McCune, 2004; Vermunt, 1998). As the importance of the differing ways in which students perceive, and react to, the same context became clear, inventories were developed to measure specific aspects of students’ experiences of teaching–learning environments. Lowyck, Elen, and Clarebout (2005) have been exploring instructional conceptions, which they describe as generalised ways in which students come to view the learning environments they encounter. But much of the research has concentrated on a level equivalent to approaches, at which group differences in perceptions of teaching (Entwistle & Ramsden, 1983) can be identified between reactions to varying teaching–learning environments, while the range of distributions of these responses indicate substantial individual variations in those perceptions. Such inventories typically invite students to indicate the teaching–learning context and activities they have experienced. The Course Experience Questionnaire (Ramsden, 1991), for example, contains scales describing clear goals and standards, good teaching, appropriate workload, appropriate assessment, and a focus on generic skills. Behind this, and other such inventories, there is an idea of what represents high-quality teaching–learning environments, and that idea, as we have seen, is generally drawn from one or other of the current theories of learning and is often referred to as a powerful learning environment (De Corte, Verschaffel, Entwistle, & van Merriënboer, 2003; Verschaffel, De Corte, Kanselaar, & Valcke, 2005).

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Techniques of Data Collection and Analysis The research using inventories involves survey methods and multivariate techniques in looking at students’ responses at different levels of analysis. Some studies look at general patterns of relationship across subject areas, while others concentrate on a specific subject area or even a single course unit. The analyses can be carried out to focus on the scales created through factor analyses or, where appropriate, on responses to individual items. The questionnaire method does, however, limit the extent to which rich descriptions of the studying of individual students can be obtained. As the focus on student learning narrows further to look at individual students’ reactions to tasks, the research methods are more likely to involve interviews and qualitative analysis of the transcripts. Much research on student learning has drawn on the phenomenographic approach to qualitative research developed by Marton (1981). Phenomenographic interviewing uses an interview schedule to ensure coverage of certain topics, but without being constraining. It is carried out in a relaxed conversational style, with the students being encouraged progressively to reflect more deeply on their experiences (Entwistle, 1997; Marton & Booth, 1997). In research on studying, individuals are typically asked about specific pieces of work they have undertaken (to avoid vague general statements), how they approached them, and why they used those methods. The relaxed interviewing style allows students to bring in additional aspects which they feel are salient, but had not been covered in the original schedule. Analysis of the interview transcripts seeks to identify major themes initially, and then to distinguish categories of description that indicate the varying ways in which students go about their work. In parallel with this approach, Halldén and his colleagues at Stockholm University (Halldén, 1988, 1999; Scheja, 2002; Wistedt & Brattström, 2004) developed a conceptualisation of student learning which focused more closely on the tasks that students are given and the meanings that students give to those tasks. These studies aimed to describe how, and explain why, students interpret specific learning tasks in different ways, and what these variations in interpretations imply for learning in different subject areas. The basic tenet of this research approach is that learning can be seen as an intentional activity where students’ intentions and personal beliefs about their own learning capabilities, in relation to perceived demands of the teaching–learning environment, strongly influence the ways in which they tackle a particular learning task or subject area. Through an active interpretive process, students contextualise the task, i.e., they put the task into a personal context of meaning to make sense of it for themselves (Halldén, 1999; Scheja, 2002). As a result, learners who are confronted with the same learning task may end up working on what amounts to different problems. To investigate this view of student learning, problem sessions are often set up in which groups of students jointly solve a learning task confronting them in a particular teaching–learning setting, with these sessions being tape- or video-recorded. Individual interviews, similar to the phenomenographic approach, may also be carried out again using an open conversational style. Analyses of the data typically focus on the meanings that students’ ascribe to given tasks, and on the personal learning goals they develop on the basis of their contextualisations of the tasks and of the situation as a whole. There is no attempt, however, to establish strict categories of description, although the main differences in response are delineated looking across the individual cases.

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We now turn to the three specific studies used to illustrate differing levels of analysis. The first study presents quantitative analyses from a large-scale, national British project, along with illustrative comments from group interviews, while the other two studies involve in-depth interviews, one in Sweden using intentional analysis and the other in Scotland using phenomenographic interviewing. Both these studies also used case studies of individual students to explore the complexities and the idiosyncratic nature of the influences on student learning.

Perceptions of Course Units and Approaches to Studying Background to the Study The first study is a large-scale investigation of teaching and learning across four contrasting subject areas — Enhancing Teaching Learning Environments in Undergraduate Courses (ETL project) within the Teaching and Learning Research Programme (TLRP) of the British ESRC (McCune & Hounsell, 2005, with working papers also at http://www.ed.ac.uk/etl). The main intention of this project has been to explore ways of enhancing teaching–learning environments in undergraduate courses in collaboration with teaching staff teaching specific modules (course units). At the start of each module, students completed a Learning and Studying Questionnaire, which asked students about their reasons for being in higher education and how they had been studying in that subject area. At the end of the unit, they filled in an Experiences of Teaching and Learning Questionnaire, which covered the perceived demands made by the unit, the students’ experiences of teaching (including the whole teaching–learning environment), and what they felt they had gained in terms of knowledge and skills. The questionnaire items describing experiences of teaching were drawn from the literature to describe a high-quality, or powerful, teaching–learning environment (De Corte et al., 2003), and were based in part on constructivist theory (Tynjälä, 1997; Vermetten, 1999). Complete data were collected from 1,950 students across the four subject areas. At the end of each unit, small groups of students were asked to discuss openly their experiences and the transcribed interviews were analysed to bring out the main themes mentioned. Here, one subject area — electronic engineering — will be used to illustrate the different levels of analyses carried out in looking at the relationships between perceptions of teaching and approaches to studying. Relationships Between Perceptions of Teaching and Approaches to Learning and Studying These analyses, although carried out at different levels, are based on a single level of conceptualisation relating to students’ perceptions of teaching and their approaches to learning and studying. The general relationships between perceptions of teaching and approaches to learning have already been well established using a variety of measures (e.g. Kreber, 2003; Richardson, 2005; Vermetten, Vermunt, & Lodewijks, 2002). All these studies indicate that perceptions of high-quality teaching–learning environments are associated with a greater reported use of deep approaches to learning. While the chain of causality is

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often assumed to extend from teaching to approaches and so on to achievement, there is other evidence that shows that pre-existing approaches also influence the perceptions of teaching. In the ETL project, at the broadest level of analysis, the whole sample was used to establish the relationships between the scales used in the two questionnaires. The first step was to explore the dimensionality of the various sections of the two questionnaires. Besides the deep approach and the surface approach, there was a composite factor showing the organised effort put into studying. Within perceptions of teaching, six main factors emerged — interest and enjoyment, clarity and coherence, encouraging learning, set work and feedback, staff enthusiasm and support, and student support. The first factor reflects the students’ general attitudes to the course unit, while the remaining five describe perceived aspects of a high-quality teaching–learning environment. Multivariate analyses have been carried out in the project, showing the expected general links between approaches to studying and perceptions of the teaching–learning environment, and also correlational analyses which show the specific relationships between individual scales (Entwistle, Nisbet, & Bromage, 2005). Substantial positive correlations were found between deep approach, organised effort, and learning outcomes, measured towards the end of the target units, and the main descriptors of a supportive teaching–learning environment, namely ‘encouraging (deep) learning’, ‘clarity and coherence’ of aims with teaching approaches, and the support for students provided through ‘set work and feedback’. These scales were equally strongly correlated, negatively, with surface approach. This pattern was also shown with ‘staff enthusiasm and support’ and ‘student support’, but less strongly. It was also found, however, that there were equivalent correlations, although with much lower coefficients, with approaches measured before the course unit began. Along with strong test–retest correlations between equivalent approach scales, these findings not only indicate that approaches have a certain consistency, through having become habitual, but also that they are clearly affected by the extent to which the teaching–learning environment is perceived to be supportive. These correlations across the whole sample do not, however, show the nature of the relationships, which can be seen more clearly by reducing the level of analysis through looking at students’ reactions to specific course units. Table 1 uses analyses of three contrasting course units in electronic engineering to examine the changes in mean scores on approaches to studying in relation to the percentage agreement with specific items describing perceptions of the teaching–learning environment (Entwistle et al., 2005). The mean change scores indicate that in Module A students reported a marked shift in their approach from deep towards surface, with a decrease in organised effort. Module B showed little change except for some decrease in organised effort, while Module C showed a totally different pattern with strong increases in deep and decreases in surface approaches. Students’ perceptions of the teaching–learning environment indicate possible reasons for these contrasting approaches to learning and studying. Three-quarters of the students in Module A and over half of those in Module B reported that the rate at which material had been introduced was too fast, while that was true for under a quarter of students in Module C. The perceived difficulty level showed even stronger differences with only 16% of students in Module A suggesting that the ideas and problems were easy. In both the second-year units, two thirds of the students thought the amount of work required was

Difference in mean scores 0.09 0.34 0.05 ⫺0.49 ⫺0.16 0.20 Percentage agreement with items

25.3 16.0 33.3

46.9 34.7 34.7

72.5 42.5 52.5

Experiences of the teaching provided in the course unit I found most of what I learned in this course unit really interesting How this unit was taught fitted in with what we were supposed to learn Plenty of examples and illustrations were given to help us to grasp things The teaching encourage me to rethink my understanding of some aspects Staff gave me the support I needed to help me complete the set work The feedback given on my set work helped to clarify things

45.3 72.0 66.7 60.0 69.3 63.7

34.7 67.3 51.0 67.3 51.0 30.6

82.5 97.5 95.0 72.5 75.0 47.5

Self-ratings of learning outcomes Knowledge and understanding about the topics covered

73.3

69.4

92.5

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Perceived easiness of the demands made by the unit The rate at which new material was introduced was easy The ideas and problems I had to deal with were easy The amount of work I was expected to do was easy

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⫺0.22 0.40 ⫺0.20

3rd Module C (N = 40)

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Deep approach Surface approach Organised effort in studying

2nd Module B (N = 49)

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Scales and items

2nd Module A (N = 75)

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Year of course within electronic engineering degrees

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Table 1: Difference in mean scale scores for approaches to studying between those prior to unit and those during unit and percentage agreement with items describing perceptions of the teaching–learning environment in three contrasting modules (A, B and C).

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demanding and a substantial proportion, particularly in Module B, did not find the work interesting. Generally, Module C attracted much more favourable responses, with the exception of the feedback provided, which was low also in Module B. Module A, in contrast, provided good feedback, along with support for set work and sufficient examples for a majority of students. Analysis of the group interviews showed that the fast pace in presenting new ideas in the lectures had affected students’ confidence in their understanding of the subject which, in turn, affected the effort they put into their work. From the students’ perspective, at least, the chain of causality, leading from experiences of teaching to a surface approach, was clear. At the beginning I was all [at sea], sort of too much information at one time… It seemed that once we’d gone over one specific network that we weren’t really given enough time to absorb the information before we were given another one, and the difficulty level increased as you went onwards. You have to focus your energy where it’s [rewarded]… You work through the tutorial problems and, for the analogue ones, you don’t get any answers out of them. I tended to [work] blindly: I knew if I [just] followed these steps, then I could come to an answer… We can teach ourselves… to do an example and have no idea what to do and we scrape by. But we probably would have got great marks had we actually understood what we were doing. The feeling indicated in the second of these extracts also reflects a phenomenon that had been identified earlier by Scheja (2002, 2006), which he labelled delayed understanding and can be seen more clearly in a comment made by a third-year student. In second year I got a better understanding of what I learnt in first year. Now in third year I’ve kind of learnt what I was supposed to know in second year. It’s a shame that I’ve never felt that I’ve learned it in the actual year [it was taught]… When you’re being taught something, you’re just desperately trying to learn it, and there’s not necessarily a whole lot of interest. You’re scrambling back to notes [in preparing for the exams], trying to understand the course. [Later on], you do get interested and [then] things start to fall into place.

Students’ Individual Contextualisations of Their Study Situation Background to the Study The first of the two interview studies investigated first-year students’ experiences of studying computer science and electronic engineering in a Swedish university of technology (Scheja, 2002, 2006). This study used an open-ended questionnaire and individual interviews to explore students’ contextualisations of their study situation. The open-ended questionnaire was used to provide an overview of first-year study experiences, focusing specifically on the students’ individual study situation and on the perceived conditions for learning and studying,

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with an invitation to take part in a subsequent interview. Of the 86 students who answered the open-ended questionnaire, 34 volunteered for interviews. On the basis of their written responses, 15 of the students were then chosen strategically to focus on the main themes emerging from the initial comments. The lengthy interviews explored the students’ experiences of studying and learning during the first year in depth, with a particular focus on how they had experienced and dealt with the demands of the teaching–learning environment. Individual Coping Strategies within a Demanding Teaching–Learning Environment An initial analysis of the written descriptions identified the main theme as being a concern about the pressure of work being experienced. Like the British second-year students, the Swedish students felt that the pace at which the material was being introduced was too fast and there were clear examples of delayed understanding (Scheja, 2006). As a result, most of the students felt they were falling out of phase with the work they had to do. Feeling overwhelmed with the work and disillusioned by their lack of understanding, not surprisingly, they became uncomfortably anxious. One of the computer studies students spoke for other students on the course, explaining that Everybody talks about [that course] saying that it’s virtually impossible to pass the exam, and the pace of the lectures is mental. Everything is so theoretically abstract that finally you don’t understand a thing… you don’t get much out of [the lectures] really. You just sit there looking at the blackboard, perhaps jotting down a few notes; you don’t know what they are talking about. Time is very scarce here… I could easily study twenty-four hours a day, but of course I don’t. When I come home I’m usually too tired to study. I often study over the weekends… I probably need to study more than I do, but what would happen to my spare time if I did? I [still] feel stressed and anxious about not studying enough, and I have fallen behind in several courses. The advantage of using individual interviews, unlike the group interviews in the ETL project, was that the individual reactions of the students to their situation could be explored more fully. The students were mostly highly motivated and worked out their own ways of coping, with three distinguishable ways of relating to their teaching–learning environment being identified among the sample, as follows. Exertion and perseverance (N = 2) These students basically saw studying as a question of disciplining themselves into putting a great deal of effort into carrying out the academic work in order to successfully deal with the perceived demands of the teaching–learning environment: I prefer to study alone. I have a method. I use a timer and then I solve problems for 50 minutes… You mustn’t give up when things start to get difficult… You have to push your way through [enough] problems [to)] pass the exams; then you’ll understand.

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Trying to keep in phase by seeking help (N = 10) For the majority of the students interviewed, their relation to the teaching–learning environment involved taking remedial measures to try to stay in phase with the course schedule, mainly by seeking help from other students. When you attend all the lectures, and go home and read through everything, … and you do all the problems recommended in the course schedule; that’s being in phase. [But the teaching] went really fast, so you could feel yourself falling behind… its hopeless. … You often have to get help from others … and that sometimes leads to copying. Autonomy and independent action (N ⫽ 3) While recognising the need to keep up with the study pace, these students nevertheless sought to detach themselves from the immediate study setting with its underlying demands, preferring to work with a certain degree of independence: I attend those lectures I’ll get something out of. I don’t bother to go to the other lectures. It’s pointless to sit there trying to understand, when you can’t understand anything… What I do is to track down my old books from school and try to find the chapter corresponding to the part we’re studying, . . . [then I can understand] what it was about. The focus of the analysis was narrowed even further by carrying out an intentional analysis (Ryve, 2004; Scheja, 2002). Through this analysis, students’ ways of accounting for their experiences could be set in a personal context which explained their strategies in terms of their intentions, beliefs, and actions as described in the interviews, and so indirectly revealed their contextualisations of studying. Looking at one student, as an example of a case study, ‘John’ who was categorised as showing ‘autonomy and independent action’, his personal contextualisation of studying in engineering could be captured by focusing on his intention, belief, and action. – Intention: To cope successfully with first-year engineering; – Belief: It is necessary to preserve autonomy in academic work: It feels a bit absurd that, when you’re studying you have to stuff everything into your head so quickly that the knowledge doesn’t stick. And then you have to start something new and something new, ... and you have to keep up a high study pace. – Action: Sets up a personal agenda rather than keeping to a course schedule: [If] you’re really ambitious, you will study every day and never have any spare time. But I could never be like that. You have to lead a happy life… studying comes secondary to that. You have to draw the line somewhere. John’s contextualisation of his studies thus involved an ambition not only to develop personal understanding of the subject matter, but also to strike a successful balance

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between studying and everyday life. While acknowledging the pressures potentially involved in studying within a constraining teaching–learning environment, John did not believe that studying in phase was a necessary requirement for success; other values seemed to be much more important to him, and he frequently expressed a conception of studying that involved developing a personally reassuring understanding of the learning material. By strategically avoiding unrewarding lectures, he could find more time to reflect on the subject matter and to develop that personal understanding; it involved setting up a personal agenda for studying and sticking to it whatever the pressures from the teaching–learning environment. From the overall analyses reported elsewhere (Scheja, 2002), it was found that the differing coping strategies could all be understood in terms of the students’ personal contextualisations of their studies, involving particular intentions and beliefs. This study thus demonstrated the advantage of individual interviews in seeing how students make sense of their own actions as they try to cope with a very demanding teaching–learning environment.

Developmental, Contextual, and Biographical Aspects of Learning Background to the Study The second of the two small-scale studies was carried out in Scotland with first-year undergraduate psychology students (McCune, 2000, 2004), and was intended to provide a rich account of the development of the students’ ways of learning, and perspectives on learning, and how these developed during their first year at university. Nineteen students were each interviewed on three occasions: First, at the beginning of their first year of undergraduate study; then, after their first piece of assessed academic work; and, finally, towards the end of the semester. The interviews were carried out using a phenomenographic approach and were analysed, firstly, for broad themes and categories and then at the level of detailed case studies. Why Students May Not Respond to Opportunities for Developing a Deep Approach Using phenomenographic analysis of the transcripts, it was possible to identify a series of themes related to the conceptions that seemed to underlie the students’ approaches to essay writing. These described the extent to which different students were taking account of the main aspects that their tutors were expecting in a psychology essay, namely a correct use of evidence in presenting arguments, a clear logical structure running through the essay, and an appropriate use of evidence in drawing conclusions. For each of these aspects, a hierarchy of categories was established which indicated progression towards a conception suggesting a deep approach to essay writing (McCune, 2004), as shown in Table 2 for one of these aspects. Interviewing at three different stages in the first year was expected to reveal progress towards more sophisticated conceptions of essay writing, but rather little development was actually found. Tutors provided written feedback on the essays intended to guide students towards ways of writing that would indicate the psychological ways of thinking expected,

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Table 2: Hierarchy of categories — students’ descriptions of using evidence in essays. Using evidence to support arguments — students explain that evidence is used to support or evaluate arguments, with none of the difficulties expressed in the ‘precursor’ category below. Precursors to using evidence to support arguments — students note that it is necessary to make evaluation of viewpoints, but they express various difficulties in relation to doing this. Including different viewpoints — students suggest that different viewpoints or arguments should be included in their essays, but they do not talk about evaluating these views. Vague ideas about evidence — students mention that research evidence needs to be used in essays, but give no explanation of how and why it should be used.

but students differed markedly in the use that they made of these comments. Some students clearly took notice of the suggestions made and decided for themselves what needed to be done. As one student commented: The first essay — that was the criticism — I hadn’t used enough references… [So] I drew on [lots] for my second essay and got a very good mark for that, so I tried again the same thing for the third one. Another student could not accept the criticism of her essay until the tutor read parts of it back to her. I was really excited about [the essay], but at the end of the day ... I was quite grumpy about the mark I got. I thought I had much better ideas than that ... Then you heard it [read] back and, well, I would have given myself exactly the same mark, if not lower, because it was really badly expressed. Other students seemed satisfied with the comments and the marks awarded and continued to write essays in the way they had done previously, thus showing little or no evidence of progression through the hierarchies. In certain cases, students knew what was important but simply could not put it into practice. The open nature of the interviews allowed students to explain at some length the reasons for their ways of studying, but the use of the categories constrained the analysis by failing to take account of other comments that explained the students’ study behaviour in more personal terms. As a result, a series of case studies was used to relate the ways of studying to the personal history of the individual. Details of the case studies can be found in McCune (2000, 2004), but can be illustrated here through the example of ‘Susan’ who was a mature student. Susan differed from most of the students interviewed as she saw a clear need to develop her learning and was keen to make these changes. Her willingness to develop seemed to

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come from a continuing lack of confidence in her current ways of learning, and a readiness to adapt and to ask for help. These reflected her previous learning experiences, but aspects of her self-image and her reasons for taking the course were also important. She appeared to see herself as someone who fought against difficulties rather than giving up; there were several instances during her interviews where she used the metaphor of learning at university as a battle to be fought. I literally scraped through (the multiple-choice examination) by the skin of my teeth and I was bitterly disappointed ... So, with renewed determination, I have come in to the Spring term ... There’s a lot of fight in me yet; I am not going to give up without a good struggle. Susan saw her degree as one of her last chances to get a good education and to do something with her life. She also felt that getting a degree would be a very significant achievement, and she described how proud her family were that she had begun these studies. Despite her positive attitude, she did not make many changes to her learning until late in her first year, due to the difficulties she faced. Firstly, she struggled to become acclimatised to the differences between university and her prior learning environment. I found that going into my first lecture here ... was just a really terrifying experience; all these people, I just felt really overwhelmed by it all ... You’re used to working in small numbers in [your previous experience of studying]; you’ve got the same class most of the time, the same people. Even when these initial difficulties had been overcome, she still had considerable problems with time management, partly due to the paid work her circumstances required her to take on. She also seemed to have seriously misconstrued the relative importance of the different criticisms made by her tutor on her first essay, focusing on minor errors without understanding its main limitations. Towards the end of the year, when these difficulties were more under control, Susan did make changes to her learning, and these led to improvements in her grades. The individual interviews in this study not only illustrated the specific aspects of essay writing that students had to master if they were to demonstrate a deep approach, it also showed the reluctance of students to change existing methods unless these were proving problematic. Finally, the case studies allowed the uneven progress that students made to be understood more fully in terms of the students own personal situation, and these provide explanations, complementary to those obtained through intentional analysis, for the ways in which different students tackle their work. Other examples relating specific approaches to studying to prior experience and personal histories can be found in the work of Haggis (2004), for example.

Discussion Much of the research on powerful learning environments has used experimental research designs to explore how mainstream psychological theories, such as cognitive apprenticeship

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or cognitive load theory, can be used to suggest ways of improving the effectiveness of instruction in educational settings (see e.g. De Corte et al., 2003). Experimental designs have the potential advantages of control over the conditions and demonstrating causality, but it proves extremely difficult, in practice, to impose theoretically derived conditions on teachers, and almost impossible to do so for university teachers (unless the changes are required by the university management). Our three studies have been conducted within authentic educational settings and have described those settings through the students’ perceptions, so as to understand reactions to contrasting teaching–learning environments. The findings indicate the crucial interactions that exist between individual students and the contexts in which they study and try to learn, and offer a distinctive perspective on teaching and learning in higher education to consider alongside the conceptualisations deriving from psychological theories. Understanding the Phenomenon in Its Context The ETL research reflected back to university teachers the perceptions of their students, using the evidence to discuss the possibility of more effective ways of constructing teaching–learning environments to support student learning. Most of the agreed changes were specific to a module, but it was still possible to describe through inventory scales and from the group interviews with students, general characteristics of supportive teaching–learning environments, including: – the clarity and coherence in teaching aims and course organisation; – the pace at which new ideas are introduced and the perceived difficulty level of those ideas; – the teachers’ enthusiasm for the subject and the level of active support provided; – teaching that directly encourages ways of thinking about the subject; – assignments which demand and reward understanding and the development of skills; – feedback that is timely and provides suggestions about how to improve learning; and – the encouragement of a supportive learning climate among the students. The correlations between the inventory scales describing these aspects of a teaching–learning environment and students’ approaches to learning, along with the analysis of the three contrasting course units and the interview comments, showed not only the interactions that exist between perceptions and approaches, but also the marked influences of the environment on student learning. In the ETL project, we have focused particularly on the extent to which the various teaching–learning activities are congruent with the main aims of the course unit and with the previous experiences and aspirations of the students (McCune & Hounsell, 2005). The analyses in electronic engineering, illustrated earlier, showed marked differences between course units presenting similar subject content, indicating certain aspects that affected the approaches to studying adopted. From an analysis of interviews with both staff and students, it was possible to identify what seemed to be the main ways of thinking and practising (WTPs) in this particular content area, while the teaching–learning activities which students found most helpful led to the notion of there being an inner logic of the subject and its pedagogy, exemplifying congruence between the WTPs and students’ experiences of the teaching (Entwistle et al., 2005).

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The distinctiveness of the differing subject areas and their pedagogies means that the general characteristics of a supportive teaching–learning environment, listed above, have to be reinterpreted, at least to some extent, for each major discipline, if the teachers in that area are to be persuaded that suggestions for enhancement are worth considering. Even then, the frequency distributions found for the individual items (Table 2) showed such a range of reactions to the same teaching–learning activities that even subject-specific suggestions about teaching could not be expected to suit all students. In designing courses, the focus remains essentially at system level, leaving a danger that the effects of the teaching on certain subgroups of students are not fully considered. Where the teaching–learning environments are over-demanding, most students will report difficulties, but even where the general ratings are high, some subgroups will still need additional support. Narrowing the level of analysis further brings into focus the reactions of individual students and makes it easier to identify groups of students who are potentially most at risk within existing course settings. Understanding the Person in Context The individual interviews in the Swedish study provided additional insights into study activity. The reactions of the Swedish students were similar to a substantial proportion of the second-year students in the ETL project: They experienced delayed understanding as a result of the pace being much too fast for them. The consequence of feeling ‘out of phase’ with the progression of the course, in both electrical engineering and computer studies, was increasing levels of frustration and anxiety. The theoretical framework used to analyse the interviews focused on how individual students contextualise their study situation — how they make sense for themselves of what they are required to do and how to complete the work to their own and to their teachers’ satisfaction. Where the teaching–learning environment creates problems for students, students develop distinctive ways of coping with the situation. The study showed that these coping strategies can be understood in terms of the intentions and beliefs that lead to particular actions, as students try to deal with their strong feelings about the situation. Approaches to studying are also conceptualised in terms of intentions that lead to differing actions, in this case learning processes, and the correlational analyses reported in the ETL project showed how existing approaches affected students’ perceptions of teaching–learning environments they then experienced, and how characteristics of those environments also changed their approaches, at least to some extent. The individual interviews in the Scottish study helped to explain why students might not respond in the expected ways to well-designed teaching. For example, earlier educational experiences determine whether students will recognise opportunities for change offered by a tutor. Students may also have firmly established beliefs about whether or not they would be able to change in the ways encouraged by the tutor and whether the effort involved would be worthwhile for them. The example of ‘Susan’ showed how her individual circumstances, as a mature student who needed to take up paid employment, restricted the time and energy available for finding ways to improve her approaches to studying. The progressive narrowing of the focus of analysis reveals more numerous, and more subtle, aspects of the relationships between approaches to studying and perceptions of the

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teaching–learning environment, making it increasingly difficult to see how general conclusions about the characteristics of supportive teaching–learning environments can be reached. However, the interplay between the results from these different levels of analysis does have some important aspects in common. The same reactions of students to certain experiences, such as too fast a pace, can be seen clearly from both questionnaire and interview responses, but it is important not to make simplistic interpretations of correlational findings. For example, substantial positive coefficients between deep approaches and experiences of teaching can be taken to show that students adopting those approaches appreciate these methods of teaching, but the same coefficients also indicate that students not adopting those approaches have not found the teaching so helpful. Looking at specific frequency distributions, however, shows the extent of any possible difficulties, while students’ comments help us to understand the nature of the problems faced by students. The Educational Implications of Studies at Different Levels of Analysis In both Britain and Sweden, government policies have been emphasising the need to recruit additional numbers of students from social groups who are currently under-represented in higher education. The implementation of these policies has led to rapid increases in the numbers of students entering higher education in recent years, without the funding required to maintain traditional teaching methods. (So far, however, the ‘additional’ students seem to be coming mainly from the social groups already over-represented, but with lower entry qualifications.) There has thus been great emphasis on the need to find new ways of teaching that will cope with the increased numbers in more economical ways. Various innovative techniques have been developed which apparently provide equivalent instruction, while also giving students more control over the instruction being provided. Many of the new instructional methods stress the importance of autonomy in studying, and yet many of the ‘additional’ students will be less well prepared for independent studying, and so will need more individual support to help them adjust to new ways of learning. It is thus important that research on the effectiveness of these innovations produces not only group-level analyses, but also ones at subgroup and individual levels to indicate how differing subgroups are adjusting to these environments. The ETL project provides an illustration of the way group-level analyses can be used in conjunction with data that bring out important subgroup differences. It has been demonstrating the advantages of obtaining detailed conceptually based information about how different students perceive the teaching–learning activities in which they are involved. The changes that staff agreed to introduce in that project were often the result of showing that there were groups of students in a class who were critical of certain aspects of the teaching. The questionnaire analyses indicated the level of disquiet being expressed, but not what changes should be made. In the group interviews, students explained why they had experienced difficulties and often suggested what specific changes would help them most. The teaching–learning environment could then be adapted, often in quite simple ways, to support a higher proportion of the students more effectively. For instance, students were often asking for better, and more timely, feedback on the set work they had completed. The group-level studies demonstrated that feedback and guidance was seen as an important part of the learning process, but the interviews suggested

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that some aspects were problematic. One difficulty with feedback is that university teachers may not appreciate that they are taking important aspects of the work for granted in their comments, creating confusion for some students. In several modules, interview comments about the feedback brought home to staff the problems being experienced by some students and made sufficient impact to encourage change. Many of the staff teaching electronic engineering, for example, was wary of providing detailed feedback on tutorial problems, which showed the steps needed to reach correct solutions. But students maintained that the lecturers’ solutions were essential if there were to fully understand what was required. There were similar worries about providing advice on revising for examinations, seeing it as ‘spoon-feeding’, and yet general advice on the most common errors made by previous students, or explanations about how specific examination of requirements imply particular ways of preparing for them, can be seen as particularly valuable for students at the greatest risk. From what we have argued, it can be seen that research at different levels of analysis serves different purposes. The group-level analyses offer guidance on general improvements to the system and also show the extent of any problems being experienced by students, while a narrower focus makes the nature of those problems much clearer and can lead directly to suggestions for improving the situation. Although the methodologies being adopted are very different, making it impossible to carry out any single integrative analysis, if a single conceptual framework is used, then findings from different analytic procedures can be brought together in ways that strengthen the conclusions reached. Our overall conclusion, therefore, is that, in trying to enhance the existing teaching–learning environments in higher education, it is equally important to understand both the phenomenon and the person — the general pattern of relationships within an interacting system and the reactions of different individuals to what they are experiencing within it. By bringing together findings from analyses working along these dimensions, we not only learn to appreciate the power of these mutually supportive streams of research, but we also gain new and valuable knowledge about the complex interplay of influences affecting student learning in higher education.

References Biggs, J. B. (1987). Student approaches to learning and studying. Australian Council for Educational Research, Melbourne. Cronbach, L. J. (1975). Beyond the two disciplines of educational psychology. American Psychologist, 30, 116–127. De Corte, E., Verschaffel, L., Entwistle, N. J., & van Merriënboer, J. (Eds). (2003). Powerful learning environments: Unravelling basic components and dimensions. Oxford: Elsevier Science. Entwistle, N. J. (1997). Introduction to the Special Issue on phenomenography in higher education. Higher Education Research and Development, 16, 127–134. Entwistle, N. J. (in press). Conceptions of learning and the experience of understanding: Thresholds, contextual influences, and knowledge objects. In: S. Vosniadou, & A. Baltas (Eds), Philosophical, historical, and psychological approaches to conceptual change. New York: Cambridge University Press. Entwistle, N. J., & McCune, V. S. (2004). The conceptual bases of study strategy inventories in higher education. Educational Psychology Review, 16, 325–346.

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Entwistle, N. J., Nisbet, J. B., & Bromage, A. (2005). Subject area report for electronic engineering. ETL Project website at www.ed.ac.uk/etl/publications.html Entwistle, N. J., & Ramsden, P. (1983). Understanding student learning. London: Croom Helm. Fransson, A. (1977). On qualitative differences in learning. IV — Effects of motivation and test anxiety on process and outcome. British Journal of Educational Psychology, 47, 244–257. Haggis, T. (2004) Meaning, identity, and ‘motivation’: Expanding what matters in understanding learning in higher education? Studies in Higher Education, 29, 335–352. Halldén, O. (1988). Alternative frameworks and the concept of task: Cognitive constraints in pupils’ interpretations of teachers’ assignments. Scandinavian Journal of Educational Research, 32, 123–140. Halldén, O. (1999). Conceptual change and contextualisation. In: W. Schnotz, S. Vosniadou, & M. Carretero (Eds), New perspectives on conceptual change (pp. 53–66). Oxford: Pergamon. Kreber, C. (2003). The relationship between students’ course perceptions and their approaches to studying in undergraduate courses: A Canadian experience. Higher Education Research and Development, 22, 57–75. Lehtinen, E., Vauras, M., Salonen, P., Olkinuora, E., & Kinnunen, R. (1995). Long-term development of learning activity: Motivational, cognitive, and social interaction. Educational Psychologist, 30, 21–35. Lowyck, J., Elen, J., & Clarebout, G. (2005). Instructional conceptions: A prospective analysis. In: J. Lowyck, E. Lehtinen, & J. Elen (Eds), Conceptions of students and the design of powerful learning environments [Special issue]. International Journal of Educational Research (in press). Marton, F. (1981). Phenomenography: Describing conceptions of the world around us. Instructional Science, 10, 177–200. Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah, NJ: Erlbaum. Marton, F., & Säljö, R. (1997). Approaches to learning. In: F. Marton, D. J. Hounsell, & N. J. Entwistle (Eds), The experience of learning (2nd ed., pp. 39–58). Edinburgh: Scottish Academic Press. Retrieved from http://www.ed.ac.uk/publications.html McCune, V. (2000). The development of first-year students’ approaches to studying. PhD thesis, University of Edinburgh. McCune, V. (2004). Development of first-year students’ conceptions of essay writing. Higher Education, 47, 257–282. McCune, V., & Hounsell, D. J. (2005). The development of students’ ways of thinking and practising in three final-year biology courses. Higher Education, 49, 255–289. Perry, W. G. (1970). Forms of intellectual and ethical development in the college years: A scheme. New York: Holt, Rinehart, and Winston. Ramsden, P. (1991). A performance indicator of teaching quality in higher education: The Course Experience Questionnaire. Studies in Higher Education, 16, 129–150. Richardson, J. T. E. (2005). Students’ perceptions of academic quality and approaches to studying in distance education. British Educational Research Journal, 31, 1–21. Ryve, A. (2004). Can collaborative concept mapping create mathematically productive discourses? Educational Studies in Mathematics, 56, 157–177. Scheja, M. E. (2002). Contextualising studies in higher education. First-year experiences of studying and learning in engineering. PhD thesis, Department of Education, Stockholm University. Scheja, M. E. (2006). Delayed understanding and staying in phase: Students’ perceptions of their study situation. Higher Education, 52, 421–445. Säljö, R. (1982) Learning and understanding. A study of differences in constructing meaning from a text. Gothersburg: Acta Universitatis Gothenburg. Tynjälä, P. (1997). Towards expert knowledge? A comparison between a constructivist and a traditional learning environment in the university. International Journal of Educational Research, 31, 357–442.

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Vermetten, Y. (1999). Consistency and variability of student learning in higher education. PhD thesis, Katholieke Universiteit Brabant, The Netherlands. Vermetten, Y. J., Vermunt, J. D., & Lodewijks, H. G. (2002). Powerful learning environments? How university students differ in their response to instructional measures. Learning and Instruction, 12, 263–284. Vermunt, J. D. (1998). The regulation of constructive learning processes. British Journal of Educational Psychology, 68, 149–171. Verschaffel, L., De Corte, E., Kanselaar, G., & Valcke, M. (Eds). (2005). Powerful learning environments for promoting deep conceptual and strategic learning (Studia Paedagogica). Leuven: Leuven University Press. Wistedt, I., & Brattström, G. (2004). Understanding mathematical induction in a co-operative setting: Merits and limitations of classroom communication amongst peers. In: A. Chronaki, & M. Christiansen (Eds), Challenging perspectives on mathematics classroom communication (pp. 173–203). Greenwich, CT: Information Age Publishing.

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Chapter 9

The ‘Unhappy Moralist’ Effect: Emotional Conflicts between Being Good and Being Successful Fritz Oser, Evi Schmid, and Lisa Hattersley The moral law however doesn’t promise happiness. I. Kant

Morality and Success: Two Interfering Worlds In recent years moral developmental research has gone beyond classical questions on stage, structure, and phases; it is becoming more and more situated. This is why in this chapter — as one of many possible questions — we would like to ask why some people feel so unhappy when they are trying to keep up moral standards, whereas others do not. On the other hand we often see that immediate success related to a necessary good, which is not attainable if someone does not go against some ethical principles, makes people selfconfident and at times even happy. Thus the questions we raise are: – – – –

What is the relationship between having success and being moral? Does morality inhibit success? Why do moral persons often feel unsuccessful? What does it mean to combine morality and success?

These questions stand in relation to the so-called good life metaphor, which states that virtue-oriented behaviour yields to a satisfaction with respect to general subjective well being. Morally good persons feel satisfied that they are embedded in an environment, which expects them to be good in every field. According to Aristotle, apart from good situational conditions and apart from having leisure time, the good life comes out of the fact that one acts according to virtues and thus, as a result, feels complete happiness. Other philosophical paradigms see morality as only one aspect of happiness; yet

Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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sometimes question even the basis of this assumption. Thus we can trace the following thinking patterns: – Whereas Aristotle connects morality with happiness, Kant assumes that if all aspects of life are submitted to practical reasoning some persons can become happy but others cannot. – The utilitarism connects these two opposing elements differently: Good is what is in the best service of others. Happiness becomes not only a by-product, but also a central goal of life. – In a post-modern world morality is connected to financial independence, which guides and supersedes this morality and thus can be interpreted only according to success (communitarism). – If morality concerning important issues is embedded in practical decision making it can lead to what we call moral unhappiness, which can be prevented by connecting morality to success in a new interpretative way. Success must be submitted to moral reflection (Seel, 1999). – Today we can see the following thinking pattern: “In confronting the question of the good life and the successful society, we encounter the vexatious question of cultural relativism. If societies have different sets of values, people in them are likely to consider different criteria relevant when judging the success of their society” (Diener & Suh, 2003, p. 3). As helpful as these reflections may be, the question we raise goes — at least partly — beyond philosophical analyses. We want to know why some people stay moral in most difficult situations, even if they feel unsuccessful (moral resilience) and even if things are negatively related to the way they act. This question bears on the field of educational psychology. We found that individuals who have decided to be moral, might be unhappy and might even face being excluded from the group. This is especially the case when success depends on being immoral and when the status of the underlying norm is not very strong, that is to say if the respective transgression belongs to the realm of the so-called weak negative behaviour (Nisan, 1986). We have so far described the problem of the ‘unhappy moralist’. The rest of the chapter is outlined as follows: The next section describes a study on fare-dodging, in which youngsters feel happy about cheating and unhappy by not doing so. The third section briefly introduces a further study on cheating and happiness. In the fourth section a study on negotiation (see Oser & Reichenbach, 2000) with great importance for the ‘unhappy moralist’ effect is introduced. The fifth section discusses the phenomenon of the ‘happy victimizer’, which is a kind of ‘mirror image’ of the ‘unhappy moralist’ effect. A ‘happy victimizer’, like a person happy about cheating, has done wrong, and children believe that he/she feels good about it. The next two sections describe in detail a new study, in which the attribution of emotions in the moral sphere is addressed from a developmental psychology angle (see Schmid, 2003). In the eighth section attention is given to new questions in the field with a special focus on different groups of norms and their possible effect on the phenomenon of the ‘unhappy moralist’. Some educational reflections are discussed in the final section.

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Happy Cheating: Never Be Excluded From a Group In an experimental study (Oser, 1999, pp. 168–219), each student of an apprentice class was influenced by two other trained students (a girl and a boy) not to use the offered money received for a tramway fare to another far away located university building in order to participate in a course, but rather to keep the money to buy a drink after the course with his/her friends and companions. The experimental conditions were such that the young protagonist did not know that if the students had been caught, the ticket would have been in the possession of the seducers because all fares for the tramway company were paid in advance. What are the results regarding the fare-dodgers? Many of them did cheat, whereas others did not. Six out of 11 students were fare-dodgers, 5 resisted to cheating (6 students of the class were trained as seducers). Results of this pilot study show that in general the fare-dodgers were on a fixed moral stage; the non-fare-dodgers were on transition, all this measured on the Kohlberg test. The fare-dodgers were rather stable emotionally, and more reality based, they had a higher self-worth, and were rather modest in their general behaviour (polarity profile). They were less severe in their judgment towards others, but more sensitive, and they rejected illusions to a lesser extent. They appeared to be less frustrated and were viewed as more popular by the group, relative to the nonfare-dodgers. On the other hand, they were less dependent on the group and even preferred working in the group more than the non-fare-dodgers. In regard to the life satisfaction scale we did find — due to the small N — only a tendency towards fare-dodgers having a higher satisfaction value than the non-fare-dodgers (m1=1.43; m2=1.25, on a scale of –2 to +2). All in all it seems that the ‘immoral’ persons, because they were successful in respect to cheating in a concrete ‘small’ situation, felt happier, more satisfied with regard to their actions and especially more integrated within the group of the other 16-year-olds than the moral ones. Conversely, the non-fare-dodgers did not feel very accepted, nor stable, and indicated dissatisfaction with their decision; especially in regard to the qualitative data (interviews after the happening), they felt less free in their decision-making process and were too afraid of being caught. In addition, some of the non-fare-dodgers said that ultimately they felt the decision was OK, but that they also felt unhappy about not being accepted and even had ill feelings toward the others. On the other hand the fare-dodgers were more satisfied that they had overcome the fear of being caught; they felt they were somehow heroes in consideration of the fact that the State was already demanding too much money from students, too much tax fare, etc. They also had many other stories about having been successful with other types of adolescent cheating behaviour. This was the first time we discovered that people with a strong moral point of view often feel dissatisfied with regard to the success in normatively loaded situations. As mentioned earlier, we called this phenomenon ‘the unhappy moralist’ effect. It depicts an emotional reaction to the fact that in some situations the conflict between morality and success cannot be balanced out. Of course in this example of cheating regarding tramway tickets, we can suggest that the reactions of the fare-dodgers are typical for stage 3 persons according to Kohlberg. Stage 3 persons stress a relational morality. Good is if I am doing what the group or my friends want me to do. However, most of the non-cheaters were also around stage 3 so that this argument does not apply fully. If we accept — as Solomon

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(2000) does — that subjects are not simply at the mercy of their emotions, but also actively design them, then emotions are personal judgments that say something about the moral motivation of a person. According to recent research, emotions do not only happen to us, they are parts of our acts, even if these acts are mere judgments. In relation to the unhappy moralists these emotions show that persons who act morally and give profit second priority, feel dissatisfied with their act and will not experience moral happiness or a ‘warmglow-effect’ (see Nunner-Winkler, 2001, p. 182) as would have been expected. This dissatisfied reaction stems — as suggested — from a conflict between a moral demand and a personal need or a personal gain. In contrast to the ‘unhappy moralists’, ‘happy victimizers’ (see the fifth section) give priority to direct personal needs or personal gains. They accept a moral transgression and believe that the wrongdoers are satisfied afterwards. Children believe that the victimizer can only be happy, whereas the victim can only be unhappy, but both dimensions are related to moral emotions, and of course thus to different aspects of such emotions. Op ’t Eynde and De Corte (2002, p. 14) state that First, emotions are based on students’ cognitive interpretations and appraisals of specific situations. Second, students construct interpretations and appraisals based on the knowledge they have and the beliefs they hold, and thus they vary by factors such as age, personal history, and home culture. Third, emotions are contextualized because individuals create unique appraisals of events in different situations. Fourth, emotions are unstable because situations and also the person-in-the-situation continuously develop. Applied to our phenomenon, ‘unhappy moralists’ are dissatisfied with their moral decision; cognitively they view the decision as ‘right’, but do not gain success from it. In addition students construct a so-called ‘information availability bias’. Since information is not balanced, and the societal and cultural norm accepts both success and morality, the student constructs a disequilibrated form of moral decisiveness. Thirdly, this is only the case when — as we said — the situation is related to a so-called weak norm and the appraisal of an event goes together with an internally or socially expected second norm system, which is related to a financial or law-oriented gain. Finally, this emotional state can change as soon someone supports the subject with regard to his/her decision. The non-‘unhappy moralist’, in comparing this gain with acting morally, denies the moral necessity and thus devaluates the consequences of his/her action as being negative for someone else.

