The Neurological Basis of Learning, Development and Discovery: Implications for Science and Mathematics Instruction (Science & Technology Education Library)

THE NEUROLOGICAL BASIS OF LEARNING, DEVELOPMENT AND DISCOVERY

Science & Technology Education Library VOLUME 18 SERIES EDITOR William W. Cobern, Western Michigan University, Kalamazoo, USA FOUNDING EDITOR Ken Tobin, University of Pennsylvania, Philadelphia, USA EDITORIAL BOARD Henry Brown-Acquay, University College of Education of Winneba, Ghana Mariona Espinet, Universitat Autonoma de Barcelona, Spain Gurol Irzik, Bogazici University, Istanbul, Turkey Olugbemiro Jegede, The Open University, Hong Kong Reuven Lazarowitz, Technion, Haifa, Israel Lilia Reyes Herrera, Universidad Autónoma de Columbia, Bogota, Colombia Marrisa Rollnick, College of Science, Johannesburg, South Africa Svein Sjøberg, University of Oslo, Norway Hsiao-lin Tuan, National Changhua University of Education, Taiwan SCOPE The book series Science & Technology Education Library provides a publication forum for scholarship in science and technology education. It aims to publish innovative books which are at the forefront of the field. Monographs as well as collections of papers will be published.

The titles published in this series are listed at the end of this volume.

The Neurological Basis of Learning, Development and Discovery Implications for Science and Mathematics Instruction

by

ANTON E. LAWSON School of Life Sciences, Arizona State University, U.S.A.

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

eBook ISBN: Print ISBN:

0-306-48206-1 1-4020-1180-6

©2003 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2003 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at:

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

TO

MATT, BOB, BETSY and KRISTINA

This page intentionally left blank

TABLE OF CONTENTS

Preface

ix

Acknowledgements

xv 1

CHAPTER 1

How Do People Learn?

CHAPTER 2

The Neurological Basis of Self-Regulation

27

CHAPTER 3

Brain Maturation, Intellectual Development and Descriptive Concept Construction

57

Brain Maturation, Intellectual Development and Theoretical Concept Construction

79

Creative Thinking, Analogy and a Neural Model of Analogical Reasoning

99

CHAPTER 4

CHAPTER 5

CHAPTER 6

The Role of Analogies and Reasoning Skill in Theoretical Concept Construction and Change

119

Intellectual Development During the College Years: Is There a Fifth Stage?

135

CHAPTER 8

What Kinds of Scientific Concepts Exist?

159

CHAPTER 9

Psychological and Neurological Models of Scientific Discovery

183

CHAPTER 7

CHAPTER 10 Rejecting Nature of Science Misconceptions By Preservice Teachers

211

CHAPTER 11 Implications for The Nature of Knowledge and Instruction

225

References

261

Index

277

This page intentionally left blank

PREFACE

A goal of mine ever since becoming an educational researcher has been to help construct a sound theory to guide instructional practice. For far too long, educational practice has suffered because we have lacked firm instructional guidelines, which in my view should be based on sound psychological theory, which in turn should be based on sound neurological theory. In other words, teachers need to know how to teach and that "how-to-teach" should be based solidly on how people learn and how their brains function. As you will see in this book, my answer to the question of how people learn is that we all learn by spontaneously generating and testing ideas. Idea generating involves analogies and testing requires comparing predicted consequences with actual consequences. We learn this way because the brain is essentially an idea generating and testing machine. But there is more to it than this. The very process of generating and testing ideas results not only in the construction of ideas that work (i.e., the learning of useful declarative knowledge), but also in improved skill in learning (i.e., the development of improved procedural knowledge). Thus, to teach most effectively, teachers should allow their students to participate in the idea generation and testing process because doing so allows them to not only construct "connected" and useful declarative knowledge (where "connected" refers specifically to organized neuron hierarchies called outstars), but also to develop "learning-to-learn" skills (where "learning-to-learn" skills refer to general rules/guidelines that are likely located in the prefrontal cortex). My interest in the neurological basis of instruction can be traced to a 1967 book written by my biologist father, the late Chester Lawson, titled Brain Mechanisms and Human Learning published by Houghton Mifflin. Although the book was written while I was still in high school, in subsequent years my father and I had many long conversations about brain structure and function, learning and development, and what it all meant for education. In fact, in that book, my father briefly outlined a theory of instruction that has subsequently been called the learning cycle. That instructional theory was put into practice by my father, by Robert Karplus and by others who worked on the Science Curriculum Improvement Study during the 1970s. My mathematician brother David Lawson has also boosted my interest in such issues. David worked on NASA's Space Station Program and is an expert in neural modeling. His help has been invaluable in sorting out the nuances of neural models and their educational implications. Given this background, Chapter 1 begins by briefly exploring empiricism, innatism and constructivism as alternative explanations of learning. Empiricism claims learning results from the internalization of patterns that exist in the external world. Innatism claims that such patterns are internal in origin. Constructivism views learning as a process in which spontaneously generated ideas are tested through the derivation of

x

expectations. The initial ideas are retained or rejected depending upon the extent that their expectations match future observations in an assumed-to-exist external world. Piaget's brand of constructivism with its theory of self-regulation is discussed as an explanation for development and learning. Piaget's self-regulation theory is based on biological analogies, largely on Waddington's theory of genetic assimilation. Genetic assimilation is described and used to explain psychological-level phenomena, specifically the development of proportional reasoning skill during adolescence. In spite of the value of self-regulation theory, an important theoretical weakness exists as the theory is based on biological analogies rather than on brain structure and function. Brain structure and function are discussed in Chapter 2 to hopefully eliminate this weakness. Chapter 2 explains visual and auditory information processing in terms of basic brain structure and function. In brief, a hypothetico-predictive pattern is identified in both visual and auditory processing. Steven Grossberg's neural modeling principles of learning, perception, cognition, and motor control are presented as the basis for construction of a neurological model of sensory-motor problem solving. The pattern of problem solving is assumed to be universal, thus is sought in the higher-order shift from the child's use of an additive strategy to the adolescent's use of a proportions strategy to solve Suarez and Rhonheimer's Pouring Water Task. Neurological principles involved in this shift and in the psychological process of self-regulation are discussed, as are educational implications. The conclusion is drawn that reasoning is hypotheticopredictive in form because that is the way the brain works. Many adolescents fail when attempting to solve descriptive concept construction tasks that include exemplars and non-exemplars of the concepts to be constructed. Chapter 3 describes an experiment that tested the hypothesis that failure is caused by lack of developmentally derived, hypothetico-predictive reasoning skill. To test this developmental hypothesis, individually administered training sessions presented a series of seven descriptive concept construction tasks to students (ages five to fourteen years). The sessions introduced the hypothetico-predictive reasoning pattern presumably needed to test task features. If the developmental hypothesis is correct, then the brief training should not be successful because developmental deficiencies in reasoning presumably cannot be remedied by brief training. Results revealed that none of the five and six-year-olds, approximately half of the seven-year-olds, and virtually all of the students eight years and older responded successfully to the brief training. Therefore, the results contradicted the developmental hypothesis, at least for students older than seven years. Previous research indicates that the brain's frontal lobes undergo a pronounced growth spurt from about four to seven years of age. In fact, performance of normal six-year-olds and adults with frontal lobe damage on tasks such as the Wisconsin Card Sorting Task, a task similar to the present descriptive concept construction tasks, has been found to be identical. Consequently, the present results support the hypothesis that the striking improvement in task performance found at age seven is linked to maturation of the frontal lobes. A neural network of the role the frontal lobes play in task performance is presented. The advance in reasoning that

xi presumably results from effective operation of the frontal lobes is seen as a fundamental advance in intellectual development because it enables children to employ hypotheticopredictive reasoning to change their "minds" when confronted with contradictory evidence regarding features of perceptible objects, a reasoning pattern necessary for descriptive concept construction. Presumably, a further qualitative advance in intellectual development occurs when some students derive an analogous, but more advanced pattern of reasoning, and apply it to derive an effective problem-solving strategy to solve the descriptive concept construction tasks when training is not provided. Chapter 4 describes an experiment testing the hypothesis that an early adolescent brain growth plateau and spurt influences the development of higher-level hypothetico-predictive reasoning skill and that the development of such reasoning skill influences one's ability to construct theoretical concepts. In theory, frontal lobe maturation during early adolescence allows for improvements in one's abilities to coordinate task-relevant information and inhibit task-irrelevant information, which along with both physical and social experience, influence the development of reasoning skill and one's ability to reject misconceptions and accept scientific conceptions. A sample of 210 students ages 13 to 16 years enrolled in four Korean secondary schools were administered four measures of frontal lobe activity, a test of reasoning skill, and a test of air-pressure concepts derived from kinetic-molecular theory. Fourteen lessons designed to teach the theoretical concepts were then taught. The concepts test was readministered following instruction. As predicted, among the 13 and 14-year-olds, performance on the frontal lobe measures remained similar, or decreased. Performance then improved considerably among the 15 and 16-year-olds. Also as predicted, the measures of frontal lobe activity correlated highly with reasoning skill. In turn, prefrontal lobe function and reasoning skill predicted concept gains and posttest concept performance. A principal components analysis found two main components, which were interpreted as representing and inhibiting components. Theoretical concept construction was interpreted as a process involving both the representation of taskrelevant information (i.e., constructing mental representations of new scientific concepts) and the inhibition of task-irrelevant information (i.e., the rejection of previously-acquired misconceptions). Chapter 5 presents a model of creative and critical thinking in which people use analogical reasoning to link planes of thought and generate new ideas that are then tested by employing hypothetico-predictive reasoning. The chapter then extends the basic neural modeling principles introduced in Chapter 2 to provide a neural level explanation of why analogies play such a crucial role in science and why they greatly increase the rate of learning and can, in fact, make classroom learning and retention possible. In terms of memory, the key point is that lasting learning results when a match occurs between sensory input from new objects, events, or situations and past memory records of similar objects, events, or situations. When such a match occurs, an adaptive resonance is set up in which the synaptic strengths of neurons increase), thus a record of the new input is formed in longterm memory. Neuron systems called outstars and instars presumably enable this to occur. Analogies greatly facilitate learning and