Cheating on Mathematics: Who Is Unhappy? As we mentioned previously, not all situations in which someone acts morally lead to the ‘unhappy moralist’ phenomenon. It is necessary that a material gain stands against the morally worthwhile act. It is also essential that the norm character is weak rather than strong (see the eighth section). (A weak norm is less absolute compared to a strong norm, which should be kept in most cases. A weak norm concerns for instance a speed regulation, a strong norm the commandment not to kill.) In addition, the chances of the outcome

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of the act becoming public have to be relatively small. Sometimes it is also a clear-cut ‘information availability bias’, in the sense that we believe that the other person knows what he or she is doing, and that we do not ask enough and so the hidden information stands against the not openly given information. As a justification for the behaviour, people might say: ‘They did not ask me; why should I give them more information.’ ‘They did not ask me’ becomes an excuse for not saying what should have been said and as such, becomes a fully justified response. Hiding information is interpreted less severely than directly lying and than stressing a kind of ‘first-order’ desire. This kind of first-order desire is in so far different from the above-mentioned judgment of children, as adults fully and consistently have knowledge of the conflict between morality and success. Within certain situations, only morally resilient people resist the temptation to hide if hiding is deemed ‘easy’ and is viewed better for the individual’s gain or success. Examples of such situations are an act of selling a product or a negotiation process. An interesting study with respect to this issue was carried out in Vienna. Although it was the main objective of the study to measure mathematical writing performances, it revealed interesting findings on cheating behaviour as well (Hanisch, 1990). In Austria, the German word for cheating is ‘Schummeln’. By definition ‘Schummeln’ is a minor form of cheating that refers to unacceptable behaviour but is not considered a criminal act. Only 7 of 191 students between 16 and 19 years reported that they did not cheat at all. There were indications that these 4% either did not need to cheat or were unhappy and somehow socially excluded from the others. This research did not focus on the ‘unhappy moralist’ phenomenon but rather on cheating methods, cheating forms, cheating motivation, reactions of the teachers, feelings of being caught, and similar issues. The findings of this study indicated that cheaters, whether girls or boys, were happy cheaters. They even see helping others through cheating as a social responsibility act and consider the risks of being caught as a ‘Kavaliersdelikt’ — a type of offence, which leads to a form of group acceptance (group morality). Characteristic of the research in this field, not enough is said concerning the noncheaters. This and similar studies could broaden our horizons with respect to mathematically related beliefs (see also De Corte, 2003). We can imagine that the task-oriented beliefs for instance could be supplemented: instead of saying ‘the most satisfying thing for me is to learn the course material in this math class’, one could also say, ‘the task can be better resolved if I prepare a crib sheet’. With respect to self-efficacy beliefs, instead of saying ‘I’m confident that I can understand even the most difficult part of the math course’, one could propose an alternative such as, ‘I am sure that cheating gives me more security with respect to a high stakes exam in math’. Although research in this area has not yet been done, it could provide insight into intercultural differences.

Moral Resilience and What it Means to not Be Unsuccessful Probably the most convincing study with respect to the ‘unhappy moralist’ phenomenon deals with hiding and devaluating information in negotiation processes (see Oser & Reichenbach, 2000). This study investigates moral resilience and the respective emotional reactions where in a negotiation case one party — besides having the task of winning and fighting for the best solution in the service of their respective clients — has to deal with

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morally negative information. This information is such that it speaks against the own client. Moral resilience in this case means a) resistance to gain or accepting a good when there is an indication that the procurement of that good is connected to something negative; b) to resist public pressure even when acting in favour of weak or persecuted people will probably lead to the consequence that this act will damage the moral subject, i.e. him- or herself, and c) to not bear witness against others when this testimony only yields an advantage for the one who is in possession of a so-called evidence but not for the one whose future is at stake (Oser & Reichenbach, 2000, 2005). Moral resilience is a precondition for the ‘unhappy moralist’ phenomenon. Subjects choose the right thing to do because their moral conscience supersedes the material gain without giving the person a moral self-worth or a high moral self-esteem. An example may help understand this: A teacher in a philosophy class discusses the question about legitimating the death penalty with a 17-year-old. The student is opposed to the death penalty, whereas the teacher is in favour. Instead of defending the teacher’s view in an exam, the student maintains his view in opposition of the death penalty. He receives a poor grade. He then feels unhappy about his decision to adhere to his own moral beliefs instead of adopting the teacher’s view. Only many years later does his decision make him feel proud, enhancing his self-esteem. Thus the student’s moral resilience was accompanied by the fact that it hindered success and made the protagonist unhappy. In the moment of the event, the student’s lack of moral self-esteem was crucial (Heid, 2004, personal communication). This is only an example that illuminates that truthfulness does not often lead to felt success. Returning now to the negotiation study, in the respective simulation divorce case on Winter vs. Winter, two lawyers defended the claim of the husband, two others the claim of the wife. Both parties received relatively clear general information. However, in the additional confidential information given to each party, Paul’s lawyers received positive information: Paul still loves his wife, he wants her to come back, he cares about the children etc. Conversely, the lawyers of Barbara received negative information: She leaves the children alone, she hits them if they wet their beds, she flirts with the boyfriends of her older daughters, she spends money for her unnecessary lessons that is intended for the children etc. The most important information, however: not one of the five children wants to stay with her if the divorce takes place, and all the neighbours think Paul would be a better custodian for the children. What is the problem? Barbara’s lawyers have information that speaks against her. She wants the children, she wants to win, she wants the money, but as her defender you know that the future lives of these children depend on your decision. From the information received you know that her husband could look after them much better than Barbara would. In our study we found that 30% of the subjects (N = 110 adults in management or higher political positions or lawyers) decide to give all the children to Paul, 12% give the custody of all the children to Barbara, 28% give the two older children to Barbara, 10% give the two older children to Paul, and 20% do not find a solution. The most challenging result is that the quasi morally resilient persons, those who use their information against the interests of their client and therefore indirectly help the attorneys of the opposite party,

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are largely unsatisfied with the result of their negotiation. They feel that they have done the right thing but are not convinced that their decision makes the world any better or that they are successful negotiators. They do not feel really successful even when they are convinced that they have done the right thing. One of them said: “I am so exhausted; I will never become a good negotiator. I think it was the right thing to do but I am wondering how we could have brought things together”. And precisely this seems to be the key issue of what we are discussing here: on the one hand the negotiator should be a winner with good tactical and economical abilities, on the other hand he should have a moral stand. The following data supports this first effect: Persons who decide to give the children to Barbara show a highly significant correlation between the statement ‘Morally, I completely did what was right’ and ‘I am satisfied with the outcome’ (.707*). When the children were separated (e.g., the older children to Barbara, the younger children to Paul), the correlation was less high (.459*). When the children were given to Paul, there was no significant correlation (.219). This again leads to the assumption that a complementary phenomenon to that of the ‘happy victimizer’ (see the fifth section) exists, namely the resilient ‘unhappy moralist’. Why resilient? It means that these persons keep their moral standards even if it is against their feeling of being unsuccessful. In other words, they work against themselves, the people who act morally correct do not show positive correlations with being content about the solution they reached. This can be sustained with another significant correlation: ‘The solution is in the interest of all concerned parties’ correlates positively with ‘We were lying’ if the children were allocated to Paul (.389*), but negatively if the children were given to Barbara (–.637*). That means that for Paul‘s defenders there is a positive relationship between lying and interests. They believe that lying could help, whereas the ‘true liars’ do not believe that. There is no significant correlation between the ones who do not find a solution (see Oser & Reichenbach, 2005). What are the reasons for such lying behaviour, respectively for the behaviour to force the other party to give the children to the person with the bad record? As mentioned above, we believe there are two qualitatively distinct effects. The first is what we called an ‘information availability bias’, and the second is an ‘information devaluation bias’. The information availability bias states that subjects — especially on Paul’s side — believe they have all the necessary information and that both parties have the same balanced problems. The information devaluation bias states — especially on Barbara’s side — that the negative information given is not so important, they believe that in general both parties are guilty and the misbehaviour of the wife is due to the overload of work and responsibility. These are precisely the reasons for giving the children to Barbara, reasons that illustrate that people want to avoid the ‘unhappy moralist phenomenon’. For the 30% who allocated all children to Paul the emotional feeling is ‘we have done the right thing but we have not been successful negotiators’. Thus the relationship between morality and success is never equally balanced. This leads to the question of how we can educationally strengthen the moral resilience and the moral courage on the one hand, and how we can build up a powerful moral self-esteem on the other.

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The Happy Victimizer: A Kind of Mirror Image We have already mentioned the notion of the ‘happy victimizer’ effect twice. In the next section, we will provide some more details on the phenomenon based on experimental studies. Using a longitudinal study carried out by Weinert and Schneider (1986), NunnerWinkler and Sodian analysed the emotions that children attributed to a moral victimizer when confronted with hypothetical situations of moral violations. The focus of the study was on showing that moral development is a process consisting of two phases. This is contradictory to Kohlberg’s supposition of cognitive–affective parallelism, which implies that both aspects develop at the same time and in the same way. But many research groups have questioned Kohlberg’s assumption (see Nunner-Winkler, 1989, 1999). Contrary to Kohlberg, Nunner-Winkler assumes that in a first universal phase, moral rule understanding is acquired. The second phase consists of a slow individual learning process, in which moral motivation is built up. Moral motivation can be understood as the readiness to do what is right; this may occur not only because one wants to do it, but also when doing what is right requires renouncing from the satisfaction of hedonistic desires (see NunnerWinkler, 1993). Thus, Nunner-Winkler and Sodian conducted their studies based on the hypothesis that attribution of emotion can be taken as an indicator for moral motivation (see NunnerWinkler, 1993). In one of their studies 4-, 5-, 6-, 7-, and 8-year-old children were presented with picture stories in which a child protagonist is confronted with a conflict between a moral rule and a hedonistic desire. After questioning the children about their knowledge and understanding of the moral rule in question, the story figure was shown violating the rule and satisfying his or her hedonistic desire. The children were then asked which emotions they would attribute to the moral victimizer. Their answer would either focus on the rule violation (‘feels bad, because he/she has done something wrong’) or on the satisfaction of the hedonistic desire (‘feels good, because he/she got what he/she wanted’). According to Nunner-Winkler’s assumption, this attribution can be seen as the indicator for moral motivation. The results show that in spite of having the necessary moral rule understanding, younger children focus on the successful outcome of the violation, judging a moral victimizer to experience positive emotions (60% of the 4- and 5-year-olds and 50% of the 6- and 7-year-olds). A majority of younger children believe a person will feel good if he/she does exactly what (s)he wants to do, regardless of whether a moral rule is violated or not. Older children attributed negative feelings to the story figure, focusing on the rule violation and the moral value of the victimizer’s action.1 Even if we could argue that there is a desirability effect with respect to older children, the readiness of younger children to attribute positive emotions to a moral victimizer is a strong effect, which is referred to as the ‘happy victimizer phenomenon’ (see Nunner-Winkler, 1993, 2001). NunnerWinkler and Sodian also presented children with a story in which the story figure abides by the moral rule and in doing so resists the temptation to satisfy his or her desire. When

1 From the age of about 10 all children, like adults, attribute negative emotions to a moral victimizer; therefore such attribution of emotion can only be seen as on indicator for moral motivation in younger children (see Nunner-Winkler, 2001, p. 178).

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asked how the story figure must feel, children assume the person will feel bad, because he or she could not satisfy his or her hedonistic desire. It therefore appears that children not only expect a person to feel good if a hedonistic desire is satisfied, but conversely, they also expect a person to feel bad if (s)he does something (s)he does not want to do or if (s)he does not do something (s)he wants to do (see Nunner-Winkler, 1999). Keller, Lourenço, Malti, and Saalbach (2003) observed similar results concerning the attribution of emotions to a hypothetical victimizer in a study with German and Portuguese children. Younger children strongly favoured hedonistic desire satisfaction in spite of their understanding of moral rules. Older children, on the other hand, gave priority to the moral rule as opposed to the hedonistic desire of the story figure (see Keller et al., 2003). It would appear that there is a phase (happy victimizer) in which moral rule understanding is present but moral motivation is not yet established. The question arises whether the other phenomenon (the ‘unhappy moralist’) can only occur once moral motivation exists. It would appear that the readiness to sacrifice hedonistic or ‘first-order’ desires in favour of what is morally right provides a possible basis for the characteristic emotions of an ‘unhappy moralist’. Should this be the case, then moral motivation would be a precondition for the ‘unhappy moralist’ phenomenon to occur and the ‘happy victimizer’ a preceding phenomenon to the ‘unhappy moralist’. Based on the research, our assumption is that there are two types of the phenomenon: (a) a situation-specific form which is independent of moral stage development, and (b) a form which is related to a lack of moral reversibility in which not being able to be successful makes people unhappy. In our studies we concentrated on the first form.

A Developmental Psychology Perspective on the Attribution of Emotions in the Moral Sphere: A New Study Until now the phenomenon of the ‘unhappy moralist’ itself was circumscribed. Demonstrating the effect through empirical evidence using a broader age range still remains to be analysed. Preliminary evidence exists in the observations that Oser and Reichenbach made of participants in negotiation courses (see the fourth section): people who behaved morally, were often unsatisfied with the result of their negotiation technique. As a consequence, the losses that were commonly suffered as a result of moral and honest conduct proved to be more important for the emotional equilibrium of the negotiator than his/her proven moral strength. A second source of information that we discussed was NunnerWinkler’s investigations into moral motivation (see the fifth section). Findings demonstrated that with the aid of attributions of emotions made by children in relation to a hypothetical moral wrongdoer, until a certain age, children are prepared to attribute only positive emotions to a wrongdoer (see Nunner-Winkler, 2001). The aim of the study described below was to investigate whether the ‘unhappy moralist’ phenomenon as well as the ‘happy victimizer’ effect can be detected in both children and teenager attributions (see Schmid, 2003). In the study, a random sample of participants ranging in age from 7 to 15 years was selected. As various studies (see Hascher, 1994; Keller et al., 2003; Nunner-Winkler, 1999) were able to show, a development takes place in children regarding the area of attribution of emotions in general, as well as, in the area of the attribution of emotions within the

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moral sphere. Therefore, it seemed reasonable to approach this study from a developmental psychology angle, using a broad age range of participants. Accordingly, participants were interviewed in order to investigate differences in the structures of their answers. At each age level (7, 9, 11, 13, and 15 years) half of the interviewees were girls and half were boys. In addition, of the 13- to 15-year-olds half attended junior secondary school (Realschule), and the other half secondary school. This factor allowed educational background to be used as a between variable. The design of the study consisted of each child being told two stories. Of the two stories, each had two versions. Although the structure of the stories was the same within each group of participants (younger/older children), the story figure was modified in order to guarantee that the children identified as closely as possible with the story figure, which was either a child or a teenager of approximately the same age as the children/teenager listening to the story. All the stories were about a child or teenager who wanted to buy something. The two versions of the story were then presented. In the first version, the sales assistant withholds information that would indicate that the object being sold is not brand new or has already been repaired. By withholding the information, the sales assistant makes a larger profit because the consumer believes the object to be new. In the second version, the sales assistant does not withhold any information; she/he is totally honest and therefore loses out financially. Each participant was presented with the two stories, with both a female and a male protagonist. These deliberately gender-specific stories were intended to indicate possible gender-related differences. After the 40 children and teenagers had been told the stories, they were asked questions about them. The first three questions were intended to investigate the dimension of ‘success’. Moreover, how the interviewees assess both the fair and the unfair sales assistant regarding her gain. With the two subsequent questions on the dimension of ‘morality’, participants were first asked which form of conduct of the two sales assistants they regarded as being good and why, and secondly they were requested in a more open question to assess how each of the two sales assistants might feel. The final question was intended to explain the dimension of ‘happiness’, in which interviewees were asked which person they regarded as more happy, the one who had behaved in a moral manner or the one who had concealed important information and had thus earned more money. The last question related directly to the hypothesis of the researchers, which was that ‘the younger children regard money as the criterion for success, satisfaction, and happiness, whereas the older children are torn between the criteria of ‘financial profit’ and ‘honesty’. Although we believed in advance that the criteria of ‘morality’ and ‘honesty’ become of increasing importance with age, data of a pilot study already showed that there was no direct shift in fixation from financial criteria to moral criteria. The older children appeared to be aware of the difficult relationship between the two dimensions and as such, attempted to find what they deemed to be a good solution. The second hypothesis states that ‘a development takes place in the area of emotion attribution in children and young people between the ages of 7 and 15: as they grow older, the number of positive emotions attributed to the immoral sales assistant declines, while the number of negative emotions increases’. The second hypothesis relates primarily to the previously mentioned studies by Nunner-Winkler and Sodian concerning the ‘happy victimizer’ phenomenon. In their longitudinal study they were able to show that 4- and 8-year-old

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children fundamentally differ in the emotions they attribute to a fictitious rule-breaker. Whereas younger children mainly focus on whether the story figure has been able to satisfy his needs, older children show that they allow themselves to be more strongly affected by moral criteria in their attribution of emotions. The third hypothesis indicates that ‘despite the amoral attribution of emotions, children and teenagers identify the conduct of the sales assistant who acts morally as correct and not the conduct of the immoral sales assistant’. This hypothesis is also based both on NunnerWinkler’s research and on the results of the aforementioned study. Nunner-Winkler was able to show through various investigations that knowledge of moral rules is found even in very small children, but that children may not always act in accordance with such knowledge (see Nunner-Winkler, 1999). Already 7-year-olds declared that the sales assistant who acted in a moral manner was the one who acted correctly.

Results of the Study In this section the most important results obtained by Schmid (2003) are presented and discussed. The first hypothesis, which stated that the younger children would be closely focused on financial criteria, while the older children would base their decision using the moral criteria, may be regarded as confirmed by the results. The responses to all the questions clearly indicate that a change of this type takes place between the ages of 7 and 15. Both the participants’ assessment of the success of the two sales assistants, as well as the assessment of the level of satisfaction regarding the sale and of the happiness of the sales assistants, indicate a clear shift in the assessment criteria from financial to moral as seen with the increasing age of the participants. In addition, confirmation was obtained that the older children and teenagers not only use moral criteria as a basis for decision making, but also that with increasing age there is an ever greater tension between morality and success. For example, the answers to the question of how the fair sales assistant feels show very clearly that almost without exception younger children focus on the financial aspects, whereas ambivalent feelings can be attributed to increasing age. While the younger children still think in a very polarized way and conclude that the fair sales assistant either feels satisfied or dissatisfied as a result of her/his honest behaviour, the older children and teenagers increasingly try to describe the situation of emotional tension in which the sales assistant finds herself/himself. As Figure 1 shows, there are no answers among the statements made by the 7-year-olds that would allow a conclusion of ambivalent feelings regarding the fair sales assistant. On the other hand, a large number of the older children interviewed describe being torn between the desire to act honestly and morally, and the necessity to be financially successful. This also seems to indicate that the older children perceive moral situations and feelings differently and possess a different vocabulary of emotions as compared to the younger children. In all age groups both an ‘unhappy moralist’ and a ‘happy victimizer’ phenomenon were detected. The majority of the children and teenagers interviewed stated that they regarded the fair sales assistant as unhappier, less successful, and more dissatisfied with the sale, whereas, they viewed the unfair sales assistant as being happier, more successful, and more satisfied with the sale. However, it is also clear that in the area of emotion attribution and

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satisfied (honest action) feels ambivalent (less money/honest action) dissatisfied (less money)

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Figure 1: How does the fair sales assistant feel? the assessment of moral and immoral situations, a development takes place between the ages of 7 and 15 years; as Figures 2 and 3 show, the amoral attribution of emotions becomes less frequent as the children grow older, and the moral attribution of emotions becomes more common. Whereas the younger participants still almost exclusively assume that the fair sales assistant is less successful, less happy, and more dissatisfied with the sales situation, with increasing age more children and teenagers assess the fair sales assistant as more successful and happier, as she/he acted honestly. The second hypothesis, which states that the amoral attribution of emotions becomes less common as one grows older, while moral attribution becomes more common, can therefore also be confirmed. The third hypothesis was confirmed too. As Figure 4 shows, the vast majority of the children and teenagers identified the conduct of the person who acted in the morally correct manner as the correct way to act, even if they attributed negative emotions to this person. In sum, these results support the findings reported in the studies by Nunner-Winkler’s studies on moral motivation. They found that the knowledge younger children have of moral rules does not necessarily mean that they also feel motivated to act in accordance with these rules. The findings also support the ‘unhappy moralist’ phenomenon, which states that the good person is ambiguous in regard to the balance between financial gains and the morally good decision. This research is important because it is the first time that the phenomenon of the ‘unhappy moralist’ was empirically confirmed in both children and teenagers. Major developmental effects in the area of moral development between the ages of 7 and 15 were also established via the research described in this chapter. In other words, the phenomenon of the ‘unhappy moralist’ has been confirmed, meaning that for the most part children

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Figure 2: Which sales assistant is more successful?

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"unfair" sales assistant 12

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Figure 3: Which sales assistant is happier? attribute negative feelings to a person who acts in a morally correct way. This attribution of emotions is primarily made by focusing on the satisfaction of basic fundamental needs (first- or second-order desire) and not on the basis of moral criteria. Individuals are more satisfied and happier if they possess more and if they have what they want. Those who do not have what they really want are dissatisfied and unhappy, even if they have deliberately refrained from acquiring what they want on the basis of moral criteria. Children and teenagers thus do not assume that a person who acts in a morally correct way feels good and satisfied because of his clear conscience and honesty. They rather assume that not being able to satisfy needs and desired gains due to the application of moral principles leads to dissatisfaction and furthers the feeling of being unsuccessful.

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Figure 4: Which sales assistant acted correctly? With this study it was also possible to show, as was expected on the basis of NunnerWinkler’s investigations into the ‘happy victimizer’, that an ‘unhappy moralist’ phenomenon is not present in the same intensity at every stage in the moral development of a child. The results show very clearly that as children grow older, moral aspects as opposed to needsrelated aspects play a more influential role in their assessment of moral and immoral persons and situations. In their answers, the younger children focused on financial and needs-oriented criteria. The older children and teenagers, however, tended to account for the moral aspects of the stories and used honesty and a clear conscience as factors in their arguments. This shows that most 13- and 15-year-olds appear to ask themselves what is ‘good’ and ‘just’, while younger children remain very one-sidedly interested in selfish and hedonistic goals. The question thus remains how influential the intensity of the first or second order desire is. In the negotiation situation many of the subjects forget the moral part when they are in the winning flow.

New Questions in the Field: Different Groups of Norms in Relation to the ‘Unhappy Moralist’ Many open questions still remain regarding the ‘unhappy moralist’ phenomenon. One central question concerns the circumstances in which the phenomenon occurs. Our new research focuses on norms or more specifically on different areas or groups of norms. The assumption is that the ‘unhappiness’ of an ‘unhappy moralist’ is connected to the strength of a norm (see Hattersley, 2005). Garz (1999) discusses five different groups of everyday

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norms; two of these groups concern strong and weak norms. According to Garz, practically everyone abides by strong norms. They are generally understood to be binding and — if violated — high consequences must be assumed. In general, the violation of a strong norm is not even taken into consideration. Weak norms however are not given as much importance and the potential consequences are not as high, which is why many smaller violations can be found in this area. It is ‘easier’ to give priority to a hedonistic desire if the violation in question concerns a weak norm. A potential violation is also more easily justified. Due to the nature of certain norms, they are adhered to without questioning and this does not entail unpleasant or bad feelings. Conversely, choosing the moral action in order to abide by a norm can result in negative emotions, such as those of an ‘unhappy moralist’. For instance, how will I feel if a bad grade replaces my good one because I mentioned a major mistake the teacher missed while correcting my exam? Will I be content if I point out to the shop assistant that he has given me far too much change? And will I be ‘unhappy’ if I receive a good grade in an essay, which I copied from my older sister? The following questions therefore arise: Within which norm groups does the ‘unhappy moralist’ effect occur? And can differences be found regarding strong and weak norms? Can further differences be found within the weak norms? Apart from the differentiation between strong norms and weak norms, a further possible distinction concerns moral and legal norms. These two groups do not seem to have the same level of obligation, just as strong and weak norms do not. To allow for more accuracy the moral and legal norms can be divided into three groups, partially based on the Domain Theory (e.g. Nucci, 2001; Turiel & Smetana, 1986): moral–legal norms, non-legal moral norms, and non-moral legal norms. Moral–legal norms can be considered both from a legal and from a moral point of view (e.g. theft). They follow from moral demands and prohibitions, but are legally defined and enforceable. Non-legal moral norms are known to be morally correct or incorrect, but, contrary to moral–legal and non-moral legal norms, they cannot be legally enforced. They can often be found in daily interpersonal situations (e.g. standing up someone). Non-moral legal norms concern actions, which are not essentially right or wrong unless they are governed by specific rules, i.e. they depend on the respective social system. For instance, driving on the right-hand side of the road, as for example in Switzerland, is not a question of morality. In Switzerland it is correct to drive on the right-hand side of the road; in England driving on the left-hand side is correct. Thus, as shown in Figure 5, six possible norm groups can be established (see Hattersley, 2005).

Weak Norms

Strong Norms 3

4

1

6 2

Moral-legal Norms

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Non-moral legal Norms

Figure 5: Norm groups.

Non-legal moral Norms

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The assumption is that the ‘unhappy moralist’ effect will only occur in the area of the weak-norm groups (4, 5, and 6). Since in the weak-norm groups the consequences following a violation are lower, and the hedonistic desire or potential personal profit is often stronger than the norm in question, more violations occur in these norm groups. If however the norm is abided by in spite of a strong hedonistic desire, it can be expected that the person will feel discontent, or in other words, the person will be an ‘unhappy moralist’. In the strong-norm groups (1, 2, and 3) on the other hand, it is clear which action should and will be chosen, which is why generally no decision has to be taken about whether to give priority to the hedonistic desire or to the norm in question. Since the norm is stronger and therefore no conflict results, the assumption is that the characteristic emotions of an ‘unhappy moralist’ will not occur in the area of the strong-norm groups. The question is of course when one considers a norm as strong or weak. In the Winter vs. Winter case many see the attribution of the children to one or the other side as a strong norm (children’s right) but others evaluate this norm as a weak one. It is conceivable that further distinctions may be perceived within the weak norms. For instance, it may be that the ‘unhappy moralist’ effect will more likely be found in the norm groups, which are to some extent moral. These would include the weak moral–legal and non-legal moral norm groups. As norms belonging to the non-moral legal group are not essentially wrong, they are expected to be violated more easily. Therefore it is less likely for a conflict to arise between the hedonistic desire and the norm, and therefore also less likely that a basis exists for the ‘unhappy moralist’ effect to occur. To summarize: distinctions between different norm groups are assumed in regard to the ‘unhappy moralist’ effect. The effect is expected to occur predominantly in the weak-norm groups as opposed to the strong-norm groups, and within the weak-norm groups it is expected to occur particularly in the moral–legal and non-legal moral norms. Thus one of the aims of the new research on this topic is to test these assumptions and to ascertain in which areas of norms the ‘unhappy moralist’ phenomenon is likely to occur.

Educational Consequences What about educational consequences? At present it is not at all clear how — on the basis of these findings — education can be conceived. We believe that two goals are central. First, teachers must choose situations and vignettes that contain issues of need/gains in contrast to issues of being moral or immoral. These situations must be as much as possible ethically loaded. Second, students — especially in adolescence — should learn that being moral has positive long-term effects, but in the short run humans often lose the strength for overcoming the immediate want and for resources to suppress a desire in order to keep morality alive. They must develop a notion of how internal and external pressures can inhibit the moral point of view. Since the ‘unhappy moralist’ effect produces a high emotional disequilibrium, we might teach our students that morality is only morality if it is in conflict with personal needs/gains that would precisely hurt this morality. They need to understand that it is this conflict that is at the core of moral emotions and that this disequilibrium is also the main source for moral education.

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References De Corte, E. (2003). Mainstreams and perspectives in research on learning (mathematics) from instruction. Applied Psychology: An international Review, 53, 279–310. Diener, E., & Suh, E. M. (2003). Measuring subjective well-being to compare the quality of life of cultures. In: E. Diener, & E. M. Shu (Eds), Culture and subjective well-being (pp. 3–11). Cambridge, MA: The MIT Press. Garz, D. (1999). “Also die Annahme, dass die Welt gerecht ist, das wäre sehr irrational”. Urteilen, Handeln und die Moral des Alltagslebens. In: D. Garz, F. Oser, & W. Althof (Eds), Moralisches Urteil und Handeln (pp. 377–405). Frankfurt: Suhrkamp. Hanisch, G. (1990). Problematik der Leistungsfeststellungen durch schriftliche Arbeiten am Beispiel der Mathematik. Habilitationsschrift, Wien: Universität Wien. Hascher, T. (1994). Emotionsbeschreibung und Emotionsverstehen. Zur Entwicklung des Emotionsvokabulars und des Ambivalenzverstehens im Kindesalter. Münster/New York: Waxmann. Hattersley, L. (2005). “Unhappy Moralist”: Doing right and feeling wrong. Eine empirische Arbeit zum Phänomen des unglücklichen Moralisten in Zusammenhang mit verschiedenen Normbereichen und anderen möglichen Einflussfaktoren. Lizentiatsarbeit, Freiburg, Schweiz: Universität Freiburg, Departement Erziehungswissenschaften. Keller, M., Lourenço, O., Malti, T., & Saalbach, H. (2003). The multifaceted phenomenon of ‘happy victimizers’: A cross-cultural comparison of moral emotions. British Journal of Developmental Psychology, 21, 1–18. Nisan, M. (1986). Die moralische Bilanz. Ein Modell moralischen Entscheidens. In: W. Edelstein, & G. Nunner-Winkler (Eds), Zur Bestimmung der Moral. Philosophische und sozialwissenschaftliche Beiträge zur Moralforschung (pp. 347–376). Frankfurt: Suhrkamp. Nucci, L. P. (2001). Education in the moral domain. Cambridge, New York, Oakleigh: Cambridge University Press. Nunner-Winkler, G. (1989). Wissen und Wollen. Ein Beitrag zur frühkindlichen Moralentwicklung. In: A. Honneth, T. McCarthy, C. Offe, & A. Wellmer (Eds), Zwischenbetrachtungen. Im Prozess der Aufklärung (pp. 574–600). Frankfurt: Suhrkamp. Nunner-Winkler, G. (1993). Die Entwicklung moralischer Motivation. In: W. Edelstein, G. NunnerWinkler, & G. Noam (Eds), Moral und Person (pp. 278–303). Frankfurt: Suhrkamp. Nunner-Winkler, G. (1999). Moralische Motivation und moralische Identität. Zur Kluft zwischen Urteil und Handeln. In: D. Garz, F. Oser, & W. Althof (Eds), Moralisches Urteil und Handeln (pp. 314–339). Frankfurt: Suhrkamp. Nunner-Winkler, G. (2001). Freiwillige Selbsteinbindung aus Einsicht — ein moderner Modus moralischer Motivation. In: J. Allmendinger (Ed.), Gute Gesellschaft? Verhandlungen des 30. Kongresses der Deutschen Gesellschaft für Soziologie in Köln 2000 (pp. 172–196). Opladen: Leske + Budrich. Op ’t Eynde, P., & De Corte, E. (2002). Accepting emotional complexity: A component systems approach of emotions in the mathematics classroom. Paper presented at the symposium “Motivation and emotion research in education: Theoretical frameworks and methodological issues” at the 2002 Annual Meeting of the American Educational Research Association, New Orleans, Louisiana. Oser, F. (1999). Die missachtete Freiheit moralischer Alternativen: Urteile über Handeln, Handeln ohne Urteile. In: D. Garz, F. Oser, & W. Althof (Eds), Moralisches Urteil und Handeln (pp. 168–219). Frankfurt: Suhrkamp. Oser, F., & Reichenbach, R. (2000). Moralische Resilienz: Das Problem des “Unglücklichen Moralisten”. In: W. Edelstein, & G. Nunner-Winkler (Eds), Moral im sozialen Kontext (pp. 203–233). Frankfurt: Suhrkamp.

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Oser, F., & Reichenbach, R. (2005). Moral resilience. What makes a moral person so unhappy? Working paper. Schweiz: Universität Freiburg, Departement Erziehungswissenschaften. Seel, M. (1999). Versuch über die Form des Glücks. Frankfurt: Suhrkamp. Schmid, E. (2003). “Unhappy Moralist”: Das Phänomen des unglücklichen Moralisten. Eine entwicklungspsychologische Arbeit zur Emotionsattribution im moralischen Bereich. Lizentiatsarbeit. Freiburg, Schweiz: Universität Freiburg, Departement Erziehungswissenschaften. Solomon, R. C. (2000). Gefühle und der Sinn des Lebens. Frankfurt: Zweitausendeins. Turiel, E., & Smetana, J. G. (1986). Soziales Wissen und Handeln: Die Koordination von Bereichen. In: F. Oser, W. Althof, & D. Garz (Eds), Moralische Zugänge zum Menschen. Zugänge zum moralischen Menschen (pp. 108–135). München: Peter Kindt Verlag. Weinert, F. E., & Schneider, W. (1986). First report on the Munich longitudinal study on the genesis of individual competencies. (LOGIC). München: Max Planck Institute for Psychological Research.

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Chapter 10

Educational Assessment: Towards Better Alignment Between Theory and Practice James W. Pellegrino and Daniel T. Hickey

Introduction The literature on educational assessment is filled with research reports, theoretical papers, policy arguments, and practical guidelines. Many of these pieces debate the pros and cons of assessment design and use from the level of the classroom to state and national testing. Often the arguments are contentious, with individuals advocating for or against specific forms of assessment and/or their uses in the educational system. Despite the fact that assessment of individual intellectual performance has a long history of use in education, dating back to the development and use of the first tests of intelligence in France by Binet and Simon early in the 20th century (and Chinese civil service tests well before that), there is often more heat than light on discussion of the topic of educational assessment. In 2001, a report was issued by the U.S. National Research Council entitled Knowing What Students Know: The Science and Design of Educational Assessment (Pellegrino, Chudowsky, & Glaser, 2001). The goal of that report was to evaluate the state of research and theory on educational assessment and establish the scientific foundations for their design and use. As argued in that volume, many of the debates that surround educational assessment emanate from a failure to understand its fundamental nature, most especially the ways in which theories and models of learning and knowing interact with and influence assessment design and use. In this chapter we review key issues regarding educational assessment raised in that report and more recent research aimed at addressing those issues. Our goal is explicating, albeit in abbreviated form, current understanding of the science and design of educational assessment, while highlighting challenges in using assessment to enhance teaching and learning. Our analysis of assessment issues and our efforts to address them largely reflects the current educational climate in the U.S. (for a perspective that includes issues operative in Europe see Chapter 11 in this volume). Our concern is ensuring that some educative value is derived from current educational reform policies that rely extensively on the use of conventional Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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large-scale tests. In particular, we consider how the negative consequences of current policies and practices can be minimized, and how the significant funds and energy invested in the use of external, accountability-oriented assessments can be more productively balanced with improving classroom assessments that are ultimately more useful and beneficial for students and teachers. We believe that the issues considered here and the insights offered regarding resolution of tensions through a more reasoned application of research and theory are relevant to matters of assessment policy and practice in most, if not all, educational systems.

The Complex Landscape of Educational Assessment Educational Assessment in Context From teachers’ classroom quizzes to nationally and internationally administered standardized tests, assessments of students’ knowledge and skills have become a ubiquitous part of the educational landscape. There is now wide recognition that assessments that are properly designed and used can provide essential information to policy makers, administrators, teachers, parents, and students. Assessment is widely understood as a critical element in the educational enterprise, along with curriculum (knowledge and skills in subject matter areas that teachers teach and students are supposed to learn) and instruction (methods of teaching and the learning activities used to help students master the content and objectives specified by a curriculum). While the importance of assessment itself is currently well understood, there is less appreciation of the need to align assessment with curriculum and instruction (e.g., NCTM, 1995, 2000; NRC, 1996; Webb, 1997). Alignment, in this sense, means that the three functions are directed toward the same ends and reinforce each other rather than working at cross-purposes. Ideally, an assessment should reflect what students are actually being taught, and what is actually being taught should reflect the curriculum one wants students to master. Many of the tensions that surround assessment are the result of asynchronies between these functions. In reality, alignment is remarkably difficult to achieve, and the role of assessment in driving the system away from important curricular and instructional goals is frequently a major point of contention (e.g., Wilson, 2004). This is especially so with respect to both the perceived and actual impact of accountability-oriented tests administered on a large-scale basis in states, provinces, and countries. While it is particularly problematic when large-scale tests undermine classroom assessment practices, classroom assessment itself can also undermine classroom instruction. These tensions are partly a reflection of the more general failure to distinguish between the purposes of assessment and the levels at which assessments function. Thus, alignment of assessment with curriculum and instruction ultimately requires alignment of the different assessment practices present in most educational contexts. Assessment Purposes and Levels One of the central points of the Knowing What Students Know report was that assessments are developed for specific purposes and the nature of their design is very much constrained

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by their intended use. The reciprocal relationship between function and design leads to concerns about the inappropriate and ineffective use of assessments for purposes beyond their original intent. We contend that continued progress in the alignment of assessment practices requires us to reconsider the continual conflating of two pervasive dichotomies. The first dichotomy is between ‘internal’ classroom assessments administered by teachers and ‘external’ tests administered by districts, states, or nations. Ruiz-Primo, Shavelson, Hamilton, and Klein (2002) showed that these two very different types of assessments are better understood as two points on a continuum that is defined by the ‘distance’ from the enactment of specific instructional activities. They defined five discrete points on the continuum of assessment distance: immediate (e.g., observations or artefacts from the enactment of a specific activity), close (e.g., embedded assessments and semi-formal quizzes of learning from one or more activities), proximal (e.g., formal classroom exams of learning from a specific curriculum), distal (e.g., criterion-referenced achievement tests such as required by the U.S. No Child Left Behind legislation), and remote (broader outcomes measured over time, including norm-referenced achievement tests and some national and international achievement measures). (A similar continuum with somewhat different points and labels was defined by Kennedy, 1999.) One of our central arguments is that different assessments should be understood as different points on this continuum if they are to be effectively aligned with each other and with curriculum and instruction. As will be shown here, broad advantages accrue when moving from alignment across just two levels of assessment to three or more levels. We will return to this point subsequently. A second pervasive dichotomy constraining assessment is the one between ‘formative’ assessments used to advance learning and ‘summative’ assessments used to provide evidence of prior learning. Often it is assumed that classroom assessment is synonymous with formative assessment and that large-scale assessment is synonymous with summative assessment. We contend that what are now widely understood as different types of assessment practices are more productively understood as different functions of assessment practice, and that summative and formative functions can be identified for most assessment activities. The recklessness in conflating assessment level and assessment function is apparent when one considers common assessment practices such as formal classroom exams (roughly akin to the proximal level). Well-structured classroom exams have substantial formative potential for students when used by teachers for refining curriculum, providing remediation for specific topics or specific students and pacing instruction. In order to serve these formative functions, such exams necessarily define a relatively summative experience for students. Furthermore, some practices intended to maximize the formative potential of proximal-level assessments (e.g., by not grading performance or using open-ended performance tasks or essays) may actually undermine that formative potential (by failing to motivate students to try in the first place or by failing to cover enough of the curriculum). As we argue next, considering the formative and summative functions within each assessment level is essential to aligning functions across multiple levels. Balancing the Formative and Summative Functions of Assessment As highlighted in influential considerations by Sadler (1989) and Black and Wiliam (1998), assessment is ultimately about feedback. These and many other articles have led to

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widespread appreciation that assessment is valuable only to the extent that it generates useful information for advancing learning and instruction, and that this information is then acted upon. A central issue is the way that gathering and using information for more summative functions undermines gathering and using information from formative functions. Efforts to address these tensions are often characterized as efforts to ‘balance’ formative and summative assessment. This includes efforts to minimize the way external assessments undermine the formative potential of classroom assessments and efforts to broaden the formative potential of external assessments. A series of studies led by the second author and funded by the U.S. National Science Foundation has attempted to identify features of assessment practice that are particularly useful for balancing formative and summative functions. In addition to the notions of level and function outlined above, this work has identified several other seemingly useful features that have yet to be widely addressed in the assessment literature. One of these features, orientation, is simply a further consideration of the different levels defined by Ruiz-Primo et al. Because the levels are points on a continuum, defining the orientation of a particular assessment practice helps clarify formative and summative functions. For the immediate, close, proximal, distal, and remote levels, one can distinguish respective orientations as events, activities, curriculum, standards, and achievement/attainment. The utility of the orientation notion is apparent in the easily overlooked distinction between ‘event-oriented’ immediate-level assessments and ‘activity-oriented’ close-level assessments. Each enactment of a given curricular activity is different. Even within the same classroom, enactments of given activities can be quite different. Hence, event-oriented assessments provide useful information about particular enactments, while activity-oriented assessments should provide useful information about the particular curricular activity, relatively independent of the many different ways the activity may be enacted. As elaborated below, this distinction is crucial for maximizing the untapped formative potential of immediate- and close-level assessments. Other useful insights are provided by the distinction between ‘standards-oriented’ distal-level assessments and ‘achievement-oriented’ remote-level assessments. One of the most important issues facing accountability-oriented reforms in the U.S. is that efforts to increase scores on criterion-referenced tests (distal-level assessments that are aligned to each state’s content standards) are associated with declining scores on norm-referenced tests (remote-level assessments that are designed to compare the academic achievement of students across the country). Consideration of assessment orientation leads to another seemingly useful aspect of assessment that has heretofore attracted little consideration. Drawing from the work of Lemke (2000), it is apparent that different assessment practices can be understood as operating at different timescales. The timescales for the five levels defined above can be characterized as minutes, days, weeks, months, and years. Timescale is important because the different competencies that various assessments aim to measure (and therefore the appropriate timing for being impacted by feedback) are ‘timescale-specific’. The cycles, or periodicity, of educational processes build from individual utterances into an individual’s lifespan of educational development. What teachers and students say in class constitute verbal exchanges; these exchanges make up the lesson; a sequence of lessons makes up the unit; units form a curriculum, and the curricula form an education. Each of these elements

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operates on different cycles or timescales: second to second, day to day, month to month, and year to year. The usefulness of timescales is apparent, for example, in further clarifying the distinction between standards-oriented distal-level assessments and achievementoriented remote-level assessments. Typical distal-level assessments in the U.S. such as criterion-referenced achievement tests are usually designed to measure whether students have met a certain criterion of performance for the content covered in the preceding school year. Such tests, and the criteria associated with them, are regularly adjusted to reflect shifting content standards and expectations for students. This is quite different than the norm-referenced remote-level tests that are designed in a way that allows the assessment of performance relative to a nationally representative sample across years. Summary In this part of our chapter, we have tried to delineate both the importance of assessment in the educational process and some of the confusion that surrounds its use, differentiating between levels and functions. The level at which an assessment is intended to function, which involves varying distance in ‘space and time’ from the enactment of instruction and learning, has implications for how and how well it can fulfil various functions of assessment, be they formative, summative, or programme evaluation. We have further shown how levels and functions can be further appreciated by considering the orientation and corresponding timescales of different assessment practices. As we have argued elsewhere (Hickey & Pellegrino, 2005; Hickey, Zuiker, Schafer, Michael, & Taasoobshirazi, 2005), it is also the case that the different levels and functions of assessment can have varying degrees of match with theoretical stances about the nature of knowing and learning. In the second part of our chapter we explore this issue and discuss how broadening our views of knowing and learning can aid efforts to balance formative and summative functions and align assessment, instruction, and curriculum. To do so, we first focus on the fundamental nature of assessment and the three critical components that contribute to the design and use of any assessment. The conception of assessment as a process of reasoning from evidence applies regardless of the context in which the assessment is pursued or the purpose it is intended to fulfil.

Assessment as a Principled and Theory-Driven Activity Reasoning From Evidence Whatever their various roles in the educational system — e.g. classroom teacher, school principal, district superintendent, state superintendent, or national education secretary — educators make provision for the assessment of students to ascertain what they know and can do, presumably for the purpose of obtaining information that can lead to improvements in learning, instructional practice, resource allocation, and/or policy. While this intent seems rather benign, it is not a simple thing to assess students well. Fundamentally, assessing student knowledge and skill is not a straightforward process, certainly not as straightforward as measuring other attributes of persons and populations such as height or weight.