xii

retention because they activate outstars (i.e., the cells that are sampling the to-belearned pattern) and cause the neural activity to grow exponentially by forming feedback loops. This increased activity boosts synaptic strengths, thus causes storage and retention in long -term memory. In Chapter 6, two hypotheses about theoretical concept construction, conceptual change and application are tested. College biology students classified at different levels of reasoning skill were first taught two theoretical concepts (molecular polarity and bonding) to explain the mixing of dye with water, but not with oil, when all three were shaken in a container. The students were then tested in a context in which they applied the concepts in an attempt to explain the gradual spread of blue dye in standing water. Next students were taught another theoretical concept (diffusion), with and without the use of physical analogies. They were retested to see which students acquired the concept of diffusion and which students changed from exclusive use of the polarity and bonding concepts (i.e., misconceptions) to the scientifically more appropriate use of the diffusion concept to explain the dye's gradual spread. As predicted, the experimental/analogy group scored significantly higher than the control group on a posttest question that required the definition of diffusion. Also as predicted, reasoning skill level was significantly related to a change from the application of the polarity and bonding concepts to the application of the diffusion concept to explain the dye's gradual spread. Thus, the results support the hypotheses that physical analogies are helpful in theoretical concept construction and that higher-order, hypothetico-predictive reasoning skill facilitates conceptual change and successful concept application. Chapter 7 describes research aimed at testing the hypothesis that two general developmentally based levels of causal hypothesis-testing skill exist. The first hypothesized level (i.e., Level 4, which corresponds generally to Piaget's formal operational stage) presumably involves skill associated with testing causal hypotheses involving observable causal agents, while the second level (i.e., Level 5, which corresponds to a fifth, post-formal stage) presumably involves skill associated with testing causal hypotheses involving unobservable entities. To test this fifth-stage hypothesis, a hypothesis-testing skill test was developed and administered to a large sample of college students both at the start and at the end of a biology course in which several hypotheses at both causal levels were generated and tested. The predicted positive relationship between causal hypothesis-testing skill and performance on a transfer problem involving the test of a causal hypothesis involving unobservable entities was found. The predicted positive relationship between causal hypothesistesting skill and course performance was also found. Scientific concepts can be classified as descriptive (e.g., concepts such as predator and organism with directly observable exemplars) or theoretical (e.g., concepts such as atom and gene without directly observable exemplars). Understanding descriptive and theoretical concepts has been linked to students' developmental stages, presumably because the procedural knowledge structures (i.e., reasoning patterns) that define developmental stages are needed for concept construction. Chapter 8 describes research that extends prior theory and research by postulating the existence of an

xiii

intermediate class of concepts called hypothetical (e.g., concepts such as subduction and evolution with exemplars that can not in practice be observed due to limits on the normal observational time frame). To test the hypothesis that three kinds of scientific concepts exist, we constructed and administered a test of the concepts introduced in a college biology course. As predicted, descriptive concept questions were significantly easier than hypothetical concept questions, than were theoretical concept questions. Further, because concept construction presumably depends in part on reasoning skill, students at differing reasoning skill levels (Levels 3, 4 and 5, where Level 5 is conceptualized as 'post-formal' in which hypotheses involving unseen entities can be tested) were predicted to vary in the extent to which they succeeded on the concepts test. As predicted, a significant relationship (p < 0.001) was found between conceptual knowledge and reasoning skill level. This result replicates previous research, therefore provides additional support for the hypothesis that procedural knowledge skills associated with intellectual development play an important role in declarative knowledge acquisition, i.e., in concept construction. The result also supports the hypothesis that intellectual development continues beyond the 'formal' stage during the college years, at least for some students. Chapter 9 considers the nature of scientific discovery. In 1610, Galileo Galilei discovered Jupiter's moons with the aid of a new more powerful telescope of his invention. Analysis of his report reveals that his discovery involved the use of at least three cycles of hypothetico-predictive reasoning. Galileo first used hypotheticopredictive reasoning to generate and reject a fixed-star hypothesis. He then generated and rejected an ad hoc astronomers-made-a-mistake hypothesis. Finally, he generated, tested, and accepted a moon hypothesis. Galileo's reasoning is modeled in terms of Piaget's self-regulation theory, Grossberg's theory of neurological activity, Levine & Prueitt's neural network model and Kosslyn & Koenig's model of visual processing. Given that hypothetico-predictive reasoning has played a role in other important scientific discoveries, the question is asked whether it plays a role in all scientific discoveries. In other words, is hypothetico-predictive reasoning the essence of the scientific method? Possible alternative scientific methods, such as Baconian induction and combinatorial analysis, are explored and rejected as viable alternatives. The "logic" of scientific discovery and educational implications are discussed. Instructional attempts to provoke preservice science teachers to reject nature-ofscience (NOS) misconceptions and construct more appropriate NOS conceptions have been successful only for some. Chapter 10 describes a study that asked, why do some preservice teachers make substantial NOS gains, while others do not? Support was found for the hypothesis that making NOS gains as a consequence of instruction requires prior development of Stage 5 reasoning skill, which some preservice teachers lack. In theory, science is an enterprise in which scientists often use Stage 5 reasoning to test alternative hypotheses regarding unobservable theoretical entities. Thus, anyone lacking Stage 5 reasoning skill should be unable to assimilate this aspect of the nature of science and should be unable to reject previously constructed NOS misconceptions as a consequence of relatively brief instruction. As predicted, the study found the predicted positive relationship between reasoning skill (Levels 3, 4 and 5) and NOS

xiv

gains as a consequence of instruction. Preservice teachers who lack Stage 5 reasoning skill can be expected to find it difficult to teach science as a process of inquiry when they become teachers. Chapter 11 begins with a brief summary of the neurological principles and research introduced in the previous chapters and with their key instructional implications. The chapter then offers a resolution to the current debate between constructivists and realists regarding the epistemological status of human knowledge. As we have seen, knowledge acquisition follows a hypothetico-predictive form in which self-generated ideas/representations are tested by comparing expected and observed outcomes. Ideas may be retained or rejected, but cannot be proved or disproved. Therefore, absolute Truth about any and all ideas, including the idea that the external world exists, is unattainable. Yet learning at all levels above the sensory-motor requires that one assume the independent existence of the external world because only then can the behavior of the objects in that world be used to test subsequent higherorder ideas. In the final analysis, ideas - including scientific hypotheses and theories stand or fall, not due to social negotiation, but due to their ability to predict future events. Although this knowledge construction process has limitations, its use nevertheless results in increasingly useful mental representations about an assumed to exist external world as evidenced by technological progress that is undeniably based on sound scientific theory. An important instructional implication is that instruction should become committed to helping students understand the crucial role that hypotheses, predictions and evidence play in learning. Further, instruction that allows, indeed demands, that students participate in this knowledge construction process enables them to undergo self-regulation and develop both general procedural knowledge structures (i.e., reasoning skills) and domain-specific concepts and conceptual systems. Examples of effective instruction are provided. As you will see, this book includes fairly detailed accounts of specific research studies. The studies provide examples of how hypothetico-predictive research can be conducted and reported in science and mathematics education. In my view, too few such studies are designed and written in this hypothetico-predictive manner, and suffer as a consequence. In fact, in my view the entire field suffers as a consequence. Thus, a secondary goal of this book is to encourage other researchers to adopt the hypotheticopredictive approach to their research and writing.