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As we shall see shortly, there are major issues regarding how to conceive of the nature of what is known that have substantial implications for the process of assessment design and use. Part of the contentiousness that often surrounds assessment focuses on the quality of the assessment in terms of what is assessed together with how and how well it is done, all of which impact the validity of the inferences that can be drawn based on the evidence obtained (e.g. Messick, 1995). The process of collecting evidence to support inferences about student knowledge represents a chain of reasoning from evidence that characterizes all assessments, from classroom quizzes and standardized achievement tests to computerized tutoring programmes and to the conversation a student has with her teacher as they work through an assignment. The process of reasoning from evidence in educational assessment can be portrayed as a triad of three interconnected elements. This has been called the assessment triangle (Pellegrino et al., 2001). The vertices of the assessment triangle represent the three key elements underlying any assessment: a model of student cognition and learning in an academic or occupational domain; a set of beliefs about the kinds of observations that will provide evidence of students’ competencies; and an interpretation process for making sense of the evidence. The three elements of cognition, observation, and interpretation may be explicit or implicit, but an assessment cannot be designed and implemented without some consideration of each. The three are represented as vertices of a triangle because each is connected to and dependent on the other two. A major tenet of the Knowing What Students Know report is that for an assessment to be effective, the three elements must be in synchrony. In fact, it is often the tacit or hidden nature of basic assumptions regarding the three foundational elements and the failure to question the assumptions about one or more of them and their interconnections that creates conflicts about the meaning and value of assessment results. The cognition corner of the triangle refers to a theory or set of beliefs about how students represent knowledge and develop competence in a domain. The theory should represent the most scientifically credible understanding of typical ways in which learners represent knowledge and develop expertise in that domain. These findings should derive from cognitive and educational research about how people learn, as well as the experience of expert instructors. As scientific understanding of learning evolves, the cognitive underpinnings of assessment should change accordingly. As discussed later, theories of student learning and understanding can take different forms and encompass several levels and types of knowledge representation that include social and contextual components. This in turn has implications for assessment design and use. It would be unrealistic to expect that assessment design could take into account every subtlety and complexity about learning in a domain that has been uncovered by research. Instead, our proposal is that assessment design should reflect contemporary psychological perspectives on knowledge, but in a manner that best accomplishes the formative and summative functions associated with the particular assessment practice. The observation corner of the assessment triangle represents a description or set of specifications for assessment tasks that will elicit illuminating responses from students. The observation model describes the stimuli presented to examinees and the products, such as written or oral responses, or the answers students have to choose among for multiple-choice

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items. In assessment, one has the opportunity to structure some small corner of the world to make observations. The assessment designer can use this capability to maximize the value of the data collected, as seen through the lens of the underlying beliefs about how students learn in the domain and what is important knowledge to assess. Finally, every assessment is based on certain assumptions and models for interpreting the evidence collected from observations. The interpretation corner of the triangle encompasses all the methods and tools used to reason from fallible observations. It expresses how the observations derived from a set of assessment tasks constitute evidence about the knowledge and skills being assessed. It includes the rules used for scoring or evaluating students’ responses. In the context of large-scale assessment, the interpretation method also usually includes a statistical model, which is a characterization or summarization of patterns one would expect to see in the data given varying levels of student competency. In the context of classroom assessment, the interpretation is often made less formally by the teacher, and is usually based on an intuitive or qualitative model rather than a formal statistical one. As will be elaborated below, in the kinds of immediate-level and close-level assessments that have the most potential for advancing student understanding, the interpretation is a largely discursive one that considers the shared knowledge that is being negotiated among all of the participants and artefacts that define the enactment of a set of instructional intentions. To have an effective assessment, all three vertices of the triangle must work together in synchrony. For instance, a cognitive theory about how people develop competence in a domain like algebra provides clues about the types of situations that will elicit evidence about that competence. It also provides clues about the types of interpretation methods that are appropriate for transforming the data collected about students’ performance into meaningful assessment results. And knowing the possibilities and limitations of various interpretation models helps in designing a set of observations that is at once effective and efficient for the task at hand. To build a credible assessment and to effectively and properly use it, all three vertices of the triangle must work together in synchrony. Central to this entire process of building a credible assessment and of effectively and properly using it are theories and data on how people learn and what students know as they are instructed and develop competence in aspects of a curriculum. This is the cornerstone of assessment design and use, and forms the basis of evidential and consequential validity (Hickey, Wolfe, & Kindfield, 2000; Messick, 1994). It has been duly noted that current assessment practices are the cumulative product of multiple factors including theories of learning and models of measurement that were developed to fulfil the social and educational needs of a different time (e.g. Pellegrino, 2004; Pellegrino, Baxter, & Glaser, 1999). Mislevy’s (1993, p. 19) aptly stated argument still holds today: “It is only a slight exaggeration to describe the test theory that dominates educational measurement today as the application of 20th century statistics to 19th century psychology”. Although the core concepts of prior theories and models are still useful for certain purposes of assessment at certain levels, they need to be augmented or supplanted to deal with newer assessment needs. Thus, it is critical to lay out the succession of theoretical perspectives on the nature of cognition that characterize the 20th century up to the present and what they imply for assessment practice.

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The Relationship Between Theories of Knowing and Learning and the Design and Use of Assessment Until recently, the assumptions underlying different assessment practices and designs were largely implicit. Many of the tensions accompanying different functions of assessment and the evidential and consequential validity of different forms of assessment are rooted in their underlying assumptions about cognition. We examine these assumptions, starting from what are generally acknowledged as the three ‘grand theories’ of knowing and learning, using widely recognized labels of behavioural/empiricist, cognitive/rationalist, and situative/socioculturalist (see e.g., Case, 1996; Greeno, Collins, & Resnick, 1996). The following is an overview of the application of this ‘comparative’ approach to assessment. Behavioural/empiricist views Empiricist views of knowing and teaching are embodied in the behaviourist models associated with Skinner. However, the initial human information-processing models following the ‘cognitive revolution’ in the 1960s also embraced empiricist assumptions within the cognitivist perspective (essentially using specific mental associations rather than specific stimulus-response associations). Empiricist perspectives are inherently reductionist (assuming that complex behaviour or concepts consist of smaller elements) and additive (assuming these smaller elements then assemble into an accurate representation of the more complex entity). Learning is seen as the process of forming, strengthening, and adjusting the specific associations presumed to define knowledge. Therefore, the transfer of learning to a new situation depends on the number and nature of the associations that are needed in the new situation, relative to the number and nature of the associations acquired in the previous environment. By demonstrating that students have made associations that are generally agreed to be useful in some transfer environment, the students are presumed to have some transferable knowledge. This can be done quite efficiently by asking students to recognize or recall those same associations or to make new higher-order associations between existing lower-level associations. Multiple-choice and short-answer testing formats are well suited for assessing the transfer of knowledge in this regard. In the classroom setting teachers routinely use such tests, often obtaining them from teacher versions of their textbooks or from supplementary materials. Because recognition-level items are generally answered quite quickly, they allow for tests that cover a broad representation of the domain. By creating large pools of such items, random collections of such items provide assessments that are not biased towards any particular curriculum. When coupled with sophisticated psychometric techniques such as Item Response Theory (IRT), empiricist assumptions about knowledge afford much of what the modern testing industry has to offer. IRT makes it possible to model the relative difficulty of specific items and the relative proficiency of individuals with respect to those items, allowing items to be substituted as necessary to create new secure test forms that efficiently and reliably compare students’ familiarity with academic domains of knowledge. As long as one assumes that the items included in such tests are presumed to be an essentially random sample of the associations that make up the domain, such assessments represent a valid assessment of the transferable associations an individual possesses. In terms of content coverage, tests using such items are often assembled with a range of ability in mind. For each content

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area, a pool is assembled with items that range in difficulty, and items are selected from that pool in order to create a test that captures a broad range of ability. While such assessments are ideal for comparing multiple curricula, they are widely believed to be less useful for refining instruction tied to a specific curriculum, for guiding remedial instruction for specific topics or individuals, or for directly advancing student learning. The obvious exception is in explicitly empiricist curricular approaches such as direct instruction in which content domains are deliberately broken down into numerous specific associations that are directly taught and assessed (e.g., Fredrick, Deitz, Bryceland, & Hummel, 2000). A rationalist view The Knowing What Students Know report pointed out that conventional achievement tests are ‘based on highly restrictive beliefs about learning and competence not fully in keeping with current knowledge about human cognition and learning’ (Pellegrino et al., 2001, p. 2). These and several other recent reports support the long-standing argument that (1) many current assessment practices are based on outdated behaviourist theoretical assumptions, (2) that these assumptions need to be acknowledged and challenged, and (3) that newer cognitive theories of knowing and learning have untapped potential for improving assessment (e.g., Gipps, 1999; Mislevy, 1993; Resnick & Resnick, 1992). These newer theories are often labelled cognitive/rationalist. Rationalist perspectives became the major focus of psychological research on learning in the 1970s. While there was a shift away from the explicitly Piagetian ‘stage-theory’ models in the 1980s, rationalist models continue to be very influential in educational and cognitive psychology. (See Case, 1996, for a detailed discussion of the shifts within each of the three perspectives.) This family of perspectives views knowledge in terms of structures of information and processes that recognize and make sense of (i.e., ‘rationalize’) symbols in order to understand concepts and exhibit general abilities. From this perspective, knowledge of a domain consists of general reasoning schemata as well as more domain-specific concepts and specific processes. The interested reader should see Bransford, Brown, Cocking, Donovan, and Pellegrino (2000) for a general summary of research and theory within the rationalist perspective. Within this perspective, when an individual demonstrates knowledge of something, she or he is presumed to do so by marshalling the various higher-level knowledge structures needed to construct a solution (i.e., make sense of) given the demands of the particular task. Such knowledge is acquired via the process of constructing the mental structures that represent those concepts. This includes the development of high-level structures used to solve very general problems as well as the construction of very specific knowledge structures that are more relevant to specific domains. When knowledge is viewed in terms of general conceptual schemata, assessment must be concerned with students’ ability to employ those schemata in a variety of ways including larger, extended tasks that differ from those that individuals have previously encountered. Thus, an appropriate environment for assessing students’ ability to transfer knowledge presents learners with new problems that require them to apply the higher-level knowledge structures that were presumably constructed in the original learning environment. In contrast to the more random process that follows from empiricist perspectives, doing so generally calls for systematic consideration of the knowledge structures that define the domain (e.g., Mislevy, Steinberg, & Almond, 2002). Evaluations of specific

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learning environments must verify that schemata presumably constructed in learning environments can be used to solve new problems in different contexts. Some types of the familiar open-ended ‘constructed-response’ items assess higher-level knowledge, and they can be obtained, administered, and scored with modest effort and high reliability. Among alternatives consistent with a rationalist perspective are the multi-step ‘performance assessments’ that generally involve some sort of inquiry activity. Their distinguishing characteristic is the need to give explanations, or rationale, for phenomena. Performance assessments are challenging to develop and use, particularly in the context of large-scale testing programmes (Solano-Flores & Shavelson, 1997). There are many collections of performance assessments marketed or available for classroom use, and many sources offer useful guidelines for creating performance assessments (e.g. Stiggins, 1997, 2001; Wiggins, 1998; Wiggins & McTighe, 1999). Because performance assessments are relatively time consuming to administer and score, they cannot sample a range of content. As such, items need to be selected and interpreted with care. From a rationalist perspective, these are simply technical problems and are addressed by thoughtful analysis of the higher-level knowledge structures that represent the desired learning outcomes (Hickey & Zuiker, 2005). The assessments that follow from a rationalist perspective seem to offer a useful balance of formative and summative functions that seem ideally suited to formal classroom assessment. Situative/sociocultural views Newer situative and sociocultural views of knowing and learning question the notion that knowledge is acquired by, and resident in, the minds of individual knowers (e.g. Greeno et al., 1996; Wenger, 1998). Rather, knowledge is viewed as being constructed through, and fundamentally residing in, ritualized cultural practices. Knowing What Students Know (Pellegrino et al., 2001) and other recent calls to broaden assessment (e.g. Mislevy et al., 2002) certainly acknowledge these views. Arguably though, their consideration and recommendations for assessment still take for granted individually oriented cognitive assumptions about knowing and learning. For example, the guidelines for representing knowledge in assessments in Knowing What Students Know rely exclusively on cognitive notions such as schema theory, expert–novice differences, and conceptual change. Doing so means that notions of context and language that have unique significance in sociocultural views are represented using conventional individually oriented cognitive views. Rather than treating collective discourse as evidence of knowledge (as in sociocultural assessment practices), classroom discourse is characterized only as another tool for helping individuals learn and assess what individuals ‘know’. Arguably then, many calls to broaden our theoretical perspective on assessment to include modern cognitive perspectives are themselves based on views of knowing and learning that others find relatively narrow (Delandshere, 2002). Consensual characterizations of sociocultural perspectives, particularly situative cognitive theory (e.g. Greeno et al., 1996), are still emerging. An essential aspect of sociocultural perspectives that is often overlooked concerns the relationship between the individual and the broader environment in which the individual operates. Both behavioural/empiricist and cognitive/rationalist perspectives make a clear distinction between the individual and the environment. Sociocultural perspectives assume a dialectical relationship between the individual and the environment, in terms of ongoing relations between the changing individual and the changing social context (Beach, 1999). This means that using knowledge changes the nature

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of that knowledge, and that knowledge is ‘stretched across’ the social and physical contexts of its use (Cole, 1991). The assumption that knowledge resides in social contexts, rather than individuals, presents challenges for conventional assessment. This view argues that the learning that occurs in a particular learning environment resides ultimately in the participatory rituals of the community, rather than in the minds of the individual participants. Thus, assessment must consider the way that knowledge rituals are adapted and appropriated by the learners, and how this ritualized participation transfers to subsequent environments. Because this participation necessarily changes that knowledge, learning is represented by the collective change in the participants and the physical and social context that supports their participation. Thus, for example, assessments from this perspective would need to recognize that students will be more knowledgeable about a particular topic when participating in subsequent activities that involve their classmates with whom they learned that topic in the first place. For these reasons, the event, rather than the individual, is the primary unit of analysis for assessing knowledge from a sociocultural perspective. Thus, the use of interpretive eventbased methods such as discourse analysis (e.g. Gee & Green, 1998) is ideally suited for assessing knowledge from this perspective. However, such methods are time intensive and do not yield the types of individual-level evidence that are often expected in many research and evaluation contexts. More importantly, because such assessment embraces an entirely different set of assumptions about making and warranting claims about knowledge, other scientific communities and policy makers are likely to dismiss any evidence gathered using such methods as anecdotal and unscientific (e.g. Shavelson, Phillips, Towne, & Feuer, 2003). Connecting Levels, Functions, and Theories Thus far we have presented various lenses that must be brought to bear in understanding issues associated with the many different forms of assessment used in the educational system. A reasonable question is whether there is a sensible way to bring together concerns about levels, functions, and theories of knowing and learning. We believe that there is. Elsewhere we have developed in some detail the argument that there is a systematic way to connect together level, function, and theoretical orientation to more productively approach the design and use of assessment. What follows is an abbreviated description of the proposed framework, focusing primarily on the first two levels. For additional details and applications, see Hickey and Pellegrino (2005) and Hickey et al. (in press). The first three columns of Table 1 show the five levels of assessment described earlier, along with their primary orientations and timescales. Our current understanding of the optimal formative and summative functions at each level are listed in the fourth and fifth columns of Table 1. While it is important to reiterate that the five levels are points on a continuum, we also contend that defining discrete levels is crucial for balancing formative and summative functions. Working with at least three such adjacent levels at a time (e.g. close, proximal, and distal) makes it possible to use formative feedback at the first level to improve outcomes at the second level (maximizing ‘consequential’ validity), while preserving the summative value of the third level (maximizing ‘evidential’ validity). We further contend that doing so requires the use of newer ‘design-based’ educational research methods, particularly as advanced by leading sociocultural theorists (e.g. Cobb, Confrey, diSessa, Lehrer, & Schauble, 2003; Collins, 1999).

Optimal summative function

Prototypical domain knowledge representation

Prototypical assessment format

Specific events

Minutes

Guide and refine enactment of specific curricular routines. Informally advance participation domain discourse.

Informally assess whether routines are enacted as intended within specific activities.

Enacted knowledge practices, discourse during a specific curricular routine.

Event-oriented observations; guidelines and exemplars for classroom discourse.

CLOSE (semi-formal classroom assessment)

Specific activities

Days

Give all students more robust understanding of the topic. Support semi-formal remediation for specific students and/or topics. Guide the refinement of specific activities.

Assess whether students can engage in discourse around the content in specific activities.

Semi-formal representation, discourse around representations similar to the curricular routines.

Activity-oriented quizzes and discursive formative feedback.

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IMMEDIATE (artefacts from the enactment of the curriculum)

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Optimal formative function

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Primary Timescale orienrelationtation ship to curricula

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Level (example)

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Table 1: Five levels of assessment (Source: Hickey & Pellegrino, 2005; Hickey et al., in press).

Formal representation of the concepts covered in the curriculum.

Curriculumoriented exams and conceptual formative feedback.

Regional Months or national content standards

Help teachers and researchers see if students can use knowledge in formal high-stakes context. Guide refinement of entire curriculum accordingly.

Assess whether students meet specific criteria, compare curricula in this regard.

Formal representation of associations drawn from the standards.

Criterionreferenced tests carefully aligned to content standards.

REMOTE (normreferenced external tests)

National achievement

Help researchers and policy makers see if curricular standards and curricular reforms are effective.

Impact of broader changes to curriculum and standards.

Formal representation of associations drawn from national samples of achievement.

Normreferenced tests.

Years

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Assess whether students learned intended content in specific curriculum.

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Help all students transfer new knowledge to more formal representation. Support formal remediation for specific students and/or topics. Guide refinement of curricular sequence.

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Weeks

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We contend that balancing between levels and functions is further facilitated when different forms of knowledge representation are explicitly acknowledged and appropriately used as an interpretive base at each level. Specifically, the claim we advance here is that the immediate-level observations of curricular enactments are more consistent with sociocultural assumptions about knowing and learning; the proximal-level problem-solving classroom assessments are more consistent with rationalist assumptions, and the remotelevel norm-referenced achievement tests are more consistent with empiricist assumptions. Our framework aims to advance assessment practice by arguing that there are actually fundamental relationships between theories and levels, and that the diverse educational goals of assessment will be better met if assessment practice recognizes and embraces them. This is especially important in avoiding persistent misunderstandings by educators, policy makers, the public and the media arising from the misuse of assessment results at one level to make evaluative judgments of educational outcomes associated with another level. Our initial characterization of the relationship between theories and levels and prototypical assessment forms is detailed in the sixth and seventh columns of Table 1. For pragmatic purposes, we choose to characterize this relationship in terms of the prototypical or ‘bestfitting’ manner for representing knowledge at each level. These are initial characterizations and will continue to need refinement. For now, we propose that assessment practices at the immediate, proximal, and remote levels prototypically need to embrace sociocultural, rationalist, and empiricist assumptions, respectively, while the close and distal levels are most likely to employ hybrid sociocultural/rationalist and rationalist/empiricist assumptions. Implicit in these characterizations is the idea that transfer across different forms of knowledge representations is unidirectional. While we have yet to prove this assumption experimentally, some of the prototypical assessments discussed in the next section emerged from efforts to maximize the consequences of formative feedback at one level for summative performance at the next level (e.g. Hickey, Kindfield, Horwitz, & Christie, 2003). These efforts have convinced us that the ‘cultural’ knowledge that results from meaningful participation in domain discourse transfers readily to ‘cognitive’ representations of that knowledge, and transfers moderately to ‘behavioural’ representations of that knowledge — but the inverse is usually not true. This means that formative feedback on proximal-level performance assessments will likely help students recognize correct associations on distal-level norm-referenced tests, but that formative feedback on external multiple-choice tests (as in the ubiquitous test-prep programmes that are now prevalent in the U.S.) will likely not help students solve problems on performance assessments (and might actually diminish participation in classroom discourse).

An Agenda for Research and Development: Increasing the Educational Value of Assessments Focusing on Formative Assessment When one examines the large research literature on assessment, it is clear that the bulk of the work that has been done is focused on large-scale assessments deployed for summative purposes. More recently, attention has shifted to the importance of formative assessment, based

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in part on the influential review by Black and Wiliam (1998). Arguably, the vast majority of work on formative assessment reflects a modern cognitive rationalist perspective. While we see great promise in the continued application of research and development rooted with the cognitive/rationalist perspective on classroom-based formative assessment, we also believe that there is untapped potential in the application of a situative/sociocultural perspective as a way of further expanding the formative potential of assessment practices. This potential is most apparent to us, and least explored by others, as it concerns immediate- and close-level assessment, particularly when these assessments are used within the newer design-based research methods as promoted by leading situative/sociocultural theorists. These ideas for enhancing teaching and learning by focusing on more cultural representations of domain knowledge are certainly not new. In many respects, these ideas mirror the suggestions that some communities of educational scholars (particularly language educators and linguists) have been making for decades. Many of these ideas draw directly from the wealth of socioculturally inspired research that has emerged in most content domain areas in the last decade. What seems unique is the way that these new practices reflect a relatively agnostic approach towards one’s characterization of the fundamental nature of knowledge and learning. The ideas presented below reflect a very ‘functional’ approach that embraces and refines whatever characterizations produce the broadest, most desirable outcomes. These ideal models of immediate- and close-level assessment emerged across several successive multi-year studies. In each study, design-based research methods were used to define and refine approaches to classroom assessment that yielded the largest gains on proximal-level classroom performance assessments and on distal-level multiple-choice achievement tests. What follows is a brief exposition of our current thinking about how this work might proceed for immediate- and close-level assessment, including references to recent and ongoing papers in which these ideas are explored in more detail. Immediate-level Event-Oriented Observations We propose that ideal immediate-level assessments assess knowledge that is represented in collective participation in the varied discourses that comprise the enactment of specific curricular routines. While this includes conversation, it also includes any interaction with the symbols and signs of the domain, regardless of whether it is collaborative or solitary. Because teachers and students can directly observe discourse, formative feedback can also directly and immediately enhance it. This feedback is also useful for providing teachers with useful guidance regarding the structure of the individual curricular routines, and guiding their refinement. As such, assessment at the immediate level should minimize formal summative functions (such as grades) because doing so will directly undermine that formative potential. Effective immediate-level assessment requires a systematic delineation of the discourses that define the domain knowledge that is represented more formally in targeted learning standards. In our ongoing work we have been developing guidelines for teachers and students that help ensure that productive domain discourse ensues when specific curricular routines are enacted (e.g. criteria for guiding formation of student explanations as tabled in Duschl & Gitomer, 1997). For example, one of our initial projects involved a curriculum that featured guided inquiry investigations that built on the sophisticated modeling technology built into the

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GenScope introductory genetics software (Horwitz & Christie, 2000). Student discourse initially focused on the specific features of the GenScope environment (the five multimedia ‘windows’ representing the different levels of biological organization, and the various traits of the fanciful ‘dragons’ that the activities involved). In an effort to increase domain discourse, a science educator/geneticist enhanced the student and teacher versions of the worksheets, including detailed descriptions of the biological phenomena and ‘key points’ using more conventional text and diagrams. Teachers and students were encouraged to use those materials when they enacted the investigations; reflecting the central vision of our multi-level model, they were reminded that doing so would ensure that students did well on the close-level quizzes that would be completed when the activity was completed. In other projects currently underway, we have been providing immediate-level support by providing teachers with print- and video-based guidelines that present specific examples of the forms of student discourse that should occur for very specific curricular routines (Anderson, Zuiker, Taasoobshirazi, & Hickey, 2005). In practice, the immediate-level assessment ends up getting rather informally ‘folded into’ the close-level assessment. Specifically, the act of crafting print- or video-based guidelines for the discourse that should emerge when an activity is enacted, as well as drafting the ‘answer explanation’ formative feedback rubrics for the close-level quizzes (described next) provides useful guidelines for the enactment of the associated curricular routines. The teachers and curriculum developers end up using those rubrics to guide their observation and refinement of the routine, in order to prepare students to succeed on the quiz. As described next, more formal efforts to facilitate participation in domain discourse can take place around the close-level assessments. Assessment at the Close Level A great deal of our effort has been invested at directly refining close-level assessments and aligning them with assessments at other levels. Our close-level quizzes are ‘activity-oriented’. This means that they represent domain knowledge using similar content and context as the curricular routines. After completing quizzes, students collaboratively review their completed assessments using a ‘learner-oriented’ formative feedback rubric. These rubrics and our efforts to use them to scaffold participation in domain discourse and argumentation are perhaps the most salient and most scalable aspect of this approach (Hickey et al., 2003). These rubrics offer detailed explanations of the reasoning behind each quiz item, without directly stating the ‘correct’ answer. Unlike conventional scoring rubrics, they also include details that are not technically ‘necessary’. Students use their completed assessments and the rubrics to discuss their understanding of the assessed topics during carefully orchestrated ‘assessment conversations’. Reflective of the largely formative function of these assessments, students need to only participate meaningfully in a feedback conversation at a level consistent with their abilities and capabilities. Although the answer explanations do have to be comprehensible, they do not need to be artificially simplified. In our vision, the familiar knowledge representations and a minimally summative administration context provide a supportive environment where students can use the answer explanation rubrics to ‘try-out’ the nuances of authentic domain discourse (e.g., Gee, 2003; Sfard, 2000) and ‘try-on’ the identities that are presumed to define domain

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expertise (e.g., Nasir, 2002). This aspect of our effort is shaped by sociocultural research on classroom culture and discourse. Broadly conceived, the feedback conversations are intended to foster a ‘third space’ for authentic interaction (Gutierrez, Rymes, & Larson, 1995). In this view, the ‘scripts’ of schooling and the scripts of academic domains intersect the ‘counter-scripts’ of students’ everyday social and epistemological experiences. Such a space is supported through design elements of the activity. One of our central goals in refining feedback conversations is ensuring that a ‘local accountability’ emerges, where students and teachers hold each other accountable for increasingly sophisticated participation in authentic domain discourse. In this regard, we assume that many of the welldocumented, negative consequences of competition and extrinsic rewards (Kellaghan, Madaus, & Raczak, 1996) stem from excessively summative assessments that highlight shortcomings in the absence of opportunity to improve (Collins, Brown, & Newman, 1989; Hickey, 1997). Conversational feedback therefore prioritizes the enhancement of student knowledge over all other functions. Unlike narrower test-preparation methods, this approach does not simply identify and correct specific lower-level associations. Rather, it is intended to scaffold the assessment-related discourse (and ultimately the broader classroom culture) towards what Bereiter and Scardamalia (1989) describe as ‘intentional learning’.

Concluding Comments: A Vision of the Future Assessment is a very critical aspect of the educational process and although it is a complicated and sometimes confusing enterprise, much has advanced in the way of theory and research to sort out many of the complexities and to offer direction for the future. It is the future that we consider here by offering a vision of what might be possible. Students will be given worthwhile opportunities to apply what they have learned and to get prompt and useful feedback. Some of these opportunities will not even be referred to as ‘assessments’ but rather will just seem like slightly more structured versions of activities that have already been completed. Other opportunities will be more formal, but students will approach those activities with confidence that their prior activities have prepared them to do well, while still appreciating that these new opportunities can help them learn even more. Ultimate and intermediate learning goals will be shared regularly with students as a part of instruction. Students will be engaged in activities such as peer and self-assessment to help them internalize the criteria for high quality work and develop metacognitive skills. Teachers will assess students’ understanding frequently in the classroom to refine the enactment of curricular activities and revise the activities themselves, and determine next steps for instruction. Teachers’ classroom practices will be grounded in principles of how expert thinking and learning develops in content domains and of assessment as a process of reasoning from evidence. They will use this knowledge to provide students with feedback about particular qualities of their work and what they can do to improve. But teachers will not be expected to design all of their classroom assessments on their own; they will have access to a variety of research-based classroom assessment tools designed to be practical for use in the classroom. Some of the tools will utilize computers and other technologies that make it feasible to provide individualized assessment and instruction to students, with the teacher serving

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as mediator. Teachers will also use summative assessments for ongoing reflection and feedback about overall progress and for reporting this information to parents and others. Policy makers, educators, and the public will understand distal-level standardized assessments as ‘indirect’ indicators of students’ knowledge, based on necessarily constrained representations of domain knowledge. In particular, they will appreciate that because such tests are oriented towards content standards rather than specific curricula, their value for directly advancing student knowledge and refining particular curricula is limited. Rather, they will understand such assessments as useful tools for comparing different curricula and evaluating policy decisions. Specifically policy makers and administrators will ensure that such tests are sufficiently aligned to proximal-level assessments used by teachers, and help ensure the evidential and consequential validity of those assessments. Efforts will be made to minimize directly teaching to specific distal-level tests, and any large-scale score increases on targeted tests will be viewed with caution. Within the education system, students, teachers, administrators, and policy makers will work from an appropriate knowledge base about how students learn subject matter and what aspects of competence are important to assess. Resource materials that synthesize modern scientific understanding of how people learn in areas of the curriculum will serve as the basis for the design of classroom and large-scale assessments, as well as curriculum and instruction, so that all the system’s components work towards a coherent set of learning goals. In many ways, the vision outlined above represents a significant departure from the types of assessments typically available today and from the ways in which such assessments are most commonly used in educational practice. Achieving this vision will not be easy since it involves numerous changes in educational policy and practice. Nevertheless, any hope of progress will continue to depend on advances in research and theory within disciplinary fields concerned with human cognition and the translation of such knowledge into effective educational practice.

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Stiggins, R. (2001). The unfilled promise of classroom assessment. Educational Measurement: Issues and Practice, Fall 2001, 5–15. Webb, N. L. (1997). Criteria for alignment of expectations and assessments in mathematics and science education (Research Monograph No. 6). National Institute for Science Education and Council of Chief State School Officers. Washington, DC: Council of Chief State School Officers. Wenger, E. (1998). Communities of practice: Learning, meaning, & identity. Cambridge: Cambridge University Press. Wiggins, G. (1998). Educative assessment: Designing assessments to inform and improve student performance. San Francisco: Jossey-Bass. Wiggins, G., & McTighe, J. (1999). Understanding by design. Washington DC: Association for Supervision and Curriculum Development. Wilson, M. (2004). Assessment, accountability and the classroom: A community of judgment. In: M. Wilson (Ed.), Towards coherence between classroom assessment and accountability. 103rd Yearbook of the National Society for the Study of Education, Part II (pp. 1–19). Chicago: University of Chicago Press.

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Learning and the Emerging New Assessment Culture Filip Dochy, David Gijbels, and Mien Segers

Introduction In recent years, education has frequently been blamed because graduates are not sufficiently able to apply their knowledge to solve complex problems in a working context. The development and implementation of instructional practices that will foster students’ skills to communicate, think, and reason effectively, make judgements about the accuracy of masses of information, solve complex problems, and work collaboratively in diverse teams, remain an important challenge for today’s higher education (Pellegrino, Chudowsky, & Glaser, 2001). Overall, it is claimed that ‘powerful’ or ‘new’ learning environments have the potential to improve these educational outcomes for students in higher education (De Corte, 2000; Lea, Stephenson, & Troy, 2003; Simons, van der Linden, & Duffy, 2000). Currently, the new teaching and assessment conception stresses the importance of the acquisition of specific cognitive, meta-cognitive, and social competencies (Dochy & Moerkerke, 1997). Feltovich, Spiro, and Coulson (1993), and use the concept of ‘understanding’ to describe the main focus of the current instructional and assessment approach. They define understanding as “acquiring and retaining a network of concepts and principles about some domain that accurately represents key phenomena and their interrelationships and that can be engaged flexibly when pertinent to accomplish diverse, sometimes novel objectives” (p. 181). In order to reach this goal of deep understanding new instructional methods were needed. A vast amount of research in cognitive psychology has influenced the instructional process (Segers, Dochy, & De Corte, 1999). As Mislevy (1996) has stated: “The cognitive revolution is a fait accompli in psychology, and it has begun to influence the ways in which the educators seek to characterize, monitor, and advance students’ learning.” (p. 411). De Corte (1990, 1996) refers to the design of powerful learning environments characterized by the view that learning means actively constructing knowledge and skills on the Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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basis of prior knowledge. Glaser (1990) and Lohman (1993) argued that the changing goals, the new methods of instruction as well as new findings and insights about novel learning environments point to the necessity of reconceptualizing current tests and assessments and critically examining their underlying theory. It is generally accepted that assessment has an important impact on instruction and learning (Gibbs, 1999; Scouller, 1998). The alignment between the objectives of the learning environment and assessment procedures that are used is viewed as a ‘magic bullet’ in improving learning (Cohen, 1987). However, the direct and indirect impacts of assessment may either be positive or negative (Crooks, 1988). The main purpose is to make the assessment congruent with the instruction and align the assessment to what students should be learning (Biggs, 2003). The traditional view that the assessment of students’ achievement is separate from instruction and only comes at the end of the learning process, is no longer tenable. As assessment, learning, and instruction become more and more integrated, there is a strong support for representing assessment as a tool for learning (Dochy & McDowell, 1997; Sambell, McDowell, & Brown, 1997). Whereas in the past, we have seen assessment primarily as a means to determine measures and thus for certification (referred to as the ‘testing culture’), there is now evidence that the potential benefits of assessment are much wider and impinge on all stages of the learning process (referred to as the ‘assessment culture’).

The Assessment Culture New assessment modes such as observations, text- and curriculum-embedded questions, interviews, over-all tests, simulations, performance assessments, writing samples, exhibitions, portfolio assessment, product assessments, and modes of peer- and co-assessment have been investigated more and more in recent years (Birenbaum & Dochy, 1996; Topping, 1998) and a set of criteria for new assessment practices has been formulated (Birenbaum, 1996; Feltovich et al., 1993; Glaser, 1990; Shavelson, 1994). Generally speaking, the current assessment culture can be characterized as follows (Birenbaum, 1996; Dochy, 2001). There is a strong emphasis on the integration of assessment and instruction. Many assessment specialists take the position that appropriately used educational assessments can be seen as tools that enhance the instructional process. Additionally, there is a strong support for representing assessment as a tool for learning. The position of the student is that of an active participant who shares responsibility in the process, practices self-evaluation, reflection and collaboration, and conducts a continuous dialogue with the teacher. Students participate in the development of the criteria and the standards for evaluating their performance. Both the product and process are being assessed. The assessment takes many forms, all of which are generally referred to as ‘unstandardized assessments embedded in instruction’ and more often there is no time pressure, and a variety of tools that are used in real life for performing similar tasks are permitted. The assessment tasks are often interesting, meaningful, authentic, challenging, and engaging, involving investigations of various kinds. Also, students sometimes document their reflections in a journal and use portfolios to keep track of their academic/vocational growth. Reported practices shift from a single score to a profile, i.e. from quantification to a portrayal (Birenbaum, 1996).

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Important Issues in the Assessment Culture In this paragraph some important issues in the so-called ‘assessment culture’ — a consequence of the need to make learning and instruction more in congruence with assessment — are discussed. We refer to the results of a recent meta-analysis, which looked at the effects of the new ‘problem-based’ learning environments from the angle of assessment, to show that there remains a lot to be done in order to fully align today’s educational goals, instructional practices, and students’ assessment. Next, different effects of assessment on students’ learning, such as pre-, post-, and true-assessment effect, are explained. Finally, recent investigations are summarised, pointing at the important relationships between assessment and student motivation, the impact of more formative assessment and the impact of assessment on students’ approaches to learning, assessment preferences and perceptions. New Learning Environments and Alignment: The Case of Problem-Based Learning Bridging the gap between new developments in the assessment culture and the daily educational and assessment practice faces a number of difficulties (Black & Wiliam, 1998). For one, many scholars and teachers still have to be convinced that they cannot use a new form of constructivist-oriented learning environment without adapting the assessments. Problem-based learning (PBL) is an example of a new learning environment, based on constructivist learning principles, which aims at educating students who are able to solve complex problems (Birenbaum, 2003; Hendry, Frommer, & Walker, 1999; Russell, Creedy, & Davis, 1994; Savery & Duffy, 1995; Segers et al., 1999). However, assessment in this new learning environment is not always fully congruent with the new learning environments’ objectives. A recent meta-analysis on the effects of PBL from the angle of assessment (Gijbels, Dochy, Van den Bossche, & Segers, 2005) included three levels of assessment: (1) understanding of concepts, (2) understanding of the principles that link concepts, and (3) linking of concepts and principles to conditions and procedures for application. In order to be congruent with its educational goals and resulting instructional principles and practices, the assessment of the application of knowledge when solving problems is at the heart of the matter in PBL. Therefore, one would expect students in PBL to perform better at these third levels when compared to students in more traditional learning environments. The results of the meta-analysis showed a difference in the reported effects of PBL between each of the three levels. Different from expectations that the effects of PBL are larger when the method of assessment is more capable of evaluating complex levels, the effect size for the third level of the knowledge structure was smaller compared to the effect size of the second level and not statistically significant. Moreover, only 8 of the 40 studies that were included in the meta-analysis focused on assessment at the third level. Most studies (n ⫽ 31) assessed at the level of understanding of concepts. These results imply an implicit challenge for new learning environments to pay more attention to the third level of the knowledge structure, both during the learning activities that take place and during students’ assessment. Concerning the latter, a situation where new learning goes hand-in-hand with traditional examinations (often directed towards reproduction of knowledge) can easily lead to what we called the auto-dissolving prophecy (Dochy & Dierick, 2001). This implies that the educational innovation will resolve itself when

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assessment is not congruent with the teaching. Since complex problem solving is considered as the core goal of higher education in general, this concern probably counts for all learning environments in the context of higher education and probably beyond. Effects of Assessment Research has shown that the nature of assessment tasks influences the approaches which students adopt to learning. Traditional assessment approaches often have effects contrary to those desired (Beckwith, 1991). Segers (1997) gives two more reasons why instruction and assessment must be linked. First, student outcomes provide information that can be used in improving educational practice only when the instruments that measure the outcomes match the instructional practices (English, 1992). Because of their static and product-oriented nature, traditional achievement tests fail to provide relevant diagnostic information that is needed to adapt instruction appropriately to the needs of the learner (Campione & Brown, 1990; Dochy, 1994; Snow & Lohman, 1989). Second, tests are diagnostic aids only when they identify the extent to which the goals are attained. This means that tests must be sensitive to how well students are able to use knowledge in an interrelated way when analysing and solving authentic problems. Tests that are inadequately linked to instruction have led to undesirable consequences such as inappropriate information about learning progress and learning difficulties, reduction of student motivation for learning, and incorrect evaluation of the effectiveness of instruction. The influence of assessment can occur on different levels and depends on the function of the assessment (summative vs. formative) (Dierick & Dochy, 2001; Gielen, Dochy, & Dierick, 2003). This aspect is also referred to as consequential validity. It implies the investigation of whether the actual consequences of assessment are really the expected consequences. The influence of summative assessment on learning behaviour is mainly proactive. The question ‘do we have to know this for the examination’ will be recognizable for nearly every teacher and illustrates that students tend to adjust their learning behaviour to what they expect to be assessed on. These effects can be described as pre-assessment effects, since the effects occur before the assessment takes place. When assessment is formative (integrated within the learning process), it can influence learning because students, after finishing their tasks, reflect on their learning outcomes and learning processes (referred to as post-assessment effects). Feedback is the most important cause for these post-assessment effects. Teachers and peers can give students information about the quality of their performance. When students have the necessary meta-cognitive knowledge and skills, they become capable enough to draw conclusions themselves about the quality of their learning behaviour (self-generating feedback or internal feedback). However, this is not always the case, certainly not in the beginning stage of their study. An important difference between the pre- and post-assessment effect is that the latter is intentional, whereas the first is rather a kind of side effect, since the main purpose of summative assessment is not support for learning (but rather selection and certification of students). Nevo (1995) and Struyf, Vandenberghe, and Lens (2001) point at a third kind of learning effect from assessment that is called the true assessment effect. Students also learn during the assessment itself, because they often need to reorganise their required knowledge, use it to tackle new problems and to think about relations between related

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aspects they did not discover yet, during studying. When assessment stimulates students to use higher-order thinking processes, it is possible that the assessment itself becomes a rich learning experience for students. This means that, contrary to the old saying “weighing the pig doesn’t fatten it”, in some cases high-quality learning is fostered by simply assessing the learning outcomes. In other words, ‘weighing can fatten the pig’. This applies to formative as well as to summative assessment. This true (pure) assessment effect is somewhat of a different kind than the two other effects, in the sense that it might provide for learning, but it does not have a direct effect on learning behaviour, unless under the form of selffeedback as we discussed earlier. Recent Research Findings Related to Assessment and Its Effects Faced with such powerful effects, assessment should be used strategically and should be designed to have educationally sound and positive influences. However, additional research is needed to understand the contextual factors that influence these effects (Hamilton, 2003). Recent investigations are summarised below, pointing at the important relationships between assessment and the motivation of students, the impact of more formative assessment and of assessment on students’ approaches to learning, assessment preferences and perceptions. Assessment and motivation Recently, the finding that assessment is steering learning has gained a lot of attention within educational research (Segers, Dochy, & Cascallar, 2003). Life-long learners have to be able to regulate their own learning. It is generally agreed that self-regulated learning refers to the degree to which students are meta-cognitively, motivationally, and behaviourally active in their learning (Boekaerts, 1999; Zimmerman, 1989). The cognitive, meta-cognitive, and resource management strategies that self-regulated learners activate in combination with their motivation help them accomplish their academic goals and overcome obstacles (Pintrich, 2000; Randi & Corno, 2000). Certainly motivation has been investigated as one of the factors that is sometimes strongly influenced by the assessment or the assessment system applied. In the past decade, research evidence showed that the use of summative tests squeezes out ‘assessment for learning’ and has a negative impact on motivation for learning. Moreover, the latter effect is greater for the less successful students and widens the gap between high and low achievers (Harlen & Deakin Crick, 2003; Leonard & Davey, 2001). Moreover, summative testing does not only affect the students’ motivation, but also teachers and their motivation. High stakes test do result in educational activities directed towards the content of the tests. As a consequence, the diversity of learning experiences for students is reduced and teachers use a small range of instructional strategies. The latter leads teachers to ‘deprofessionalization’ (Rigsby & DeMulder, 2003). Firestone and Mayrowitz (2000) state: “What was missing … was the structures and opportunities to help teachers reflect on their teaching and develop more effective practices” (p. 745). With respect to the effect of new modes of assessment on the motivation of students, research is scarce. Kane, Khattri, Reeve, and Adamson (1997) concluded from their interviews in 16 schools using new modes of assessment that students ‘exhibit a greater motivation to learn and a greater amount of engagement with performance tasks and portfolio assignments

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than with other types of assignments’ (p. 201). These results are in line with the findings of McDowell (1995). Nevertheless, we should not be too enthusiastic and we agree with Nevo (2003, personal communication) that students might find new modes of assessment motivating and interesting not necessarily because of the characteristics of such new modes, but perhaps because they severely dislike and are demotivated by traditional testing methods. Formative assessment: Assessment for learning As the culture is shifting from testing to assessment, one should also try to change the culture in students. An important step towards this goal has been set by the Council of Europe’s Language Policy Division in developing the European Language Portfolio. Its key aims are to motivate students by acknowledging their efforts to extend and diversify their language skills at all levels and to provide a record of the linguistic and cultural skills they have acquired (Council of Europe, n.d.). Also, in mathematics education much attention has been paid to the development and implementation of realistic mathematics during recent decades, including ‘didactical assessment’ intended to support the teaching and learning process (Clarke & Stephens, 1996; Van den Heuvel-Panhuizen, 1996). Much more formative assessment will be needed in a broad range of domains in order to convince students that assessment has two main purposes. Firstly, showing students their strong points, weaknesses, and growth and, secondly, guiding students towards the achievement of the learning goals. The topic of formative assessment has been reviewed by Black and Wiliam (1998). From their synthesis of quantitative studies they concluded that efforts to improve teachers’ formative assessment capabilities lead to significant learning gains for the students. Feedback on students’ importance and advice on how to improve seem to be crucial for positive effects of formative assessment. Assessment and student’s approaches to learning The literature and research on students’ approaches to learning suggests that deep approaches to learning are encouraged by assessment methods and teaching practices which aim at deep learning and conceptual understanding, rather than by trying to discourage surface approaches to learning (Trigwell & Prosser, 1991). The research on the relation between approaches to learning and assessment was strongly influenced by three groups: the Swedish Research Group around Marton and Säljö, the Scottish group around Entwistle, and the English/Australian group around Biggs, Ramsden, Trigwell, and Prosser. Originally, Marton and Säljö (1997) gave the kickoff and conducted a series of studies in which they tried to influence the students’ approaches to learning towards a deep approach to learning. These studies revealed that the students’ perceived assessment requirements tend to have a strong relation with the approach to learning a student adopts when tackling an academic task. Similar findings emerged from the Lancaster investigation (Ramsden, 1981) in relation to a whole series of academic tasks and also to students’ general attitudes towards studying. Students often explained surface approaches or negative attitudes in terms of their experiences of excessive workloads or inappropriate forms of assessment. The experience of learning is made less satisfactory by assessment methods, which are perceived to be inappropriate. High achievement in conventional terms may mask this dissatisfaction and also hide the fact that students have not understood material they have learned as completely as they might

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appear to have done (Ramsden, 1997). Inappropriate assessment procedures encourage surface approaches, yet varying the assessment questions may not be enough to evoke fully deep approaches (Struyven, Dochy, & Janssens, 2005). An interesting question in this respect pertains to the relationship between students’ approaches to learning and their assessment scores. Recently, Watkins (2001) conducted a cross-cultural meta-analysis in which the relationship between students’ approaches to learning and their academic performance was one of the central questions. It was hypothesized that surface approaches to learning would be significantly negatively correlated with students’ grades, whilst the deep approach would be positively related with academic achievement. The results of his study were rather disappointing, although in the expected direction, with correlations of ⫺0.11 for surface and 0.16 for deep approaches. Although a deep approach to learning is generally expected to lead to higher achievement (both in terms of higher quality outcomes and grades), the assessment system does not always seem to reward the deep approach (Biggs, 1987; Marton & Säljö, 1997; Scouller, 1998; Scouller & Prosser, 1994). Entwistle, McCune, and Hounsell (2003, p. 90) suggest that research findings vary ‘due to differences in the extent to which understanding is explicitly rewarded in the assessment procedure’. However, recent studies by Minbashian, Huon, and Bird (2004) and Gijbels, van de Watering, Dochy, and Van den Bossche (2005) could not confirm the hypothesis that a deep approach would be more effective for questions of higher cognitive order than for questions of lower cognitive order. Students’ assessment preferences and perceptions Research on students’ assessment preferences and perceptions has focused on the format of assessment and its relationship with students’ approaches to learning. According to the studies of Ben-Chaim and Zoller (1997), Birenbaum and Feldman (1998), Traub and MacRury (1990), Van de Watering, Gijbels, Dochy, and Van der Rijt (2005), and Zeidner (1987), in general, students prefer the multiple-choice format or the simple and decontextualised questions over the essay type of assessment or constructed-response type of questions. Birenbaum (1994) introduced a questionnaire to determine students’ assessment preferences (Assessment Preference Inventory) for various facets of assessment. Using the questionnaire, Birenbaum (1997) found that differences in assessment preferences correlated with differences in learning strategies. In another study, Birenbaum and Feldman (1998) found that students with good learning skills, who have high confidence in their academic ability, tend to prefer the essay type of assessment over the multiple-choice of examinations. And vice versa, students with poor learning skills, who tend to have low confidence in their academic ability, prefer the choice type over the constructed-response type of assessment (Birenbaum & Feldman, 1998). Also Entwistle and Tait (1990) reported that students describing themselves as surface learners preferred teaching and assessment procedures which supported that approach; whereas, students describing themselves as deep learners preferred courses which were intellectually challenging and assessment procedures which allowed them to demonstrate their understanding. According to Birenbaum and Rosenau (2006), students’ perceptions of assessment refer to opinions, attitudes, and preferences towards the assessment and its properties. Struyven, Dochy, and Janssens (2003) interpret perceptions as a constructivist act of creating meaning in which perceptions are seen as beliefs, opinions, interpretations, ideas, preferences,

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images, and conceptions as a result of experience. In both cases, preferences are seen as a factor in determining the students’ perceptions. Recently, several researchers have investigated students’ perceptions of assessment practices. Scouller (1998) and Scouller and Prosser (1994) found that success in multiple-choice examinations was related to the perception of the questions as assessing lower levels of cognitive processes and the nonemployment of deep strategies. Although a recent review on students’ perceptions of new modes of assessment indicated that students’ perceptions of assessment have considerable influences on students’ approaches to learning (Struyven et al., 2003), Lindblom-Ylänne and Lonka (2001) found no differences in students’ perceptions of the examination procedures between four groups with different ‘approaches to learning-profiles’. All students criticised the examination practices as calling too much for memorising instead of understanding and application of knowledge.