xv Acknowledgements I would like to thank William Cobern, Series Editor, for asking me to write this book, Michel Lokhorst, Publishing Editor of Kluwer Academic Publishers, for his expert help in seeing the project to completion, Irene van den Reydt of Kluwer's Social Sciences Unit for helping with the review process, Chula Eslamieh for her help in preparing the final manuscript, and two anonomous reviewers for their many helpful comments. Thanks also to Anne Rowsey, Laural Casler and Cameo Hill of the Arizona State University Life Sciences Visualization Laboratory for their graphic illustration work that appears in the book and to several colleagues who have contributed to the ideas and research presented. These include John Alcock, Souheir Alkoury, William Baker, Russell Benford, Margaret Burton, Brian Clark, Erin Cramer-Meldrum, Lisa DiDonato, Roy Doyle, Kathleen Falconer, Bart James, Margaret Johnson, Lawrence Kellerman, Yong-Ju Kwon, David Lawson, Christine McElrath, Birgit Musheno, Ronald Rutowski, Jeffery Sequist, Jan Snyder, Michael Verdi, Warren Wollman and Steven Woodward. An additional thank you is due to the National Science Foundation (USA) under grant No. DUE 0084434 and to the editors and publishers of the articles appearing below as several of the chapters contain material based on those articles: Lawson, A.E. & Wollman, W.T. (1976). Encouraging the transition from concrete to formal cognitive functioning - an experiment. Journal of Research in Science Teaching, 13(5), 413-430. Lawson, A.E. (1982). Evolution, equilibration, and instruction. The American Biology Teacher, 44(7), 394405. Lawson, A.E. (1986). A neurological model of problem solving and intellectual development. Journal of Research in Science Teaching, 23(6), 503-522. Lawson, A.E., McElrath, C.B., Burton, M.S., James, B.D., Doyle, R.P., Woodward, S.L., Kellerman, L. & Snyder, J.D. (1991). Hypothetico-deductive reasoning and concept acquisition: Testing a constructivist hypothesis. Journal of Research in Science Teaching, 28(10), 953-970. Lawson, A.E. (1993). Deductive reasoning, brain maturation, and science concept acquisition: Are they linked? Journal of Research in Science Teaching, 30(9), 1029-1052. Lawson, D.I. & Lawson, A.E. (1993). Neural principles of memory and a neural theory of analogical insight. Journal of Research in Science Teaching, 30(10), 1327-1348. Lawson, A.E., Baker, W.P., DiDonato, L., Verdi, M.P. & Johnson, M.A. (1993). The role of physical analogues of molecular interactions and hypothetico-deductive reasoning in conceptual change. Journal of Research in Science Teaching, 30(9), 1073-1086. Lawson, A.E. (1999). What should students learn about the nature of science and how should we teach it? Journal of College Science Teaching, 28(6), 401-411. Musheno, B.V., & Lawson, A.E. (1999). Effects of learning cycle and traditional text on comprehension of science concepts by students at differing reasoning levels. Journal of Research in Science Teaching, 36(1), 23-37. Kwon, Yong-Ju & Lawson, A.E. (2000). Linking brain growth with scientific reasoning ability and conceptual change during adolescence. Journal of Research in Science Teaching, 37(1), 44-62.

xvi

Lawson, A.E. (2000). The generality of hypothetico-deductive reasoning: Making scientific thinking explicit. The American Biology Teacher, 62(7), 482-495. Lawson, A.E., Clark, B., Cramer-Meldrum, E., Falconer, K.A., Kwon, Y.J., & Sequist, J.M. (2000). The development of reasoning skills in college biology: Do two levels of general hypothesis-testing skills exist? Journal of Research in Science Teaching, 37(1), 81-101. Lawson, A.E., Alkhoury, S., Benford, R., Clark, B. & Falconer, K.A. (2000). What kinds of scientific concepts exist? Concept construction and intellectual development in college biology. Journal of Research in Science Teaching, 37(9), 996-1018. Lawson, A.E. (2000). How do humans acquire knowledge? And what does that imply about the nature of knowledge? Science & Education, 9(6), 577-598. Lawson, A.E. (2001). Promoting creative and critical thinking in college biology. Bioscene: Journal of College Biology Teaching, 27(1), 13-24. Lawson, A.E. (2002). What does Galileo's discovery of Jupiter's moons tell us about the process of scientific discovery? Science & Education, 11, 1-24.

Anton E. Lawson Department of Biology Arizona State University Tempe, AZ, USA 85287-1501 September, 2002 [email protected]

CHAPTER 1 HOW DO PEOPLE LEARN?

1. INTRODUCTION Years ago while teaching junior high school math and science, two events occurred that made a lasting impression. The first occurred during an eighth grade math class. We had just completed a chapter on equivalent fractions and the students did extremely well on the chapter test. As I recall, the test average was close to 90%. The next chapter introduced proportions. Due to the students' considerable success on the previous chapter and due to the similarity of topics, I was dumbfounded when on this chapter test, the test average dropped below 50%. What could have caused such a huge drop in achievement? The second event occurred during a seventh grade science class. I cannot recall the exact topic, but I will never forget the student. I was asking the class a question about something that we had discussed only the day before. When I called on a red-haired boy named Tim, he was initially at a loss for words. So I rephrased the question and asked again. Again Tim was at a loss for words. This surprised me because the question and its answer seemed, to me at least, rather straightforward, and Tim was a bright student. So I pressed on. Again I rephrased the question. Surely, I thought, Tim would respond correctly. Tim did respond. But his response was not correct. So I gave him some additional hints and tried again. But this time before he could answer, tears welled up in his eyes and he started crying uncontrollably. I was shocked by his tears and needless to say, have never again been so persistent in putting a student on the spot. However, in my defence, I was so certain that I could get Tim to understand and respond correctly that it did not dawn on me that I would fail. What could have gone wrong? Perhaps you, like me, have often been amazed when alert and reasonably bright students repeatedly do not understand what we tell them, in spite of having told them over and over again, often using what we believe to the most articulate and clear presentations possible, sometimes even with the best technological aids. If this sounds familiar, then this book is for you. The central pedagogical questions raised are these: Why does telling not work? Given that telling does not work, what does work? And given that we can find something that does work, why, in both psychological and neurological terms, does that something work? In short, the primary goal is to explicate a theory of development, learning and scientific discovery with implications for teaching mathematics and science. The theory will be grounded in what is currently known about brain structure and function. In a sense, the intent is to help teachers better

1

2

CHAPTER

1

understand effective teaching methods as well as provide both psychological and neurological level explanations for why those methods work. We begin with a brief look at three alternative views of how people learn. This will be followed by a discussion of initial implications for higher-order cognition and for math and science instruction. Chapter 2 will introduce neural network theory with the intent of explaining learning in neurological terms. Subsequent chapters will expand on these and related ideas in the context of math and science instruction and in the context of scientific discovery. 2. EMPIRICISM, INNATISM AND CONSTRUCTIVISM An early answer to the question of how people learn, known as empiricism, claims that knowledge is derived directly from sensory experience. Although there are alternative forms of empiricism espoused by philosophers such as Aristotle, Berkeley, Hume and Locke of Great Britain, and by Ernst Mach and the logical positivists of Austria, the critical point of the empiricist doctrine is that the ultimate source of knowledge is the external world. Thus, the essence of learning is the internalization of representations of the external world gained primarily through keen observation. Innatism in its various forms stands in stark opposition to empiricism. Innatism's basic claim is that knowledge comes from within. Plato, for example, argued for the existence of innate ideas that "unfold" with the passage of time. For a more modern innatist view see, for example, Chomsky and Foder (in Piattelli-Palerini, 1980). A third alternative, sometimes referred to as constructivism, argues that learning involves a complex interaction of the learner and the environment in which contradicted self-generated behaviors play a key role (cf., Piaget, 1971a; Von Glasersfeld, 1995; Fosnot, 1996).1 What are we to make of these widely divergent positions? Consider the following examples. Van Senden (in Hebb, 1949) reported research with congenitally blind adolescents who had gained sight following surgery. Initially these newly sighted adolescents could not visually distinguish a key from a book when both lay on a table in front of them. They were also unable to report seeing any difference between a square and a circle. Only after considerable experience with the objects, including touching and holding them, were they able to "see" the differences. In a related experiment, microelectrodes were inserted into a cat's brain (Von Foerster, 1984). The cat was then placed in a cage with a lever that dispensed food when pressed, but only when a tone of 1000 h2 was produced. In other words, to obtain food the cat had to press the lever while the tone was sounding. Initially the electrodes indicated no neural activity due to the tone. However, the cat eventually learned to press the lever at the correct time. And from that point on, the microelectrodes showed significant neural activity when the tone sounded. 1 A philosophical examination of alternative forms of constructivism can be found in Matthews (1998). Discussion of some of these alternatives will be saved for Chapter 11. For now it suffices to say that the present account rejects extreme forms of constructivism that in turn reject or downplay the importance of the external world in knowledge acquisition.

HOW DO PEOPLE LEARN?