New Developments We conclude this contribution with some reflections on the future developments in assessment. Current assessment practices mainly tend to focus on assessment ‘of’ (and not ‘for’) learning and seem to even hamper students’ motivation, well-being, and learning. A better alignment of learning, instruction, and assessment should have a more positive influence on students’ learning. Recognising this supports new developments in the emerging assessment culture, i.e. the notions of blended assessment, new lines in edumetrics, and the engineering of assessment, which will be further outlined in the final part of this chapter. Blended Assessment Blended assessment is usually defined as a combination of a variety of assessment modes, e.g. paper and pencil tasks, online assessment tasks, peer-assessment, overall assessment, etc. A blended assessment system refers to a combination of both normreferenced tests and standard-based tests in one decision-making system. Recent research points at different new needs for optimising learning in schools. Blended assessment seems to correspond more to mainstream new learning environments. As Rigsby and DeMulder (2003) state: “Teachers question whether one standardized test administered at a single point in time, and drawing on a single mode of demonstrating learning could even produce a fair assessment for all children” (pp. 12–13). Objective tests are sometimes useful for certain purposes, although they should not dominate an assessment program. Increasingly, measurement specialists recommend so-called balanced or pluralistic assessment programs, where multiple assessment formats are used (Birenbaum, 1996; Clarke & Stephens, 1996; Dierick & Dochy, 2001; Ridgway & Schoenfeld, 1994). Surely, we should not abandon knowledge-oriented assessments completely. Despite the current denigration of ‘mere facts’, decades of research have shown convincingly that holding the key domain knowledge is a basis for excellence of experts (Chi, Glaser, & Farr, 1988). This key domain knowledge certainly refers to a larger extent to key concepts and jargon in a domain than to mere facts. Nevertheless, a good diversification and balance in assessment is essential.

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New Lines in Edumetrics It should not be surprising that a new learning society and, consequently, a new instructional approach and a new assessment culture cannot be evaluated solely on the basis of the criteria that were developed a long time ago for mainly ‘psycho’-metric purposes (and not in educational settings). Quality control issues are important for formative assessment and crucial in summative assessment. These issues refer to the accuracy (reliability) of the assessment scores as well as to the validity of the inferences drawn. Research has shown that the new modes of assessment tend to compare unfavourably to standardized testing with respect to these psychometric criteria of reliability and validity (Dunbar, Koretz, & Hoover, 1991; Koretz, Stecher, Klein, & McCaffrey, 1994; Linn, 1994). Questions have been raised whether the traditional psychometric criteria are the most suitable and the only criteria that do fit with the new assessment culture (Birenbaum, 1996; Dierick & Dochy, 2001). According to Birenbaum (2003), this complies with criticism raised regarding the applicability of psychometric models to this type of assessment (Birenbaum, 1996; Delandshere & Petrosky, 1998; Dierick & Dochy, 2001; Moss, 1994, 1996) and in general to the context of classroom assessment (Dochy & Moerkerke, 1997). Efforts to conceptualize more suitable criteria for quality control with respect to new modes of assessment have recently been presented. Dierick and Dochy (2001) and Segers et al. (2003) suggested an ‘edumetric approach’ (instead of the ‘psychometric approach’) that expands the traditional concepts of validity and reliability to include assessment criteria that are sensitive to the intricacy of the teaching–learning process. These assessment criteria are the cognitive complexity of tasks, the authenticity of tasks, the directness of assessment, fairness, and the transparency of the scoring criteria. Each of these will be further explained. A first criterion that distinguishes new assessment modes from traditional tests is the extent to which the assessment task measures problem solving, critical thinking, and reasoning. This criterion is called cognitive complexity (Linn, Baker, & Dunbar, 1991). To judge whether assessment tasks meet this criterion, we can analyse whether there is a consistency between the processes required for solving the tasks and those used by experts in solving the problems. Next, it is also necessary to take into account students’ familiarity with the problems and the ways in which students attempt to solve them (Bateson, 1994). Another criterion for evaluating assessment tasks is authenticity. Shepard (1991) describes authentic tasks as the best indicators for having attained learning goals. Indeed, traditional tests assume always an interpretation from student answers to competence in a specific domain. When using authentic assessment, interpretation of answers is not needed, because assessment is a direct indication of competence. The criterion ‘authenticity of tasks’ is narrowly related to the directness of assessment. Powers, Fowles, and Willard (1994) argue that the extent to which teachers can judge competence directly is relevant evidence of the directness of assessment. In their research, teachers were asked to give a global judgement about the competence ‘general writing skill’ of writing tasks, without scoring them. Thereafter, trained assessors, following predetermined standards scored these works. Results indicated that there was a clear correlation between the global judgement of competence by the teachers, and the rewarded marks by the assessors. When scoring assessment, the criterion fairness (Linn et al., 1991) plays an important role. The

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central question is whether students had a fair chance to demonstrate their real ability. ‘Bias’ can occur because of several problems. First, tasks might not be congruent with the received instruction/education; second, students might not have had equal opportunities to demonstrate their real capabilities on the basis of the selected tasks (e.g. because they are not accustomed with the cultural content that is asked for), and third, because of prejudgment in scoring. Beside this, it is also important that students understand the criteria that are used in assessment. ‘Meeting criteria improves learning’: communicating these criteria to students at the moment the assignments are given improves their performance, as they can develop clear goals to strive for in learning (Dochy, 2001). A last criterion that is important when evaluating assessment is its transparency. Following Frederiksen and Collins (1989), the extent to which students can judge themselves and others as equally reliable as trained assessors provide a good indication for this criterion. However, in order to further operationalize these criteria more research is needed into their applicability and the impact of their implementation (Birenbaum, 2003). Assessment Engineering There is a strong need to rethink assessment towards more formative, authentic, and context-embedded assessment that is flexible and integrated into the curriculum. ‘Assessment engineering’ is necessary in multiple senses: aligning assessment, learning and instruction, blending different modes of assessment, avoiding earlier pitfalls such as concluding that assessments within learning environments are largely comparable with assessment of human intelligence and other psychological phenomena. Assessment engineering can be defined as the engineering or re-engineering of the assessment, both at the classroom and program level, in order to reach full alignment with learning and instruction, a balance between assessment of learning and assessment for learning, a balance between different modes of assessment within a well-articulated assessment policy of the school or training program. As such, assessment engineering serves a dual purpose — assessment for learning and assessment of learning — and addresses the needs of both learners and teachers; the process of assessment engineering is informed by research findings, piloted, evaluated, and revised according to learner and teacher needs; it takes into account factors affecting learning outcomes such as intellectual abilities, use of resources, learning opportunities, assessment modes, approaches to learning, and views of learning; it promotes ‘learning lasting for life’ (Dochy, 2005) and the needs of today’s information societies; it is meant to be economical as it reduces the burden on overstretched examining organisations (Birenbaum, et al., 2006). Six interrelated key principles for assessment engineering can be formulated: (1) the learners participate in the assessment process; (2) assessment is contextual and responsive — it is aligned to instruction; (3) assessment is what the learners know and are able to do and consequently allows to plan a learning route in order to build further on his potential (it is not focusing primarily on gaps in learner knowledge and performance); (4) both learning processes and learning products are assessed; (5) assessment criteria are transparent to individual learners and teachers; and (6) learners and teachers get high-quality feedback. Properly engineered assessment systems will allow teachers to spend more time on developing the teaching of the curriculum and will provide them with useful information

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about individual learners’ progress. Students can use assessment as a tool for learning, and this can be less stressing and more motivating (Birenbaum et al., 2006). Continuing along this line involves efforts from different players in the field. Firstly, departmental audits or accreditation audits should not be limited to the screening of external standards in summative tests. They should also include an inventory of the amount and nature of formative assessments and new modes of assessment, and consider to what extent students’ learning is supported and to what extent the principles of good teaching practice are realized. Secondly, teacher pre-service and professional development programmes should include instruction in how students learn and how learning can be assessed for the purpose of learning as a major component in most programmes. The focus should be on the proper integration of learning and assessment in teachers’ educational experience (Hamilton, 2003; Pellegrino et al., 2001). Finally, teachers should use assessment strategically to support students’ learning. Three issues related to assessment can help teachers in doing this (Gibbs & Simpson, in press). First, assessment can influence the quantity and distribution of student effort. This is the case when the assessed tasks capture sufficient study time and effort and distribute this effort evenly across the topics and weeks. Second, assessment can influence the quality and the level of the students’ effort. When the tasks engage students in productive learning activities and communicate clear and high expectations to the students, assessment fully supports student learning. Third, assessment can be accompanied by timely and sufficient feedback (from the teacher or the peers). Feedback then should be of high quality, should focus on learning, be understandable for the students, and linked to the purpose of the tasks and the criteria. It is obvious that the emerging new assessment culture in its current meaning, referring to new modes of assessment, assessment for learning, assessment of competence, etc. is still in an early phase of widespread use in educational practice (Segers et al., 2003). In educational programmes, assessment will need to be much more systematically engineered. Questions that need to be addressed at the classroom level are: Which modes are in line with my instruction? How to combine different modes in my class? How many assessment tasks can I include in one course? Is it manageable for the teacher and the students? Will the assessment foster and not hamper students’ learning? At the programme level one should create a sound assessment policy, ensuring that all modes of assessment are in line with each other in the complete program and that the edumetric quality is sufficient. The science of ‘assessment engineering’, trying to fill the gaps we find in aligning learning and assessment, asks for more research within many different fields.

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The Difficult Marriage Between Education and Technology: Is the Marriage Doomed? Gavriel Salomon and Dani Ben-Zvi

Introduction We begin with two assertions upon which we will elaborate in this chapter: The first assertion is that technology in education has yet to prove its unique and worthwhile contributions to learning and instruction. Our second assertion is that such contributions of technology to education, particularly Information and Communication Technology (ICT), will be realized to the extent that it comes to serve novel learning environments, based on novel principles of teaching and learning. The history of media and technology in education is long and mainly painful. It is long since it began in full swing in the early twentieth century with such devices as instructional radio, then film, followed by learning machines, educational TV, and finally — computers. It is a painful history because — by and large — the promises that were stated with the introduction of each technology far exceeded its actual contribution to learning and teaching. As argued by Olson in 1976, the effects of media on learning are either unknown or simply negligible. The overwhelming finding of studies comparing the use of this or that technology with regular face-to-face instruction was ‘no significant difference’, a finding that is repeated today in comparisons of distance learning with regular classroom instruction (e.g. Russell, 1999). Consider some typical promises, as follows: The future holds many promises for the growth of internet education … . Soon it seems that actually ‘going’ to class will not be necessary. All of the knowledge needed for a particular course may be stored on a Web page… no need for the traditional classroom-style teaching, since it could all be done on-line. … Anything could be possible through the Web … . The horizons are endless for internet education. (Schnitzler, 2001)

Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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Gavriel Salomon and Dani Ben-Zvi … The future will see more and more domain-specific Highly Interactive Intelligent Computer-Assisted Learning (HIICAL) systems that are more effective (students learn better and faster) than one-on-one human tutoring. And, keep in mind that one-on-one human tutoring is far more effective than one teacher per 20 to 30 or more students that we have in conventional classrooms. (Moursund, 2004, p. 77) By breaking through the constraints of space and time, ICTs can in principle allow learning anywhere and at any time, making them a supremely powerful lever for educational change. For many educational experts, new digital technologies are making a learning revolution possible by enabling children to become more active and independent learners trough the newfound opportunities for collaborating on projects across frontiers and cultures, learning from one another, and accessing a wide range of information. (Guttman, 2003, p. 27)

Such promises ignited the imagination of educators who were quick to introduce the technology into their classrooms. But much too often, and with very important but few exceptions to which we will return later on, the prevailing metaphor of earlier days of computing as a Trojan Horse was ignored. That metaphor meant that computers are capable of ‘making a difference’ not for their own attributes but for the hidden (pedagogical) baggage they carry with them (e.g., Salomon & Perkins, 1996). Expecting computing to affect learning in and of themselves necessarily led to disappointment. Oppenheimer (1997) spoke of the ‘Computer delusion’, and Sherry Turkle (1995), not a newcomer to computing in education, concluded: “The possibilities of using this thing poorly so outweigh the chance of using it well, it makes people like us, who are fundamentally optimistic about computers, very reticent” (p. 48). Others have reached similar verdicts also more recently, as for example: In sum, based on our findings and on national data, we maintain confidently that, contrary to the dreams of most techno-promoters, technology has simply become a small and largely peripheral element of a familiar, longrunning high school routine. True, computers and other technologies greatly affect the experience of the school day for as much as 5% of the student population. … High-end technology has simply not had the type of widespread, fundamental effect on students that most techno-promoters covet. (Peck, Cuban, & Kirkpatrick, 2002, p. 479) Research tends to support such voices of disappointment. For example, Becker, Ravitz, and Wong (1999) found that while 30% of English teachers and 43% of elementary school teachers in the USA assign computer work frequently, only about 16% of science teachers, 12% of math teachers, and 10% of social studies and fine arts teachers do. Cordes and Miller (1998) carried out a meta-analysis of studies on computers and K-12 children and concluded their report by labelling it ‘Fool’s Gold’. Van Boekel and Stegers (2003) found in a survey study carried out in the Netherlands that 22% of elementary school teachers

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and 53% of high school teachers use computers in their classrooms no more than 2 hours a week. On the other hand, only 10% of elementary school teachers and 8% of high school teachers use computers between 10 and 15 hours a week. Concerning learning attainments, a systematic review of a large number of meta-analytic studies and reviews of computers and learning carried out by British scholars (Higgins, 2003) concludes that the link between ICT use and achievements is generally very weak, that other interventions such as peer tutoring, reciprocal teaching, or metacognitive instruction lead to far better achievements, and that ICT can be more effective when properly used. Salomon, Kosminsky, and Asaf (2003) concluded their review of the effects of word processing on writing ability, stating: “that technology, in and of itself, does not really matter that much for children’s writing; instruction does”, thus echoing a point made much earlier by Clark (1983). Coll, Onrubia, and Mauri (2005) of the University of Barcelona, take an activity theory position. They point out correctly that ICT can uniquely mediate the relationships between learners and contents and can mediate the communication interactions among the learners themselves. However, they also point out that these potentialities can become realized only by the uses that learners make of the technology. Yet these usages, as surveys and more focused research show, leave a lot to be desired as the innovative learning practices afforded by ICT do not seem to become manifested very often (Becker, 2000). Findings are not much different when computer-based distance learning is compared with face-to-face settings. Russell (1999) examined all relevant studies he could find and showed that out of 393 comparisons, 374 ended up with ‘no significant differences’ and among the 19 with significant differences, half were in one direction and half in the other. A more recent meta-analysis of 252 studies was carried out between 1985 and 2002 by Bernard et al. (2003). Their three primary findings were that on average, distance learning equals classroom teaching on two primary measures: Achievement and attitude; that distance learning has a lower success rate (higher attrition); that conditions that promote interactivity and synchronicity are beneficial, and that there is great diversity in the effects of distance learning. Conclusions of another meta-analysis carried out by Cavanaugh, Gillan, Kromrey, Hess, and Blomeyer (2004) reached similar conclusions: “ … Distance education can have the same effect of measures of student academic achievements when compared to traditional instructions”, and that “No factors were found to be related to significant positive or negative effects.” (p. 4). However, the overall picture is not as straightforward as this brief review might imply. In fact, the effects of ICT on learning vary widely. Waxman, Lin, and Michko (2003) carried out a meta-analysis of 42 recent controlled studies and found an effect size of 0.42, which is more than twice that of previous meta-analyses which they reviewed. But the effect sizes obtained by Waxman et al. ranged from 0.464 to ⫺0.091, which is typical of the field. Lest the reader dismisses our brief but sad review by countering our assertion with exemplary cases of extraordinary integrations of ICT into education, we hasten to admit that such do exist (we will turn to them later on) but that these islands of excellence do not constitute continents. There is a vast ocean out there of wasted good intentions and mediocre usages of ICT and only a few islands of success scattered here and there. By and

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large, the marriage between instruction and computing is still not a stable or satisfying one. After more than 35 years of computing, its overall effects are still negligible. How can we explain this state of the field? Numerous explanations have been offered, ranging from the shortage of computers to teachers’ reticence, and from the inherent incompatibility between technology and education to the inadequacy of available programs. We believe the reasons for the strained relations between ICT and education are deeper than those and although they have already been discussed in the professional literature (e.g., Cuban, 2001) we nevertheless feel that they need to be discussed again in some detail. In what follows, we present three classes of reasons that may explain the situation just described. This will then lead us to discuss the conditions which we believe are necessary for a healthier and more fruitful marriage between education and technology. The three classes of reasons we discuss below are trivialization of ICT, omnipotency attributed to ICT, and misleading research.

The Trivialization of ICT On the basis of a transmission view of education, instruction is maintained as a top-down process whereby good learning means the accumulation of facts and procedures to be rehearsed and stored (Perkins, 1992). E.D. Hirsch’s (1987) call for Cultural Literacy: What every American needs to know, as well as the basic tenets of Computer Assisted Instruction (CAI) and the ‘Back to basics’ movement fit this approach well. Thus, anything that is likely to rock the educational boat by requiring or even just implying a shift of responsibility for learning to the students, a change of the teacher’s authoritative role, or the introduction of a more constructivist (i.e. diversity-oriented) approach, is easily taken as a threat. The role of ICT, having potentially subversive characteristics, is thus reduced to serve only benign functions. Petraglia (1998) thus wrote of the ‘domestication of computers’ and Matti Sinko (1998) of Finland stated that the new learning paradigm “has stayed in the rhetoric” rather than in practice. Indeed, when ICT is used for drill and practice, for e-mail communication, or for simple computational work, one may say that its great and unique potentials have been trivialized. As the studies mentioned earlier suggest, this is still the dominant state of affairs in many of the schools (e.g. InfoDev, 2005).

The Attribution of Omnipotency to ICT The other side of trivializing ICT is attributing to it omnipotency under the assumption that once you have computers, new developments are likely to follow more or less on their own. It is often assumed that the introduction of as powerful a technology as ICT is bound to affect instruction, curriculum, social activity, and teachers’ roles (e.g. Maeroff, 2003). Indeed, the mastery of computing skills was seen by teachers as more important than mastering history, science, and social issues such as drugs (Oppenheimer, 1997). Similarly, as a recent study showed (Mor, 2001), teacher trainees, while gaining first hand experience with the design of constructivist learning environments, still rated mastery of computing as most significant, far beyond the mastery of the new pedagogy.

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Perhaps most importantly is the observation that the technology itself comes to occupy centre stage and to reshape the very nature of knowledge as perceived and understood. Simon (1982) suggested that in the age of computer-mediated easy accessibility to knowledge the very meaning of knowledge changes from a noun connoting possession to a verb connoting access. It is not that important any more what people carry around in their heads as is what they can access when needed. Knowledge ceases to be a commodity available when required; it becomes a potential to be realized upon demand. Thus, the skills of access become more important to acquire than the skills of knowledge retention. March (1987) alluded to a similar change: It is conceivable that computers and information technology will have an impact comparable to that of books. If they do, however, it will not be because they are particularly efficient systems for teaching what we now teach, but because they change the way we organize knowledge and our relation to knowledge. That is, the most far-reaching potential effect of new information technology [is] … on the nature of knowledge itself. (p. 24) These ideas point to a change in the status of knowledge and its nature. But accessibility, the hallmark of the Internet age, is not to knowledge but to information. And knowledge and information are not the same! While information can be discrete, decontextualized, and handed down ready-made, knowledge is organized in web-like networks, is greatly context dependent, and is to be constructed, not ‘internalized’ ready-made. Think of “Timbuktu”. What do you know of it? Initially, it is just a name of a place (City? Where?), a rather meaningless piece of information. But then you discover that it is a city at the edge of the Sahara desert, in the African state of Mali and that it used to be the gate for nomads and caravans venturing through the Sahara desert. Now you have more than one piece of information, a small web of interconnected items and a context of geography to which additional pieces of information can be added on: Africa, desert, caravans, heat, camels, thirst, etc. It would be a different context if we would speak of Timbuktu as a metaphor for far away, desolate places, as it is mentioned in poetry, or by pop singers. It also would have a very different meaning for a traveller stuck in a remote hotel in the city as compared with the meaning for a geography scholar studying urban development around deserts. Considering ICT as having self-propelled transformational powers for education ignores the role played by the learner and the learning environment. The distinction between information and knowledge becomes particularly critical in this respect when we think of ICT as a source of knowledge. Can it indeed provide knowledge or can it only serve to provide information, while the transformation of the information into knowledge is left to the learner’s constructive activities? The very essence of constructivism favours the latter possibility. Thus, it follows that ICT, and certainly e-learning (Salomon, 1999) cannot and should not be given centre stage because when it comes to instruction and learning the roles of the learner and that of the learning environment are at least as crucial. Contrary to the claim that ICT can transform education in and of itself, it can only provide the information, afford certain activities, and set the stage for the design of novel learning environments. There is nothing omnipotent about the role of ICT and no real change in and of education can take all on its own.

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Misleading Research ICT, as was the case with previous technologies, is intensively studied. But some of that research is based on questionable or at least naive assumptions and thus ends up being misguided and misleading. Of particular interest are the very many studies that continue to compare ICT with ‘traditional’ classes and e-learning with face-to-face instruction (e.g. Russell, 1999, carried out a meta-analysis of 393 studies and Bernard et al., 2003, did the same with another 252 studies). Such comparisons continue an old tradition of comparison dating back to the studies on instructional radio and instructional film and are based on the assumption that learning outcomes can be compared across media, methods or technologies. Underlying this assumption is the idea that all media or technologies come to serve the attainment of the same learning outcomes and differ only in respect to speed, depth, cost or sustainability. It would seem that there is no other way to compare learning achievements except for by using the same evaluation criteria, which, more often than not, are of the more traditional type. But comparison of some learning outcomes across two entirely different media or learning environments, where, for example, one environment requires passive attention and the other affords active team-based problem solving, has to use a common criterion of achievement. Such a common criterion constitutes, by necessity, the lowest common denominator. While using a common criterion for learning would sound right and reasonable (do learners in a constructivist, team-based problem solving environment understand the material as well as those learning in a ‘traditional’ classroom?), it misses the main point: If the two media, methods, technologies or learning environments are truly different — they necessarily serve the attainment of different learning goals. Let us unpack this statement. First, we want to claim that people learn mainly from what they are doing; but they learn even more from what they are thinking about what they are doing (e.g. Bransford, Brown, & Cocking, 1999). Second, different media, methods, and learning environments afford different activities, and they, in turn, afford different thoughts about those activities (e.g. Salomon, 1994). It follows then that if different media, methods or learning environments afford different kinds of learning activities, and if learning is the outcome of the thinking that learners’ activities activate, one would expect also different media, methods or learning environments to lead to the attainment of qualitatively different learning outcomes. These arguments fit the idea that alternative modes of assessment (such as portfolios) cannot be evaluated on the basis of the same criteria of traditional testing (such as reliability in the sense of internal consistency). Different types of criteria or other types of reliability are needed for that (Segers, Dochy, & Cascallar, 2003). Once we accept this line of reasoning it becomes evident why cross-media or technology comparisons are suspect as long as the same criteria for learning are employed. Indeed, a team-based problem solving learning environment such as the Jasper project designed and studied by the Cognition and Technology Group at Vanderbilt (1997) yields particularly impressive learning outcomes in the domain of problem solving while a more traditional classroom addresses more successfully the attainment of calculation. If a common criterion is employed in the comparison between the two learning environments, the results would be misleading. The same might be said of the many studies yielding no significant differences between media or environments. Not only do they ignore the possibility of strong disordinal

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interactions with learners’ aptitudes, contents, and settings, they compare the different environments in light of the same learning outcomes. A recent meta-analysis of 32 studies by Rosen and Salomon (in press) supports this argument: Technology-intensive constructivist learning environments in elementary and high schools were found to lead to superior constructivist attainments such as problem-solving ability over traditional classrooms (average effect size of 0.902). But such learning environments were found to have hardly any advantage over traditional environments when the attainment of more traditional goals such as memory of facts are evaluated (average effect size of 0.107). In other words, it may well be the case that ICT does contribute uniquely to learning but that its differential contributions are masked by the use of the wrong measurement criteria, thereby misleading the community to its disappointment with ICT.

The Other Half of the Glass: Promising Cases of ICT On the basis of the brief review presented above, we could conclude that the case of ICT in schools is not very promising. To paraphrase Cuban’s words (2001): Technology is oversold, misused, and wrongly assessed. But this would constitute an unfair overgeneralization. We need to distinguish between the typical attainments of ICT and that which ICT, in its best manifestations, can be made to attain. Unlike the studies on which the previous review was based, the exemplary cases described below illustrate what ICT can be made to accomplish. Three principles guide the examples below: (a) An updated (usually constructivist and/or sociocultural) conception of real life-like problem-based learning as a intentional and mindful process, (b) the design of learning environments that afford and encourage the desired kind of learning, and (c) the design of technology that can uniquely serve that kind of learning within the designed learning environment. We shall present two examples, sharing the following principles: Their conception of learning emphasizes the construction of knowledge rather than its rehearsal and memorization by isolated learners (Salomon, 2000); the design of the learning environment emphasizes the integration of socially-distributed activities and student-propelled learning (Cobb, Stephan, McClain, & Gravemeijer, 2001); and the technology is designed to afford team-based activities of search, design, construction, and communication, activities that cannot be carried out otherwise (Koschman, 1996). In light of these principles, learning goals and outcome criteria are often very different from those used in standard testing or in typical cross-environment comparisons. Example 1: CSILE and the Knowledge Forum — Technology Supports Knowledge Building in Group-Based Environments One major, long-term effort that exemplifies many of the promising features of collaborative technology is the Computer-Supported Intentional Learning Environment (CSILE) and its continuing platform — the Knowledge Forum (http://www.knowledgeforum.com). For the past two decades, Bereiter and Scardamalia, and their colleagues have been researching and developing how to create knowledge-building classroom environments (Scardamalia, 2002; Scardamalia & Bereiter, 2003). The first environment — CSILE — was

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started by Scardamalia and Bereiter at the Ontario Institute for Studies of Education. This technology, originally developed in a research setting, became in the years 1995–2002 part of a national Canadian initiative called TeleLearning Network of Centres of Excellence. These research-based innovations continue developing under the Institute for Knowledge Innovation and Technology (IKIT, http://ikit.org/), which conducts research, develops technology to help build communities aimed at advancing beyond ‘best practice’ in education, knowledge work, and knowledge creation. CSILE and the Knowledge Forum are problem-centred collaborative media that operate over a computer network. The goal of CSILE and Knowledge Forum is to support structured collaborative knowledge building by having students communicate their ideas and criticisms — in the form of questions, statements, and diagrams — to a shared database classified by different types of thinking. As a class, students are trying to understand some aspects of how the world works by producing conceptual artifacts — ideas that represent a continual improvement in what the class knows. Students are not focused or distracted by the need to produce a product or project to demonstrate their learning. Instead their ongoing work in their Knowledge Forum database is both the product and the impetus for further investigation. By classifying the discussion in this way, students become more aware of how to organize their growing knowledge. The computer system thus provides the organization and support for the complex array of individual and group discourse and development of ideas that constitutes a working knowledge-building community. In the best of these knowledge-building classrooms, we see students taking off with an idea that carries them into intellectual realms that adults find exciting. The students approach problems from multiple perspectives; engage in knowledge transforming discourse aimed at reconstructing their ideas both in Knowledge Forum and in face-to-face dialogue; and they work collaboratively to advance the knowledge of the class over a sustained period of time. Students learn to identify their own beliefs, bring those beliefs into contact with others’ beliefs, and are proud of being in charge of their own learning (Lamon, Reeve, & Scardamalia, 2001). In knowledge building classrooms, we see teachers who may not know all the answers in advance but because they are knowledge builders themselves they continuously research the domain looking for resources that will help the community advance. The teacher is not a guide or a coach but rather is someone whose understanding is regarded as an authoritative resource on the subject along with other sources. And so, the teacher’s own knowledge does not circumscribe what students will investigate. What are the advantages of the knowledge-building approach and supporting technology? As students develop their knowledge they need to learn facts and procedures to help them advance. In the process of knowledge building they are mastering the key principles that underlie science and so are able to go well beyond learning the facts. In addition students learn how to become knowledge builders. They begin to identify their own ideas and to compare and contrast their ideas with those of others; they need to look for inconsistencies, strengths, weaknesses, applications, limitations, and potential for further development between their ideas and those of others (Bereiter, 2002). This kind of discourse brings with it a metacognitive strength — knowing one’s own mind, identifying skills and needs in how one approaches problems, monitoring one’s own and others’ conceptual progress, and taking charge of one’s own growth in understanding.

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Students in K–12 classes who use CSILE for science, history, and social studies perform better on standardized tests and create deeper explanations than students in classes without this technology (Scardamalia, Bereiter, McLean, Swallow, & Woodruff, 1989). Gains have also been found for students participating in CSILE projects at the university level (see, e.g., Scardamalia & Bereiter, 1996). Although all students show improvement, positive effects are especially strong for students categorized as low or middle achievers (Bryson & Scardamalia, 1991). Many additional types of learning networks have been created for use in classrooms at all levels. For example, the International Education and Resource Network (iEARN), which is a large non-profit global network that enables young people to use the Internet and other new technologies to engage in collaborative educational projects. Learning Circles project (http://www.iearn.org/circles/) uses computer networking for multicultural and multilingual highly interactive, project-based partnerships collaborative learning by partnering a small number of classrooms located throughout the world to produce newsletters or other writing projects (Riel, 1995). Reports from researchers and teachers suggest: “students who participate in computer-connected learning networks show increased motivation, a deeper understanding of concepts, and an increased willingness to tackle difficult questions” (Roschelle et al., 2000, p. 81). Example 2: Interactive Geometry Software — Learning through Exploration, Frequent Interaction, and Feedback Research suggests that learning proceeds most rapidly when learners have frequent opportunities to apply the ideas they are learning and when feedback on the success or failure of an idea comes almost immediately (cf. Anderson, 1996). In contrast, students in traditional classrooms typically have limited time to interact with instructional materials, with each other, or with the teacher, and receive restricted or untimely feedback on their work and ideas. Unlike other media, computer technology can encourage rapid interaction and feedback and engage students for extended periods on their own or in small groups. This can create more time for the teacher to give individual feedback to particular children (Schofield, 1995). One major, long-term effort that exemplifies many of the promising and unique features of technology in supporting exploration, frequent interaction, and feedback is the Geometric Supposer software series (started by Schwartz & Yerushalmy, 1986), and its continuing counterparts The Geometer’s Sketchpad (Key Curriculum Press) and the Cabri (Texas Instruments). In high school geometry, educators continue to debate the relative emphasis that formal proof should play. Some argue that we should continue the traditional focus on axiomatic systems and proof. Some believe that we should abandon proof for a less formal investigation of geometric ideas. Others believe that students should move gradually from an informal investigation of geometry to a more proof-oriented focus (Hanna, 2000). Consistent with the alternatives to axiomatic approaches, the focus of the Geometric Supposer is to facilitate students’ making and testing conjectures. The Supposer allows students to choose or create a primitive shape, such as a triangle or quadrilateral, and perform measurement operations and geometric constructions on it. The software records sequences of constructions performed on shapes and can repeat the action on other shapes.

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The software permits the user to construct a shape, change it, and then maintain any constructions that were made. Thus, it permits students to explore the generality of the consequences of constructions. The Supposer provides a dynamic construction and exploration-learning environment that enables students to explore and understand mathematics in ways that are simply not possible with traditional tools. Students can construct with the computerized tool an object and then explore its mathematical properties by dragging the object with the mouse. All mathematical relationships are preserved, allowing students to examine an entire set of similar cases in a matter of seconds, leading them to consider generalizations. As a result, this technology encourages a process of discovery in which students first visualize and analyze a problem and then make conjectures before attempting a proof. Thus, allowed to wander intellectually with the Supposer environment, students can devise a new piece of mathematics, can pose questions, suppose, explore, and create. They are never directed to a ‘right’ answer, or to any answer. Within the limited domain of geometry, they are free to wander at will. If interesting challenges are posed to them by the teacher, they can go far and have the all too rare experience of making new knowledge. In short, the unique feature of this class of software is that it does not focus only on the already known but rather on the unknown, allowing students to pose and solve new problems, to cherish old knowledge, and to make new knowledge based on their own explorations. Research has demonstrated the effectiveness of such construction programs. In one evaluation, students using the Supposer software performed as well as or better than their nonSupposer counterparts on geometry examinations (Yerushalmy, Chazan, & Gordon, 1987). Moreover, students’ learning went beyond standard geometry content as they invented definitions, made conjectures, posed and solved significant problems, and devised original proofs. Making conjectures was not easy for students, but eventually nearly all students made conjectures and justified their generalizations. Supposer-based activities helped students move away from considering measurement evidence as proof (e.g., Hannafin, Burruss, & Little, 2001). Unlike textbook theorems, which students can assume as true ‘because they are in the book,’ students believed that theorems generated with Supposer software needed to be proved before they could be accepted as true. Students using this software also made gains in understanding diagrams. They were flexible in their approach to diagrams, treated a single diagram as a model for a class of shapes, were aware that this model stood for a class of shapes, and were aware that this model contained also characteristics not representative of the class (Yerushalmy & Chazan, 1988; Yerushalmy et al., 1987).

Is the Marriage of Education and Technology Necessarily Doomed? If we were to answer this question on the basis of exemplary cases of the kind presented above, we would answer that the marriage is far from being doomed. It is a very promising marriage, provided at least three necessary conditions are met. First, if technology is to have a unique effect on learning it cannot be trivialized to serve outdated learning goals. Technology is not a means for the attainments of learning goals designed at the preconstructivist age of print and television. If technology is to be used, it must be allowed to flex its unique muscle, that is — allow students to engage in collaborative, design- and

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problem-solving oriented activities. Nearly by necessity, these call for team-based activities, for authentic problems to deal with, and for relatively open-ended processes of exploration. Does this mean that all learning in school must always be technology-based and thus team- and problem-solving oriented? No, not at all. There is hardly ever a single method, approach, medium or instructional paradigm that fits all contents, all ages, and all students. As Bronfenbrenner (1977) has so succinctly put it, our main effects are likely to be interactions. This applies to technology in education as it applies to most everything else in education. Some topics, for some time at some stages of mastery might be handled didactically while other topics at other times at other stages of mastery might be best served by the kinds of learning environment that ICT can stimulate. Second, while technology is not to be trivialized by serving goals designed by a different approach, it can also not be treated as if its very employment is sufficient to make a difference. As is commonly understood today, it is not the technology per se that can make the difference but rather the activities that the learning environment affords and brings to life. To the extent that the learning environment activates both unique individuals’ cognitive as well as socially distributed learning-related processes, to that extent will unique learning outcomes be attained. The programs described above — Knowledge Forum and the Geometric Supposer meet this condition and hence, indeed, make a difference in learning not duplicated in any other way. Third, as ICT stimulates the design of new kinds of learning environments and becomes embedded in them, it also comes to serve the attainment of new kinds of learning such as the skills of team work, conflict resolution, accessing information and integrating it, designing criteria for information selection, ways of solving new problems, and their likes. These are not the kinds of commonly aimed at and measured learning outcomes. If we were to assess the contribution of ICT and the learning environments in which it is embedded, we would need to assess such achievements rather than the standard ones. Are the former worth attaining? Much depends on one’s point of view. On the one hand, an appreciation of the kinds of knowledge and skill that a high school graduate would need for proper functioning in the twenty-first century, suggests that such skills are essential (e.g., Simon, 1982). On the other hand, one might still argue that a solid base of wellchosen disciplined knowledge is what proper functioning in today’s society requires (e.g., Gardner, 1999). Probably, in the spirit of main-effects-as-interactions, a combination of the two might well be the answer. All said, education and technology have a difficult marriage, but it is not a doomed one. While as Sarason (1984) has pointed out, not everything possible, wondrous as it might be, is necessarily desirable, we might add that not everything desirable is necessarily impossible. ICT can be made to have unique and worthwhile effects on learning, provided that not easily attained but possible conditions are met.

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Becker, H. J., Ravitz, J. L., & Wong, Y. T., (1999). Teacher and teacher-directed student use of computers and software. Retrieved from http://www.crito.uci.edu/tlc/findings/computeruse/html/ startpage.htm Bereiter, C. (2002). Education and mind in the knowledge age. Mahwah, NJ: Erlbaum. Bernard, R., Lou, Y., Abrami, P., Wozney, L., Borokhovski, E., Wallet, P., Wade, A., Fiset, M., & Huang, B. (2003). How does distance education compare to classroom instruction? A metaanalysis of the empirical literature. Montreal: CSLP Report. Retrieved from http://scholar. google.com/scholar?hl=en&lr=&q=cache:JHon3Rnd4e0J:doe.concordia.ca/cslp/assets/pdfs/ 1-RER-Master-Jan11b-04.pdf+bernard+%26+meta+%26+distance Bransford, J., Brown, A., & Cocking, R. (Eds). (1999). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press. Bronfenbrenner, U. (1977). Toward an experimental ecology of human development. American Psychologist, 32, 513–530. Bryson, M., & Scardamalia, M. (1991). Teaching writing to students at risk for academic failure. In: B. Means, C. Chelemer, & M.S. Knapp (Eds), Teaching advanced skills to at-risk students: Views from research and practice (pp. 141–167). San Francisco: Jossey-Bass. Cavanaugh, C., Gillan, K. J., Kromrey, J., Hess, M., & Blomeyer, R. (2004). The effects of distance education on K-12 student outcomes: A meta-analysis. Retrieved from http://www.unf.edu/ ~ccavanau/EffectsDLonK-12Students1.pdf Clark, R. E. (1983). Reconsidering research on learning from media. Review of Educational Research, 53, 445–459. Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. Journal of the Learning Sciences, 10(1–2), 113–164. Cognition and Technology Group at Vanderbilt (1997). The Jasper project: Lessons in curriculum, instruction, assessment, and professional development. Hillsdale, NJ: Erlbaum. Coll, C., Onrubia, J., & Mauri, T. (2005). Technology and pedagogical practice: The ICT as joint activity mediation tools. Paper presented at the Annual Meeting of the American Educational Research Association, Montreal, Canada. Cordes, C., & Miller, E. (1998). Fool’s gold: A critical look at computers and children. Retrieved from http://www.allianceforchildhood.net/projects/downloads/frontmatter.pdf Cuban, L. (2001). Oversold and underused: Computers in the classroom. Cambridge, MA: Harvard University Press. Gardner, H. (1999). The disciplined mind: Beyond facts and standardized tests, the K-12 education that every child deserves. New York: Simon & Schuster. Guttman, C. (2003). Education in and for the Information Society. Paris: UNESCO. Retrieved from http://portal.unesco.org/ci/en/ev.php-URL_ID=12846&URL_DO=DO_TOPIC&URL_ SECTION=201.html Hanna, G. (2000). Proof, explanation, and exploration: An overview. Educational Studies in Mathematics, 44(1–2), 5–23. Hannafin, R. D., Burruss, J. D., & Little, C. (2001). Learning with dynamic geometry programs: Perspectives of teachers and learners. Journal of Educational Research, 94(3), 132–144. Higgins, S. (2003). Does ICT improve learning and teaching in schools? Retrieved from http://www.bera.ac.uk/publications/pdfs/ICT%20PUR%20MB%20r-f-p%201Aug03.pdf Hirsch, E. D. (1987). Cultural literacy: What every American needs to know. Boston: Houghton Mifflin. InfoDev. (2005). Knowledge map on information and communication technologies in education. Retrieved from http://www.infodev.org/files/1157_file_KnowledgeMap_ICTsEducation_tools. pdf Koschman, T. (1996) Paradigm shifts and instructional technology: An introduction. In: T. Koschman (Ed.), CSCL: Theory and Practice (pp. 1–23). Mahwah, NJ: Erlbaum.