3

In other words, the cat was "deaf" to the tone until the tone was of some consequence to the cat! In more general terms, it appears that a stimulus is not a stimulus unless some prior "mental structure" exists that allows its assimilation. What about the innatist position? Consider another experiment with cats. In this experiment one group was reared in a normal environment. Not surprisingly, cells in the cats' brains became electrically active when the cats were shown objects with vertical lines. Another group was reared to the same age in an artificial environment that lacked vertical lines. Amazingly, the corresponding cells of these cats showed no comparable activity when they were shown identical objects. Thus, in this case at least, it would seem that the mere passage of time is not sufficient for the cat's brain cells to become "operational," i.e., for their mental structures to "unfold." Next, consider a human infant learning to orient his bottle to suck milk. Jean Piaget made several observations of his son Laurent from seven to nine months of age. Piaget (1954, p. 31) reports as follows: From 0:7 (0) until 0:9 (4) Laurent is subjected to a series of tests, either before the meal or at any other time, to see if he can turn the bottle over and find the nipple when he does not see it. The experiment yields absolutely constant results; if Laurent sees the nipple he brings it to his mouth, but if he does not see it he makes no attempt to turn the bottle over. The object, therefore, has no reverse side or, to put it differently, it is not three-dimensional. Nevertheless Laurent expects to see the nipple appear and evidently in this hope he assiduously sucks the wrong end of the bottle.

Laurent's initial behavior consists of lifting and sucking whether the nipple is properly oriented or not. Apparently Laurent does not notice the difference between the bottom of the bottle and the top and/or he does not know how to modify his behaviour to account for presentation of the bottom. Thanks to his father, Laurent has a problem. Let's return to Piaget's experiment to see how the problem was solved. On the sixth day when the bottom ofthe bottle is given to Laurent".... he looks at it, sucks it (hence tries to suck glass!), rejects it, examines it again, sucks it again, etc., four or five times in succession" (p.127). Piaget then holds the bottle out in front of Laurent and allows him to simultaneously look at both ends. Laurent's glare oscillates between the bottle top and bottom. Nevertheless, when the bottom is again presented, he still tries to suck the wrong end. The bottom of the bottle is given to Laurent on the 11th, 17th, and 21st days of the experiment. Each time Laurent simply lifts and sucks the wrong end. But on the 30th day, Laurent "...no longer tries to suck the glass as before, but pushes the bottle away, crying" (p. 128). Interestingly, when the bottle is moved a little farther away, "...he looks at both ends very attentively and stops crying" (p. 128). Finally, two months and ten days after the start of the experiment when the bottom of the bottle is presented, Laurent is successful in first flipping it over as he "...immediately displaces the wrong end with a quick stroke of the hand, while looking beforehand in the direction of the nipple. He therefore obviously knows that the extremity he seeks is at the reverse end of the object" (pp. 163-164). Lastly, consider a problem faced by my younger son when he was a 14-month old child playing with the toy shown in Figure 1. Typically he would pick up the cylinder

4

CHAPTER 1

sitting at the top left and hunt for a hole to drop it in. At first, he was unable to locate the correct hole even though it was directly below where he had just picked up the cylinder. Even, if by chance, he happened to find the correct hole, he was unable to orient the cylinder to make it fit. Nevertheless, with my help, he achieved some success. When he placed the cylinder above the correct hole, I gently pushed the object so that it would fit. Then, when he let go, the cylinder dropped out of sight. He was delighted. Success! Next, he picked up the rectangular solid. Which hole do you think he tried to drop it in? Should he drop it into the hole below the rectangular solid? He did not even consider that hole even though (to us) it clearly is the correct choice. Instead, he tried repeatedly to drop it into the round hole. Presumably this was because that behavior (placing an object above the round hole and letting go) had previously led to success. In other words, he responded to the new situation by using his previously successful behavior. Of course when the rectangular object was placed over the round hole, it did not fit. Hence, his previously successful behavior was no longer successful. Instead it was "contradicted." Further, only after numerous contradictions was he willing to try another hole. I tried showing him which holes the various objects would go into, but to no avail. He had to try it himself - he had to act - to behave. In other words, the child learned from his behaviours. Only after repeated incorrect behaviors and contradictions did he find the correct holes.

The previous examples suggest that knowledge acquisition is not merely a matter of direct recording of sensory impressions, nor is the mere passage of time sufficient for

HOW DO PEOPLE LEARN?

5

innate structures to become functional. Rather, acquiring new knowledge appears to involve a complex "construction" process in which initially undifferentiated sensory impressions, properties of the developing organism's brain and the organism's unsuccessful (i.e., contradicted) behaviors interact in a dynamic and changing environment. 3.

AN EXPLORATION INTO KNOWLEDGE CONSTRUCTION

To provide an additional insight into the knowledge construction process, take a few minutes to try the task presented in Figure 2. You will need a mirror. Once you have a mirror, place the figure down in front of it so that you can look into the mirror at the reflected figure. Read and follow the figure's reflected directions. Look only in the mirror - no fair peeking directly at your hand. When finished, read on.

6

CHAPTER 1

How did you do? If you are like most people, the task proved rather difficult and frustrating. Of course, this should come as no surprise. After all, you have spent a lifetime writing and drawing without a mirror. So what does this mirror-drawing task reveal about learning? I think it reveals the basic knowledge construction pattern depicted in Figure 3 and described as follows: First, the reflected images are "assimilated" by specific mental structures that are currently part of your long-term memory. Assimilation is an immediate, automatic and subconscious process. The activated mental structure then drives behavior that, in the past, has been linked to a specific consequence (i.e., an actual outcome of that behavior when used in the prior contexts). Thus, when the structure is used to drive behavior in the present context, the behavior is linked to those prior consequences. In this sense, the behavior carries with it an expectation, a prediction, i.e., what you expect/predict you will see as a consequence of the behavior. All is well if the behavior is successful - that is if the actual outcome matches the expected outcome. However, if unsuccessful, that is if the actual outcome does not match the expectation/prediction (e.g., you move your hand down and to the right and you expect to see a line drawn up and to the left, but instead you see one drawn up and to the right), contradiction results. This contradiction then drives a subconscious search for another mental structure and perhaps drives a closer inspection of the figure until either another structure is found that works (in the sense that it drives successful, noncontradicted behavior), or you become so frustrated that you quit. In which case, your mental structures will not undergo the necessary change/accommodation. In other words, you won't learn to draw successfully in a mirror. The above process can be contrasted with one in which the learner first looks at a reflected image. But not being certain how to draw the image, s/he looks again and again. With each additional look, the learner gathers more and more information about the image until s/he is confident that s/he can draw it successfully. Finally, at this point, the learner acts and successfully draws the reflected image. In contrast with the trialand-error process depicted in Figure 2, this view of learning can be characterized as inductive. Which process best characterizes your efforts at mirror drawing? Quite obviously, mirror drawing is a sensory-motor task that need not involve language. Nevertheless, if we were try to verbalize the steps involved in one attempt to draw a diagonal line, they may go something like this: If...I have assimilated the present situation correctly, (initial idea) and...I move my hand down and to the right, (behavior) then...I should see a diagonal line go up and to the left. (expectation) But...the actual line goes up and to the right! (actual outcome) Therefore...I have not assimilated the situation correctly. I need to try something else. (conclusion) The important point is that the mind does not seem to work the way you might think. In other words, the mind does not prompt you to look, look again, and look still

HOW DO PEOPLE LEARN?

7

again until you somehow derive a successful behaviour from the environment in some sort of inductivist manner. Rather, the mind seems to prompt you to look and as a consequence of this initial look, the mind generates an initial idea that then drives behavior. Hopefully the behavior is successful. But sometimes it is not. In other words, you tried something and found it in error. So the contradicted behavior then prompts the mind to generate another idea and so on until eventually the resulting behavior is not contracted. In short, we learn from our mistakes - from what some would call trail and error.

8

CHAPTER 1

4. IS THE IF/THEN/THEREFORE PATTERN ALSO AT WORK IN PRACTICAL PROBLEM SOLVING? Can we find this pattern of If/then/Therefore thinking in cases of everyday problem solving? Consider a personal example that we might call the case of the unlit barbecue. Before I arrived home one evening, my wife had lit the gas barbecue in the backyard and put some meat on for dinner. Upon arriving, she asked me to check the meat. When doing so, I noticed that the barbecue was no longer lit. It was windy so I suspected that the wind had blown out the flames - as it had a few times before. So I tried to relight the barbecue by striking a match and inserting its flame into a small "lighting" hole just above one of the unlit burners. But the barbecue did not relight. I tried a second, and then a third match. But it still did not relight. At this point, I suspected that the tank might be out of gas. So I lifted the tank and sure enough it lifted easily - as though it were empty. I then checked the lever-like gas gauge and it was pointed at empty. So it seemed that the barbecue was no longer lit, not because the wind had blown out its flames, but because its tank was out of gas. What pattern of thinking was guiding this learning? Retrospectively, it would seem that thinking was initiated by a causal question, i.e., why was the barbecue no longer lit? In response to this question, my reconstructed thinking goes like this:

If...the wind had blown out the flames, (wind hypothesis) and...a match is used to relight the barbecue, (test condition) then...the barbecue should relight. (expected result) But...when the first match was tried, the barbecue did not relight. (observed result) Therefore...either the wind hypothesis is wrong or something is wrong with the test. Perhaps the match flame went out before it could ignite the escaping gas. This seems plausible as the wind had blown out several matches in the past. So retain the wind hypothesis and try again. (conclusion) Thus, if...the wind had blown out the flames, and...a second match is used to relight the barbecue, then...the barbecue should relight. But...when the second match was used, the barbecue still did not relight. Therefore...once again, either the wind hypothesis is wrong or something is wrong with the test. Although it appeared as though the inserted match flame reached the unlit burner, perhaps it nevertheless did get blown out. So again retain the wind hypothesis and repeat the experiment. But this time closely watch the match flame to see if it does in fact reach its destination. Thus, if...the wind had blown out the flames, and...a third match is used to relight the barbecue while closely watching the flame,

HOW DO PEOPLE LEARN?

9

then...the flame should reach its destination and barbecue should relight. But...when the third match was used while closely watching the flame, the flame appeared to reach its destination, but the barbecue still did not relight. Therefore...apparently there was nothing wrong with the test. Instead the wind hypothesis is probably wrong and another hypothesis is needed. Perhaps the tank was out of gas. Thus, if...the tank is out of gas, (empty-tank hypothesis) and...the tank is lifted, then...it should feel light and should lift easily. And...when the tank was lifted, it did feel light and did lift easily. Therefore...the empty tank hypothesis is supported. Further, if...the tank is out of gas, and...the gas gauge is checked, then...it should be pointed at empty. And...it was pointed at empty. Therefore...the empty-tank hypothesis is supported once again. 5. THE ELEMENTS OF LEARNING

The introspective analysis suggests that learning (i.e., knowledge construction) involves the generation and test of ideas and takes the form of several If/then/Therefore arguments that can be called hypothetico-predictive (or hypothetico-deductive if you prefer). However, notice that the attainment of evidence contradicting the initial wind explanation (i.e., hypothesis) did not immediately lead to its rejection. This is because the failure of an observed result to match an expected result can arise from one of two sources - a faulty explanation or a faulty test. Consequently, before a plausible explanation is rejected, one has to be reasonably sure that the test was not faulty. In short, learning seems to involve the following elements: 1. Making an Initial Puzzling Observation - In this case, the puzzling observation is that the barbecue is no longer lit. The observation is puzzling because it is unexpected (i.e., I would not expect my wife to be trying to cook meat on an unlit grill). Unexpected observations are cognitively motivating in the sense that they require an explanation. Of course in this instance, motivation can also come from one's hunger and/or a desire to keep one's wife happy. 2. Raising a Causal Question - Why is the barbecue no longer lit? In this case, the causal follows more or less automatically from the puzzling observation. However, in other instances, generating a clear statement of the causal question may be much more difficult. 3. Generating a Possible Cause (an explanation) - In this case the initial explanation (i.e., hypothesis) was that the barbecue was no longer lit because the

10

4.

5.

6.

7.

CHAPTER 1

wind had blown out its flames. The process of explanation/hypothesis generation is seen as one involving analogies, analogical transfer, analogical reasoning i.e., borrowing ideas that have been found to "work" in one or more past related contexts and using them as possible explanations/solutions/hypotheses in the present context (cf., Biela, 1993; Bruner, 1962; Dreistadt, 1968; Finke, Ward & Smith, 1992; Gentner, 1989; Hestenes, 1992; Hoffman, 1980; Hofstadter, 1981; Holland, Holyoak, Nisbett & Thagard, 1986; Johnson, 1987; Koestler, 1964; Wong, 1993). Presumably the wind explanation was based on one or more previous experiences in which the wind had blown out flames of one sort or another including the barbecue's flames. Presumably the empty-tank explanation was similarly generated. In other words, a similar experience was recalled (e.g., a car's gas empty tank led to a failure of its engine to start) and used this as the source of the empty-tank explanation used in the present context. Supposing that the Explanation Under Consideration is Correct and Generating a Prediction - This supposition is necessary so that the tentative explanation can be tested and perhaps be found incorrect. A test requires imagining relevant condition(s) that along with the explanation allows the generation of an expected/predicted result (i.e., a prediction). This aspect of the learning process is reminiscent ofAnderson's If/and/then production systems (e.g., Anderson, 1983). Importantly, the generation of a prediction (sometimes referred to as deduction) is by no means always automatic. People often generate explanations that they fail to test either because they do not want to or because they cannot derive/deduce a testable prediction. Conducting the Imagined Test - The imagined test must be conducted so that its expected/predicted result can be compared with the observed result of the actual test. Comparing Expected and Observed Results - This comparison allows one to draw a conclusion. A good match means that the tested explanation is supported, but not proven. While a poor match means that something is wrong with the explanation, the test, or with both. In the case of a good match, the explanation has not been "proven" correct with certainty because one or more un-stated and perhaps un-imagined alternative explanations may give rise to the same prediction under this test condition (e.g., Hempel, 1966; Salmon, 1995). Similarly, a poor match cannot "disprove" or falsify an explanation in any ultimate sense. A poor match cannot be said to falsify with certainty because the failure to achieve a good match may be the fault of the test condition(s) rather than the fault of the explanation (e.g., Hempel, 1966; Salmon, 1995). Recycling the Procedure - The procedure must be recycled until an explanation is generated, which when tested, is supported on one or more occasions. In the present example, the initial conclusion was that the test of the wind hypothesis was faulty. Yet on repeated attempts and a closer inspection of the test, the wind hypothesis was rejected, which allowed the generation, test, and support of the empty-tank hypothesis.

HOW DO PEOPLE LEARN?

11

In this case at least, learning required feedback from the external world (albeit filtered through sense receptors). Thus, the fact that the barbecue would not relight, in spite of repeated attempts, was the key sensory evidence that eventually led to rejection of the wind hypothesis. And only after the wind hypothesis was rejected, was the alternative empty-tank hypothesis generated and tested.

6. TWO TYPES OF KNOWLEDGE Cognitive science distinguishes two types of knowledge that can be constructed, declarative and procedural, also referred to as figurative and operative (e.g., Piaget, 1970). The distinction is essentially between knowing that (e.g., I know that London is the capital of the United Kingdom, and animals inhale oxygen and expel carbon dioxide) and knowing how (e.g., I know how to ride a bicycle, to count, to conduct a controlled experiment). According to Anderson (1980): "Declarative knowledge comprises the facts that we know; procedural knowledge comprises the skills we know how to perform" (p. 222). Declarative knowledge is explicit in the sense that we generally know that we have it and when it was acquired. The word "learning" is often used in conjunction with the acquisition/construction of declarative knowledge (e.g., I just learned that Joe and Diane got married last Thursday) and its conscious recollection depends on the functional integrity of the medial temporal lobe (Squire & Zola-Morgan, 1991). On the other hand, procedural knowledge, which is expressed through performance, is often implicit in the sense that we may not be conscious that we have it or precisely when it was acquired. The word "development" is often used in conjunction with the acquisition/construction of procedural knowledge (e.g., Ralph has developed considerable golfing skill during the past few years; some students are better at solving math problems than others). Importantly, storage and recollection of procedural knowledge is independent of the medial temporal lobe, thus depends on other brain systems such as the neostriatum (Squire & Zola-Morgan, 1991). As we have seen, the acquisition/construction of declarative knowledge (e.g., the cause of the unlit barbecue is a lack of gas) depends in part on one's ability to generate and test ideas and reject those that lead to contradicted predictions. Thus, as one gains skill in generating and testing ideas, declarative knowledge acquisition/construction becomes easier. This view is consistent with Piaget's when he claimed that "learning is subordinated to development" (Piaget, 1964, p. 184), a view supported by numerous studies that have found that, following instruction, students who lack reasoning skill do more poorly on measures of conceptual understanding than their more skilled peers (e.g., Cavallo, 1996; Lawson et al., 2000; Shayer & Adey, 1993). But all of this is getting us somewhat ahead of the story. Let's first discuss Piaget's brand of constructivism in some detail before we consider what might be taking place inside the brain in neurological terms.

12

CHAPTER 1

7. PIAGET'S CONSTRUCTIVISM Bringuier: In fact, there's a single word for the whole of your work - a word I once heard you use; it's "constructivism." Piaget: Yes, that's exactly right. Knowledge is neither a copy of the object nor taking consciousness of a priori forms predetermined in the subject; it's a perpetual construction made by exchanges between the organism and the environment, from the biological point of view, and between thought and its object, from the cognitive point of view. (Bringuier, 1980, p. 110)

Because Piaget was one of the first and foremost investigators attempting to answer epistemological questions by scientific means, his brand of constructivism with its selfregulation theory deserves special consideration. Piaget began his professional studies as a biologist. So, not surprisingly, his psychological views were inspired by biological theories, particularly those of embryology, development, and evolution. In fact, Piaget's thinking was firmly grounded in the assumption that intelligence is itself a biological adaptation. Thus, he believed that the same principles apply to biological evolution and to intellectual development. As Piaget put it: "Intelligence is an adaptation to the external environment just like every other biological adaptation" (Bringuier 1980, p. 114). In other words, Piaget's basic assumption is that intellectual development can be understood in the same, or analogous, terms as the evolutionary acquisition of a hard protective shell, strong leg muscles, or keen vision. In Piaget's view there are at least two biological theories that should be considered to explain the evolutionary development, hence, by analogy, there at least two psychological theories that should be considered to explain intellectual development. The biological theories are neo-Darwinism and genetic assimilation. Piaget (1952) referred to the respective psychological theories as pragmatism and self-regulation (sometimes equilibration). Neo-Darwinism (neo because Darwin knew nothing ofthe mechanics of genetics or mutations at the time he wrote Origin of Species) proposes that evolution occurs through the natural selection of already-existing genetic variations initially produced by spontaneous mutations. In other words, mutations in the genome cause changes in observable characteristics that are then selectively evaluated by the environment (Figure 4). Pragmatism, the psychological analogue to neo-Darwinism, claims that random, non-directional changes in mental structures occur. A new mental structure then drives a new behavior. The new behavior is either successful and retained or unsuccessful and relinquished. Thus, new mental structures are internal in origin but the environment plays an active role by selecting only the appropriate structures for retention.