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Lamon, M., Reeve, R., & Scardamalia, M. (2001). Mapping learning and the growth of knowledge in a knowledge building community. Paper presented in the American Educational Research Association meeting, Seattle, Washington. Maeroff, G. I. (2003). How online learning is changing our schools and colleges: A classroom of one. New York: Palgrave Macmillan. March, J. G. (1987). Old colleges, new technology. In: S. B. Kiesler, & L. S. Sproull (Eds), Computing and change on campus (pp. 16–28). Cambridge: Cambridge University Press. Mor, N. 2001. Changes in the conception of learning as a function of experiencing novel learning environments. Unpublished doctoral dissertation, University of Haifa, Israel. Moursund, D. (2004). Planning, forecasting, and inventing your computers-in-education future. Retrieved from http://darkwing.uoregon.edu/~moursund/InventingFutures/FuturesMSWord.doc Olson, D. (1976). Media and symbols: The forms of expression, communication, and education. In: The NSSE Yearbook (pp. 383–406). Chicago: National Society for the Study of Education. Oppenheimer, T. (1997). The computer delusion. Atlantic Monthly, 280, 45–62. Peck, C., Cuban, L., & Kirkpatrick, H. (2002). Techno-promoter dreams, student realities. Phi Delta Kappa International, 83, 472-480. Retrieved from http://www.pdkintl.org/kappan/k0202pec.htm Perkins, D. (1992). Smart schools: From training memories to educating minds. New York: The Free Press. Petraglia, J. (1998). Reality by design: The rhetoric and technology of authenticity in education. Mahwah, NJ: Erlbaum. Riel, M. (1995). Cross-classroom collaboration in global learning circles. In: S. Leigh Star (Ed.), The cultures of computing (pp. 219–242). Oxford: Blackwell Publishers/The Sociological Review. Roschelle. J. M., Pea, R. D., Hoadley, C. M., Gordin, D. N., & Means, B. M. (2000). Changing how and what children learn in school with computer-based technologies. Children and Computer Technology, 10(2), 76–101. Rosen, Y., & Salomon, G. (in press). The differential learning achievements of constructivist technology-intensive learning environments as compared with traditional ones: A meta-analysis. Journal of Educational Computing Research. Russell, T. L. (1999). The no significant difference phenomenon. Chapel Hill, NC: Office of Instructional Telecommunication, North Carolina State University. Sarason, S. (1984). If it can be studied or developed, should it? American Psychologist, 39, 477–485. Salomon, G. (1994). Interaction of media, cognition and learning. Mahwah, NJ: Erlbaum. Salomon, G. (1999). Higher education facing the challenge of the information age. European Journal for Education Law and Policy, 3, 1–6. Salomon, G. (2000). Learning today: Not the computer alone…. Invited IBM Chair address at Louvain-la-Neuve. Retrieved from http://www.ipm.ucl.ac.be/ChaireIBM/Salomon.pdf Salomon, G., Kosminsky, E., & Asaf, M. (2003). Computers and writing. In: T. Nunes, & P. Bryant, (Eds), Handbook of children’s literacy (pp. 409–442). London: Kluwer. Salomon, G., & Perkins, D. N. (1996). Learning in wonderland: What computers really offer to education. In: S. Kerr (Ed.), Technology and the future of education (pp. 111–130). NSSE Yearbook. Chicago: University of Chicago Press. Scardamalia, M. (2002). Collective cognitive responsibility for the advancement of knowledge. In: B. Smith (Ed.), Liberal education in a knowledge society (pp. 67–98). Chicago: Open Court. Scardamalia, M., Bereiter, C., McLean, R. S., Swallow, J., & Woodruff, E. (1989). Computer supported intentional learning environments. Journal of Educational Computing Research, 5, 51–68. Scardamalia, M., & Bereiter, C. (1996). Computer support for knowledge-building communities. In: T. Koschman (Ed.), CSCL: Theory and practice of an emerging paradigm (pp. 249–268). Mahwah, NJ: Erlbaum.

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Scardamalia, M., & Bereiter, C. (2003). Knowledge building. In: Encyclopedia of education (2nd ed., pp. 1370–1373). New York: Macmillan Reference, USA. Schnitzler, K. (2001). Comprehensive study of education on the internet. Retrieved from http://ucsub.colorado.edu/~schnitzk/Home6.html Schofield, J. W. (1995). Computers and classroom culture. New York: Cambridge University Press. Schwartz, J. L., & Yerushalmy, M. (1986). The Geometric Supposer Series. Pleasantville, NY: Sunburst Communications. Segers, M., Dochy, F., & Cascallar, E. (Eds). (2003). Optimizing new modes of assessment: In search of qualities and standards. Dordrecht: Kluwer. Simon, H. A. (1982). The sciences of the artificial. Cambridge, MA: The MIT Press. Sinko, M., 1998. Education for the information society — The state of the art: Results of the national education ICT assessment project. Line, 4, 215–220. Turkle, S. (1995). Life on the screen: Identity in the age of the internet. New York: Simon & Schuster. Van Boekel, S., & Stegers, E. (2003). ICT-gebruik docenten behoeft brede ondersteuning! Onderzoek naar ICT-gebruik onder docenten in het primair en voortgezet onderwijs [The use of ICT by teachers needs support! Research into the ICT usage of teachers in primary and secondary education]. Retrieved from http://www.ictopschool.net/ictos/onderzoek/publicaties/ uitgaven/ ICTOSFile.2004-01-08.4909/file/ Yerushalmy, M., & Chazan, D. (1988). Overcoming visual obstacles with the aid of the supposer. Cambridge, MA: Educational Technology Center, Harvard Graduate School of Education. Yerushalmy, M., Chazan, D., & Gordon, M. (1987). Guided inquiry and technology: A year long study of children and teachers using the Geometric Supposer: ETC final report. Newton, MA: Education Development Center. Waxman, H.C., Lin, M.-F., & Michko, G. M. (2003). A meta-analysis of the effectiveness of teaching and learning with technology on student outcomes. Learning point associates. Retrieved from http://www.ic.unicamp.br/~wainer/cursos/impactos2004/waxman.pdf

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Chapter 13

Computer Support for Collaborative Learning Environments Heinz Mandl, Bernhard Ertl, and Birgitta Kopp

Introduction During the last decade, computers have become a fundamental tool for learning. Today, through connection to the Internet, they provide access to worldwide communication and information. Alongside these new possibilities, computers have become a pedagogical tool, e.g. used for students’ scientific inquiry or for their collaborative knowledge construction. This is reflected in the widespread utilization of computers in education. Computers can be found in elementary school classrooms, in universities, and in many other kinds of adult education. Computers are not only used in a general sense for learning, but may also provide specific tools for supporting collaborative learning environments. The very use of the term learning environment implies that learning is dependent on various environmental factors. According to Mandl and Reinmann-Rothmeier (2001), a learning environment is made up of a specific composition of teaching strategies and methods, learning material, and media. Learning environments target more than just knowledge acquisition. According to De Corte (2003), powerful learning environments also target the transfer of knowledge. Transfer means that the knowledge acquired does not remain inert (see Renkl, Mandl, & Gruber, 1996). Furthermore, transfer implies the productive use of the knowledge and skills acquired. Therefore, powerful learning environments usually involve situated learning scenarios (see Lave & Wenger, 1991), which rely on a moderate constructivist approach to learning. Such learning scenarios focus on learner’s active knowledge construction. They start with authentic problems and consider the social context of learning. In situated learning scenarios, learners usually work in small groups, which enables them to view the learning material from multiple perspectives. In these scenarios, the learning partners engage collaboratively in knowledge construction and negotiate with one another to reach a shared understanding about a particular topic. However, simply providing the forum for active knowledge construction may be ineffective as a stand-alone measure, because this often results in excessive demands being placed on the Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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learners. For this reason, Mandl and Reinmann-Rothmeier (2001) stress the need for instructional support, particularly through providing the learners with guidance during their knowledge construction. This is reflected in the approach of problem-based learning environments (see Dochy, Segers, van den Bossche, & Gijbels, 2003). Problem-based learning environments provide both problems to solve and instructional resources for the learners (Reinmann-Rothmeier & Mandl, 2001; also Ertl, Winkler, & Mandl, 2006). In these environments, the problems are the driver for the learner’s active knowledge construction, while the instructional resources provide guidance during the learners’ process of knowledge construction. In the context of learning environments, the computer can provide tools for learners’ collaborative knowledge construction as well as tools for learners’ instructional guidance during this process. With respect to the learner’s collaborative knowledge construction, the computer mainly provides tools that facilitate communication between the learners. We will illustrate this point in the first part of this chapter. With respect to instructional guidance for the learners, the computer offers a foundation for introducing advanced instructional methods to the collaborative learning environment. These methods would hardly be possible without the use of a computer.

Computer Support for Collaborative Knowledge Construction In collaborative learning environments, particularly when learners are separated by distance, the computer can facilitate communication between the learners. In recent years, numerous tools for enabling communication between learners have emerged. These tools allow for either an asynchronous or a synchronous mode of communication. The modes affect the selection of the learning scenario. Synchronous communication requires learners to be online at exactly the same time, whereas asynchronous communication allows learners to be online any time they choose. Besides simply providing tools for communication, the computer often provides learners with the opportunity to share the interface of the learning environment — even when in different locations. This means that learners work in the same learning context and have a shared screen in the learning environment. Different levels can be distinguished within the shared screen. The basic level simply provides learners with the same interface structure and contents when accessing the learning environment; however, learners do not necessarily see the same picture at the same time (see Weinberger, 2003). The enhanced level supports learners by having them to share one application simultaneously (application sharing). This allows learners to work collaboratively and simultaneously using the same application. They can view the actions of their learning partners and often coordinate their activities using another communication channel (e.g. chat, audio; see Dillenbourg & Traum, 1999; Ertl, Fischer, & Mandl, 2006; Pata, 2005). The level of screen sharing used often depends on the mode of communication. In asynchronous communication, learners mostly share the structure of the learning environment, whereas when communicating synchronously, they often use application sharing. In the following, we will describe two learning environments that offer different modes of communication. In the first scenario, learners communicate asynchronously through

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discussion boards. In the second scenario, learners communicate synchronously through videoconferencing. After describing both examples, we will highlight the similarities and differences found in each. A Learning Environment Using Asynchronous Communication When the computer provides asynchronous communication, learners often communicate through discussion boards in the learning environment. Such learning environments are quite commonly used for virtual seminars in higher education (see Koschmann, Suthers, & Chan, 2005; Schnurer, 2005; Weinberger, 2003). Using the discussion board, learners express themselves by typing statements into the computer interface. Learners can post messages to the system and also have the opportunity to read and reply to the messages of their learning partners. The communication is asynchronous, which means that there is no immediate reply to each learner’s contribution. However, this method also provides enough time for learners to compose thoughtful replies to other learners’ contributions (see Schnurer, 2005; Weinberger, 2003). The written messages are permanent and usually allow for later access (see Pächter, 1996). Furthermore, many systems allow learners to edit and improve their contributions (see Clark & Brennan, 1991; Dennis & Valacich, 1999). The advantage of discussion boards and other asynchronous learning scenarios is that each learner can proceed with the learning process at his/her own pace. This means that learners have time to think when writing contributions because there is no immediate need for response (Ellis, 2001; Lipponen, Rahikainen, Lallimo, & Hakkarainen, 2003). On the other hand, learners are often dependent on each other’s contributions, e.g. when working on a team assignment collaboratively. It is often necessary for learners who depend on one another to have a ‘similar pace’ for their collaborative work (see Fischer & Waibel, 2002). This means that learners should contribute to the discussion in a timely manner so that the other learners have the chance to pick up statements and reply to them. The first sample learning environment was comprised of a collaborative learning scenario for three learners working to gain a more in-depth understanding of the attribution theory (see Weinberger, 2003). They worked on three authentic learning cases and used the attribution theory to identify the causes for some pupils’ problems in school. In this scenario, learners worked independently on an initial case solution and then worked as a group to further develop the best solution. In collaboration with their co-learners and by referring to individual resources, learners discussed their analyses and other ideas to develop the most suitable solution for each case. Thus, students invested much effort in exploring the learning material on an individual basis and also shared their own perspectives during collaboration. Using the discussion board, learners composed an initial analysis and posted it to the learning environment. The learning environment provided three discussion boards for the discussion of the learners’ analyses, one for each case. The learners composed messages about case diagnoses and commented on each other’s contributions. Following these analyses, one learner prepared a final solution for each case. In this scenario, the asynchronous learning platform enabled learners to communicate and reply to each other’s comments with a temporal delay. Yet, because the learners were highly dependent on one another for composing the collaborative case solution, they worked within a fixed timeframe for their collaborative negotiation.

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A Learning Environment Using Synchronous Communication The computer can provide synchronous communication in the form of a chat or videoconferencing tool. In this learning scenario, learners are permanently connected with one another throughout the learning process. They communicate either by typing statements or sentences when using computer chat or by speaking into a microphone during videoconferencing. The communication partners receive these communication acts instantly. In this way, synchronous communication enables highly frequent learner interaction. In our example, we analyze a learning environment that uses videoconferencing. Videoconferencing enables learners to communicate in spoken words through an audio and a video channel (see Ertl, Fischer, & Mandl, 2006). The audio channel transmits spoken discourse and the video channel generally provides an image of the head and the chest of the learning partners. In such collaboration scenarios, learners often find a shared application on their screen. This shared application functions as a tool for making the contents of the spoken communication permanent, which is an important aspect when dealing with demanding learning tasks. In the second example, two learners were engaged in collaborative problem solving (see Fischer, Bruhn, Gräsel, & Mandl, 2000). The learners used videoconferencing to work collaboratively on a problem-solving task about motivational theories. They found themselves in the role of teachers, who were tasked with developing a lesson plan. In this scenario, they had to deal with different styles of cooperative assignments for the pupils and were to provide incentives for the pupils to cooperate. When developing the lesson plan, they were asked to consider which assignment could best motivate learners for a certain purpose. Using the videoconference, learners collaborated intensely to create the most suitable lesson plan. The mode of communication (videoconferencing) enabled the learners to communicate in spoken words, as they would on the telephone. Additionally, the learners had a slightly delayed image, which showed the head and the chest of their learning partner, and a shared application (whiteboard) for taking notes collaboratively. During their joint effort, they had to consider how different group assignments would affect the pupils’ motivation and discuss the pros and cons of each of the different assignments. Furthermore, they had to decide collaboratively on the design of the lesson plan and document this lesson plan in the shared application. Learners utilized the shared application both to note the pros and cons of each of the different assignments and to document the final lesson plan. Similarities and Differences of Each of the Learning Environments We have chosen examples of both asynchronous and of synchronous communication to show the extent to which the computer may provide different tools for quite similar learning scenarios. The particular features of each tool offered learners different communicational aspects for their task-specific negotiation. In the first example, the tool offered a discussion of contributions, whereas the second one provided fast responses and highly frequent interactions for the learners to collaborate together on a solution and to make decisions about how to document their solutions in the shared application. Considering the different features of each tool, the question revolves around the degree to which the learners were able to reach their learning goal using each of the respective tools. When considering this issue,

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Weinberger (2003) as well as Fischer et al. (2000) report that learners were able to reach their learning goal using each of the respective learning environments. More specifically, they found beneficial effects with respect to both the collaborative work on the task and individual learning outcomes. Learners improved their knowledge about the particular learning material during their activity in both learning environments (see Fischer et al., 2000; Weinberger, 2003). In addition, Weinberger (2003) emphasizes that learners acquired beneficial collaboration strategies and Fischer et al. (2000) refer to the better use of theoretical concepts. These results indicate that learners may achieve different goals by using different tools for communication. Focusing on the discussion of individual solutions resulted in the use of an asynchronous communication tool, in particular a discussion board. Focusing on the collaborative strategy led to the use of a synchronous communication tool, in this case videoconferencing. This difference in synchronicity evokes quite different learner interactions. In synchronous scenarios, the communication is quite intense. Learners talk or ‘chat’ with each other while learning collaboratively and can react instantly to their partners’ statements. In contrast, during asynchronous communication, partners have to wait until a statement has arrived. Therefore the communication flow is not as intense (see Weinberger, Ertl, Fischer, & Mandl, 2005). This means that synchronous communication features highly frequent interaction and coordination, whereas asynchronous communication evokes more thoughtful and comprehensive replies (see e.g. McGrath & Hollingshead, 1994). Consequently, when designing a learning environment, consideration should be given to the relationship between the learning scenario and the mode of communication. Learning scenarios that require highly frequent interaction — for example, collaborative problem solving — may be better served with a tool for synchronous communication. Thoughtful case analyses, on the other hand, may be better served by a tool for asynchronous communication (see also McGrath & Hollingshead, 1994; Pächter, 2003). Such interrelations have recently become hot topics in communication research. Researchers have worked to compare users’ performance on the same task using different communication tools (see e.g. Anderson et al., 1997; Bernard et al., 2004; O’Connaill, Whittaker, & Wilbur, 1993; Pächter, 2003; Piontkowski, Böing-Messing, Hartmann, Keil, & Laus, 2003). This research resulted in several theories and taxonomies about media choice (see e.g. Daft & Lengel, 1984; Dennis & Valacich, 1999; McGrath & Hollingshead, 1994). However, these research results and the theories are rather descriptive and quite specific. Moreover, the rapid development in communication technologies and problem-based learning environments are not yet reflected in current meta-reviews in this area (e.g. Bernard et al., 2004). Thus, research has only just begun to answer questions about learning scenarios and beneficial tools for communication. However, to obtain a satisfying answer, it is important to ask the right questions. To do this, one should follow Clark’s (1994) argumentation, which states that the type of instruction influences the learning much more than the medium, i.e. the communication tool. Considering that each tool has its own associated affordances and constraints, the question is not about which tool is best for communication, but rather how to design a learning environment in which the learners perform optimally, using a specific communication tool. As seen in each of our examples, communication occurs differently when using asynchronous or synchronous communication. However, the instruction provided may even out these differences (see Clark, 1994) by introducing important tasks and strategies for

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collaboration. Specific instruction may facilitate the learners’ ability to reach the particular learning goals. In the example of asynchronous communication, instruction may focus on problems that occur when the schedule is too flexible. In such cases, some learners take too much time for making their contributions. Due to the late arrival of these contributions, the other learning partners may miss the chance to take these contributions into account. To counteract this problem, the instruction could provide a timeframe for the learners’ activities. This timeframe could, to a certain extent, synchronize the learners’ pace in the learning environment. This kind of synchronization may help learners finish their collaborative task in a timely manner while giving consideration to the contributions of all collaborating partners (see e.g. Fischer & Waibel, 2002; Schnurer, 2005; Weinberger, 2003). In the videoconferencing example, one could introduce individual phases to provide learners with an opportunity for individual reflection during the synchronous communication (see Ertl, Reiserer, & Mandl, 2005; Rummel & Spada, 2005). This could even out problems, which may arise during highly frequent interaction and could also support thoughtful individual reflections. Another possibility would be to introduce a shared application during which the learners would have the opportunity to record any important contents of their collaboration: the swift contents of synchronous discourse become permanent when they are fixed in the shared application and therefore provide a lasting foundation for collaborative reflection (see Ertl, Reiserer, & Mandl, 2005; Pächter, 1996). This shared screen may thereby offer both a resource and a space for communication between the collaborating partners to support their collaborative activities and their knowledge construction (see Bell, 2002; Schnurer, 2005; Weinberger, 2003). Furthermore, the contents displayed on the shared screen may focus the learners’ discourse and may therefore receive increased attention from the learners (see Ertl, Fischer, & Mandl, 2006; Suthers & Hundhausen, 2003). In summary, the instruction and the learning scenario indicate which communication tool is best for promoting learners’ knowledge construction. Furthermore, instruction may stem from several support methods, which can further improve learners’ performance within each specific learning environment.

Instructional Guidance for Computer-Supported Learning Environments When the computer supports the instructional guidance of a learning environment, it mainly offers a tool for implementing advanced instructional methods. In this context, the main feature of the computer is the shared screen. We have already mentioned that this shared screen can serve as a permanent knowledge base, thus facilitating the learners’ collaborative knowledge construction. In addition, it can also introduce advanced instructional methods to collaboration, which would not be realizable without the use of the computer. These advanced instructional methods have their roots in methods for supporting traditional learning scenarios. They are tailored to the specifics of collaborative learning environments and therefore often take on a particular significance (see Bromme, Hesse, & Spada, 2005; Fischer, Mandl, Haake, & Kollar, 2007). Methods for improving learning environments focus on the learner and the learner’s performance within the environment.

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The focus is on potential problems that learners may encounter during the learning process. To address problems that occur during collaborative work on the task, the methods focus both on difficulties with working to solve the collaborative task and on difficulties with structuring its content. In the following, we will show approaches for improving computer-supported collaborative learning environments that relate to both aspects. However, because these methods focus on the learners’ performance within the learning environment, they also may depend on their individual prerequisites. This aspect will be discussed at the end of this section. Facilitating the Work on the Collaborative Task Solution Methods that aim to improve the work on the collaborative task solution are often based on approaches such as scripted cooperation (see O’Donnell & King, 1999). These scripts sequence learners’ work on the task. Furthermore, they may provide roles for the learners and encourage them to apply beneficial strategies for solving the task. From this perspective, scripts have two main purposes: they structure the collaborative negotiation as well as the work to determine a solution for the task. Applying scripts in face-to-face scenarios mainly aims to evoke beneficial cognitive and meta-cognitive strategies from the learners. One example is the method of scripted cooperation by O’Donnell and Dansereau (1992). This script sequenced the learner’s collaboration process in four phases for individual text reading, recall from memory, peer-feedback, and elaboration. However, although this script structures the work on the task, the main motor for the comprehension processes lies in the strategies applied during each of the different phases (see also Rosenshine & Meister, 1994). Furthermore, learners take on different roles that correspond to the application of particular strategies within each phase. For example, one learner takes on the role of recaller, while the other functions as questioner. This example also shows how scripts depend rather marginally on the content of the text: the scripted cooperation method can be applied to texts within different content areas. However, the script is specific to the learning task. Recently, scripts have gained in importance in the field of computer-supported collaborative learning (see Fischer et al., 2007). In contrast to scripts used in face-to-face scenarios, the scripts used in computer-supported learning contexts do not necessarily structure both the collaboration process and the actual work on the task. For example, Baker and Lund (1997) describe a script that directed only the collaboration process. Using speech act buttons in the shared application, the collaborating learners had to agree on any modifications made by other learners in the shared application before they were allowed to continue. Weinberger et al. (2005) described a different script that guided learners through various discussion boards without specifying how to collaborate. However, most scripts use a mixture of both aspects and sequence specific strategies for handling a task. Ertl, Reiserer, and Mandl (2005, see Table 1) described one example for scripting in videoconferencing. In this learning environment, two learners were given the task of teaching theories of educational science to one another. To do this, they first worked independently and expanded their knowledge about a particular theory. The learners then entered the videoconferencing session for collaborative teaching. During this videoconferencing session, the learners also had a shared application for making notes about important aspects. Furthermore, half of the collaborating dyads received instructional

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Table 1: Script for collaborative teaching in videoconferencing (Source: Ertl, Reiserer, & Mandl, 2005). Teacher’s role Phase 1: Communicate Phase 2: Expanding their understanding Phase 3: Reflection Phase 4: Discussion

Learner’s role

Explaining the text material Asking comprehension questions Supporting the learner Rehearsing and typing the information received into the shared application Individual reflection and elaboration, based on the shared application Discussing on the basis of Discussing on the basis of reflection with the partner reflection with the partner and capturing the results of the discussion in the shared application

support in the form of a script. The aim of this script was to improve learning during the task of collaborative teaching. The script structured the collaborative work on the task, the roles of the learners, and the application of beneficial strategies for collaborative negotiation. Results of the study show that the script was able to facilitate learners’ negotiation with theoretical concepts during the collaboration process. For individual learning outcomes, the script specifically helped learners in the learner role acquire new theoretical knowledge (see Ertl, Reiserer, & Mandl, 2005). Other studies also report the beneficial effects that scripts have on learning processes (see Baker & Lund, 1997; Weinberger, 2003) and on individual outcomes in computer supported learning environments (see Rummel & Spada, 2005). Baker and Lund (1997) were able to show that applying a script could foster the learner’s collaboration processes. Weinberger (2003) reported that scripts used to facilitate learning resulted in more homogeneous work on the task as well as a higher individual learning outcome, measured by a higher score in an individual post-test case. Furthermore, Rummel and Spada (2005) reported that the script was able to support learners’ acquisition of beneficial collaboration strategies. Facilitation Relating to the Structure of the Content In contrast to the approach of scripts, which mainly concentrate on the work involved in solving the task and collaboration-specific strategies, content-specific facilitation is directed at a conceptual level. It aims to facilitate learners’ understanding of a particular problem. For this purpose, content-specific facilitation highlights central characteristics of the learning material by representing important content structures. According to Zhang and Norman (1994), this representation of content influences the learners’ ability to deal with the content. When provided with a beneficial representation, learners may perceive the

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problem in a different manner. This may then enable them to deal with its content more swiftly (see Zhang & Norman, 1994). In computer-supported learning environments, the shared screen provides an ideal forum for realizing content-specific support (see Ertl, Fischer, & Mandl, 2006). Prestructuring the shared screen can make important task characteristics salient and can thereby function as a representational guide for content-specific negotiations (see the concept of representational guidance, e.g. in Suthers & Hundhausen, 2003). The broad variety of structures for conceptual representation (see Löhner & van Joolingen, 2001) has led to a wide variety of facilitation methods. These methods mainly differ in the degrees of freedom that learners have and in the degree of support the learners receive when working with them. For this reason, one can differentiate between different classes of support: templates and conceptualization tools. Templates prestructure the content domain (see Brooks & Dansereau, 1983; Ertl, Winkler & Mandl, 2006; Suthers & Hundhausen, 2003). They provide categories, mainly in the form of tables, which are particularly important for content-specific negotiation. Learners fill in the empty spaces in the template and thereby focus on important categories. However, learners cannot change the structure of the template or model new relationships. Templates therefore basically aim to facilitate the understanding of important aspects or categories within a subject area. Conceptualization tools allow learners to model relations. When these tools are used, they provide objects of different style and different relations important for the content area. Learners are able to create their own representation of the structure of a particular content (see Fischer, Bruhn, Gräsel, & Mandl, 2002; Suthers & Hundhausen, 2003). Consequently, conceptualization tools aim at facilitating the deeper understanding of structures within a particular subject area. Ertl, Fischer, and Mandl (2006) present one example for improving content-specific aspects of the learning environment using a template (see Figure 1). In this scenario, three learners collaborated through videoconferencing. The subject was attribution theory and it was the learners’ task to solve a case, which used the attribution theory to describe a pupil’s problems with math. Learners were asked to search within the case material for possible causes for the problem. They adopted different perspectives and tried to analyze the case with respect to attribution theory. To do this, they had to deal with information about consensus and consistency and formulate attributions (see Ertl, Fischer, & Mandl, 2006). To develop a good solution to this case, learners had to integrate their different perspectives and substantiate their claims according to attribution theory (see Kopp, 2005). All groups used a shared text editor for documenting their solution to the case. Furthermore, half of the groups received a supporting template, which was included in the shared application. The template aimed to support learners by providing them with a framework for performing attributions. To this end, the learning environment contained a template, which aimed to focus learners on aspects important for formulating attributions, particularly the information about consensus and consistency and attribution patterns. It is important to note that such a template can change the learners’ perception of the task. In contrast to the naïve strategy of simply focusing on causes, learners using the template may use the strategy of justifying their attributions based on case information. Such a strategy change may be permanent and may prove effective in a later situation — e.g. a post-test — without facilitation (see Ertl, Fischer, & Mandl, 2006).

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Information Consensus

Consistency

Attribution according to Kelley

Heider

Figure 1: Content-specific facilitation in template style (Source: Ertl, Reiserer, & Mandl, 2005). The results of the study show that the template was able to focus learners on the important aspects of their attribution. When compared to a control group, they determined the attribution pattern for each cause and justified each attribution through case information regarding consensus and consistency. This resulted in a higher score for learners’ collaborative and individual learning outcomes (see Kopp, Ertl, & Mandl, 2004). The effect of the support on the individual outcomes is of particular importance since learners completed the individual post-tests without support. Many other studies have also described the beneficial effects of content-specific facilitation in computer-supported learning environments (see Ertl et al., 2005; Fischer et al., 2002; Suthers & Hundhausen, 2003). Ertl, Reiserer, and Mandl (2005) were able to show that a template focused learners’ collaborative knowledge construction on contents that they neglected without the template. Suthers and Hundhausen (2003) reported that a template helped learners to describe the relationships between theoretical concepts and evidence. Furthermore, Fischer et al. (2000) found that learners who used conceptualization tools also converged regarding the knowledge acquired. This means that the post-test scores of learners who had been provided with support were much more similar than the scores of the other learners. Facilitation and Learners’ Prerequisites In several studies, collaboration-specific and content-specific support measures have proven themselves beneficial for learning. However, the decision to employ a support measure should be driven by the specific characteristics of the learning scenario. Solid theoretical considerations and aspects of usability, rather than technical feasibility, should be the driving force for the design of facilitation. Not all of the opportunities that facilitation methods offer may have the desired effects (see Weinberger et al., 2005). The key for this issue often lies in the learners’ individual prerequisites, e.g. prior knowledge (Dochy, 1992; Ertl, Kopp, & Mandl, 2005; Shapiro, 2004), cognitive abilities (Sweller, van Merriënboer, & Paas, 1998), or motivational aspects (Deci & Ryan, 1992). These prerequisites mean that scripts and content-specific support may have a varied impact. With respect to scripts, there is the risk that excessive rigidity may have a negative impact on learners’ motivation (see Deci & Ryan, 1992). This could also have a detrimental impact on learning processes and outcomes (see Weinberger, 2003). Dillenbourg (2002) introduced the term of ‘over-scripting’ a learning environment, which means that too much structure in the learning process may hinder the exchange of information and reduce the beneficial effects of scripts on the learning processes (see also Cohen, 1994).

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With respect to content-specific facilitation, methods that provide learners with too much freedom might prove too complex for beneficial activities (see Dobson, 1999). When applying complex conceptual facilitation, such methods may exceed learners’ cognitive abilities and lead to cognitive overload (see Sweller et al., 1998), which may negate the facilitation effect. This means that complex methods, which allow a high degree of freedom, may be best suited for highly experienced learners, while rather restricted, highly structured methods provide most benefits for inexperienced beginners. Therefore, it becomes clear that the learners’ skills and their prior knowledge must be taken into consideration (see Ertl, Kopp, & Mandl, 2005; Reiserer, 2003; Shapiro, 2004). On the other hand, if facilitation methods oversimplify the task, this could lead to decreased mental activity in the learners and therefore to lower learning outcomes (see also Salomon, 1984). Because the learners’ cognitive activities are the key to their understanding, facilitation methods might paradoxically make the task more difficult. The greater level of difficulty then works to evoke increased mental activity and may improve learning outcomes (see Reiser, 2002). Therefore, combining different facilitation methods may benefit the learning environment (see Ertl, Fischer, & Mandl, 2006).

Conclusions In this chapter, we have focused on the computer as a tool for supporting collaborative knowledge construction and for introducing advanced instructional methods to collaborative learning environments. In doing so, we have discussed the constraints and affordances relating to both aspects. Regarding collaborative knowledge construction, we showed the extent to which the learning scenario and the mode of communication relate to one another. However, we also showed the degree to which instruction could influence this relationship. With respect to instruction, we illustrated how the support method depends on the learner’s individual prerequisites. Yet, there is one additional aspect to consider, which lies between the learning environment and learners’ progress in this environment. In learning environments that exist over a longer time period, e.g. a whole course term, learners repeatedly work within the same learning scenario. One could expect that, over time, through repeatedly working in the same learning environment that learners internalize the structure and the particular facilitation methods applied. In terms of the interaction processes between the learners’ prerequisites and support measures, this additional experience raises their individual prerequisites and may thereby reduce the need for support after several learning sessions. Consequently, computer-supported learning environments should also provide a fading mechanism based on the cognitive apprenticeship approach (see Collins, Brown, & Newman, 1989; Puntambekar & Hübscher, 2005). This fading mechanism should reduce the amount of support learners receive to the amount they actually need. This would reduce the structure of the learning environment and enable more self-directed learning over time. Using such a procedure could increase the learners’ awareness of the self-regulation strategies that are needed and counteract loss of motivation as well as course dropout, which occur when learners work in a computer-supported learning environment for longer periods (see Deci & Ryan, 1992). Future research should focus on the question of how to apply facilitation methods in a flexible manner. This

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includes facilitation strategies adapted to the learners’ requirements. As learners gain experience, the facilitation should be faded. The success of computer-supported collaborative learning scenarios has its origins in two sources: in learners’ collaborative knowledge construction and in the specific instructional support provided to the learners. To achieve this success, the computer can be a powerful tool by providing communication, advanced instructional methods, and an array of valuable and authentic resources for the collaborative learning environment. Thus, learning environments should not only use the new technology, they should also benefit from the new instructional methods that are enabled by this technology. The goal for using computer-based learning should be to create powerful learning environments that facilitate both beneficial learning activities and fruitful social interactions between learning partners (see De Corte, Verschaffel, Entwistle, & van Merriënboer, 2003).

Acknowledgment This work was funded by Deutsche Forschungsgemeinschaft (German science foundation, DFG), grant nos. MA 978/13-1, MA 978/13-3, and MA 978/13-4.

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Chapter 14

E-pedagogies for Networked Learning Robert-Jan Simons and Maarten de Laat

Introduction Networked learning is an emerging interdisciplinary field with its focus on learning through computers. It is a term more prevalent in the U.K. than in the U.S.A. and continental Europe. By networked learning we mean the use of information and communication technologies (ICT) to promote collaborative or co-operative connections between learners in a community, their tutors, and learning resources (Steeples & Jones, 2002) in order to enhance the efficacy of learning among its members. Deliberately, we chose for the term ‘networked learning’ and not, as most Europeans do, for computer-supported collaborative learning (CSCL). We did this because (a) computer-supported learning focuses, in our view, too much on the role of the computer, whereas we believe that computer networks are the more important carriers; (b) instead of collaborative learning with its connotations of learning together we prefer a broader perspective with an open eye for individual and collective learning; (c) we believe that networked learning fits better into work-related learning than CSCL which is thus far mostly connected to school and university contexts. To provide an overview of the developments in the field of networked learning is a formidable challenge. Despite the fact that it is a relatively young field (though it has a longer tradition as it emerged out of computer-assisted learning approaches), it has witnessed, and actively contributed to, changing the way we currently think about teaching and learning. In this chapter we would like to put the pedagogical approach to online teaching and learning to the centre of our attention and describe how pedagogies in networked learning have developed. The term e-pedagogy denotes this pedagogical approach to e-learning, both in on-line courses and integrated in face to face courses. We will connect these pedagogies to learning metaphors (mental constructions people develop about learning). First, we will present an analytical scheme of five learning metaphors to be used in the next paragraphs to analyse connections between technical approaches to networked learning and pedagogical approaches. Second, we will sketch the history of the use of computers in education from the point of view of learning and instruction. Finally, we will discern two stages of networked learning: teacher-centred approaches and community-centred Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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approaches. In each stage we will describe prototypical examples of networked learning. Which metaphors are found in networked learning and which one is leading in the two stages described: technology or pedagogy?

Learning Metaphors According to Lakoff and Johnson (1980), a metaphor is a mental construction that helps us to structure our experience and to develop our imagination and reasoning. Simons and Ruijters (2003) distinguish five metaphors of learning: the acquisition metaphor, the participation metaphor, the discovery metaphor, the apperception metaphor, and the exercising metaphor. Fifteen components in which the metaphors could differ were deduced from the literature and practice: (a) situations in which one learns; (b) relations with others; (c) dealing with mistakes; (e) the role of emotions; (f) acquiring knowledge; (g) guidance; (h) allergies; (i) preferences in training; ( j) who determines learning; (k) how to organise it; (l) what is annoying; (m) what makes you think; (n) reaction to unknown situations; (o) kinds of knowledge; (p) what makes you think. For each of these components, the metaphors have differences. Emotions related to learning are, for instance, inspiration and curiosity (discovery), safety and trust (experimentation and participation), clarity and certainty (acquisition), and stress and work pressure (imitation). Allergies are, for instance, boredom (imitation), people who withdraw from collaboration (participation), lack of knowledge (acquisition), acting without feeling competent (experimentation), and lack of room for initiatives (discovery). Dealing with mistakes varies as follows: I learn a lot from my mistakes (experimentation), mistakes keep me alert (discovery), I try to prevent mistakes through a good preparation (acquisition), I do not learn a lot from mistakes (imitation). The first two metaphors relate to the distinctions made by Anna Sfard in her article ‘On two metaphors for learning and the danger of choosing just one’ (Sfard, 1998). Learning as the acquisition of something is probably the most common view of learning. The Oxford Reference dictionary even refers to learning as ‘knowledge acquired by study’. Knowledge of the world is treated as the objective truth that can be transmitted from one person to another (Bruner, 1996). Theoretically, the acquisition metaphor stems from and resides in the tradition of cognitive psychology, which focused on the storage, organisation, and retrieval of information in memory (Anderson, 2000; Anderson, Reder, & Simon, 1996). In educational psychology, especially Ausubel (1963) worked in the tradition of the acquisition metaphor. The participation metaphor examines learning as a process of participation in various cultural practices and shared learning activities. The focus is on activities and not so much on outcomes or products of learning. Knowledge does not exist either in a world of its own or in individual minds but is an aspect of participation in cultural practices (Brown, Collins, & Duguid, 1989; Lave, 1988; Lave & Wenger, 1991). Cognition and knowing are distributed over individuals and their environments, and learning is ‘situated’ in relations and networks of distributed activities of participation. Knowledge and knowing cannot be separated from situations where they are used or where they take place. Learning is a matter of participation in practices, enculturation, or legitimate peripheral participation (Lave & Wenger, 1991).

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Simons and Ruijters (2003) refer to Paavola, Lipponen, and Hakkarainen (2002) who argued convincingly that the distinction between the acquisition metaphor and the participation metaphor should be supplemented with a third metaphor: the discovery metaphor. They base this on an analysis of three recent theories of knowledge creation, the ones from Engeström (1999), Bereiter (2002), and Nonaka and Takeuchi (1995). Hager (2004) independently suggested a similar third metaphor: the construction metaphor, seeing learning as a process of (re)construction. The fourth metaphor is the apperception metaphor, focusing on implicit learning through observation and imitation. Role models, best practices, and learning under pressure in the real world are key aspects of this metaphor. Theoretically, this way of learning relates mostly to the social learning theory of Bandura (1986) focusing on observation, imitation, and modelling as vehicles for learning. The fifth metaphor (exercising) is a metaphor of learning that resides more in the learning organisation literature (Senge, 1990). It is explicit learning, that is, however, not focusing on knowledge (as the acquisition metaphor), but on skills, attitudes, and expertise. For learning, one needs guidance by experts and collaboration with others in safe environments. In learning organisations, not only the organisation as such and the teams in it, but also, or even especially, the individuals should work on their learning abilities. If individual employees have high learning abilities, the organisation can change quicker than competitive organisations (Senge, 1990). Another theoretical approach that underlies this final metaphor is Ericssons’ deliberate practice theory. This theory describes how musicians, sport people, and workers practice deliberately on a regular basis in order to reach higher levels of expertise or competence (Ericsson, Krampe, & Tesch-Romer, 1993). Table 1 characterizes these five metaphors of Simons and Ruijters (2003) with some key words. Simons and Ruijters considered the five to be metaphorical in a true sense, meaning that they had a holistic nature with various kinds of overlap on dimensions of learning. Moreover, the overlap could also be a source of information. Acquisition and exercising overlap, for instance, in their emphasis on explicit deliberate learning. The other three metaphors overlap in that they focus on implicit spontaneous learning. Participation and

Table 1: Five metaphors of learning. Learning by Apperception Participation Acquisition Exercising Discovery

Key words Role models, best practice, real life, pressure, implicit learning, imitation, observation Dialogue with others, collaboration, discourse, trust, enculturation, communities of practice Objective facts, transmission, knowledge from experts, theories Safe environment, practising, skills, attitudes, simulations, explicit learning, role playing Meaning, deep understanding, inspiration, self-regulation, knowledge creation, productive, designing

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exercising overlap in their focus on learning with others in a good climate. Apperception and discovery overlap in their focus on complexity and real life, etc. In analysing the developments, these overlapping patterns are what we are looking for. These five metaphors will be used in this chapter to sketch changes in thinking about learning over the years as appearing from research and development of ICT in education in general and networked learning in particular. We assume that historical periods differ with respect to the patterns of learning metaphors that are dominant. Theories of learning came and went, and thinking about learning and education underwent important changes. The causal mechanisms, however, are unclear. Do theories influence thinking in practice? Are societal developments influencing the popularity of certain theories? We don’t know. These changes in thinking about learning will also become apparent, so is our expectation, in e-pedagogies used in education and in networked learning. Technology probably ‘pushed’ certain developments in thinking (and the related metaphors of learning), and these changes in thinking probably ‘pulled’ the development of new technological applications. Is it technology push or pull? And was this the same in various historical periods? Examples of technology-related concepts as related to the metaphors are as follows: – Participation: Communities of practice (implicit social learning); videotaped practices; learning communities (learning at the foreground) — blended learning. – Apperception: The Shell mentoring approach (see shell.live_wire.uk/mentor) — access to examples and role models from outside the department; learning from best practice sites, worked out examples, role models, talking heads. – Acquisition: Knowledge management — archiving and restructuring existing information; traditional e-learning modules; on-line tutorials. – Exercising: Peer feedback (e.g. 360-degree feedback) and supervisor feedback in an eHRD-environment; competence-based approaches; learning to learn in learning communities; virtual action learning; electronic portfolios. – Discovery: Problem solving, design, research, decision making, meaning construction through ICT; change laboratories; active training approaches in e-learning. In remaining of this chapter, we will first sketch the history of ICT in education in relation to the five metaphors. Then, we will turn to (two stages of) networked learning and the metaphors that are dominant there.

A Brief History of ICT in Education The history of the use of computers in education and training may be divided in three periods: 1960–1975, 1975–1990, and 1990–2005. What were the main learning metaphors during these stages? The three stages have some overlap, and clear demarcation lines between them cannot be drawn. Some of the older systems and habits remain popular over the years, whereas other disappear or are replaced. Sometimes there are developments that are ahead of their time. During the first period, ICT was mainly present in higher and military education and running on mainframe computer systems. Researchers tried to develop ‘machines’ through which the learning and instruction process can be supported. In fact they were so enthusiastic about

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the power of the machine that during that stage the ambition grew to develop machines to replace the teacher. ‘After all, a machine that can do this job is, by definition, a good teacher’ (Galanter, 1959, p. 1). In fact, in his edited book Automatic Teaching these teaching machines were seen as a theory of teaching and learning, because the structure of a machine or its program is a set of operations that describe its initial state, and the subsequent states that can be derived by the rules of transformation, which is in fact the characterisation of a learning theory (Galanter, 1959). Some features of these machines were the ability to; (a) respond to the student; (b) make plans for itself; (c) diagnose the plans and ideas that the student has formed (Galanter, 1959). The central idea was to create a teaching machine that would respond to the needs of the student. This could be done when the machine could offer alternative plans or programs by breaking down the subject matter into its minimal elements (referred to as atomic items). The number of paths through the subject matter will then be based on the available elements in the program. The order of elements will be fixed, but errors made by students, as they go through the program, will be deciding factors for the path the student takes through the program. The better student can skip ahead, but when the error rate is high the machine should return to earlier material (Galanter, 1959). Much of the later developed computer-assisted instruction (CAI) material is still based on these principal rules. Early experiments of automated individual and group instruction were used to automate the teaching of large groups of students. At IBM they developed the IBM 650 Inquiry Station (Rath, Anderson, & Brainerd, 1959), used in binary teaching, which is a typewriter and a console (or terminal) capable of transmitting typed information to the computer and receiving information from the computer in return. The student sits at the Inquiry Station. The program of instructions in the computer presents a problem to the students by way of the typewriter. The student types his answer, which is sent to the computer for checking and returns to subsequent steps on the basis of the teaching program. In 1960 Donald Bitzer (see Alpert & Bitzer, 1970) developed the PLATO system (Programmed Logic Automated Teaching Operations). On the basis of Skinner’s behaviourist learning model, over 15,000 hours of instruction was developed for this system. During the 1960s, PLATO was a small system for a single classroom of terminals, but around 1972 new mainframe technology supported its transition to a system capable of serving up to 1000 simultaneous learners. On-line chat and bulletin board notes features were added in the early 1970s, long before the Internet. The PLATO system used special terminals, connected through a satellite link (Computer Museum, 2005). Another well-known system was TICCIT (Time-Shared Interactive Computer Controlled Instructional Television). It was based on David Merrill’s (see Merrill, Schneider, & Fletcher, 1980) instructional concept of Component Display Theory (CDT). The difference with the PLATO system was that the student was offered full control. The TICCIT system followed an instructional sequence independent of the subject matter. The lessons had a variety of information presentations, examples, practice problems, tests, and a map of the structure of the curriculum. The second period (1975–1990) was the time where microcomputers became available rapidly. The teaching machines developed into more advanced computer-based programs to support learning. This movement became known as computer-assisted learning (CAL). In CAL the computer is used interactively so that the exchanges between the computer and student resemble a conversation (Tawney, 1979). The use of CAL can be roughly divided

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into three main categories; learning with the computer, learning around the computer, and learning through the computer (Crook, 1994). The instructional methods used when learning with the computer were based on the approach of the programmed instruction discussed earlier. This form is called CAI, where the subject matter is taught through a tutorial dialogue in small steps, provided with immediate feedback based on the student’s responses; when successful the student is rewarded; if not, the error is diagnosed and the student is led back to the correct answer (Tawney, 1979). Learning and instructional models were based on providing instructions through tutorials (tutorial dialogues) and drill and practice. CAI was used mainly in the following ways (see the most influential book of that time: Alessi & Trollip, 1985): tutorials, drills, simulations, instructional games, tests, computercontrolled video, and problem-solving environments. In tutorials, information is presented via the computer screen and the student is guided through the initial use of the information. Drills refer to a sequence of questions that students have to answer or a series of problems that they have to solve in order to reach a sufficient level of proficiency. Simulations refer to systems that imitate a phenomenon in order to teach the student about it. Tests are computerised systems for administering and scoring tests. Instructional games are systems that challenge students by increasing the level of difficulty. Computer-controlled video refers to systems where the computer is used to control the sequence of video screens. Problem-solving environments, finally, aim to teach children’s thinking skills in certain areas that can then be applied to other areas like mathematics or science. The most famous problem-solving environment was Papert’s (1980) Logo. Children learned how to let a turtle move (for instance in the form of a square). The goal was to teach children problemsolving and mathematical skills that could be applied in many other areas like maths, science, and social studies by teaching the child to program the computer. General skills were taught in the hope that transfer to more domain specific areas would occur automatically (see De Corte & Verschaffel, 1989). Later on more complicated Legologo, Logowriter, and Microworlds, succeeded the classic Logo environment. Apart from CAI, there was also computer-managed instruction (CMI), which managed the learners’ progress in ‘courseware’ and computer-managed learning (CML), which offered help to learners on the basis of their responses or detailed profiles (Stockinger & De Pablo, 1999). Learning around the computer refers to a student or a group of students using the computer to simulate or model a kind of theory or application. Here the students are stimulated to talk with each other (or with the teacher) about what is happening when manipulating certain variables or parameters. Nevertheless, in these early days, the emphasis was on using simulations to provide individualised learning. Learning and instruction was based on cognitivist theories of learning, where the emphasis is on perception, information processing, and thinking. Learning is seen as an active process that occurs within the learner, depending on how information is structured, presented, and processed by the student. The students are stimulated to diagnose problems, form concepts through experience, learning by doing, and discovery learning (Tawney, 1979). Models for learning and instruction were based on teaching principles focusing on information processing. Tawney (1979, see pp. 111–113) formulated teaching principles such as the following: existing teaching practice should be supplemented rather than replaced; learning should be active, enabling student participation in a dialogue between student and computer; the focus should be experience

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driven, emphasising handling knowledge instead of transmitting knowledge; previous acquired knowledge should be restructured, linking new knowledge to a longer established structure of knowledge; high-level learning should be stimulated where the activities are application and evaluation of knowledge (as opposed to recall of knowledge); what the student does should be controlled, a tutorial dialogue ordering the way a student learns more than a book does. Designing CAL programs based on these principles imposes the problem of task structure and guidance. One can decide to program a linear route where the student can only progress or repeat earlier completed steps, or the students can be given a set of options that branches out of previously made decisions, or the students can be given full control and can select at any time from the menu what they want to do. In general, students do not like to follow a detailed set of instructions, yet at the same time complete freedom is not appreciated either. Students welcome a well-defined task where a structure is imposed by a task rather than a series of small questions or general comments on what to do next (Tawney, 1979). Learning through the computer later on branched into CML aimed to create connections between learners, teachers, and learning resources, now known as networked learning, which will be discussed in the next paragraph. In the case of CML the emphasis is on managing learning events or the routing of students through a course, each being advised on their next step, based on the strength of their aims, interests and, most importantly, past performance. The emphasis here is more on offering a personalised learning experience and on the organisational, planning, and monitoring side of learning instead of learning and instructional processes. The third period (1990–2005) is the time where email and Internet entered the field. CAI became web-based instruction. This also made networked learning possible. Email became an important addition to many courses for the interaction between teachers and students. Electronic learning environments like BlackBoard and WebCt were implemented on a large scale. Typically, these electronic learning environments form places where all the information (documents, powerpoint sheets, readings, assignments, etc.) is archived. It is the place where teachers and students interact with each other. There are also possibilities for students to interact with each other in discussion forums or through email. Internet became an enormous collection of resources that people can use to learn and teachers can use to teach. E-learning and blended learning became the new buzzwords in the beginning of the 21st century. Somewhere in this third period, an important shift occurred from teacher-centred to community-centred approaches. It is impossible to say when this happened and it did not occur everywhere yet, still there are many signs that this shift occurred. At first, ICT was used to replace or support teaching without changing the basic approach to teaching as presenting information, guiding the student, practicing, and assessing student learning. Later on, community-centred approaches became more popular, focusing on new ways and new sequences of learning, centring around the needs and inputs from students learning together. When we look at the three stages from the perspective of the learning metaphors, it seems clear that the acquisition and exercising metaphors were dominant in the first period. In the second stage, some first signs of the discovery metaphor appeared (Logo for instance) next to especially the acquisition metaphor. It is only in the third stage that the participation metaphor entered the scene and the discovery metaphor became more important. Table 2 presents a summary of the three stages of computer use in education.

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Table 2: Three stages of computer use in education and learning metaphors. Stage

Key focus

Dominant learning theory

Dominant learning metaphors

1960–1975

Technology replacing teaching/teaching machines

Behaviourism

Exercising and acquisition

1975–1990

Learning with computers: conversation between learner and computer Learning around computers: optimal information processing Learning through computers: beginnings of networked learning

Cognitivism

Acquisition and discovery

1990–2005

Teacher-centred approaches to networked learning

Cognitivism, constructivism, and social interactionism

Discovery, acquisition, and participation

Community-centred approaches to networked learning

Constructivism and social interactionism

Participation and discovery

When we now turn to networked learning, we may discern two stages in the use of ICT in networked learning: a stage where networked learning was embedded in teacher-centred approaches and a stage where community-centred approaches are becoming dominant. In the following paragraphs, we will treat these two stages from the perspective of e-pedagogies.

Teacher-centred Approaches to Networked Learning In the first two stages of the use of ICT in education, the main idea was that elements of the teaching processes could be taken over by technology, where even in some cases, it was the aim to replace the teacher. However, this approach was not very successful and the teacher nowadays still plays a vital role in the educational process. Computers became more powerful and with the increasing possibilities of networking, their presence in education grew out of the experimental stage and became more or less mainstream. Learning with computers (traditions as CAI) became less dominant and the focus was on exploring the possibilities of learning through computers, aimed at making connections between learners, teachers, and learning materials (referred to as networked learning). Cognitivist learning theories made place for social interaction and constructivist learning theories, which place even more emphasis on the active role of the student in learning and instruction (De Corte, 1990). Learning is

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seen as a process of knowledge construction where the learner is in charge of its own learning experience, combined with reflection and social interaction. The emphasis was on implementing computer-mediated communication (CMC) in education and this stage was focused on assisting teachers adopting these new forms of learning successfully in their courses. In the late 1980s and continuing in the 1990s, learning through computers was driven by CMC to foster co-operative or collaborative learning and distance learning. These developments led to the implementation of groupware and virtual learning environments in education. Learning and instructional models were influenced by this orientation towards group learning, where students are stimulated to work together on a common problem in discourse communities (Glaser, Ferguson, & Vosniadou, 1996). Popular learning environments are Blackboard and WebCT. These packages are mostly concerned with providing education via on-line and were introduced to bridge traditional institution-based education with web-based learning (as clearly reflected by the name ‘Blackboard’). A popular instructional model (see Figure 1) to support teachers to moderate learning in virtual learning environments was developed by Salmon (2000). The role of the teacher (or moderator) is essential to the design and implementation of networked

Figure 1. Model of teaching and learning online (Source: Salmon, 2000).

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learning and student outcomes and this model aims to guide teachers on how to successfully teach and moderate on-line learning. The first stage of this model is focused on setting up the virtual learning environment, through the design and preparation of on-line learning activities: welcoming the students and introducing them to this way of learning and working together. Stage two is one of on-line socialisation and building identities: stimulating students to send messages through which they can get to know each other and learn how to operate in an on-line discussion environment. During stage three, the focus shifts more towards the actual course. Students are invited to articulate their personal goals, submit information relevant to the course to each other as well as to use the resources available in the virtual learning environment, like course material, content, web-links, and information presented by their fellow learners. The role of the teacher is to provide structure, overview, and keep the online activities organised. At stage four, the students start the course-related group discussions and the interaction becomes collaborative. The teachers’ role is to connect messages sent by the students with the course content and aims, summarize the discussions but also move the students to new topics when needed. At stage five, the students are encouraged to take responsibility for their own learning. Students look for more benefits from the system to help them achieve personal goals. The teacher stimulates the students to discuss concepts and ideas at a deeper level. Salmon’s (2000) five-stage model is a constructivist approach to learning and instruction, based on the following principles: (a) build upon learning objectives of the learner; (b) stress the importance of problem-solving objectives; (c) assessment and evaluation is part of the experiential cycle and interwoven in the learning process; (d) look for assessment criteria that are in line with the objectives put forward by the learners. The use of ICT in education had a great impact during this stage and challenged the way institutions approached education. Laurillard (2002) wrote a book with the title Rethinking University Teaching offering a teaching (or instructional) strategy based on a conversational framework, which can also be used to categorize different kinds of media used in education. According to her, the best strategy for learning and instruction is to create an iterative dialogue between the teacher and the student focused on a topic or goal. Laurillard admits that this is a prescriptive strategy, but it aspires, according to her, to prescribe a form of interaction between teacher and student. We may conclude that in this stage, the role of the students during the learning has become an active one where both the teacher and the students are stimulated to take charge of the learning. However, the pedagogical models for learning and instruction are still teacher driven. It is the teacher who is the prime person responsible for designing and offering the learning experiences, though the student is invited to take partly control of this process. There are beginning signs of the participation metaphor, focusing on the importance of conversations and dialogues as well as of the discovery metaphor, emphasising the importance of construction of knowledge by students themselves. But this shift is not yet complete, because of the dominance of teacher control.

Community-Centred Approaches to Networked Learning The traditional relationship between the teacher and the student is, however, changing (De Laat, Lally, Simons, & Wenger, 2005); the role of the teacher is moving away from

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‘the sage on the stage to a guide on the side’, allowing the students to move to the centre and become self-regulated learning communities. We believe that this development is partly initiated by adopting the community of practice model (Wenger, 1998) in networked learning. Applying the principles of communities of practice or learning communities means that institutions create open learning spaces where students are explicitly invited to take charge of their own and collaborative learning experience. Where in the previous stage, the focus was more on teachers implementing networked learning in their courses; in this new emerging stage we see that students are gradually taking over and designing networked learning together and in dialogue with teachers. Currently we are in the middle of this community-centred stage and it is difficult to reflect on it as a whole or retrospectively. In this paragraph we will therefore present emerging issues based on research in networked learning practice. An early example of networked learning is the concept of the knowledge-building community (Scardamalia & Bereiter, 1992). Knowledge-building communities are familiar to scientific research communities and operate on the basis of constructivist principles (knowledge is a human construction and not something that is to be revealed or transmitted), sociocultural activity (as the medium through which knowledge construction takes place), and apprenticeship (skills of young scientists are acquired by working with a more mature scientist). Scardamalia and Bereiter developed a networked learning environment called CSILE (computer-supported intentional learning environments) that embedded a number of design principles to support learning and instruction (Scardamalia & Bereiter, 1992, pp. 44–46). They treat knowledge as objects that can be criticized, modified, compared, related, and regarded from different viewpoints, in different contexts. Higher order representations and integrations of knowledge are encouraged rather than the proliferation of loosely connected items. Contributions to the communal database should be visible, not solely in terms of their independent merits, but also of their contribution to advancement of the group’s knowledge. Learning collaboratively or co-operatively are relatively new learning attitudes for both students and teachers. Co-operative learning (Johnson & Johnson, 1999) methods such as the jigsaw approach (Brown & Campione, 1994) have proved to be successful to foster interactions amongst students, but these methods were not widely adopted, neither in classroom nor in on-line education. In many instances of networked learning, both teachers and students are experimenting with various forms of collaborative learning, and teachers express a need for pedagogical methods to make this a success. Studies conducted by Hewitt (1996) show that students made most progress when the teacher was actively coaching, structuring, and participating in the knowledge-building communities. Although CSILE was meant to be (an early) community-centred approach, in practice it was often very teacher centred (see also the research of Veldhuis-Diermanse, 2002). In an attempt to synthesise research findings in networked learning (De Laat, Lally, Simons, & Wenger, 2005) we found clear indicators that the traditional teacher–student relationship is changing (see for instance McConnell, 1999). Owing to the openness of the networked learning environment and a community approach to learning and instruction, the traditional boundaries are fading and a shift in the balance of power is apparent as both teachers and students actively engage in a learning relationship (De Laat & Lally, 2003). De Laat et al.’s review showed that students, when learning collaboratively in

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networked learning communities, develop rules, shared responsibilities, roles, learning tasks, goals, and leadership styles to organise and regulate their learning (see for instance Light, Nesbitt, Light, & Burns 2000; Vonderwell, 2003). They actively engage in creating their own learning agenda and learning style by negotiating the tension between their personal desired direction and the direction of the entire group (see McAteer, Tolmie, Duffy, & Corbett, 1997). In other words, students take on both learning and teaching responsibilities and seek to develop ways in which they can coordinate and plan their learning (Gustafson, Hodgson, Mann, & Olsen, 2004). This form of group regulation of learning is, perhaps, a logical extension of the self-regulated learning behaviour, but it seems to require new skills and knowledge of metacognitive learning and group dynamics. Knowledge about one’s own learning style alone is not enough in this context. It has become important to develop awareness of other participants’ learning styles and strategies. This requires developing a form of ‘inter-metacognitive’ knowledge (knowledge of the cognitive processes and strategies of the group) to be able to actively engage in group regulation of learning. Our review (De Laat, Lally, Simons, & Wenger, 2005) also points out that students need to be familiarised and properly introduced in this way of working and learning together. Taking part in an on-line discussion requires the ability to exercise attitudes and competencies and it takes time for students to develop these. Students need to be explicitly informed and socialised in community-based constructivist learning (i.e. Cramphorn, 2004). They have to learn to become active learners and need time to develop confidence to act as constructive learners and gain learner autonomy. It is clear that providing a community forum by itself is not enough. The role of the teacher is to create appropriate conditions in their instruction and course design to develop a sense of community where students are made aware that there are complex group dynamics involved in learning together. Students need to learn to act as a community where they take on active responsibility for their learning and teaching processes as well as manage the group’s cohesion, well-being, trust, emotion, spirit, and motivation (Rovai, 2002). Sorensen (2005) presents a model for learning and instruction to facilitate networked learning based on the social theory of learning by Wenger (1998) and an orientation towards participant cultures in terms of experiences and competencies. This model aims at emphasising the role of experiences and practices of the individual students as a means to support the development of group identity and shared culture through participation and mutual engagement. Sorensen (2005) uses the concept of culture shock as a way to enhance learning, because she argues that the shock of new culture often stimulates cognitive and emotional dissonance, which in turn results in a better understanding of others and ourselves. On the basis of these perspectives, she presents an open instructional process that is student centred, where knowledge resources enter dynamically from all sides via the participants as well as the teacher(s). This approach, which is process driven, aims to stimulate a dynamic interchange between teacher and learner roles. McConnell and Lally (EQUEL Position Paper, 2004), amongst others, have designed a learning and instruction model inspired by constructivist and community-based learning principles to host a masters course in e-learning. This model is based on the idea that collaborative learning and community-based learning principles provide an open learning environment where students can construct knowledge together. When learning collaboratively

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students create the opportunity to share and discuss their experiences and knowledge in a way that both the individual and the community can benefit from this. Learning in communities is a process where both individual- and collective-learning goals and agendas are carefully and constantly being negotiated, around a topic or domain that has the interest of each participant. This way networked learning communities enable the learners to develop a space for a shared activity in which their learning is situated, where they connect ideas, share problems and insights in a constructive way with concepts they are already familiar with, with new knowledge that is collaboratively constructed through their dialogues and social interactions on-line. This view of socio-culturally mediated, situated, and constructive community-based learning were the main theoretical perspectives that drove the design of the Masters in Networked Learning course at Sheffield University, offered since 1996. A means for achieving this is exposure to other participants’ development within the learning community. Members participate in developing the learning community perspective, which is based on participants and tutors taking collective responsibility for the (re)design and evaluation of the programme (EQUEL Position Paper, 2004). We may conclude from the research reviewed in this section that there is a change from teacher-centred to community-centred e-pedagogies. Instead of teachers in charge of everything, communities of students and teachers together determine how learning takes place. In terms of our learning metaphors, there is a shift away from the acquisition and exercising metaphors in the direction of the participation and discovery metaphors.

Conclusions and Discussion New pedagogical models in the community-centred approach should, in our view, focus on stimulating networked learning readiness and collaborative learning competencies. This way students will be warmed up to the idea not only to regulate their learning but also to be able to think strategically about their learning goals and needs and how to organize the collaborative learning experience to get out of it what they want. There is, so we conclude, a clear need for new pedagogical models to support the learning and instruction processes from a community-centred perspective. Group theory or group dynamics theory and conversational or dialogical learning theories as well as theories on identity formation, communities, and culture will become increasingly more important to understand and guide networked learning processes and practices. We believe that students need to develop new competencies to become participants in design, act as both teachers and learners, use intraand inter-metacognitive knowledge and skills, develop and manage individual and collective learning styles, apply leadership roles, create structures to guide their learning, and manage self-regulation and group regulation of learning. Furthermore, we think, it is the teacher’s task to both introduce and support students in this way of working because it is important to carefully introduce students into taking over these responsibilities (Simons, Van der Linden, & Duffy, 2000). It is a form of process-oriented teaching where there is a need to manage the interplay between self-regulation and external regulation (Vermunt & Verschaffel, 2000) of the learning and instruction processes. Looking at stages of networked learning — learning around the computer, teacher- and community-centred networked learning — the following picture emerges: In the first

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stage, there was dominance of the acquisition metaphor in the drill and practice programs and in the teaching machines. Some signs of the discovery metaphor showed up (already) in these days, for instance in the work by Papert (1980). In the beginning, stages of the teacher-centred stage of networked learning, email, and the electronic learning environments were mainly used for the interaction with the teacher, combining the acquisition and exercising metaphors. Gradually, in this teacher-centred stage, the exercising metaphor became more important than the acquisition metaphor: ICT was now used for assignments that could be executed with (virtual) fellow students. In the third stage that we called the community-centred stage, it became more and more the participation and the discovery metaphors that dominated the field. Another way to look at the learning metaphors in relation to the stages of networked learning is to relate them to three kinds of interaction with ICT (after Moore, 1989): with learning content, with teachers, and with fellow learners. The dominance of these three kinds of interaction varies in the five learning metaphors. In the acquisition and discovery metaphor the interaction with content is central, whereas in the apperception and exercising metaphors the interaction with teachers is more important. In the participation metaphor the interaction with fellow students is primary. When we look at the changes over time during the three stages of networked learning, there is a change from a focus on content (acquisition and discovery) in the beginning, followed by a focus on the teacher (exercising) to, finally, a focus on fellow students (participation). How can we explain these changes over time? Did the introduction of computers and networks cause changes in thinking about learning or was it the other way around: did changes in thinking about learning bring about new uses of ICT in education? Our impression is that causality went in both directions. At times technology pushed changes in the dominance of certain learning metaphors. Because new technologies entered the scene, new ways of thinking became possible. This was, for instance, the case when the introduction of Logo and microworlds influenced thinking about learning in the direction of the discovery metaphor. Another example is the use of computer networks in education in the teacher-centred stage of networked learning. Technological possibilities (Internet and other networks) made it possible to increase collaborative learning and discussion forums in education, facilitating a first shift in the direction of participation learning. At other times, however, technologies were used in new ways because of changes in thinking that were going on in parallel to technological changes. This seemed especially the case when community-centred networked learning started to become more important. New uses of technology were invented to make the further shift towards the participation metaphor possible. Probably, thus the best answer to the question about causality is that it went in both directions: sometimes technology pushed, sometimes changes in the dominance of certain learning metaphors pulled.

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Stockinger, P, & De Pablo, E. (1999). The Archimed Knowledge Village. Archimed Telematics project PL961060. Tawney, D. A. (Ed.). (1979). Learning through computers: An introduction to computer assisted learning in engineering, mathematics and the sciences at tertiary level. London: McMillan Press. Veldhuis-Diermanse, E. A. (2002). CSCLearning?: Participation, learning activities and knowledge construction in computer-supported collaborative learning in higher education. Doctoral dissertation, University of Wageningen, The Netherlands. Vermunt, J., & Verschaffel, L. (2000). Process-oriented teaching. In: P. R. J. Simons, J. Van der Linden, & T. Duffy (Eds), New learning (pp. 209–225). Dordrecht: Kluwer Academc Publishers. Vonderwell, S. (2003). An examination of asynchronous communication experiences and perspectives of students in an online course: A case study. Internet and Higher Education, 6, 77–90. Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. Cambridge: University Press.

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Chapter 15

From Individual Learning to Organizational Designs for Learning Lauren B. Resnick and James P. Spillane

Introduction Instructional psychology is devoted to building a special kind of science of learning, one capable of guiding interventions to improve learning. Over several decades of trying to build a practically useful science of instruction, psychologists have recognized again and again that ‘context’ — the environment, organization, and general beliefs that surround any particular designed intervention in learning — matters a great deal. Mostly, however, psychologists have treated context as a ‘limiting factor’ in the effects they hope they understand and document. Only very recently have psychologists of learning found common cause with scholars of other disciplines — scholars who specialize in studying, and sometimes intervening in, the social and organizational aspects of learning environments that are the context for learning. At the same time, some scholars of education policy and organizational design are reaching toward psychology for constructs that might help them understand organizations’ ‘sense-making’ efforts. In this chapter a psychologist reaching toward social and organizational theory to understand her own intervention science and an education policy researcher using psychological principles to understand educational organizations join forces to consider the complexities of disseminating both the knowledge of cognitive and learning processes that psychologists have amassed and the growing body of social and organizational theory relevant to education.

Strategies for Transferring Knowledge The first obvious question is a broad one: How does one distribute scientific knowledge about instruction and environments for learning? Especially, how do we circulate this Instructional Psychology: Past, Present, and Future Trends: Sixteen Essays in honour of Erik De Corte Copyright © 2006 by Elsevier Ltd. All rights of reproduction in any form reserved. ISBN: 0-08-045021-0

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knowledge in a manner that creates change not just in ideas, but also in the behaviour and performance of individuals and organizations? There are at least four broad possibilities: (1) We could tell people what we know about learning and instruction or about organizations, and leave to ‘practitioners’ (teachers and other education professionals) the full task of making the knowledge useful — taking care to ‘translate’ our technical and scientific language into terms accessible to people who are not trained in psychology. (2) Alternatively, or in addition, we could build study tools explicitly designed to support specific kinds of professional learning communities. This would still leave implementation details to users, but would provide extended examples and discussion or study guides linking the theoretical ideas directly to professional practices. (3) Providing even more guidance for practitioners, we could create protocols of practice that, if used appropriately, would constitute good ‘applications’ of our science. (4) Finally, we could also try to change the organizations in which people work and learn so that they become optimal environments for professional learning and practice. These four are not mutually exclusive. The first three have been used by psychologists and policy theorists – perhaps most diligently by those aiming to use their disciplines as a foundation for improvement of school-level education. But because each is expensive and complex, particular research and development groups tend to focus on one or the other, rather than on the mix of strategies likely to be most effective. What is more, as scholars in our disciplines, we are much more comfortable with some strategies than with others. Psychology as a discipline is particularly undeveloped with respect to the fourth strategy — organizational change. In examining these four strategies, we will suggest that unless we can optimally combine them, our disciplines may become marginalized as nations and societies increasingly place education at the center of their social policies. This is especially true for the ‘older’, more mature discipline of psychology. If psychology does not step up to the challenge, new multidisciplinary fields may emerge that will accept the challenge and in the process undermine psychology’s relevance in the world of learning. Telling What We Know This is the method of sharing our knowledge at which we as scholars are most adept. We regularly write research articles and give presentations. For the most part, though, presentations at professional meetings are aimed at ‘the choir’: other researchers and scholars. We may reach out to interdisciplinary groups, but not — except perhaps in our teaching within professional schools — to potential users of scientific and scholarly analyses. Only through books and articles written specifically for practitioners do we aim to make our language and concepts accessible to audiences who are not specialists. In the field of education, future practitioners experience an educational process in which they read selections from what we write — sometimes in the original scholarly

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versions, more often in versions intended for practitioners. In this way, a kind of canon of texts on psychological principles of learning and instruction has been developed and most practitioners in the field can remember the names and claims of a few major theorists. However, the links between these theoretical findings to what educators actually do in their work are weak. As we visit schools and classrooms today, we find very little practice that matches the principles of learning and instruction being taught in teacher preparation programmes. The same goes for principles of educational leadership and organizational design. Our vocabulary of distributed leadership, or ‘learning communities’, can be heard at professional meetings, but is hard to recognize in practice. This limited impact is not for lack of sophisticated attempts to improve the telling process. For example, the cognitive research community in the United States has worked over the past 10 years to communicate the most important findings of cognitive science research to policy makers and practitioners. It started with a National Research Council (NRC) Committee on Learning in 1996 that produced a book entitled How People Learn (Bransford, Brown, & Cocking, 1999) that quickly became the point of reference for scholars in the U.S. and other countries. Within a few months a more accessible version for educators appeared (Donovan, Bransford, & Pellegrino, 1999). Through workshops and meetings with practitioners, the NRC launched a serious effort to carry the principles of How People Learn into classroom use. Most recently, a new volume has been published that includes detailed examples of how to apply the principles in teaching history, science, and mathematics (Donovan & Bransford, 2005). These are sophisticated attempts by leading psychology researchers to tell education practitioners what the research says and to make the telling relate to practice. Study Tools for Professional Learning Communities Telling can begin the process of delivering knowledge, but it can never complete it, especially when the new knowledge we want to disseminate to the world of practice departs significantly from existing understandings. Indeed, if we heed our own research about learning we would realize that telling as a strategy has serious limitations because, when faced with new knowledge, the human sense-making process tends to conserve existing understanding. Something more than even sophisticated and audience-friendly reportage is needed; something that fits into what we now understand about the role of learning in communities as a crucial aspect of how people can change their practices. A powerful possibility, one just beginning to be systematically explored, is to build study tools for educators that teams of professionals can use ‘on the job’ to learn principles directly relevant to their work. Over the past dozen years, one of us (Resnick) has been working directly ‘in the field’ of education practice, bringing her own past immersion in cognition and learning research along with her. Working with a growing team of highly accomplished professionals in the Institute for Learning at the University of Pittsburgh’s Learning Research and Development Center, she and the Institute have formed alliances with leading U.S. school districts – the large ‘urban’ ones that contain the preponderance of poor, minority, and immigrant students, those most in need of strong science of learning. Educators there were hungry to learn what guidance the cognitive research of the past 25 years or so could provide. But they wanted

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this knowledge to come in forms that were tightly tied to their own work, not forcing them to first learn a bulky theory and only later focus on educational practice. They wanted to become skilled ‘reflective practitioners’ (Schon, 1987), not (once again) novice university students studying for exams. The Institute began with an analysis of the kinds of professional knowledge and skills educators would need in order to lead the kind of ‘knowledge-based constructivist’ (Resnick & Hall, 1998) learning environments that psychological research tells us we need to develop. From there, the institute built a series of study tools for professional learning communities (Resnick, Lesgold, & Hall, 2005). The tools differ from the usual linear presentation of knowledge in several key ways. First, they do not prescribe a particular order of activity for learners. Instead, they provide an array of linked resources that learning communities can access as they explore questions and develop knowledge and ‘stances’ toward their work. Second, the ‘toolkit’ contains multiple learning resources: cases to analyse, rubrics for analysis and discussion, commentaries and questions to guide discussion, and suggested structures for organizing study — along with relatively short stretches of descriptive text aimed at helping users glimpse the underlying theoretical knowledge base. These tools are embedded in a series of CD-ROMs around nine Principles of Learning distilled from 25⫹ years of cognitive research on teaching and learning (http://www. instituteforlearning.org/develop.html). The CDs are intended for use by study groups of 6 to 10 education practitioners, possibly including an expert facilitator. An introductory CD, Principles of Learning: Study Tools for Educators (Resnick, Hall, & Fellows of the Institute for Learning, 2001) is mainly designed to set forth the core theories and build common ways of using the language of teaching and learning. Additional CDs focusing on individual Principles of Learning — Clear Expectations: Putting Standards to Work in the Classroom (Resnick & Bill, 2001) and Accountable Talk: Classroom Conversation that Works (Michaels, O’Connor, & Hall, 2002) — provide study groups with the means of further developing a shared theory of instruction and learning. Each CD set presents an overview of the principle, either in text format or as an extended video presentation, as well as materials for in-depth study of specific aspects of the principle. Each also contains extended case studies. All are supported by suggested activities for individuals and study groups, along with observation sheets (to be printed out) to help ground the conversation and provide a record of issues discussed. (See Resnick et al., 2005, for a fuller description and examples of the CDs and their uses.) In sessions led by Institute for Learning fellows, most of whom had helped to design the CDs, participants experienced vibrant learning situations and there was considerable excitement about the study tool’s potential. The next step was to use the study tools to bring new forms of educational thinking to entire schools and school districts. The experience was sobering. Evaluations of our tools as used in three different districts made it clear that providing good tools and time for study is not enough to ensure that our dissemination of psychological knowledge will be well-received. Evaluator observations led to radically different assessments in the three districts. In one district, active study groups used the CDs in some schools, and principals and teachers in many schools reported successful use of the CD. There was considerable — although not universal — enthusiasm for the CD as a powerful tool for supporting teacher study of the Principles of Learning. In the two other districts, by contrast, the CDs were rarely used.

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The evaluators eventually determined that the differences were due to organizational variances in how the Principles of Learning study tools were situated in the ‘official’ work of the district. In the high-use district, participants were given ‘homework assignments’ in which they were asked to lead study sessions using the CD. They were expected to collect ‘artefacts’ from these sessions — filled-out activity sheets, e.g. — that would be discussed at the next principals’ meeting. Several cycles of assignments and artefact discussion ensued, making it highly likely that even the initially reluctant principals would find a way to launch the CD project. There was no such social facilitation and demand in the two low-use districts. There, at the end of the introductory sessions, principals were told that the CDs could help establish ongoing professional development in their schools, but no particular expectations for use were established and there was no follow-up. Since principals were not asked to report on how they were using the tools and how teachers were responding, their acceptance of the new tool was as varied as their leadership practices. Some principals initiated study groups. Others did not. Only a few participated in teachers’ study sessions. With no accountability created for participation, this new form of learning failed to take root. Protocols for Communities of Professional Practice Even where the CD-based study groups did take root, the tools provided could only begin the process of creating communities of professional practice. Transcripts, videos, and tailored study protocols can open an avenue to reflective practice, but in the real world, no externally provided example of teaching ever neatly matches a local experience. Multiple things can happen in a classroom in just a few minutes. Teachers may pose problems and start discussions, but — with rare exceptions — matters do not unfold according to a script. Students’ responses may lead in unanticipated directions. Efforts to make expectations clear to students may appear to interfere with students’ managing their own learning. A planned complex and academically rigorous lesson may become much less demanding in the teacher’s attempt to help weak or shy students. Different students may react differently to the same teacher-proposed activities. This variety and complexity means that it cannot be enough to teach educators specific strategies for effective teaching and learning — even when these are well-illustrated by carefully selected examples from practice. Educators also need to learn how to analyse the ‘messy’ instructional practice of the real world — deciding which principles of learning are illustrated (or violated) and learning how to discuss examples of practice that may be headed toward, but are still distant from, ‘best practices’. They also need to learn how to function ‘in community’ — i.e. how to treat discussion of instructional cases as legitimate opportunities for comparing ideas and sharpening concepts rather than as evaluations of teaching practices. This shift in attitude toward analysis and reflection and away from evaluative judgment is a substantial challenge, given the traditions of today’s school systems. One approach to building communities of instructional practice is for groups of educators to visit classrooms together and then confer about what they have seen. A skilled facilitator can guide the discussion; and shared protocols for observation can help to direct the initial observations in productive directions; Such protocols are designed to fit into the flow

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of daily practice, enabling educators to accomplish work that is central to their job. For example, a protocol might be designed to help school principals monitor classroom instruction (a key leadership function) in order to enable them to ‘see’ dimensions of instruction that are critical to student learning. In using the protocol over time, the hope is that practitioners will learn what constitutes effective reading or mathematics or science instruction. The Institute for Learning has developed a structured set of protocols for this kind of communal, interactive classroom visitation, which we have dubbed the LearningWalk (Goldman et al., 2004). LearningWalks are organized visits to a series of classrooms using the Principles of Learning to focus on the instructional core. Educators in a number of U.S. school districts have been trained in the processes of facilitating these visits. The ‘walkers’ observe interactions between students and teachers, examine artefacts such as displayed student work and written assignments, and talk directly with students — all guided by the semi-structured protocol. After each classroom visit, the walkers gather in the school hall and use another protocol to discuss and analyse what they have seen, always focused on trying to understand, rather than evaluate, observed practices. The LearningWalk helps build professional learning communities by focusing participants on teaching and learning, breaking down classroom isolation, developing insight into what students are learning, and providing a basis for designing professional development for the school members. Tools such as classroom observation protocols are not mere accessories for practice. Well-designed, these protocols enable and constrain practice and thereby contribute to defining it. Like other tools (Vygotsky, 1978), they mediate individuals’ interactions with others and effects on the world. One way in which structured protocols such as the LearningWalk contribute to defining practice is by framing the interactions among practitioners. Hence, the protocols that are used in the LearningWalk focus the ‘walkers’ observations on key aspects of instruction — e.g. the extent to which quality expectations for student work are made clear, the content and form of classroom discourse, the extent to which core disciplinary concepts are the focus of teaching. The protocols frame the dialogue among the walkers, directing attention to certain key aspects of classroom life and thereby enabling a conversation that is centred on core learning questions such as the complexity of the academic tasks that students are engaged in. Of course, tools do not directly determine practice but rather are made and remade in and through practice. Some ‘remakes’ can actually work against the intended learning. For example, school leaders with little experience of new forms of community building often assimilate the LearningWalk into a form of classroom visitation with which they are more familiar: evaluation of teacher performance. They convert the discussion protocols into checklists for use by supervisors, and skip much of the discussion with other ‘walkers’ and teachers. When this happens, teachers who are used to professional privacy inside their classrooms often become resistant to the process. Thus, it requires constant attention to matters of organizational design and functioning to maintain the professional learning intention of professional practice protocols.

From Tools and Protocols to Organizational Design As the prior examples illustrate, psychology provides articulated theories of learning and some demonstrations that these theories work for education when faithfully applied.

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However, when we try to apply psychologically derived theories, programmes, and tools in a more systemic manner, we encounter blockages. Our ideas and practices seem to gain a toehold among people whom we have met and worked with personally, but the new ideas and processes do not become the standard way of doing things. We have partial success at most, and only rare experiences of sustainability. Indeed, this lack of spread and sustainability is a dominant finding in most research on education policy and school reform. To create more sustainable use, to guard against our psychological knowledge being stashed away in the closet after the externally funded party is over, we need to understand what causes the blockages. Psychologists have a favourite set of blockage explanations, all focused on the individuals within the organizations they are trying to influence. They point, for example, to difficulties of motivation. New ideas are difficult at first and people do not want to make the extra effort to apply them. This analysis calls for using various motivational techniques to build loyalty to the new processes and to keep people working in the new ways. Incentives may be offered for persistence — tangible rewards or merely the camaraderie of participating with others. Other blockages, according to psychologists’ analyses, come from participants’ beliefs. These may be beliefs about the nature of teaching and learning, which can lead teachers to resist modifications to established educational programmes. For example, teachers in Germany (Staub & Stern, 2002), Israel (Strauss & Shilony, 1994), and probably in most countries believe teaching as a form of ‘transmitting’ knowledge and are likely to find recommendations to have students explore topics in order to arrive at an understanding uncomfortable or at least unproductive. In addition, many teachers have been heavily schooled in the ideas of ‘mastery learning’ (Bloom, 1971); they believe that students should keep working on a new skill or concept until they master it, and only then go on to the next topic. Carefully designed reading and mathematics programmes that rely instead on a principle of ‘spiral learning’ (Bruner, 1960) — returning again and again to a concept so that full mastery is built only over repeated, time-separated exposures — run against the grain of this belief and teachers may reject such programmes. Even when they accept the new programmes, educators’ ‘sense-making’ interpretations of new information (Spillane, 2004) may lead them to fit the new programmes into their existing scripts for instruction. For example, they may teach a math concept at greater length than the programme designers intended — so that all children seem to master it — and then skip the conceptual revisiting and extension built into the spiral plan. The psychologist’s remedy for this kind of disbelief or distortion is likely to be training programmes in which the theory of spiral learning is taught to teachers, along with training in the details of how to implement a particular curriculum. These are both solutions aimed at what individuals know and believe. An alternative or complementary approach would adjust how spiral curricula fit into the overall distribution of time, personnel, and material resources within a school or school district and might build formal benchmarks of student progress in spirally organized teaching programmes. Teachers may also have strong beliefs about which students can learn which kind of material and which students are ‘ready’ for investments in learning. Beliefs about who can learn what run deep in our schooling systems and our societies. Despite substantial research showing that ability to learn can be acquired (Resnick & Nelson-Le Gall, 1997), educators in most western countries continue to believe that intelligence and aptitude set

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limits on learning and we invest heavily in tests to detect that aptitude. Many psychologists respond to belief blockages by trying to intervene directly on the belief systems of students, teaching them to attribute success and failure more to their efforts than to their abilities (Dweck, 2003). They use group investigation strategies in an effort to enhance motivation (Shachar & Fischer, 2004), or focus on developing student self-regulated learning (Boekaerts, 2002). An alternative or supplemental approach might adjust institutional arrangements — e.g. basing access to advanced placement and other high-level courses on students’ willingness to do the work involved, rather than on grades and aptitude test scores.

Interdisciplinary Resources for Organizational Design All these blockage analyses and potential responses are psychological explanations and solutions. They focus on what individuals in education systems know, believe, or can learn. Such analyses are indeed part of the picture, but are likely not the whole story (Ball, 1994). Finding powerful solutions to the education and learning problems that we face requires looking beyond individuals, and thus beyond what psychology alone can offer. If we really want to apply psychology to instruction in the real world, our psychological explanations focused on individuals need to be matched with explanations and interventions that take account of the social groups and organizations in which people live and work (Choo, 1998; Mabey & Iles, 1994; Senge, 1994; Sparrow, 1998). Other social sciences can offer complementary frameworks that will help build organizational as well as individual capacity. Let us examine some of these interdisciplinary resources. Anthropology and Sociocultural Theory Probably the best known to psychologists of all the social sciences is the branch of anthropology known as ‘sociocultural’ theory (see Cole, Yrjo, & Olga, 1997; Lave & Wenger, 1991; idenger, 1998) or, in its variants closest to psychology, ‘situated learning’ (Greeno, Collins, & Resnick, 1996). In the 1970s, driven partly by the rediscovery of the work of Vygotsky (1978) and partly by collaborations of learning, developmental, and instructional psychologists with anthropologists, a new way of thinking about learning began to develop (see Hutchins, 1995; Resnick, Levine, & Teasley, 1991; Rogoff, GoodmanTurkanis, & Bartlett, 2001). The new theories of situated cognition treated learning as not simply a matter of individual brains at work acquiring new knowledge or skills, but as persons coming to function effectively in specific, socially defined situations. Cognition came to be viewed as a social activity, ‘stretched over’ individuals, tasks, and tools. Mind and motivation, skills, and self-concepts were linked in an essentially ‘sociocognitive’ theory of learning and development. This sociocognitive stance has become increasingly influential among psychologists of development, cognition, and instruction. For learning and instructional psychologists, it introduces, or reinforces, a stance that goes beyond individual minds acquiring personal skills and knowledge. However, with only rare exceptions (e.g. Engeström & Middleton, 1999), sociocultural analyses are largely silent on the organizations within

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which interactive groups function. It is as if the broad societal culture — along with the purview of anthropology as a discipline — is carried by individuals into their interactive groups, without an institutional or organizational mediation. For more help in designing learning organizations, we will have to turn to other fields of research, each rooted in sociology. Institutional Theory Beginning with Max Weber in the 19th century, sociologists have sought to understand how formally constituted organizations work and why they come into being. Weber focused on explaining how bureaucratic structures (governmental and private) were efforts to rationalize and make more efficient the work and accountability of large organizations, where personal relationships could not sufficiently govern actions (Weber, 1947). Weber’s theories were taken up by students and colleagues worldwide; variants of this rationalist theory dominated social science thinking about organizations throughout the first half of the 20th century. They were used to prescribe organizational designs in both public (government) agencies and private businesses. In the U.S., bureaucratic principles travelled from business into education along with the general principles of scientific management that were applied to industrial production (Tyack, 1974). In other countries, similar principles of rational management entered educational practice through governmental agencies. For multiple reasons the Weberian rationalist analysis lost favour among sociologists in the 1960s and 1970s. But more recently, a ‘new institutionalism’ theory has developed (Meyer & Rowan, 1977; Powell & DiMaggio, 1991) that has much to offer those interested in seeing their ideas used. This research tells us that organizations operate within a set of ‘taken-for-granted’ (institutionalized) beliefs, practices, and structures. Organizations mostly conform to these constraints, adopting ritualistic forms and structures that compete with efficiency, thus enabling survival over time. Organizations can also challenge these ritualized practices, becoming more effective in meeting reform goals but reducing the odds of survival. Among the institutionalized practices for public service organizations (such as education systems) are professions that control entry and advancement, labour agreements, expectations for transparency and consultation outside the organization, avoidance of evaluation, and the decoupling of the technical core from management and policy. Many education reform analyses show how institutionalization limits effective change in established organizations. Of particular note is the way in which new processes, informed by psychological research, are treated as temporary ‘pilot’ studies and not allowed to enter the organization’s core policy or practice. In this way, education organizations can appear very ‘progressive’ while in fact maintaining institutionalized practices that prevent new programmes from penetrating beyond a few ‘experimental’ sites. Some research on reform efforts, however, suggests that certain forms of institutional redesign can overcome some of the expected resistance to new practices (see e.g. DiMaggio & Powell, 1991; Perrow, 1986; Rowan, 2002; Rowan & Miskal, 1999; Spillane & Burch, in press). A decade plus of educational reforms involving systemic, standards-based curricula and intensified instructional guidance for local schools in Great Britain and the U.S.