HOW DO PEOPLE LEARN?

13

7.1 How Do Limnaea Snails Adapt to Changing Environments? The validity of neo-Darwinism as an explanation for organic evolution is undisputed among modern biologists, yet many readily acknowledge that natural selection is by no means the final word. There are a number of instances of biological

14

CHAPTER 1

adaptation that cannot be explained solely terms of natural selection. Piaget himself investigated the adaptation of a variety of aquatic snails to wave-pounded and calm environments in which changes in shell shape cannot be explained solely in terms of after-the-fact natural selection (Piaget, 1929a;1929b). We will consider these data in some detail. Snails of the genus Limnaea are found in almost all European lakes including those in Switzerland where Piaget made his initial observations. The snails are famous for their variability in shell shape. Those living in calm waters are elongated while those living on wave-battered shorelines have a contracted, more globular, shape (Figure 5).

Piaget found that offspring of the elongated form, when reared in laboratory conditions simulating the wave-battered shoreline, developed the contracted form. The contracted form is due to a contraction of the columellar muscle that holds the snails more firmly to the bottom whenever a wave threatens to dislodge them. As a consequence of muscle contraction, the shell develops the contracted form as it grows. Thus, in the lab the contracted shell form is a phenotypic change. However, when the eggs of the contracted form were taken to the laboratory and reared in calm conditions, the offspring retained the contacted phenotype through several generations. This means that the phenotypic change has become genetically fixed. Therefore, we have an

HOW DO PEOPLE LEARN?

15

excellent example of a characteristic that can be acquired in the course of a lifetime that has become genetically fixed. Can this phenomenon be explained by neo-Darwinian theory? Piaget argues that it cannot because in the past when the elongated forms moved into wave-battered environments there would have been no need for natural selection of the contracted form to make it a genotypic trait (Piaget, 1952; 1975; 1978). In fact, natural selection for snails having the contracted genotype would presumably be impossible because there would have been nothing to select. In wave-battered environments, all of the snails with either genotype would be contracted! How then could the contracted phenotype have become incorporated into the genome?

7.2 Waddington's Theory of Genetic Assimilation The generally accepted answer to this question among evolutionary biologists draws heavily on the work of C. H. Waddington and his theory of genetic assimilation (Waddington, 1966). Although Waddington's theory allows for the assimilation of genes insuring the inheritance of initially acquired characteristics, it does so through natural selection, but not of the relatively simple sort envisioned by Darwin. In this sense, genetic assimilation represents a differentiation of neo-Darwinism rather than a contradiction to it. Genetic assimilation involves the natural selection of individuals with a tendency to develop certain beneficial characteristics. As such, genetic assimilation is a widely accepted theory of gene modification that appears as matter of course in modern textbooks of evolutionary biology. To understand genetic assimilation, we first need to consider embryological development and Waddington's concept of canalization. Canalization. The fertilized egg is a single cell. As egg cell divides, the resulting cells differentiate into a myriad of cell types such as skin, brain, and muscle cells. The developing embryo has a remarkable ability to buffer itself against environmental disturbances to insure that "correct" cell types are produced. This is evidenced even before the first cell divides. For example, the egg cell contains definite regions of cytoplasm. When an egg cell is centrifuged, the cytoplasmic regions are displaced. But if the egg is then left alone, the regions gradually move back to their original locations. This self-righting (self-regulating) tendency is also found in eggs cut in half. Identical human twins are produced by one egg cell that divides such that each twin arises from what one might expect to produce only half of an individual. The term Waddington gave to the developing organism's ability to withstand perturbations to the normal course of development was canalization. As Waddington (1966) described it: The region of an early egg that develops into a brain or a limb or any other organ follows some particular pathway of change. What we have found now is that these pathways are 'canalized,' in the sense that the developing system has a built in tendency to stick to the path, and is quite difficult to divert from it by any influence, whether an

16

CHAPTER 1

external one like an abnormal temperature or an internal one like the presence of a few abnormal genes. Even if the developing system is forcibly made abnormal - for instance, by cutting part of it away - it still tends to return to the canalized pathway and finish up as a normal adult. (p. 48)

Waddington pointed out that canalization is not complete. The developing system will not always end up as a properly formed adult. Yet the important point is that it has the tendency toward self-regulation, toward a final end product, even in the face of considerable variance in the paths taken. Waddington likened canalization to a ball rolling downhill with several radiating canals (Figure 6). As the ball rolls, internal (genetic) or external (environmental) factors can deflect it into one or another canal with the ball ending up at the bottom of only one canal. Waddington called the system of radiating canals the epigenetic landscape. To describe the development of an entire organism, a large number of epigenetic landscapes would be required - one for each characteristic.

Suppose, for example, an epigenetic landscape were constructed to represent the development of an individual's sex. The landscape would contain two canals, thus would dictate one of two end points - male or female. Genetic factors operate to deflect the ball into one canal. Thus, the normal adult ends up male or female (but not somewhere in between) despite intrusions at intermediate points that cause the ball to roll part way up the side of one canal. The environment might also cause the ball to be deflected into the other canal. Presumably this occurs in the marine worm Bonellia where the environment determines the individual's sex, but canalization usually insures

HOW DO PEOPLE LEARN?

17

a male or female - not an intersex. Figure 7 shows the female and male Bonellia worms. The larvae are free-swimming. If a larva settles down alone, it develops into a female. If, however, it lands on the proboscis of a female, it develops into a dwarf male.

According to Waddington, organisms vary in their ability to respond to environmental pressures due to differences in their epigenetic landscapes (e.g., the degree of canalization, the heights of thresholds, the number of alternative canals). Some individuals have well-canalized landscapes with few alternatives, hence are relatively unresponsive to environmental pressures. Compare the two epigenetic landscapes shown for the two first-generation individuals in Figures 8(A) and 8(B). Both have well-canalized landscapes with two alternatives, yet the threshold in early development of landscape H is higher than that in landscape L. Hence, an

18

CHAPTER 1

environmental pressure, depicted by the non-shaded arrow, will most likely fail to force the ball over the high threshold in H to produce the developmental modification (WA). On the other hand, in landscape L with its lower threshold, the same environmental pressure is more likely to push the ball over the threshold into another canal, thus produce the modification.

HOW DO PEOPLE LEARN?

19

Because of such differences, individuals vary in their ability to respond to environmental pressures. Some may acquire beneficial modifications, while others may acquire non-beneficial modifications, and still others may not change. Of course, individuals that acquire beneficial modifications have a better chance of survival and will be more likely to leave offspring. On the other hand, the poor responders are likely to die out. Hence landscape L with its ability to respond in a beneficial way is selected. As shown, the population becomes one in which all members have landscape L. At this point only the slightest genetic mutation (shaded arrow) will now push the ball over the threshold into the new canal. Once this happens the organism will develop the welladapted phenotype WA with or without the environmental pressure. In a sense, the selection for landscape L has put the developmental machine on hair trigger. Thus, several gene mutations, which appear random in terms of molecular structure, are likely to produce the well-adapted phenotype. Therefore, such mutations are not random in their adaptive effect. Instead, they produce positive modifications in the genome. The end result is that beneficial characteristics initially acquired in response to specific environmental pressures become assimilated into the genome. Although Waddington (1975) has stated that Piaget's studies of Limnaea represent one of the most thorough and interesting examples of genetic assimilation in naturally occurring populations, the biological literature is replete with additional natural and experimental examples (e.g., Clausen, Keck, & Hiesey, 1948; Waddington, 1959; Rendel, 1967; Futuyma, 1979). 8. PSYCHOLOGICAL SELF-REGULATION2 Figure 9 explicates psychological self-regulation as a process analogous to genetic assimilation. The analogue of the changing genotype during evolution is one's developing mental structures. The epigenetic landscape (itself shaped by the genes) corresponds to one's predisposition to acquire new behaviors determined by what Piaget (1971a, p. 22) has called "assimilation schemata." The phenotype corresponds to 2 The following discussion of psychological self-regulation differs in subtle ways from Piaget's conception. Piaget's conception of self-regulation is based upon his theory of biological phenocopy (see Piaget 1975, pp. 216-217; Piaget 1978. pp. 78-83; and Bringuier 1980, p. 113). As far as I am aware, phenocopy theory has not received favor among biologists. Therefore, the present discussion will be confined to self-regulation's relationship to genetic assimilation.