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shows that policy reform focused directly on curriculum and backed by testing and accountability can shape the technical core in schools — although not always in precisely the ways intended by the reformers (Resnick & Zurawsky, 2005). Variants arise because policy implementation is also shaped by the sense-making interpretations of educators (Spillane, 2004), which are themselves dependent on the authority (as distinct from power) that the reform policies carry in the eyes of working educators. In addition, institutionalized norms linked to specific subject-matter subcultures contributed to distinct patterns of tight and loose coupling. In particular, some dimensions of instruction (e.g. topics covered in mathematics) may respond more quickly to policy prescriptions than others (e.g. classroom discourse or the mathematics representations used in teaching) (Spillane & Burch, in press). Organizational Resources: Human and Social Capital For several decades, social scientists have worked to extend the power of resource analysis from purely financial forms of capital to other kinds of resources that affect organizational accomplishment. Economists tend to be especially interested in ‘human capital’: What people in the organization know and know how to do (Harbison & Hanushek, 1992). Human capital is measured by credentials, performance observations, and individual outputs. Some recent work using more refined measures of teacher knowledge also shows a significant positive relationship between teacher knowledge and student achievement (Hill, Rowan, & Ball, 2005). Economically oriented reformers promote programmes — usually of salary incentives and hiring policies — aimed at attracting and holding the most qualified and productive education professionals. In the U.S., several experiments are now underway — e.g. the Denver school system’s new ProComp pay for performance system linking such incentives to specific training and instructional programmes. ‘Social capital’ is a term introduced by sociologists (Becker, 1964; Coleman, 1988) referring to the opportunities that some people have, and that organizations can create, for acquiring knowledge from others. The term has expanded to include social networks, trustful relationships, and co-construction of knowledge and practices (Adler & Kwon, 2002; Nahapiet & Ghoshal, 1998). A number of sociologists studying processes of education reform have begun to document links between social capital (e.g. groups of teachers professionally engaged with one another within a school) and the forms of knowledgebased constructivism that cognitive and sociocognitive instructional theory recommends (e.g. Bryk & Schneider, 2002; Gamoran et al., 2003; McLaughlin & Talbert, 2001; Newman & Associates, 1996). Organizational Leadership Building social capital within a school requires leadership, and the development of effective leadership is a priority of many reform efforts. Most psychologically inspired theories of leadership focus on the personal styles, scripts, and dispositions of the official leader of a school – the ‘principal’, ‘head teacher’, or ‘school director’ (Leithwood & Steinbach, 1990; Yukl, 1981). However, building on work in situated and distributed cognition as well as sociocultural theory, a concept of distributed leadership is being developed (Spillane, 2005). A distributed perspective presses us to rethink leadership in

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organizations. Rather than focusing only on those with formal leadership designations, the distributed perspective acknowledges all individuals who have a hand in leadership, whether or not they are formally designated leaders. At the same time, it foregrounds the interactional and situational aspects of leadership — the ways in which decisions and directions of practice unfold in interactions among leaders and followers. The concept of distributed leadership has sometimes been misunderstood as simply delegating functions to individuals within an organization, thus missing the crucial interactive element. There are various ways in which distributed leadership can help frame ways of building new organizational processes (Spillane, 2005). However, there is no simple prescription for developing a distributed leadership organization. For example, there are likely optimal numbers of participants for any one leadership routine. Involving more people may result in diminishing returns, but we do not know how to establish the parameters for optimal involvement at this time. Further, distributing leadership beyond those at the top of the organization is no guarantee for building social capital. While distributing leadership can increase opportunities for individuals in the organization to be networked with one another, whether it will build social trust among individuals ultimately depends on the nature of the interactions. Organizational Identity Though chiefly applied in examinations of individuals, research also applies the construct of identity to organizations (Albert & Whetten, 1985). Organizational identity refers to those characteristics that organizational members believe to be the central, distinctive, and enduring aspects of their organization. Organizational identity is a powerful construct for capturing what the organization stands for and where it intends to go (Albert, Ashforth, & Dutton, 2000). Recent work as part of the Distributed Leadership Study (www.distributedleadership.org) uses the construct of organizational identity to examine elementary schools and their efforts to innovate and change. We analyse stories that teachers, administrators, and parents tell about their schools to explicate the school’s identity as an organization. Stories are important because they touch on basic issues of who we are as a school (Spillane, Benz, & Mandel, 2004). A story’s uniqueness comes from its ability to convey meaning and express human intentionality in a particular context (Bruner, 1986; Gardner, 1995; McAdams, 1993). The stories told about schools illustrate the underlying values of the people working there, showing how they identify with their organization and the purpose and meaning that drives the teachers, staff, and administrators to do their jobs (Spillane et al., 2004). Narratives of organizational identity both guide the actions of people in organizations and frame their interpretations of new information. Organizational identity helps us understand what organizational structures, routines, and tools enable learning and innovation. Organizational Routines and Bounded Rationality A very particular and influential response to the observed limits of Weberian rationalism has been the ‘Carnegie School’ of organizational theory (March & Simon, 1993). March and Simon argued that people cannot manage fully rational or reasoned decision-making.

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Instead, they satisfice — i.e. find a workable but not necessarily perfect solution — rather than optimize. Organizations do the same. Groups and individuals in the organization develop routines (standard operating procedures or SOPs) that constitute the normal ways in which work gets done. These SOPs are not necessarily what the organizations’ official manuals say should be done. Rather, they are inventions by organization members that allow them to perform satisfactorily, in the judgement of clients and supervisors and for their own self-satisfaction. They often involve adaptation to institutional constraints of the kind discussed above and may also recruit the power of informal ‘below the radar’ work groups, as documented by sociocognitive research (Orr, 1996; Suchman, 1996). March and Simon’s concept of organizational routines gives us a particularly powerful perspective for thinking about organizational change. In the bounded rationality analysis of organizations, what systems ‘know’ is their routines of practice. Organizational learning is a change in these routines. To help an organization learn, then, we would need to help an organization analyse its formal and informal routines, including their sources of authority and control and who is most closely associated with each routine. We also would need to examine whether and how identified routines connect with core organizational functions and explore whether and how they connect with the technical core — teaching and learning. Moving from diagnosis to design, we might then pick initial targets for SOP changes that are likely to succeed quickly and to affect other routines, thus exercising leverage on the entire organization.

Diagnosing and Designing Learning Organizations We have used the bounded rationality approach to begin a process of thinking about how to diagnose and design learning organizations. The challenge and the opportunity, however, reach well beyond one particular theory of organizational functioning. More broadly, we want to apply the full range of sociocultural, institutional, and organizational insights to the redesign of education organizations to make them more receptive to knowledge gained from instructional research. We assume a continuous interaction between diagnosis (study) of organizations and targeted efforts to introduce change. Rather than detailing a script for these efforts, we offer some broad principles to guide this work. Map Routines and SOPs at the Outset Delineating the organization’s SOPs involves not only figuring out the routines (a sometimes difficult task, since they are often hidden), but also who cares about them. Also needed are analyses of which routines are blocking improvement in organizational performance and which might support desired changes. A detailed inventory of routines might focus on the following questions: – What tasks or activities are involved in each routine? – Who is responsible for executing these tasks and why? – What tools are used to complete these tasks and how do they frame participant interaction? – What organizational functions or goals are these routines intended to address?

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Introduce a Small Number of New ‘Kernel’ Routines As part of this step, establish leadership for the new routines and incentives for taking risks associated with organizational change. These kernel routines might involve redesigning existing routines to address new organizational functions through the use of new tools and the involvement of new leaders. In formulating new kernel routines instructional leaders should: – Attend first to routines that are likely to win early allegiance from many different actors and enable early successes for the organization. – Create rituals that will celebrate and highlight these successes. – Build alliances — both inside the organization and among outside ‘stakeholders’ — that allow the broadest possible band of people to join the effort and take some credit for successes. Build Social Capital by Distributing Leadership and Engaging Leaders in Instructional Activities This includes extending technical knowledge and expertise ‘upward’ in the organization, in order to limit the decoupling of technical expertise from management/political activity. In school systems, for example, principals might participate in new forms of classroom visitation, direct teaching of students, or coaching of teachers — activities that had formerly been crowded out by management duties. Leadership and authority should also be extended ‘downward’ so that those who are the first to practice new processes can play a role in spreading them across the organization. A distributed perspective on leadership can help frame ways of building new processes and then stabilizing them within the organization. Focus on Understanding and Developing Practice It is not enough to announce new policies and routines. They must be nudged into practice and then shaped into sustained forms of social and individual behaviour. We might ask of the new routines we are introducing: – How are the routines co-practiced among groups of actors? – How do tools and protocols frame interactions among those leading the routine and among those involved in the routine? – Who claims the new routines as essential to their own and their organization’s core identity? – How are knowledge and expertise distributed among those involved in a routine? – Is some knowledge essential for best practice missing?

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Create Learning Opportunities for Everyone in the Organization In a period of change everyone in the organization will be challenged to alter their practices. Hence, they need opportunities to learn the new practices. Training and professional development in a transforming organization require substantial amounts of money and, perhaps most important, of time during the work day devoted to learning. Consequently, work structures may need to be changed to create time for learning. Establish Two-Way Accountability for Every Unit in the Organization As the organization evolves, members will be responsible for behaving in new ways. But they cannot be expected to learn the new ways without organizationally sponsored opportunities. Accountability in a transforming organization thus needs to flow in two directions at once: Members of a work group (e.g. teachers) are accountable to their supervisors (principals) for learning the new practices. At the same time, they have the right to hold their supervisors accountable for providing working conditions, learning opportunities, and resources that enable the new ways of working. Keep in mind that two-way accountability will probably require two-way monitoring — evaluations of supervisors by the supervised and vice versa. In this and other ways, two-way accountability and distributed leadership are intertwined. Develop a Strong and Shared Organizational Identity While building new infrastructures — routines, learning opportunities, accountability mechanisms — is necessary for organizational change, more is needed. Many schools have similar infrastructures — the same external partners, identical routines or SOPs, similar staff and clients — yet organizational well-being and productivity differ significantly. New routines and tools will work to the extent to which individuals identify with the organization through some shared sense of direction and purpose. However, shared organizational visions are often little more than bulleted wish lists. A first step to an effective shared vision involves examining the stories teachers and administrators tell about their school to get a sense of whether there is a shared identity that enables organizational improvement, or what work needs to be done to build such an identity. Engage External Partners in the Change Process Even well-managed organizational shifts involve pain and disorder. Mistakes and aroused emotions that can block successful adaptations are inevitable. External partners can help in several ways. First, they can gather information about what is really going on more quickly and more reliably than senior management can. Compared to even a well-liked insider, outsiders can talk to everyone and will often hear a more honest version of events. Second, they are freer to express their views honestly — to ‘speak truth to power’. Third, because they have encountered similar changes in other organizations, experienced outsiders can guide senior managers through difficult choices. Finally, another function of outside partners, one that many managers of change welcome but rarely discuss, is the possibility, if things go badly wrong, of ‘blaming’ the outsider, dismissing him or her, and

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making a fresh start. Such ‘sacrifices’ are common in organizations. ‘Scapegoating’ — an ancient practice of laying the sins of a community on a sacrificial animal — opened the door to a community’s purification and renewal. Outside partners of organizations in transition should be prepared to play this role.

Conclusion The principles of organizational change and design sketched here are inferences from social science theories that are just beginning to be systematically applied in practice. They do not carry the weight of the principles of individual learning with which we began this chapter because they have not been tested over decades in multiple laboratories, nor crafted in extended discourse between scholars and practitioners. Yet they can, we believe, serve as a starting point for building organizations that are better suited to using effectively what is known about human learning. In a few years it may be possible to provide empirical documentation for a revised and tested set of organizational principles. Psychologists have had considerable influence on recent theories of organizational change, but there is little chance that psychologists or social scientists will be able to do this new form of work independently. We will have to build new routines and procedures for ourselves, as well as for our clients and collaborators. We encourage caution in applying whole-cloth constructs from psychology, which focus mostly on the individual as learner, to organizations. The learning challenge for organizations cannot be solved by thinking about organizational learning solely in terms of individual learning. One cannot arrive at an understanding of the whole — the group or the organization — by aggregating from individuals. Nor, in fact, can the challenge be addressed by considering learning only at the level of the organization or collective. Approaches from each level have to be combined, informing each other to allow for a synthesis of the two. Hence, we urge caution, sophistication, and skepticism in the application of constructs and theories from the psychology of individual learning to organizational learning.

Acknowledgment The preparation of this chapter was supported in part by a grant from the National Science Foundation to the University of Pittsburgh and the University of Wisconsin (EHR 0227016) for a Mathematics & Science Partnership project called System-wide Change for All Learners and Educators (SCALE) Partnership. Any opinions, findings, or conclusions are those of the author and do not necessarily reflect the view of the supporting agency.

References Adler, P. S., & Kwon, S. (2002). Social capital: Prospects for a new concept, The Academy of Management Review, 27(1), 17–40. Albert, S., Ashforth, B., & Dutton, J. (2000). Organizational identity and identification: Charting new waters and building new bridges. The Academy of Management Review, 25(1), 13–17.

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Chapter 16

From Plato to Brown and Beyond: Theory, Practice, and the Promise of Design Experiments Denis C. Phillips and Jonathan R. Dolle

Introduction It has been remarked that Western philosophy is nothing but a series of footnotes to Plato, and the same might be said about educational theory. For his great book The Republic is credited by historians in the West as being the first work to pay detailed attention to the design of an educational program — in his case the program extended from early childhood until about the age of 50, and it was expected to culminate in the production of a small number of Guardians (philosopher–rulers). Plato’s work raised many issues that have stimulated debate for more than two millennia, but sometimes overlooked is his assumption that the issues surrounding educational design could be resolved on rational or philosophical grounds. He eschewed empirical inquiry, for such inquiry necessarily would be rooted in the changing natural realm which was fit only for the practical inquiries of tradesmen but which could not be the realm where genuine knowledge could be generated. Truth and understanding could only be attained by contemplating a transcendental realm. Over the ages and down to the present there have been many who have followed Plato in thinking that empirical inquiry at best can yield only trivial conclusions, and who have held that key educational and social issues can be resolved conceptually or philosophically (see Phillips, 2005, for a discussion of this attitude among some contemporary philosophers of education). However, as the modern era dawned and brought with it the naturalistically oriented natural sciences, there was something of a spillover into education: A rival tradition to the Platonic developed that not only advocated but practiced the empirical study of educational phenomena. It is hard to be precise about the date of its origin — which probably was sometime in the eighteenth century — for the tradition seems to have grown slowly from humble roots in unsophisticated observation of children and also from the writings of early empiricist philosophers such as John Locke (see Cleverley & Phillips, 1986).

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From their inception, the empirical natural sciences had a double aim — first to throw light on the causal mechanisms that are at work in nature (an endeavour that in part relates to the innate human desire to achieve understanding) and second, via this knowledge or causal insight, to contribute to the improvement of the human condition by eradicating disease and hunger and by developing practically useful technologies (not to mention developing technologies useful in the pursuit of warfare and conquest). Overall, the natural sciences have been spectacularly successful in this double-sided quest. For more than two centuries, the empirical or scientific study of educational phenomena similarly has had two aims — the achievement of deep theoretical insight into educationally relevant phenomena (most notably, perhaps, the nature of human learning and the pattern of human development), and the improvement of educational practice that (it was supposed) would go hand-in-hand with the development of successful theories. It is here that the history of the natural and educational sciences diverges, for (it has been charged) while the former has flourished and has moved a long way toward achieving its double aim, the latter endeavour has languished and has made little if any headway. Skeptics, then, have some justification in claiming that Plato must have been right, for empirical educational research has run up a spotty record of achievement. Historian of education Karl Kaestle pointed in 1993 to the longstanding “awful reputation of educational research” (Kaestle, 1993), and a few years later David Labaree suggested that educational researchers must live with “a lesser form of knowledge” due to the vagaries of the domain being studied (Labaree, 1998), but these are the tip of an enormous iceberg that extends back through much of the twentieth century. There have been some — such as N.L. Gage — who have presented a more optimistic picture (see Gage, 1985), but these are in the minority. The picture is clouded, too, by the fact that critics have not agreed in their diagnoses of educational research; some have held that the problem lies in the ivory-tower obsession with theory and the subsequent neglect of practice, while others have suggested the opposite. In the following discussion, we first attempt to situate design studies within the wider tradition of classroom research. In this endeavour we find Donald E. Stokes’ discussion of Pasteur’s Quadrant illuminating. We then go on to discuss the work of two educational researchers, Ann L. Brown and Allan Collins, who were pioneering advocates of design experiments. Finally, we conclude with a critical analysis of the difficulties facing researchers conducting design experiments and make several recommendations for facing these challenges, endorsing certain of Erik De Corte’s views.

Approaches to Studying Practice The natural sciences have had an advantage not always possessed by educational research: natural phenomena often can be taken out of in situ and located in the artificially simple setting of the laboratory where they can be manipulated for study, and this can be done without completely converting them into useless artifacts. And the reverse is also true: generalizations from the laboratory to the natural world hold better than in the social and behavioral sciences. Thus Galileo’s revolutionary work on natural motion in a gravitational field (which, of course, was not his way of phrasing it) was successful because of his breakthrough ideas of studying balls rolling down an inclined plane or swinging at the end

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of pendulums instead of studying them in free fall (in effect he was still studying forms of natural motion); his experimental setup enabled him to vary such things as the angle of the plane and to measure both time taken and distance traveled. The resulting insights were fruitful when applied back to natural settings. In contrast, when learning theorists took to the laboratory, their work on mastery of nonsense syllables (to cite one obvious example) was so “ecologically invalid” that usually the results were not fruitfully transposable to students attempting to learn meaningful subjects like math or biology or physics, in real (and hence complex) classroom settings in which a teacher and other students were also located. (For an influential call for a more ecologically valid cognitive psychology, see Neisser, 1976.) Yet for many decades of the twentieth century the attitude of researchers appeared to have been that laboratory (or laboratory-type) studies would yield results that could then be translated into directives for classroom practitioners to follow or “apply,” in much the way that engineering applied the findings of natural sciences and mathematics (see Mayer, 2002; Tyler, 1965). Ellen Condliffe Lagemann traced the history of education research in the United States during the twentieth century, describing the “contested terrain” researchers in education occupy (Lagemann, 1997). As demand for professional educators and administrators grew in the early part of the twentieth century, colleges, schools, and departments of education likewise began to emerge within the academy, riding the wave of optimism for the progress of science. Perhaps unsurprisingly, university educationists were not warmly welcomed by their academic colleagues. When Paul Hanus, Harvard’s first professor of the history and art of teaching, arrived on campus, philosopher George Herbert Palmer famously quipped that, sadly, “Professor Hanus … bore the onus of his subject with him” (Kuklick, 1977, p. 247). But, despite the skepticism with which the early education research community was viewed, Lagemann reports that “by the end of World War I, it was widely seen as playing an important, positive role in school improvement” (1997, p. 8). Early approaches to educational research were shaped by three factors: the burgeoning science of survey measurement techniques, the common public perception that effective school management was the major factor in improving education, and the emerging discipline of empirical psychology, which even from its earliest days had learning as one of its major foci. And as school enrollment grew, more attention was paid to the school curriculum, leading many more researchers into the classroom. The resulting curriculum revision projects forged new partnerships between university education faculty and school-based educators (Lagemann, 1997). But — crucially — even when researchers eventually abandoned (or partially vacated) the laboratory and moved into classrooms, they took with them their predetermined observation protocols and measuring instruments. An influential case in point was N. L. Gage’s process–product model of educational research that spawned many studies, in a few of which the participating teachers even had to follow predetermined scripts (the teachers in the experimental group followed one script, while the control-group teachers adhered to another) — a methodological feature used by other researchers as well, with the aim of controlling as many variables as possible. Such minutely controlled studies were not able to capitalize upon the facts that good teachers often departed from preset plans to take advantage of “teachable moments” that arise in their classrooms, and that when a plan was failing they drew upon their wealth of

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experience to formulate a new line of classroom activity. The realization slowly dawned upon researchers that life in real classrooms was complex and does not follow a simple script-line, and it became widely appreciated that studies in real-life settings needed to have a degree of methodological flexibility. Gradually, then, open-ended research in classrooms (and in the surrounding community) became fashionable — ethnographers and some psychologically oriented education researchers studied classroom culture and discourse (e.g. Heath, 1983); since the time of Thorndike, educational psychologists and others have studied students learning specific topics within the standard disciplines that make up the school curriculum and this approach is becoming increasingly popular (e.g. Ball & Bass, 2000); and sociologists studied the dynamics within classroom working groups and the learning that occurs therein (e.g. Cohen, 1986). Such work had high ecological validity, but skeptics felt that there were deficits with regard to traditional validity issues — there was lingering concern that whatever findings emerged could not be trusted because there were so many uncontrolled confounding factors. And, of course, this led to doubts about the generalizability of the findings from this type of research, even if they were valid for the settings in which they were found. (It is worth noting that Lee J. Cronbach famously argued that social generalizations are set within a network of interacting effects and thus decay over time; see Cronbach, 1975.) These various concerns led, at the end of the twentieth century, to a vigorous reaction that took the form of renewed interest in the view that had been advocated powerfully in the early 1960s by Campbell and Stanley — the view that studies embodying rigorous randomized field trials (RFTs) were by far the most reliable ways to build a stock of causal knowledge about the effectiveness of programs or treatments upon which educational policy could be based (the so-called evidence-based or research-based policy movement). At the dawn of the 21st century in the United States, the vast bulk of Federal Educational Research dollars has been redirected toward the RFT, and also to related efforts such as the website that rates studies according to how well they approximate the RFT (the “What Works Clearinghouse” at W-W-C.org). The “power of the purse-strings” has been used, to put it starkly, to dampen enthusiasm for “less scientific”, more open-ended research in classrooms and schools. This Federal policy has provoked a storm of controversy and ran against the advice given in a report produced by an expert National Academy of Sciences panel (NRC, 2002). However, the course of history — like events in a classroom — rarely follows a simple script. Roughly at the time when the move back to the RFT was germinating, research in classrooms was spawning something new, so-called “design research” (DR) or “design experiments” (DEs). The strength of DEs lies in the very areas where the RFT and the evidence-based policy movement are weakest, for supporters of DEs aim simultaneously to design effective programs and contribute to relevant theory — and crucially they aim to accomplish these goals by doing rigorous work in an open-ended way in real-life and often uncontrolled educational settings. As Erik De Corte and Lieven Verschaffel put it, DEs are “a lever for the simultaneous pursuit of theory building and practice innovation” (2002, p. 519, emphasis in original). This is an astonishingly ambitious agenda, beset by obvious methodological and practical difficulties but also (perhaps) with great promise.

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Stokes and Working in “Pasteur’s Quadrant” One way to conceptualize the development of a DE is that its advocates have been struggling to find a more ecologically valid mode of research than the laboratory study, or than treating classrooms merely as “proxies” for the laboratory — that is, treating them as settings in which to carry out rigorous controlled experimental studies. Furthermore, it is not fanciful to view the advocates of DEs as having inherited the two aims of naturalistic social science inquiry — namely, the achieving of theoretical insight while at the same time making improvements in prevailing social practices and processes. The work of Donald Stokes provides a way of thinking about DEs in this broader scientific and social context. In his book Pasteur’s Quadrant: Basic Science and Technological Innovation, Stokes (1997) offers a reconceptualization of the relationship commonly held to obtain between pure and applied research. His book … reexamines the link between the drive toward fundamental understanding and the drive toward applied use, shows how this relationship is often misconceived and the price we pay for this, proposes a revised view of the interplay of these goals of science and of the relationship between basic science and technological innovation, and shows how this revision could lead to a clearer view of several aspects of science and technology policy. (p. 5) Among other things, Stokes was critical of “the endlessly popular” linear model, according to which basic research is first undertaken, and then, later, some of the resulting advances are converted into practical applications (1997, p. 10); this model has been dominant not only in the natural sciences, but, as we sketched above, also in educational research throughout much of the twentieth century. Stokes, however, made a major contribution by stressing that many important advances in basic scientific understanding have been the result of studies that initially were “use-inspired”; Pasteur’s work provides many examples of his investigations into the spoilage of milk, wine, beer, and vinegar and his work on rabies and other diseases that led to major breakthroughs in the infant science of microbiology. Stokes summarized his argument in the form of a “two-by-two” table; the horizontal axis was the dimension “considerations of use” (low to high), and on the vertical axis was “quest for fundamental understanding” (again low to high). Thus one of the four resulting boxes or quadrants was high on considerations of use but low on the quest for fundamental understanding, and this was illustrated by the work of Edison; the box high in the quest for fundamental understanding but low in considerations of use was illustrated by the work of Bohr; and the box or quadrant high on both dimensions — use and understanding — was identified with Pasteur’s research, hence “Pasteur’s Quadrant.” It seems apparent, then, that design researchers are working in Pasteur’s quadrant — they aim to contribute to improvement in educational practice, but at the same time they aim to contribute to our fundamental understanding of learning and instruction. This dual aim comes to the forefront in what key advocates of DR have written about their intentions, as we now shall see.

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Brown, Collins, and De Corte on Design Experiments: An Introductory Survey Many of the initial methodological principles of DEs were laid out by Collins (1992) and focused on the design of learning environments. Collins suggested that several “desiderata” were essential to the development of a methodology of DEs. His revised list (Collins, 1999) contrasts the characteristics of traditional psychological methods (first) and design–experiment methods (second): (1) Laboratory settings versus messy situations; (2) a singledependent variable versus multiple-dependent variables; (3) controlling variables versus characterizing the situation; (4) fixed procedures versus flexible design revision; (5) social isolation versus social interaction; (6) testing hypotheses versus developing a profile; and (7) experimenter versus coparticipant design and analysis (1999, pp. 290–293). The ultimate goal of this work was “to construct a design theory for technological innovation,” such that “all the variables that affect the success or failure of different designs” are identified (1992, p. 19). On Collins’ early view, DEs are a kind of exercise in optimization: once all the variables are identified and their relationship to one another understood, researchers could begin investigating the interaction between independent variables as well as their impact on various dependent variables. The result would be a theoretical framework that could guide the design of instructional environments and learning technologies. To illustrate this approach, consider the development of a coin-flipping machine. The designer wants to create a device that can be adjusted such that it will flip a fair coin (with a known starting position) to land heads or tails at the operator’s direction. Building such a machine requires tinkering around with different variables (coin weight, size, starting position, the flipping force’s direction and magnitude, height, distance, etc.) to discover how the variables are related (e.g. flipping force and the coin’s height). The end result, in addition to having a nifty machine to entertain friends, would be a model relating all the variables that could be used to predict whether a fair quarter, flipped with a force of x in direction y, would land heads or tails. Collins’ recent work suggests a more flexible (if less ambitious) future for DEs, given the complexity of the educational processes. When moving from the laboratory to the classroom, the number of variables increases and the control over the classroom environment decreases. As a result, education researchers encounter some of the same difficulties faced by particle physicists: the very act of measuring impacts the behaviour of the object being measured. Werner Heisenberg, the founder of quantum physics, famously described an analogous problem in the following terms: the more precisely the position of a subatomic particle is determined, the less precisely the momentum is known. This came to be known as the Heisenberg Uncertainty Principle. (It is important to note that the reasons for uncertainly in each case are different, though the basic features are similar, for education researchers must deal with the agency of minds — a problem physicists happily never face when hunting for quarks!) Shortly after the publication of Collins’ (1992) early paper, Brown (1992) published a widely cited article in which she described her previous decade of work as moving toward DEs. Brown’s work offered a concrete picture of what DEs might look like and a more systematic treatment of their methods and goals. For Brown, DEs could be used to accomplish the dual goals of fundamental understanding and application (thus working in Pasteur’s

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quadrant). They can probe fundamental understanding, on this account, by developing new theories of learning and teaching based on “first-principles” (Brown & Campione, 1994) and by studying the implementation of various interventions (Brown & Campione, 1996). These goals are interrelated; as Brown and Campione put it, “the notion of ‘implementation as evolution (Majone & Wildavsky, 1978) constrained by first principles’ is our eventual goal” (1994, p. 264). The most famous example of this approach was a product of Brown and Campione’s “Fostering a Community of Learners” project (FCL), namely, the development of the technique of reciprocal teaching that was a pedagogical approach involving “learning dialogues in which teachers and students [take] turns leading the discussion of segments of text” (Palincsar, 2003, p. 465). Initially piloted in a laboratory setting, the study was soon shifted into classroom contexts where Brown and colleagues could study longer periods of intervention with greater ecological validity. Palincsar notes that “With this transition, a host of new issues arose: namely, an examination of the quality of instruction, and the relationships among the quality of instruction, the nature of the learner, the composition of the groups, the demands of the text, and the outcomes of instruction” (2003, pp. 465–466). The study of reciprocal teaching as practiced in the classroom also raised new research questions; for instance, did the intervention make a difference in student performance in a variety of subject matter courses? In the FCL study, the first principles of learning included the following themes: the active, strategic nature of learning; metacognition; multiple zones of proximal development; dialogic base; legitimizing differences; community of practice; and contextualized and situated learning (Brown & Campione, 1994, p. 266). Although initially developed in a single context, Brown and colleagues gradually tested FCL’s various components in other classroom contexts. As reciprocal teaching became more widely known and widely copied and applied by practitioners, it suffered the fate of many innovations: “lethal mutations” of the approach started to appear. Teachers started to describe their own pedagogical process as “reciprocal teaching” when, in fact, only surface features of the approach were used, and the first principles were ignored. As Brown and Campione noted: If one looks closely at reciprocal teaching as practiced outside the control of the originators, however, the first principles of learning it was meant to foster are often lost, or at best relegated to a minor position. What is practiced are surface rituals of questioning, summarizing, and so on, divorced from the goal of fostering understanding that the procedures were designed to serve. Teachers and students nationwide practice the ‘strategies’, sometimes even out of the context of reading authentic texts. Rarely are the procedures modified and extended to enhance the learning principles upon which they were based. (Brown & Campione, 1994, p. 265) However, when Brown’s work is carefully examined a doubt arises about whether, in fact, it illustrates that the two aims of DEs were achieved simultaneously; if it turns out that this suspicion is valid, it opens the issue of how to accurately characterize DEs. Certainly on a superficial reading it appears that two products did result — (i) an artifact,

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the practical method of reciprocal teaching, was developed, and (ii) the theoretical insights were developed that became formulated as a set of principles about learning. But did in fact the principles evolve from the DR, or were these principles pre-existing — were they there from the outset, guiding the directions the DEs took? It can be argued that DEs — like any research — are always guided by pre-existing assumptions or presuppositions or guiding principles; even Pasteur was working within a framework of assumptions (Kuhn might have said, within a paradigm), but the theories he eventually constructed about microbiological processes were not mere restatements of the assumptions with which he started. The point that concerns us in this discussion is not the practical usefulness of the artifacts that Brown and other practitioners of DEs in educational contexts have produced — which we readily acknowledge — but rather whether the design of effective artifacts (such as FCL) has dominated educational DR, and whether the other stated aim underlying DEs (the establishing of new scientific understanding) has thereby been given shortshrift. For our concern, as philosophers, is whether the simultaneous attainment of both goals is possible (and if so, under what conditions), and it is not fully clear to us that Brown’s work should count as a successful example — indeed, as an exemplar — of how to attain both goals at once. To give some substance to our concerns here, consider the following passages from Brown’s writings. The first is one that supports what we have identified above as the superficial reading: “This theory or, more precisely, set of learning principles … has evolved over the course of the project” (Brown & Campione, 1996, p. 290), words that suggest the project and learning principles developed simultaneously. But this is contradicted by other passages; they state that the teaching procedures devised by the theorists and practitioners in their Facilitating Communities of Learners project “are based on, and embody, specific learning principles” ( p. 291, emphasis added), a passage that strongly implies that the principles were pre-existing. This interpretation is reinforced by other words on the same page: “It is for these reasons that we have been concerned with the development of a set of first principles of learning to guide research and practice” ( p. 291, emphasis added).1 Further doubt that the principles were developed simultaneously with the development of the teaching procedures and the research program is fostered by the table containing the principles themselves (Table 11.5, p. 318) and the surrounding prose; the principles are, by and large, versions of ideas developed earlier in the twentieth century by John Dewey, Lev Vygotsky, and Jerome Bruner! It needs to be stressed again that we are not questioning the validity of these principles, or the role they played in the impressive research and development program steered by Brown and Campione; our concern is, first, to investigate the claim of those who engage in DEs that simultaneous advance can be made in reaching several diverse goals at the same time, and second, that the work of Brown constitutes an “existence proof.”2 1 Ed Haertel led the evaluation of the FCL project. In a personal communication (October 19, 2005), he explained the evaluation was largely unsuccessful because the FCL learning principles evolved throughout the project. For a discussion of this and related challenges emerging from the FCL project, see Ginsburg’s Report (2001). 2 There is an additional issue, which we do not have space to address here, about whether the practical technology is generalizable across settings. Thanks to Richard Shavelson for directing our attention to this additional challenge.

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So, moving beyond the rhetoric, the question again surfaces: What else (apart from this rhetoric) distinguishes DEs from various other forms of research? Eamonn Kelly recently emphasized the importance of producing an artifact (the thing being designed) as an outcome of DEs (Kelly, 2004, p. 116), which is an account that is at variance with the characterization of DEs given by Brown, Collins, and De Corte and Verschaffel. Perhaps Kelly is correctly pointing to what, in actual fact, is in most cases the main or even the sole product of DEs. In fact, it appears to us that DEs — particularly when focused on understanding adaptation and implementation and improvement of curricula, pedagogical processes, or instructional technologies — often strongly resemble varieties of formative evaluation research, which is a genre of work that aims to improve artifacts (such as programs) but which usually does not aim to make contributions to theory (although this may occasionally be an ancillary benefit, e.g. when a researcher undertakes a formative evaluation in order to understand the vagaries of working in particular settings and then these understandings are later incorporated into his or her theoretical work). Our concern about the unequal attainment of the dual goals of DR has its source in the difficulties associated with the stress on simultaneity. Design-based research as practiced by Brown and others may, indeed, have had greater ecological validity and in many instances greater practical payoff, but the goal of simultaneously contributing to theory has to face several methodological difficulties that are rarely discussed in depth by adherents of DEs. It is certainly the case that in her classic paper, Brown (1992) discussed at length a single particular problem or objection, one that certainly is of concern but as will be seen subsequently is not our main concern (although it is related to it); the one she tackled in 1992 was the charge that the results of her work were “merely” a product of the Hawthorne effect (named after the well-known experiment at Western Electric’s Hawthorne plant), where the very presence of the researchers tended to have a positive impact on worker productivity. Brown rejected this criticism of the positive effect of the research team. Nevertheless, a genuine difficulty persists: when studying interventions cooperatively with teachers, the researcher (or research team) effectively do become part of the treatment. This can seriously hamper the ability of researchers to generalize their findings about the treatment, for (presumably) researchers will not always be present. Similarly, if willingness to regularly and actively collaborate with researchers is a precondition in the selection of teachers and classrooms, this is likely to bias the sample significantly, further limiting the external validity of the study. As we will soon argue, this is the tip of a serious methodological iceberg. Before turning to discuss this iceberg in more depth, it is worth noting for the record that in the broad literature on DEs, multiple uses or functions or contexts of use of DEs are depicted — and this heightens the suspicion alluded to earlier, namely that DEs may not in practice often or usually attain both the stated goals at the one time. Thus: (i) In some cases DEs function much like an intervention pilot study, the goal being to obtain an early indication of the effectiveness of a treatment or a sense of the relevant variables. (ii) In other cases DEs can also look a lot like formative evaluation, where data collected about the treatment is used to make immediate improvements. The research of De Corte and Verschaffel on the creation of “high-powered learning communities” is a DE that might

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fall into this category — their results were positive and contributed to the improvement of practice, but because of the many uncontrolled interacting factors they were forced to conclude that “it is impossible to establish the relative importance of the different components of the interventions in producing the positive effects on the use and transfer of cognitive and metacognitive strategies” (2002, p. 529). (iii) There is also a “family resemblance” between DR and the so-called “action research” paradigm that dates back to the work by Kurt Lewin but which has had more recent advocates such as Chris Argyris and his colleagues (Argyris, Putnam, & Smith, 1985). It is also worth noting that following the initial proselytizing by Collins and Brown, the DE approach seemed so promising that there was something of a ‘bandwagon effect’ around the end of the twentieth century, but the approach remained (and remains) controversial because of the unresolved central methodological issue. However, it is to the credit of the advocates of the approach that this issue has not been completely ‘swept under the rug’. Thus, e.g. De Corte and Verschaffel write forthrightly that there is often considered to be a “methodological weakness” in DEs — a tension between “the disciplinary versus the educational orientation” (i.e. between the drive to contribute to theory and the drive to improve practice). They continued by stressing the classroom relevance and ecological validity of the DE, but significantly they added that: … this is not to say that the systemic approach cannot be beneficially complemented by more analytic research, such as studies in which different versions of complex learning environments are systematically contrasted and compared with a view to identification of those aspects which contribute to their high power and success. (De Corte & Verschaffel, 2002, p. 529) To the eyes of a skeptic, however, the reference in this passage to “complementing” might well be read as adding fuel to our skeptical doubt — as being something of a retreat from the strongly worded promise made earlier in the same essay to engage in “simultaneous pursuit” of theory building and practical innovation. DEs are completely uncontroversial — and far less novel — if they are seen as sequences of design and implementation that spawn (or are accompanied or complemented by) separate rigorously designed and executed research studies (Shavelson, Phillips, Towne, & Feuer, 2003). Whoever has doubted that this type of work is possible? The claim of Collins, Brown, and De Corte is far more exciting: it is that the two logically disparate aims (product or artifact development, and the scientific establishment of knowledge-claims) can be achieved in the one integrated or seamless (“simultaneous”) study, and it is a claim that sets the bar very high! And so the debate rages on: In 2003–2004, no fewer than three major educational research journals published special issues dedicated entirely to discussion and debate of design-based research: Educational Researcher, Journal of the Learning Sciences, and Educational Psychologist. Clearly, then, there is much here that is of great interest, and that is deserving of further discussion. In the following section, we shall outline two issues that seem to us to be particularly pressing; the second of these is the methodological iceberg to which we have been referring.

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Further Perspectives on Two Key Issues What, Then, is a Design Experiment? One thing is amply clear from the literature about DR of the past 15 years, and from the numerous examples of studies that have been given this label by those who have performed them: There is no agreed-upon model or template or exemplar of what constitutes “proper” DR; and even individuals who hold to the “classic” account about simultaneity put forward by Collins, Brown, and De Corte, in practice usually do not deliver both sets of goods. In some cases the design element is in the foreground, and the aim is to produce a program or artifact (e.g. a curriculum unit, or a piece of educational software) that is an advance over what is currently available; in other cases the aim apparently is to study or document the design process itself, so that the process might be carried out more effectively in the future. Sometimes the design of the product or artifact takes a back seat, and the stated aim is to study the learning that takes place as students interact with the new material, but this can be done in a variety of ways — sequential phases of design and implementation followed by a phase of testing, observation, and interviewing, followed by another round of design and implementation; sometimes the development and implementation sequence runs in parallel to the research activities, or the research may take the form of a traditional pre- and postintervention study. Indeed, sometimes the researchers and developers seem to be working within a fairly traditional educational design, evaluation or research framework and are merely taking advantage of a faddish new label for their work in what is possibly an attempt to appear to be on the “cutting edge.” (One of the authors was commentator at a recent AERA conference session on DR where the work of the different presenters fell readily into one or other of these categories.) The conclusion seems inescapable that — at least at present — DEs do not constitute what philosophers call a “natural kind”; they do not form a well-bounded species having one or a small number of species-defining characteristics in common. DR is a category made by humans for intellectual and “political” and self-promotional purposes; like a hard disk folder labeled “miscellaneous,” it has a lot of different things crammed into it. Thus it might not be productive to spend much time trying to come up with a simple account that ends all controversy about what DEs really are, for there is no one thing that they really are! (Just as, to take a roughly parallel case, there is no one thing that formative evaluations really are; the difference is that all cases of formative evaluation seem to have the same purpose.) To put some philosophical meat onto this stark bone of a conclusion, the category “DR” seems to be a “cluster concept” of the kind that the philosopher Ludwig Wittgenstein illuminated with his notion of “family resemblances.” (He had categories like “democracy” in mind; see Wittgenstein, 1953) This may be illustrated by the following homely (and timely) example: Consider the Bush family — the first President Bush, the second and current President, the current President’s brother (the Governor of Florida) and his family, and the current President’s two daughters. There might be a “Bush family likeness,” defined by a number of features — voice, hair, nose, chin, eyes, forehead, mannerisms and bearing, and the like. All members of the family possess the family likeness,

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but not all of them have the same collection of features, indeed some of them might have three or four of the features and others might have a different set, so that two members of the family might not share any of the features. Like the Bush family, and like various governmental systems that are called “democracies,” cases of DEs might draw from the family “cluster” but might have little if anything significant in common. This analysis explains the diversity among the specific instances of studies bearing the DE label, and it also explains why there is some overlap between DEs and action research and formative evaluation (that have at least some of the characteristics of the DE family). But without good, clear, paradigmatic examples of DEs, it is impossible to know whether or not any particular research study is a DE, and it obscures what the central features of a well crafted and rigorously executed DE look like. But we now need to turn to the ideal or rhetoric of simultaneous attainment of theoretical insight and the making of a practical advance in the form of a new superior artifact. For, as we have signaled several times above, even the attempt to carry out two studies at the one time — two integrated but logically disparate studies, rather than two that run in tandem — takes us into tricky methodological territory. The “Methodological Iceberg”: Confounded Variables and the X-1 Solution It seems beyond dispute that having a team of competent applied social scientists or educational researchers working on formative evaluation can be of great benefit to program staff, as they work on developing or strengthening their program; arguably this is a key reason why the program Sesame Street met with such great initial success (Cook et al., 1975). The same can be said about DEs: Having an Ann Brown or an Erik De Corte working alongside teachers and curriculum developers can be a great boon. But the success of the resulting program — a major achievement in its own right — is not evidence by itself that the theoretical claims about learning or about the nature of instruction are valid. Research evidence, which passes muster according to the canons of science, rather than evidence of success of the program or artifact, is required to make this case (as De Corte recognized fully well). And it is here that the serious methodological difficulty of confounding of variables arises, one that is paid surprisingly little attention by many advocates of DEs. This problem arises in all work that attempts to simultaneously design and produce a superior artifact and achieve theoretical understanding about such matters as why the artifact works as it does. A lot is happening more-or-less at once in such work. For example, a curriculum is being adapted or designed; teachers and subject-matter experts and sometimes the students are having input, the students (and the teachers “delivering” the curriculum) differ in ability and interest and are situated in real classrooms with all the trials and tribulations associated with real settings, there are gender and ethnic and socio-economic differences amongst the students (and the teachers), researchers are observing and testing and interviewing (interventions in themselves) and are giving input to the designers and teachers. Which of these many factors are to take credit — or blame — for any effects that emerge? The philosopher of science Karl Popper put it well, in the context of his discussion of the importance of making small, gradual changes to a program — what he called “piecemeal social engineering”:

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The piecemeal engineer knows, like Socrates, how little he knows. He knows that we can learn only from our mistakes. Accordingly, he will make his way, step by step, carefully comparing the results expected with the results achieved, and always on the look-out for the unavoidable unwanted consequences of any reform; and he will avoid undertaking reforms of a complexity and scope which make it impossible for him to disentangle causes and effects, and to know what he is really doing. (Popper, 1985, p. 309) Another way to put this is in terms of the philosopher Hans Reichenbach’s classic distinction between the “context of discovery” and the “context of justification.” Temporally, these two contexts of activity (making the initial discovery, and testing or warranting it) might occur very close together, but nevertheless they are logically different. As goals of a research program, basic and applied research need not be the least bit incompatible (just as there need not be any inherent tension between so-called “qualitative” and “quantitative” research methodologies). But DEs do not and — given their supposed flexibility and openness — cannot constitute a coherent research program; rather, they are better understood as one valuable approach (among many) in the tool belt of the educational researcher. As Burkhardt and Schoenfeld (2003) have suggested, the design stage is usually just the first stage of a larger development program, which (if successful) is followed by a series of field trials and finally large-scale testing. In this progression, typical of fields like engineering and pharmacology, discovery happens largely in the early stages, while rigorous justification through testing is the goal of the later stages. A clear and enlightening real-life example comes from the field of aeronautical engineering. Shortly after the end of World War II, the US military and other government agencies were under pressure to design a plane that could regularly and safely fly faster than sound, a project that involved careful documentation and cautious experiment involving sequences of minor modifications and rigorous testing (there had been some loss of life as planes went out of control at speeds near Mach 1). The aim of some of the developers — notably those aeronautical scientists from the precursor of NASA — was to understand the physics involved in breaking the sound barrier, and this was a time-consuming exercise; after each modification of the plane, they wanted a period of careful testing and measurement before the next modification was made. On the other hand, the military and its chief test pilot Chuck Yeager — a brash ‘can-do’ individual — were determined for geopolitical and other reasons to break the barrier as soon as possible. To this end, Yeager and his crew of mechanics would tinker and sometimes make numerous small modifications to the plane (the X-1) at the end of each flight, in an attempt to coax a few more miles-per-hour out of the plane for the next day’s flight. The two endeavours — cautious accumulation of theoretical understanding, and rapid development of a successful product — were incompatible, and considerable tension developed in the X-1 project. This was resolved by having two planes, one for slow, meticulous measurement and experiment and one for Yeager to fly as fast as he could at his own peril! Obviously, a similar solution is not possible in cases of educational DR, but the X-1 tension is ever-present here as well. At this stage, an actual example of an educational DE is worth discussing; it shows how complex educational settings can be and thus how difficult this methodological

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problem can be — and it shows, too, that Erik De Corte was once again forthrightly honest in acknowledging the difficulty. He discussed this case in his Presidential Address to Division 5 of the International Association of Applied Psychology (De Corte, 2000). The study concerned the design of “a powerful teaching-learning environment for mathematical problem solving” with fifth graders (2000, p. 259). The complexity of this piece of DR becomes quickly apparent: The major changes in the classroom learning environment related to the following components: the content of learning and teaching, the nature of the problems, the instructional techniques, and the classroom culture. (2000, p. 259) The learning environment focused on the acquisition by the students of “an overall metacognitive strategy” for solving certain mathematical problems; five stages and eight heuristics were involved. A varied set of specially designed realistic and complex open problems were used with the students; the students were of mixed ability. A varied set of “activating instructional techniques” was used. An innovative classroom culture was created “through the establishment of new socio-mathematical norms about learning and teaching mathematical problem solving, and aiming at fostering positive mathematics-related attitudes and beliefs not only in children, but in teachers as well” (2000, p. 260). The sequence of 20 lessons was spread over 10 weeks, and there were three groupings of lessons. Regular meetings were held between the researchers, the teachers of the four experimental classes, and their principals. The researchers used a variety of instruments and concluded that as a result of the intervention(s) the students became more “mindful” in their “approach toward mathematical problem solving” (2000, p. 262). It hardly needs stressing that a lot of things were happening here, moreor-less simultaneously; it seems clear that this study was not an example of Popperian “piecemeal social engineering.” Crucially for the point we have been making, near the end of his account of this extremely complex work, De Corte notes: “Of course, further inquiry is needed to possibly identify the crucial aspects of the learning environment which contribute especially to its success” (2000, pp. 262–263, emphasis added). This frank statement fuels our suspicion that DR can produce important practical innovations or artifacts (just as Yeager’s tinkering with the X-1 led fairly quickly to successful breaking of the sound barrier), but to discover the reasons for the effectiveness of the resulting artifacts or programs requires work that adheres more closely to the traditional research advice to “control the variables”! Having developers and researchers working at the one time on the educational equivalent of the one X-1 is not quite the way to satisfy our scientific concerns — although it certainly can generate many important leads for us to pursue in subsequent work. It is time to abandon the rhetoric of simultaneity and the notion that DEs can serve as a self-contained research program. We strongly endorse the sentiment expressed by De Corte and Verschaffel (2002) quoted earlier — a sentiment that is so important that it bears repeating; they concluded that DEs

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… [can] be beneficially complemented by more analytic research, such as studies in which different versions of complex learning environments are systematically contrasted and compared with a view to the identification of those aspects which contribute especially to their high power and success. (p. 529)3.