20

CHAPTER 1

overt behaviors. Thus, Figure 9(A) represents a situation in which the individual with assimilation schemata H is unresponsive to pressures imposed by experience and does not develop a new mental structure (WA). Interaction with the environment does not produce "disequilibrium" or subsequent mental accommodation. The individual is not "developmentally ready" because the assimilation schemata available are inadequate to assimilate the new experience. Presumably the available assimilation schemata are built up by the interplay between the individual's powers of coordination and the data of experience.

HOW DO PEOPLE LEARN?

21

Figure 9(B) on the other hand, represents an individual with assimilation schemata L able to respond to environmental pressures and acquire a new behavior. However, the newly acquired behavior has not yet been assimilated into a mental structure (i.e., the mental structure remains PA). The new behavior and the person's previous ways of thinking have not yet been integrated. The result is mental disequilibrium. With removal of environmental pressure, the individual is apt to revert to previous inappropriate behaviors just as the offspring of genetically elongated but phenotypically contracted snails will develop into the elongated form if reared in a calm environment. In the classroom students may be able to correctly solve a proportions problem if the teacher is there to suggest the procedure or if the problem is similar enough to ones previously solved. But if left on their own, use of the proportions strategy may never occur to the students because they have failed to comprehend why it was successful in the first place (i.e., it has never been integrated with previous thinking). Thus, Figure 9(B) represents a state of disequilibrium because a mismatch exists between the poorly adapted mental structure and the only occasionally successful behavior. Finally Figure 9(C) represents the restoration of equilibrium through a spontaneous, internal, yet directional, reorganization of a mental structure allowing the complete assimilation of the new behavior pattern into an accommodated mental structure. Thus, psychological assimilation corresponds to the entire process of the incorporation of new well-adapted behavior patterns (phenotypes) into one's mental structure (the genome) by way of a spontaneous accommodation of mental structure (the mutation). Hence, one does not have assimilation without accommodation. Piaget was fond of quoting the child who, when asked about the number of checkers in two rows of unequal length, responded correctly and reported, "Once you know, you know forever." Here is a child with an accommodated mental structure who had completely assimilated the notion of conservation of number.

9. INSTRUCTIONAL IMPLICATIONS The instructional importance self-regulation theory can be stated simply. If one adopts the pragmatic approach to education, then one is forced to wait until

22

CHAPTER 1

spontaneous and non-directional reorganizations of mental structures occur before learning can take place. The process is internal and not amenable to environmentalinstructional shaping. The teacher is relegated to the relatively unimportant position of simply telling a student when his ideas are right or wrong and cannot shape the direction of the student's thinking. But if one adopts self-regulation theory, then the teacher is not placed in a position of sitting idly by waiting for change to occur. Rather, the teacher knowledgeable of developmental pathways can produce the environmental pressures that place students into positions in which they can spontaneously reorganize their thinking along the path toward more complex and better-adapted thought processes. The teacher can be an instigator of disequilibrium and can provide pieces of the intellectual puzzle for the students to put together. Of course the ultimate mental reorganization will have to be accomplished by the students but the teacher is far from passive. He or she can set the process on hair trigger just as the directional natural selection of Waddington sets the genome on hair trigger. The key point is that external knowledge (that presented by the teacher) can become internalized if the teacher accepts the notion that self-regulation is the route to that internalization. This means that students should 1) be prompted to engage their previous ways of thinking about the situation to discover inadequacies, and 2) be given ample opportunities to think through the situation to allow the appropriate mental reorganization (accommodation), which in turn allows successful assimilation of the new situation. Let's consider how this might play out in the classroom. Many high school students and even a significant fraction of college students employ an additive strategy to solve the proportionality problem shown in Figure 10. As you can see, the problem involves two plastic cylinders equal in height but unequal in diameter. The students note that water from the wide cylinder at the fourth mark rises to the sixth mark when poured into the narrow cylinder. When asked to predict how high water at the sixth mark in the wide cylinder will rise when poured into the narrow cylinder, many students respond by predicting mark 8, "Because it raised 2 marks last time so it will raise 2 marks again."

HOW DO PEOPLE LEARN?

23

How can these additive students learn to use a proportions strategy? According to self-regulation theory, they must first discover the error of their previous thinking. In this case this they can simply pour the water into the narrow cylinder and discover that the water rises to mark 9 - instead of mark 8 as predicted. Even without pouring, the error can be discovered through a thought experiment. Suppose the water is poured from mark 6 in the narrow cylinder into the empty wide cylinder. Students using the additive strategy will predict a rise to mark 4 (i.e., 6 - 2 = 4). Suppose water is now poured from mark 4 in the narrow cylinder into the empty wide cylinder. Using the additive strategy students now predict a rise to mark 2 (i.e., 4 - 2 = 2). Finally, suppose that water is poured from mark 2 in the narrow cylinder into the empty wide cylinder. Use of the additive strategy leads one to predict a rise to mark 0 (i.e., 2 - 2 = 0). The water disappears! Of course additive students see the absurdity of the situation and are forced into mental disequilibrium. A more formal explication of the students' reasoning may look something like this: If...the difference in waters levels is always 2 marks, (initial strategy) and...water at mark 2 in the narrow cylinder is poured into the wide cylinder, then...it should rise to mark 0 (i.e., 2 - 2 = 0). In other words, the water should disappear. But...water cannot disappear merely by pouring it from one cylinder to another. Therefore...the difference in water levels must not always be 2 marks. At this point, the students are prepared for step 2, introduction of the "correct" way to think through the problem. Keep in mind, however, that according to the analogy, the students themselves must undergo a mental reorganization to appreciate your suggestions and assimilate the new strategy. This will not happen immediately. Rather, experience suggests that this requires considerable time and a repeated experience with the same strategy in a number of novel contexts (cf., Lawson & Lawson, 1979; Wollman & Lawson, 1978). The fact that the use of a variety of novel contexts is helpful (perhaps even necessary) is an argument in favor of breaking down traditional subject matter distinctions. For example, in a biology course one should not hesitate to present problems that involve proportions in comparing prices at the supermarket, altering recipes in cooking, comparing the rotations of coupled gears, balancing weights on a balance beam, estimating the frog population size in a pond, comparing the relative rates of diffusion of chemicals, and estimating gas mileage. If the range of problems types were confined to traditional biology subject matter, many students would fail to undergo the necessary mental reorganization and internalize the proportions strategy, hence learning and transfer would be limited. Although the previous example dealt with proportional reasoning (an aspect of logico-mathematical knowledge), self-regulation theory also deals with causal relationships. As Piaget (1975, p. 212) points out, "Now it is essential to note that this tendency to replace exogenous knowledge by endogenous reconstructions is not confined to the logico-mathematical realm but is found throughout the development of

24

CHAPTER 1

physical causality." Minstrell (1980) provides a lovely classroom example of using the theory to help students acquire physical understanding. Minstrell was trying to teach his high school physics students about the forces that keep a book "at rest" on a table. Before simply telling the students that the book remains at rest due to the presence of the equal and opposite forces of gravity (downward) and the table (upward), Minstrell asked his students what forces they thought were acting on the book. Many of the students believed that air pressing in from all sides kept the book from moving. Others imagined a combination of gravity and air pressure pushing downward. A few students also thought that wind or wind currents "probably from the side" could affect the book. The most significant omission seemed to be the students' failure to anticipate the table's upward force. Although some students did anticipate both downward and upward forces, most believed that the downward force must total more than the upward force "or the object would float away." After the crucial first step of identifying the students' initial misconceptions, Minstrell then took the class through a carefully planned sequence of demonstrations and discussions designed to provoke disequilibrium and initial mental reorganization, stopping along the way to poll the students for their current views. The key demonstrations included piling one book after another on a student's outstretched arm and hanging a book from a spring. The student's obvious expenditure of energy to keep the books up led some to admit the upward force. When students lifted the book already supported by the spring, the initial response was surprise at the ease at which it could be raised. "Oh my gosh! There is definitely a force by the spring." Although Minstrell admits that the series of demonstrations was not convincing to all, in the end about 90% of his students voiced the belief that there must be an upward force to keep the book at rest. Of course, instruction did not stop there. Nevertheless, the majority of Minstrell's students were well on the way to the appropriate mental accommodation. In short, the teacher who takes self-regulation theory to heart becomes a poser of questions, a provider of hints, a provider of materials, a laboratory participant, a class chairman and secretary. He/she gathers the class together and solicits data gathered and their meaning. Most importantly, the teacher is not a teller. He/she is a facilitator and director of learning. If materials are well chosen, good questions are posed, timely ideas are suggested, and students are prompted to think through questions, alternatives answers, and data, then much can be done to encourage the acquisition of more adaptive mental structures. In spite of the value of self-regulation theory for instruction, an important theoretical weakness exists in its origins. As discussed, the theory is based on biological analogies and on Piaget's belief that biological and intellectual development can be understood on the same or at least on analogous terms. Although analogies can be suggestive, they remain just that - suggestive. Further, no matter how suggestive Piaget's analogy may seem, the fact of the matter is that to understand classroom learning, intellectual development, and scientific discovery, we need to consider the organ in which that learning, development, and discovery actually take place. In other

HOW DO PEOPLE LEARN?