References Argyris, C., Putnam, R., & Smith, D. M. (1985). Action science (1st ed.). San Francisco: JosseyBass. Ball, D. L., & Bass, H. (2000). Making believe: The collective construction of public mathematical knowledge in the elementary classroom. In: D. C. Phillips (Ed.), Constructivism in education: Opinions and second opinions on controversial issues (Vol. 99(1), pp. 193–224). Chicago, IL: University of Chicago. Brown, A. L. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. The Journal of the Learning Sciences, 2(2), 141–178. Brown, A. L., & Campione, J. C. (1994). Guided discovery in a community of learners. In: K. McGilly (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice (pp. 229–309). Cambridge, MA: MIT Press. Brown, A. L., & Campione, J. C. (1996). Psychological theory and the design of innovative learning environments: On procedures, principles, and systems. In: L. Schauble, & R. Glaser (Eds), Innovations in learning: New environments for education (pp. 289–325). Mahwah, NJ: Erlbaum. Burkhardt, H., & Schoenfeld, A. H. (2003). Improving educational research: Toward a more useful, more influential, and better-funded enterprise. Educational Researcher, 32(9), 3–14. Cleverley, J. F., & Phillips, D. C. (1986). Visions of childhood: Influential models from Locke to Spock. New York: Teachers College Press. Cohen, E. G. (1986). Designing groupwork: Strategies for the heterogeneous classroom. New York: Teachers College Press. Collins, A. (1992). Toward a design science of education. In: E. Scanlon, & T. O’Shea (Eds), New directions in educational technology (pp. 15–22). Berlin: Springer. Collins, A. (1999). The changing infrastructure of educational research. In: E. C. Lagemann, & L. S. Shulman (Eds), Issues in education research: Problems and possibilities (1st ed., pp. 289–298). San Francisco: Jossey-Bass. Cook, T., Appleton, H., Conner, R., Shaffer, A., Tamkin, G., & Weber, S. (1975). “Sesame Street” revisited. New York: Russell Sage. Cronbach, L. J. (1975). Beyond the two disciplines of scientific psychology. American Psychologist, 30, 116–127. De Corte, E. (2000). Marrying theory building and the improvement of school practice: A permanent challenge for instructional psychology. Learning and Instruction, 10, 249–266. De Corte, E., & Verschaffel, L. (2002). High-powered learning communities: Design experiments as a lever to bridge the theory/practice divide. Prospects, 32, 517–531. Gage, N. L. (1985). Hard gains in the soft sciences: The case of pedagogy. Bloomington, IN: Phi Delta Kappa. 3

Helpful formative advice was provided by the editors and by Richard Shavelson.

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Ginsburg, H. (2001). The Mellon Literacy Project: What does it teach us about educational research, practice, and sustainability? (Working Paper No. 177). New York: Russell Sage. Heath, S. B. (1983). Ways with words: Language, life, and work in communities and classrooms. Cambridge: Cambridge University Press. Kaestle, C. F. (1993). The awful reputation of education research. Educational Researcher, 22(1), 26–31. Kelly, A. E. (2004). Design research in education: Yes, but is it methodological? The Journal of the Learning Sciences, 13(1), 115–128. Kuklick, B. (1977). The rise of American philosophy, Cambridge, Massachusetts, 1860–1930. New Haven: Yale University Press. Labaree, D. F. (1998). Educational researchers: Living with a lesser form of knowledge. Educational Researcher, 27(8), 4–12. Lagemann, E. C. (1997). Contested terrain: A history of education research in the United States, 1890–1990. Educational Researcher, 26(5), 5–17. Majone, G., & Wildavsky, A. B. (1978). Implementation as evolution. In: H. E. Freeman (Ed.), Policy Studies Review Annual (Vol. 2, pp. 103–117). Beverly Hills, CA: Sage. Mayer, R. (2002). 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. 2001 Yearbook of the NSSE (pp. 34–75). Chicago: University of Chicago Press. National Research Council (NRC). (2002). Scientific research in education. Washington, DC: National Academy Press. Neisser, U. (1976). Cognition and reality: Principles and implications of cognitive psychology. San Francisco: W. H. Freeman. Palincsar, A. S. (2003). Ann L. Brown: Advancing a theoretical model of learning and instruction. In: B. J. Zimmerman, & D. H. Schunk (Eds), Educational psychology: A century of contributions (pp. 459–475). Mahwah, NJ: Erlbaum. Phillips, D.C. (2005). The contested nature of empirical educational research (and why philosophy of education offers little help). Journal of Philosophy of Education, 39(4), 577–597. Popper, K. (1985). Popper selections (David Miller, Ed.). Princeton, NJ: Princeton University Press. Shavelson, R. J., Phillips, D. C., Towne, L., & Feuer, M. J. (2003). On the science of educational design studies. Educational Researcher, 32(1), 25–28. Stokes, D. E. (1997). Pasteur’s quadrant: Basic science and technological innovation. Washington, DC: Brookings Institution Press. Tyler, R. (1965). The field of educational research. In: E. G. Guba, & S. M. Elam (Eds), The training and nurture of educational researchers (pp. 1–12). Bloomington, IN: Phi Delta Kappa. Wittgenstein, L. (1953). Philosophical investigations. New York: Macmillan.

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Contributors

Neville Bennett

University of Exeter, UK

Dani Ben-Zvi

University of Haifa, Israel

Monique Boekaerts

University of Leiden, The Netherlands

Dirk De Bock

University of Leuven and EHSAL — European University College Brussels, Belgium

Andreas Demetriou

University of Cyprus, Cyprus

Filip Dochy

University of Leuven, Belgium

Jonathan R. Dolle

Stanford University, USA

Ann-Charlotte Eklund

Göteborg University, Sweden

Noel Entwistle

University of Edinburgh, UK

Bernhard Ertl

Bundeswehr University, Munich, Germany

David Gijbels

University of Antwerp, Belgium

Brian Greer

Portland State University, USA

Minna M. Hannula

University of Turku, Finland and Cornell University, USA

Lisa Hattersley

University of Fribourg, Switzerland

Daniel T. Hickey

Indiana University, USA

Birgitta Kopp

Ludwig Maximilian University, Germany

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Maarten de Laat

Utrecht University, The Netherlands and University of Exeter, UK

Erno Lehtinen

University of Turku, Finland

Åsa Mäkitalo

Göteborg University, Sweden

Heinz Mandl

Ludwig Maximilian University, Germany

Rob Martens

University of Leiden, The Netherlands

Velda McCune

University of Edinburgh, UK

Fritz Oser

University of Fribourg, Switzerland

Areti Panaoura

University of Cyprus, Cyprus

James W. Pellegrino

University of Illinois at Chicago, USA

Denis C. Phillips

Stanford University, USA

Lauren B. Resnick

University of Pittsburgh, USA

Roger Säljö

Göteborg University, Sweden

Gavriel Salomon

University of Haifa, Israel

Max Scheja

Stockholm University, Sweden

Evi Schmid

University of Fribourg, Switzerland

Mien Segers

University of Leiden, The Netherlands

Robert-Jan Simons

Utrecht University, The Netherlands

James P. Spillane

Northwestern University, USA

Xenia Vamvakoussi

National and Kapodistrian University of Athens, Greece

Wim Van Dooren

University of Leuven, Belgium

Lieven Verschaffel

University of Leuven, Belgium

Stella Vosniadou

National and Kapodistrian University of Athens, Greece

Elizabeth Wood

University of Exeter, UK

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Author Index Adams, S., 3, 6, 10–11 Adamson, R. J., 195 Adler, P. S., 268 Albert, S., 269 Alessi, S. M., 244 Alexander, E., 6, 10 Alibali, M. W., 49 Almond, R. G., 177–178 Alpert, D., 243 Anderson, A. H., 227 Anderson, C. W., 268 Anderson, J. R., 12, 40, 55–56, 59, 217 240 Anderson, K., 184 Anderson, N. S., 243 Anderson, R. A., 40 Anning, A., 4, 9 Appleton, H., 288 Argyris, C., 286 Asaf, M., 211 Ashforth, B., 269 Ashmann, S., 268 Asoko, H., 57 Attfield, J., 8–9, 11 Aubrey, C., 6 Ausubel, D. P., 240 Backen Jones, L., 47 Baillargeon, R., 58 Baker, E., 199 Baker, M., 229–230 Ball, D. L., 268, 280 Ball, S., 266 Band, G. P. H., 24 Bandura, A., 241 Baroody, A. J., 51

Bartlett, L., 266 Baruk, S., 74 Bass, H., 280 Bastiaens, Th., 114, 116–117 Bateson, D., 199 Baumeister, R. F., 126 Baxter, G.P., 175 Beach, K. D., 178 Beach, K., 42 Becker, G., 268 Becker, H. J., 210–211 Beckwith, J. B., 194 Beekhoven, S., 120 Behne, T., 49 Behr, M. J., 66 Bekkering, H., 45 Bell, D., 3, 10–11 Bell, P., 228 Belmont, M. J., 121 Ben–Chaim, D., 197 Bennett, N., 3–4, 6–7, 9–10, 12, 14 Benz, E., 269 Bereiter, C., 56, 185, 215–217, 241, 249 Biggs, J. B., 132 Biggs, J., 192, 197 Bill, V. L., 26, 262, 264 Binks, M. G., 77 Bird, K. D., 197 Birenbaum, M., 192–193, 197–201 Bitzer, D. L., 243 Black, P., 171, 183, 193, 196 Blomeyer, R., 211 Bloom, B., 265 Bloom, P., 26 Blum, W., 91, 95 Boaler, J., 95, 106

295

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Author Index

Boekaerts, M., 116, 121, 125, 127, 195, 266 Bogaerts, H., 42, 102 Böing–Messing, E., 227 Bond, M.A., 12 Booth, S., 50, 133 Borba, R., 27 Borghart, I., 101 Brainerd, R. C., 243 Bransford, J. D., 40–41, 177, 214, 261 Brattström, G., 133 Brennan, S. E., 225 Breuer, K., 200–201 Brewer, W. F., 57–58 Brizuela, B., 65 Bromage, A., 135, 143 Bromme, R., 228 Bronfenbrenner, U., 219 Brooks, L. W., 231 Broström, S., 5, 8 Brousseau, G., 100 Brown, A., 214 Brown, A. L., 177, 249, 261, 282–285 Brown, J. S., 56, 185, 233, 240 Brown, R. A. J., 43 Brown, S., 192 Bruhn, J., 226–227, 231–232 Bruner, J., 240, 265, 269 Bryant, P., 27 Bryceland, J. A., 177 Bryk, A. S., 268 Bryson, M., 217 Burack, J. A., 24 Burkhardt, H., 91, 289 Burns, J. R., 250 Burruss, J. D., 218 Call, J., 49 Campione, J. C., 249, 283–284 Caravita, S., 57–58 Carey, S., 57 Carpenter, M., 49 Carpenter, T. P., 59, 74 Carr, M., 7 Carraher, D. W., 43, 65, 76 Carraher, T. N., 43, 76

Carroll, J. B., 20 Cascallar, E., 195, 199–201, 214 Case, R., 22–23, 176–177 Cavanaugh, C., 211 Chan, C., 225 Chazan, D., 218 Chi, M. T. H., 60, 198 Chiang, W., 26 Choo, C., 266 Christie, J. F., 9, 11 Christie, J., 9 Christie, M. A., 182, 184 Christou, C., 24, 29 Chudowsky, N., 169, 174, 177–178, 191, 201 Church, R. B., 49 Clarebout, G., 132 Clark, H. H., 225 Clark, R. E., 116, 211, 227 Clarke, D. J., 196, 198 Clements, D. H., 66 Cleverley, J. F., 277 Clinton, K. A., 88 Clyde, M., 13 Cobb, P., 43, 100, 179, 215 Cocking, R. R., 177, 214, 261 Cognition and Technology Group at Vanderbilt 214 Cognition and Technology Group at Vanderbilt., 102 Cohen, E. G., 232, 280 Cohen, S. A., 192 Cole, M., 76, 87, 179, 266 Coleman, J. S., 268 Coll, C., 211 Collins, A. M., 56, 176, 178, 179, 185, 233, 240, 266, 282 Collins, J. S., 56 Computer Museum., 243 Confrey, J., 179 Conner, R., 288 Cook, T., 288 Cooper, B., 100, 103 Corbett, J., 250 Cordes, C., 210

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Author Index Corno, L., 116, 125–126, 195 Coulson, R. L., 191–192 Cowie, B., 7 Cramphorn, C., 250 Creedy, D., 193 Cronbach, L. J., 131, 280 Crook, C., 244 Crooks, T. J., 192 Crowson, H., 127 Cuban, L., 210, 212 Cullen, J., 4–5, 7–9, 12 Curcio, F. R., 101 Daal, M., 115 Daft, R. L., 227 Dahlberg, G., 4–5 Dansereau, D. F., 229, 231 Davey, C., 195 Davis, J., 93 Davis, R. B., 95 De Bock, D., 59, 64, 96, 101, 104 De Corte, E., 40, 42, 55–56, 64, 73–76, 91–92, 95–97, 99–102, 105, 132, 134, 143, 152–153, 191, 193, 223, 234, 244, 246, 280, 286, 290 de Croock, M., 116 De Laat, M., 248–250 De Pablo, E., 244 De Vries, R., 8 Deakin Crick, R., 195 Deci, E. L., 113, 122–123, 127, 232–233 DeFranco, T. C., 101 Dehaene, S., 22, 25, 45–46, 51 Deitz, S. M., 177 Delandshere, G., 178, 199 Demetriou, A., 20–22, 24–25, 27–29, 31–32, 34–35 DeMulder, E. K., 195, 198 Dennis, A. R., 225, 227 Derryberry, W., 127 Detterman, D. K., 40–42, 44 Deutsch, A., 74 Diener, E., 150 Dierick, S., 194, 198–199 Dillenbourg, P., 224, 232

297

DiMaggio, P. J., 267 diSessa, A. A., 57–58, 179 Dobson, M., 233 Dochy, F., 115, 191–195, 197–201, 214, 224, 232 Doerr, H. M., 93 Doherty Sneddon, G., 227 Donald, M., 77 Donovan, S., 177, 261 Dori, Y., 200–201 Driver, R., 57 Drummond, M. J., 6, 10 Duffy, C., 250 Duffy, T. M., 114, 191, 193, 251 Duguid, P., 56, 240 Dunbar, S. B., 199 Duschl, R. A., 183 Dutton, J., 269 Dweck, C. S., 266 Easley, J., 57 Edwards, C., 8 Efklides, A., 20, 29 Elen, J., 114, 127, 132 Ellis, A. B., 41, 49 Ellis, A., 225 Engeström, Y., 13–14, 241, 266 English, F.W., 194 English, L., 102 Entwistle, N. J., 117, 121, 132–135, 143, 197, 234 Eppes, F., 126 Ericsson, K. A., 47, 241 Ertl, B., 224, 226–233 Farr, M., 198 Feigenbaum, E. A., 41 Feigenson, L., 45–46, 51 Feldman, R. A., 197 Feltovich, P. J., 60, 191–192 Fennema, E., 59 Ferguson, E. L., 247 Feuer, M. J., 179, 286 Filak, V. F., 121, 127 Firestone, W. A., 195

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Author Index

Fischbein, E., 60 Fischer, F., 224–229, 231–233 Fischer, S., 266 Fisher, J., 95 Fleer, M., 4, 7–9 Fleming, A. M., 227 Fletcher, K. A., 243 Forman, G., 8 Fowles, M., 199 Frankel, G. W., 47 Fransson, A., 132 Fredrick, L. D., 177 Frederiksen, J. R., 200 Fredrickson, B. L., 121 Frommer, M., 193 Frye, D., 24 Fuson, K. C., 26, 51 Gage, N. L., 278 Galanter, E., 243 Galbraith, P., 104 Gallistel, R., 26 Gamoran, A., 268 Gandini, L., 8 Gardner, H., 219, 269 Garz, D., 162 Gauvain, M., 49 Gee, J. P., 179, 184 Gelman, R., 26, 58–59 Gelman, S. A, 51 Gerofsky, S., 95 Gertzog, W. A., 57 Ghoshal, S., 268 Gibbs, G., 192 Gibson, E. J., 46–47, 49 Gielen, S., 194 Gijbels, D., 115, 193, 197, 224 Gilden, R., 3, 10–11 Gillan, K. J., 211 Ginsburg H., 284 Gipps, C., 177 Gitomer, D. H., 183 Glaser, R., 60, 169, 174, 175, 177–178, 191–192, 198, 201, 247 Gleissner, B., 45

Goetz, Th., 121 Goffman, E., 76 Goldin–Meadow, S., 49 Goldman, P., 264 Gollwitzer, P. M., 124 Goncu, A., 41 Goodman-Turkanis, C. G., 266 Gordon, M., 218 Graeber, A. O., 60 Gräsel, C., 226–227, 231–232 Gravemeijer, K., 93, 102–103, 215 Green, J., 179 Greeno, J. G., 12, 40, 49, 59, 176, 178, 266 Greer, B., 55–56, 73–76, 91–92, 95, 97, 99, 105 Griffin, S., 27 Grossman, P., 65 Gruber, H., 223 Gulikers. J., 114, 116–117 Gustafson, J., 250 Gustafsson, J. E., 20 Gutierrez, K., 185 Gutstein, E., 106 Guttman, C., 210 Haake, J. M., 228–229 Hager, P., 241 Haggis, T., 142 Hakkarainen, K., 225, 241 Hall, J. W., 26 Hall, M. W., 262 Halldén, O., 57–58, 133 Hamilton, H., 195, 201 Hamilton, L., 171 Hanisch, G., 153 Hanna, G., 217 Hannafin, R. D., 218 Hannula, M. M., 48–50 Hanushek, E., 268 Harbison, R., 268 Harlen, W., 195 Hartmann, J., 227 Hartnett, P., 59 Hascher, T., 157

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Author Index Hatano, G., 77, 100 Hattersley, L., 162–163 Hayek, F. A., 42 Healy, L., 27 Heath, S. B., 280 Hedges, H., 5, 8 Hendry, G. D., 193 Hess, M., 211 Hesse, F.–W., 228 Hessels, A., 59, 64, 96 Hewitt, J. G., 249 Hewson, P. W., 57 Hickey, D. T., 124, 173, 175, 178–180, 182, 184–185 Higgins, S., 211 Hill, H., 268 Hindman, A., 12 Hirsch, E. D., 212 Hirschfeld, L. A., 51 Hodgson, V., 250 Hollingshead, A. B., 227 Hoover, H. D., 199 Horwitz, P., 182, 184 Hounsell, D. J., 134, 143, 197 Hoyles, C., 27 Hübscher, R., 233 Hummel, J. H., 177 Hundhausen, C. D., 228, 231–232 Huon, G. F., 197 Hurry, J., 6 Husman, J., 127 Hutchins, E., 266 Huttenlocher, J., 48 Ikeda, T., 94 Ikospentaki, K., 61, 66 Iles, P., 266 InfoDev., 212 Ioannides, C., 58 Ioannidou, I., 58 IREM de Grenoble, 95 Jacob, E., 95 Janssens, D., 59, 64, 96, 101, 104 Janssens, S., 197–198

Järvelä, S., 114 Jensen, A. R., 20 Johnson, D. W., 249 Johnson, J. E., 9, 11 Johnson, M., 240 Johnson, R. T., 249 Johnston, J., 264 Jones, C., 239 Kaestle, C. F., 278 Kail, R., 23 Kane, M. B., 195 Kanselaar, G., 132 Kaput, J. J., 88 Karmiloff–Smith, A., 31, 45, 51 Kasanen, E., 44 Kazi, S., 22, 24–25, 27–28, 31–32 Keil, W., 227 Keitel, C., 105 Kellaghan, T., 185 Keller, M., 157 Kelly, A. E., 285 Kennedy, M. M., 171 Khattri, N., 195 Kilpatrick, J., 100 Kindfield, A. C. H., 175, 182, 184 King, A., 229 Kinnunen, R., 43–44, 131 Kirkpatrick, H., 210 Kirschner, P. A., 116, 120 Kitsantas, A., 120 Klein, S., 171, 199 Kollar, I., 228–229 Kopp, B., 231–233 Koretz, D. M., 199 Koschman, T., 215, 225 Kosminsky, E., 211 Kouka, A., 58 Krampe, R. T., 241 Krapp, A., 123 Kreber, C., 134 Krebs, G., 27 Kromrey, J., 211 Kuhl, J., 123 Kuhn, T., 57

299

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Kuklick, B., 279 Kumpulainen, K., 43 Kwon, S., 268 Kyrkos, C., 58 Labaree, D. F., 278 Lagemann, E. C., 279 Lai, M.–L., 51 Lakoff, G., 66, 240 Lallimo, J., 225 Lally, V., 248–250 Lambert, E. B., 13 Lamon, M., 216 Lampert, M., 76 Langton, S., 227 Larson, J., 185 Lasure, S., 42, 75, 95–97, 101–102 Laurillard, D., 248 Laus, F., 227 Lave, J., 40–44, 75–76, 95, 100, 223, 240, 266 Lea, S. J., 191 Leach, J., 57 Lehman, A. C., 47 Lehrer, R., 102, 179 Lehtinen, E., 40–44, 48–51, 60, 114, 127, 131 Leithwood, K., 268 Lemke, J. J., 172 Lenat, D. B., 41 Lengel, R. H., 227 Lens, W., 127, 194 Leonard, F., 59 Leonard, M., 195 Lesgold, A., 262 Lesgold, S., 26 Lesh, R., 93, 102 Levesque, 122 Levine, J. M., 266 Levine, S. C., 48 Lewalter, D., 123 Light, P., 250 Light, V., 250 Lin, M.–F., 211 Lindahl, M., 47

Lindblom–Ylänne, S., 198 Lindquist, M. M., 74 Linn, R. L., 199 Lipponen, L., 225, 241 Little, C., 218 Lobato, J., 41–43, 47, 49 Lodewijks, H. G., 134 Lodewijks, J., 114 Lodewyk, K. R., 115 Lohman, D. F., 192 Lohman, F. D., 194 Löhner, S., 231 Lomax, R., 127 Lonka, K., 198 Lourenço, O., 157 Lowyck, J., 114, 127, 132 Lund, K., 229–230 Luria, A., 87 Mabey, C., 266 MacNaughton, G., 5, 12 MacRury, K., 197 Madaus, G. F., 185 Maeroff, G. I., 212 Magone, M. E., 59 Majone, G., 283 Malara, N., 60 Malti, T., 157 Mandel, E., 269 Mandl, H., 223–224, 226–233 Mandler, J. M., 45 Mann, S., 250 March, J. G., 213, 269 Martens, R. L., 114–117, 120, 127 Marton, F., 50, 132–133, 196–197 Mason, J., 91 Matthews, W., 74 Mattinen, A., 48, 50 Mauri, T., 211 May, H., 7 Mayer, R., 279 Mayrowitz, D., 195 McAdams, D., 269 McAteer, E., 250 McCaffrey D., 199,

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Author Index McCaslin, M., 124 McClain, K., 215 McCloskey, M., 57 McConnell, D., 249 McCune, V. S., 132, 134, 140–141, 143, 197 McDowell, L., 192, 196 McGrath, J. E., 227 McLaughlin, M. W., 268 McLean, R. S., 217 McMillen, S., 66 McTighe, J., 178 Meck, E., 58 Megalakaki, O., 58 Meister, C., 229 Meltzoff, A. N., 45 Merenluoto, K., 44, 60 Merrill, M. D., 243 Messick, S., 174–175 Metallidou, Y., 25, 27–28 Meyer, J., 267 Michaels, S., 262 Micheaux, D., 264 Michko, G. M., 211 Middleton, D., 266 Miettinen, R., 13 Miller, E., 210 Miller, K. F., 77 Miller, L., 3–4 Minbashian, A., 197 Minnaert, A., 127 Miskal, C. G., 267 Mislevy, R. J., 177–178, 191 Mistry, J., 41 Mix, K. S., 48, 51 Miyake, Y., 77 Moerkerke, G., 191, 199 Moll, H., 49 Moore, J. L., 40, 49 Moore, M., 252 Mortimer, E., 57 Moser, J. M., 26 Mosier, C., 41 Moskal, B. M., 59 Moss, P. A., 199 Moss, P., 4–5

301

Moursund, D., 210 Moyles, J., 3, 6, 10–11 Mukhopadhyay, S., 105 Mullin, J., 227 Muñoz, R., 41, 49 Musgrove, A., 3, 6, 11 Mutanen, M., 43 Muttock, S., 3, 10–11 Nahapiet, J., 268 Nasir, N. S., 185 Neisser, U., 279 Nelson, K., 45 Nelson–Le Gall, S., 265 Nesbitt, E., 250 Nesher, P., 59 Neumann, R., 60 Nevo, D., 194 Newlands, A., 227 Newman, F. M., 268 Newman, S. E., 56, 185, 233 Nichols, J. D., 122 Niemivirta, M., 125 Nisan, M., 150 Nisbet, J. B., 135, 143 Niss, M., 91, 95, 102–104 Nonaka, I., 241 Norman, D. A., 78, 230–231 Novak, J. D., 57 Nucci, L. P., 163 Nunes, T., 27 Nunez, R., 66 Nunner–Winkler, G., 152, 156–157, 159 Nuttall, J., 5, 8–9, 15 O’Connaill, B., 227 O’Connor, M. C., 262 O’Donnell, A. M., 229 O’Halloran, K. L., 74 O’Malley, C., 227 Ohlsson, S., 40–42, 51 Olga, V., 266 Olkinuora, E., 43–44, 131 Olmsted, P., 3–4 Olsen, S., 250

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Olson, D., 209 Omanson, S., 59 Onrubia, J., 211 Op ’t Eynde, P., 152 Oppenheimer, T., 210, 212 Orr, J., 270 Ortega, R., 13 Oser, F., 150–151, 153–155 Overtoom, C. C. E., 24

Powell, W. W., 267 Powers, D., 199 Prosser, M., 196, 198 Pugh, G., 4, 10 Punamaki, R.–L., 13 Puntambekar, S., 233 Putnam, R., 286

Paas, F. G. W. C., 232–233 Paavola, S., 241 Pachaury, A., 25, 27–28 Pächter, M., 225, 227–228 Palincsar, A. S., 283 Palm, T., 101 Papert, S., 252 Pata, K., 224 Peck, C., 210 Pekrun, R., 121 Peled, I., 59 Pellegrino, J. W., 169, 173–175, 177–180, 191, 201, 261 Pence, A., 4–5 Penn, H., 3, 5 Perkins, D. N., 40–41, 210, 212 Perrow, C., 267 Perry, R. P., 121 Perry, W. G., 132 Peterson, B., 106 Petraglia, J., 212 Petrosky, A. R., 199 Phillips, D. C., 179, 277, 286 Piaget, J., 25, 35, 48 Pick, A. D., 46–47 Pintrich, P. R., 57, 113, 119, 195 Piontkowski, U., 227 Plato, 88 Platsidou, M., 20, 24, 29 Poelmans, P., 115 Popkewitz, T. S., 9 Popper, K., 289 Posner, G. J., 57 Posner, M., 47 Post, T. R., 66

Raczak, A., 185 Radatz, H., 74, 95–96 Raftopoulos, A., 35 Rahikainen, M., 225 Ramsden, P., 132, 196–197 Randi, J., 195 Räsänen, P., 48, 50 Rath, G. J., 243 Ratinckx, E., 42, 102 Ravitz, J. L., 210 Reder, L. M., 12, 40, 55–56, 59, 240 Reeve, A. L., 195 Reeve, R., 216 Reichenbach, R., 150, 153–155 Reinmann–Rothmeier, G., 223–224 Reiser, B. J., 233 Reiserer, M., 228–230, 232–233 Renkl, A., 223 Renshaw, P. D., 43 Resnick, D. P., 177 Resnick, L. B., 26, 59, 176–178, 262, 264–266, 268 Reusser, K., 74, 95, 100–101 Richards, J., 26 Richardson, J. T. E., 134 Ridgway, J., 198, 200–201 Riel, M., 217 Rigsby, L. C., 195, 198 Riley, J., 6 Rochelle, J., 57–58 Rogers, S., 6–7, 14 Rogoff, B., 41, 266 Romberg, T. A., 44, 59 Roschelle, J. M., 217 Rosenau, S., 197

Quiroz, P. A., 268

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Author Index Rosenshine, B., 229 Rosenthal, H., 125–126 Roskos, K., 9 Rothbart, M., 47 Rovai, A., 250 Rowan, B., 267–268 Rozendaal, J. S., 127 Ruijters, M., 240–241 Ruiz–Primo, M. A., 171 Rummel, N., 228, 230 Russell, A. L., 193 Russell, T. L., 209, 211, 214 Ryan, R. M., 113, 122–123, 232–233 Ryan, R., 122 Rymes, B., 185 Ryve, A., 139 Saalbach, H., 157 Sadler, D. R., 171 Säljö, R., 74–77, 101, 132, 196–197 Salmon, G., 247 Salomon, G., 40–41, 210–211, 213–215, 233 Salonen, P., 43–44, 131 Sambell, L., 192 Samuelsson, I. P., 47 Sarason, S., 219 Savery, J. R., 193 Saxe, G. B., 76 Scardamalia, M., 185, 215–217, 249 Schallert, D. L., 126 Schauble, L., 102, 179 Scheja, M. E., 133, 137–140 Scheminsca, A., 25 Schliemann, A. D., 43, 65, 76 Schmid, E., 150, 157, 159 Schneider, B., 268 Schneider, E. W., 243 Schneider, W., 156 Schnitzler, K., 209 Schnurer, K., 225, 228 Schoenfeld, A. H., 3–4, 12–13, 15–16, 32, 55, 67, 198, 289 Schofield, J. W., 217 Schommer, M., 117

303

Schon, D., 262 Schwartz, D. L., 40–41 Schwartz, J. L., 217 Scott, P., 57 Scouller, K., 192, 197–198 Secada, W. G., 268 Seel, M., 150 Segers, M., 115, 191, 193–195, 199, 201, 214, 224 Seitz, A., 264 Senge, P., 241, 266 Sethole, G., 103 Sfard, A., 13–14, 42, 55, 184, 240 Shachar, H., 266 Shaffer, A., 288 Shaffer, D. W., 88 Shapiro, A. M., 232–233 Shapiro, L. J., 74 Shavelson, R. J., 171, 178–179, 192, 286 Shayer, M., 13 Sheldon, K., 121, 127 Shepard, L., 199 Shilony, T., 265 Siebert, D., 41–42 Silver, E. A., 74 Simon, H. A., 12, 40, 55–56, 59, 213, 219, 240, 269 Simons, J., 127 Simons, P. R. J., 114, 116, 191, 240–241, 248–251 Singley, M. K., 40 Siraj–Blatchford, I., 3, 10–11 Skinner, E. A., 121 Skopeliti, I., 61, 66 Smetana, J. G., 163 Smith, D. M., 286 Smith, D. R., 40, 49 Smith, J. P., 57–58 Smylie, M A., 124 Snow, R. E., 194 Solano–Flores, G., 178 Soler, J., 3–4 Solomon, R. C., 151 Sorensen, E. K., 250 Spada, H., 228, 230

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Spanoudis, G., 24, 29 Sparrow, J., 266 Spelke, E. S., 26, 44–49, 51, 58 Spillane, J., 265, 268–269 Spiro, R. J., 191–192 Squire, S., 27 Stafylidou, S., 59 Stanek, L., 122 Starkey, P., 26 Staub, F. C., 44, 265 Stebler, R., 74, 95, 100–101 Stecher, B., 199 Steeples, C., 239 Stegers, E., 210 Steinbach, R., 268 Steinberg, L. S., 177–178 Stephan, M., 215 Stephens, M., 94, 196, 198 Stephenson, D., 191 Stern, E., 44, 265 Sternberg, R. J., 41 Stiggins, R. J., 178 Stigler, J. W., 77–78 Stillman, G., 104 Stockinger, 244 Stodolsky, S. S., 65 Stokes, D. E., 281 Strauss, S., 265 Strijbos, J. W., 116, 120 Strike, K. A., 57 Struyf, E., 194 Struyven, K., 197–198 Suchman, L., 270 Suh, E. M., 150 Suthers, D. D., 225, 228, 231–232 Swallow, J., 217 Sweller, J., 232–233 Sylva, K., 3–4, 6, 10–11 Szeminska, A., 48 Taasoobshirazi, G., 184 Tait, H., 197 Takeuchi, H., 241 Talbert, J. E., 268 Tall, D., 28

Tamkin, G., 288 Tate, W. E., 106 Tawney, D. A., 243–245 Teasley, S. D., 266 Tesch–Romer, C., 241 Thatcher, R. W., 22–23 Tiberghien, A., 58 Tirosh, D., 60 Titz, W., 121 Tolmie, A., 250 Tomasello, M., 49 Topping, K., 192 Towne, L., 179, 286 Traub, R. E., 197 Traum, D., 224 Trigwell, K., 196 Trollip, S. R., 244 Troy, J., 191 Tsaparlis, G., 58 Turiel, E., 163 Turkle, S., 210 Turner, J. E., 126 Tyack, D., 267 Tyler, R., 279 Tynjälä, P., 134 Undheim, J. O., 20 Usiskin, Z., 105 Valacich, J. S., 225, 227 Valcke, M., 115, 132 Vamvakoussi, X., 59–63 Van Boekel, S., 210 Van de Watering, G., 193, 197 Van den Bossche, P., 115, 193, 197, 224 Van den Heuvel–Panhuizen, M., 196 Van der Linden, J., 114, 191, 251 Van der Molen, M. W., 24 Van der Rijt, J., 197 Van der Velden, J., 227 Van Dooren, W., 59, 64, 96, 101, 104 Van Joolingen, W., 231 Van Merriënboer, J. J. G., 116, 127, 132, 134, 143, 232–234 Van Vaerenbergh, G., 42, 102

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Author Index Vandenberghe, R., 194 Vansteenkiste, M., 127 Vauras, M., 43–44, 131 Veldhuis–Diermanse, E. A., 249 Verbaten, M. N., 24 Vermetten, Y. J., 114, 134 Vermunt, J. D., 114, 132, 134, 251 Verschaffel, L., 42, 55–56, 59, 64, 73–76, 91–92, 95–97, 99–102, 104–105, 132, 134, 143, 234, 244, 251, 280, 286, 290 Viennot, L., 57 Vlassis, J., 59 Volet, S., 114 Vonderwell, S., 250 Vosniadou, S., 56–63, 66–67, 97, 247 Vurpillot, E., 24 Vygotsky, L. S., 13, 76, 264, 266 Waibel, M. C., 225, 228 Walker, R. A., 193 Wardle, F., 9, 11 Wasik, B. A., 12 Watkins, D., 197 Waxman, H.C., 211 Webb, N. L., 170 Weber, M., 267 Weber, S., 288 Weinberger, A., 224–225, 227–230, 232 Weinert, F. E., 156 Wenger, E., 13–14, 178, 223, 240, 248–250, 266 Wertsch, J. V., 87 Whetten, D., 269 Whittaker, S., 227 Wiese, H., 26 Wiesemes, R., 200–201 Wiggins, G., 178

Wilbur, S., 227 Wildavsky, A. B., 283 Wiliam, D., 171, 183, 193, 196 Willard, A., 199 Williams, T., 268 Wilson, J. W., 60 Wilson, M., 170 Winkler, K., 224, 231 Winne, P. H., 115–117 Wistedt, I., 133 Wittgenstein, L., 287 Wolfe, E. W., 175 Wolters, C. A., 125–126 Wong, Y. T., 210 Wood, E. A., 3–12, 14–15 Woodruff, E., 217 Wyndhamn, J., 74–75, 101 Wynn, K., 26, 48 Wyse, D., 6 Xu, F., 26 Yackel, E., 43, 100 Yerushalmy, M., 217–218 Yong–Di, Z., 59, 65 Yowell, C. M., 124 Yrjo E., 266 Yujing, N., 59, 65 Yukl, G., 268 Zeidner, M., 197 Zelazo, P. D., 24 Zhang, J., 230–231 Zimmerman, B. J., 120, 195 Zoller, U., 197 Zuehlke, A., 122 Zuiker, S. J., 173, 178, 184 Zurawsky, C., 268

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Subject Index achievement, 3, 5, 8, 10, 13, 14, 76, 135, 171–174, 177, 182, 183, 192, 194, 196, 197, 211, 214, 219, 268, 278 affect, 11, 32, 60, 117, 118, 120, 121, 123, 131, 195, 210, 212, 224, 226, 268, 270, 282 arithmetic mental arithmetic, 77–83, 86, 87 written arithmetic, 77–81 assessment assessment culture, 191–199, 201 assessment engineering, 200–201 authentic assessment, 199 formative assessment, 171, 182, 183, 193, 195, 196, 199, 201 self-assessment, 114, 185 summative assessment, 171, 172, 185, 186, 194, 195, 199 attentional processes, 39, 47, 48–51 autonomy, 115, 116, 122, 123, 124, 127, 139, 145 behaviourism, 246 beliefs, 4, 8, 12, 16, 22, 55–57, 64, 66, 102, 114, 116–118, 120, 122, 125, 127, 133, 139, 140, 144, 153, 154, 174, 175, 177, 197, 216, 259, 265, 290 cognitivism, 246 cognitive apprenticeship, 56, 142, 233 comparative perspectives, 7, 8, 11–14 competence, 5, 13, 15, 26, 87, 116, 119, 122, 125, 127, 174, 175, 177, 186, 199, 201, 241, 242

computer computer assisted learning, 239, 243 computer managed instruction, 244 computer simulation, 114, 244 computer supported collaborative learning, 120, 223–234, 239 computer supported learning, 223–234, 239 computer uses in education, 239, 242, 252 conceptual change, 44, 55–67, 178 context contexts of discovery and justification, 289 contextualisation, 15, 133, 137, 139, 140 control of variables, 282, 290 culture cultural factors, 59 cultural tools, 9, 14, 49, 58, 77, 86, 88 curriculum, 3–13, 15, 16, 35, 64, 101, 114, 117, 170–177, 183, 184, 186, 192, 200, 212, 243, 265, 268, 279, 280, 287, 288 design experiments, 277–290 development cognitive development, 19–35, 51 moral development, 149–164 education adult education, 223 early childhood education, 3–16 elementary education, 65, 91, 94–96, 101, 102 higher education, 113–117, 120, 123, 127, 131, 134, 143, 145, 146, 191, 194, 225 secondary education, 65, 91

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e-pedagogies, 239–252 empiricism expertise, 41, 56, 95, 101, 103–106, 174, 185, 241, 271 adaptive expertise, 91, 95, 100 routine expertise, 100 evaluation formative evaluation, 171–174, 178, 179, 194, 195, 199, 285, 287, 288 summative evaluation, 171–174, 178, 179, 186, 194, 195, 199 foundation stage, 4–6, 10, 11 group learning, 247 happy victimizer, 150, 152, 156–159, 162 identity, 12, 40, 250, 251, 269, 272 individual differences, 19, 22, 24, 30, 34, 39, 48, 49, 131 innovation, 114, 116, 193, 269, 286 institution, 76, 247–249, 266, 267, 270 intelligence, 31, 32, 35, 169, 200, 265 interactive geometry software, 217–218 knowledge knowledge and information, 213 knowledge building, 56, 215, 216, 249 metacognitive knowledge, 250, 251 learning active learning, 113, 114 collaborative learning, 114, 120, 217, 223–225, 228, 229, 233, 234, 239, 247, 249–252 cooperative learning, 247, 249 learning communities, 242, 249–251, 260–262, 264, 285 learning environment, 7, 10, 13, 55–57, 64, 102, 113, 115–117, 120, 132, 142, 177–179, 191–193, 209, 213–215, 219, 223–234, 245, 247–250, 259

learning strategies, 113, 115, 117, 197 learning theory, 12, 88, 241, 243, 246 motivated learning, 113–127 networked learning, 239–252 mathematics mathematical modelling, 91–106 mathematical problem solving, 102, 290 mathematical thinking, 20, 30, 32, 47 mathematics education, 42, 43, 55, 64–66, 95, 103–105, 196 mathematics learning, 42, 43, 51, 55, 59, 64, 65, 73, 74 mental tools, 73–88 metacognition, 14, 283 metaphors, 14, 42, 56, 66, 124, 142, 149, 210, 213, 239–242, 245, 246, 248, 251, 252 mind, 19–21, 24, 27, 32, 34, 176, 216, 266 morality, 149–153, 155, 158, 159, 163, 164 moral emotions, 152, 164 unhappy moralist, 149–155, 157, 160, 162–164 motivation, 13, 14, 31, 43, 49, 55, 57, 59, 102, 113–122, 124, 125, 127, 128, 152, 153, 156, 157, 160, 193–195, 198, 217, 226, 232, 233, 250, 265 multimedia, 115, 127, 184 number concept rational number concept, 59–66 numeracy, 6, 8–11, 13, 14, 49 numerosity, 25–27, 47–50 organization, 19, 22, 25, 120, 216, 259, 267–273 organizational designs for learning, 259–273 pedagogy, 3–16, 143, 212, 239, 240 performance, 3, 6, 20, 24, 32, 41, 62, 63, 75, 76, 79, 80, 84, 102, 115, 120, 121, 125, 169, 171, 173, 175, 178, 182, 183, 192, 194, 195, 197, 200, 227–229, 245, 260, 264, 268, 270, 283

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Subject Index play, 4, 6 –11, 14, 16 policy reform, 3, 5, 15, 268 problem problem solving, 19, 21, 22, 24, 27, 34, 51, 55, 73, 78, 81, 87, 95, 97, 100, 102, 182, 194, 199, 214, 215, 219, 226, 227, 242, 244, 190 problem-based learning, 113, 115, 193, 215, 224, 227 realistic problems, 42 word problem, 74 –76, 78, 79, 88, 95, 96, 98–105 relatedness, 122, 123, 127 representation external representation, 61, 66, 67 research qualitative research methods, 133, 289 quantitative research methods, 289 research methods, 45, 133, 179, 183, 277–291 school performance, 20, 32, 33 science education, 57 script, 229, 230, 263, 270, 279, 280 self-concept, 21, 32, 266 self-regulation, 35, 113, 114, 116, 119, 120, 123–126, 233, 241, 251 sense making, 74, 76, 78, 99, 259, 261, 265, 268

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situationism situated knowledge, 16, 42– 44 sociocultural perspective, 7, 77, 81, 86, 88, 131, 178, 179, 183 socioconstructivism, 114, 116, 118, 122 student student learning, 116, 131–134, 143, 146, 174, 177, 201, 245, 264 studying, 132–145, 195, 196, 213, 259, 262, 268, 278, 279, 283, 285 teacher technology educational technology, 209, 212 information and communication technology, 114, 115, 209, 211–215, 219, 239, 242, 245, 246, 248, 252 transfer, 14, 39–51, 56, 176, 177, 179, 182, 223, 244, 260, 286 university, 114, 115, 117, 122, 131, 132, 140, 142, 143, 146, 151, 217, 239, 248, 262, 279 validity, 174–176, 179, 186, 194, 199, 280, 283, 284, 285, 286 volition, 114, 120, 123–128 young children, 5–10, 15, 39, 45, 48, 50, 51, 58, 102

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