25

words, we need to consider what might be happening in the brain as knowledge is constructed. Hence, understanding the neurological basis of self-regulation will be the primary aim of Chapter 2.

This page intentionally left blank

CHAPTER 2 THE NEUROLOGICAL BASIS OF SELF-REGULATION

1. INTRODUCTION Chapter 1 argued that learning and development are constructive processes involving complex interactions within the maturing organism, its behaviors, and the environment. Piaget's theory of self-regulation explains much of what goes on during knowledge construction. However, as pointed out, Piaget's theory is based largely on evolutionary and developmental analogies, rather than on neural anatomy and physiology. Thus, the goal of the present chapter is to provide a more solid theoretical footing by exploring brain structure and function and their relationship to self-regulation. A considerable amount of progress has been made during the past 30 or so years in the related fields of neural physiology and neural modeling that allows us to begin to connect psychological phenomena with its neurological substrate. We begin with a discussion of how the brain processes visual input.

2. HOW DOES THE BRAIN PROCESS VISUAL INPUT? How the brain spontaneously processes visual input is the most thoroughly researched and understood area of brain research. In general, that research aims to develop and test neural network models that have become known as parallel distributed processing or connectionist models. As reviewed by Kosslyn & Koenig (1995), the ability to visually recognize objects requires participation of the six major brain areas shown in Figure 1. How do these six areas function to identify objects? First, sensory input from the eyes produces a pattern of electrical activity in an area referred to as the visual buffer, located in the occipital lobe at the back of the brain. This pattern of electrical activity produces a spatially organized image within the visual buffer (e.g., Daniel & Whitteridge, 1961; Tootell et al., 1982). Next, a smaller region within the occipital lobe, called the attention window, performs detailed processing (Possner, 1988; Treisman & Gelade, 1980; Treisman & Gormican, 1988). The activity pattern in the attention window is then simultaneously sent along two pathways on each side of the brain, one that runs down to the lower temporal lobe, and one that runs up to the parietal lobe. The lower temporal lobe, or ventral subsystem, analyses object properties, such as shape, color and texture, while the upper parietal lobe, or dorsal subsystem, analyses spatial properties, such as size and location (e.g., Desimone & Ungerleider, 1989; Farah, 1990; Haxby et

27

28

CHAPTER 2

al., 1991; Maunsell & Newsome, 1987; Ungerleider & Mishkin, 1982). Patterns of activity within the lower temporal lobe are matched to patterns stored in visual memory (e.g., Desimone et al., 1984; Desimone & Ungerleider, 1989; Miyashita & Chang, 1988). If a good match is found, the object is recognized. Otherwise, it is not. The dorsal subsystem of the parietal lobes encodes input used to guide movements such as those of the eyes or limbs. The neurons in that region fire just before movement, or register the consequences of movements (e.g., Andersen, 1987).

Outputs from the ventral and dorsal subsystems come together in what Kosslyn and Koenig call associative memory. Associative memory is located primarily in the hippocampus, the limbic thalamus and the basal forebrain (Miskin, 1978; Miskin & Appenzeller, 1987). The ventral and dorsal subsystem outputs are matched to patterns stored in associative memory. If a good match between output from visual memory and the pattern in associative memory is obtained, then the observer knows the object's name, categories to which it belongs, sounds it makes and so on. But if a good match is not obtained, the object remains unrecognized and additional sensory input must be obtained. Importantly, the search for additional sensory input is far from random. Rather, stored patterns are used to make a second hypothesis about what is being observed, and this hypothesis leads to new observations and to further encoding. In the words of

THE NEUROLOGICAL BASIS OF SELF-REGULATION

29

Kosslyn and Koenig, when additional input is sought, "One actively seeks new information that will bear on the hypothesis... The first step in this process is to look up relevant information in associative memory" (p. 57). Information search involves activity in the prefrontal lobes in an area referred to as working memory. Activating working memory causes an attention shift of the eyes to a location where an informative component should be located. Once attention is shifted, the new visual input is processed in turn. The new input is then matched to shape and spatial patterns stored in the ventral and dorsal subsystems and kept active in working memory. Again in Kosslyn & Koenig's words, "The matching shape and spatial properties may in fact correspond to the hypothesized part. If so, enough information may have accumulated in associative memory to identify the object. If not, this cycle is repeated until enough information has been gathered to identify the object or to reject the first hypothesis, formulate a new one, and test it" (p. 58). For example, suppose Joe, who is extremely myopic, is rooting around the bathroom and spots one end of an object that appears to be a shampoo tube. In other words, the nature of the object and its location prompt the spontaneous generation of a shampoo-tube hypothesis. Based on this initial hypothesis, as well as knowledge of shampoo tubes stored in associative memory, when Joe looks at the other end of the object, he expects to find a cap. Thus he shifts his gaze to the other end. And upon seeing the expected cap, he concludes that the object is in fact a shampoo tube. Or suppose you observe what your brain tells you is a puddle of water in the road ahead. Thanks to connections in associative memory, you know that water is wet. Thus, when you continue driving, you expect that your tires will splash through the puddle and get wet. But upon reaching the puddle, it disappears and your tires stay dry. Therefore, your brain rejects the puddle hypothesis and generates another one, perhaps a mirage hypothesis. The pattern of information processing involved in these examples can be summarized as follows: If... the object is a shampoo tube, (shampoo-tube hypothesis) and... Joe looks at the other end of the object, (imagined test) then... he should find a cap. (predicted result) And... upon looking at the other end (actual test), he does find a cap. (observed result) Therefore... the hypothesis is supported; the object is most likely a shampoo-tube. (conclusion) And for the second example: If... the object is a puddle of water, (puddle hypothesis) and... you continue driving toward it, (imagined test) then... your tires should splash through the puddle and they should get wet. (predicted result) But... upon reaching the puddle (actual test), it disappears and your tires do not get wet. (observed result)

30

CHAPTER

2

Therefore... the hypothesis is not supported; the object was probably not a puddle of water. (conclusion) In other words, as one seeks to identify objects, the brain generates and tests stored patterns selected from memory. Kosslyn and Koenig even speak of these stored patterns as hypotheses (although we should keep in mind that the term "hypothesis" is being used here its broadest sense and not as it is generally used in the sciences - to refer to a possible cause of some puzzling observation). Thus, brain activity during visual processing utilizes an If/then/Therefore pattern that can be characterized as hypothetico-predictive. One looks at part of an unknown object and the brain spontaneously and immediately generates an idea of what it is - a hypothesis. Thanks to links in associative memory, the hypothesis carries implied consequences (i.e., expectations/predictions). Consequently, to test the validity of the hypothesis, one can carry out a simple behavior to see if the prediction does in fact follow. If it does, one has support for the hypothesis. If it does not, then the hypothesis is not supported and the cycle repeats. Of course this is the same hypothetico-predictive pattern that we saw previously in the mirror drawing.

3. IS AUDITORY INPUT PROCESSED IN THE SAME

HYPOTHETICO-PREDICTIVE WAY? The visual system is only one of several of the brain's information processing systems. Is information processed in a similar hypothetico-predictive manner in other brain systems? Unfortunately, less is known about other systems, but the answer appears to be yes. For example, with respect to understanding the meaning of individual spoken words, Kosslyn & Koenig (1995) state: "Similar computational analyses can be performed for visual object identification and spoken word identification, which will lead us to infer analogous sets of processing subsystems." (p. 213) After providing details of their hypothesized word identification subsystem, Kosslyn & Koenig (1995) offer the following summary of what presumably happens when verbal input is inadequate to provide an initial match with verbal representations in associative memory: ...if the input is so degraded that there is no good match in the pattern activation subsystem, or there are several potential matches, the best-matching word will be sent to associative memory and treated as a hypothesis. The categorical look-up subsystem then accesses a description of distinctive properties of the sound of the word, which is used to prime the auditory pattern activation subsystem and to guide the auditory window to select additional properties represented in the auditory buffer. These properties are then encoded into the preprocessing subsystem and then the pattern activation subsystem, where they are included in the match process; this information is integrated with that extracted from the whole word, and serves to implicate a specific representation. This top-down search process is repeated until a single representation is matched, just as in vision. (pp. 237-238)

THE NEUROLOGICAL BASIS OF SELF-REGULATION

31

For our purposes, the details of this hypothesized word recognition subsystem are not important. Rather, what is important is that word recognition, like visual recognition, presumably involves brain activity in which hypotheses arise spontaneously, immediately, unconsciously and before any other activity. In other words, the brain does not make several observations before it generates a hypothesis of what it thinks is out there. The brain does not appear to operate in some sort of enumerative inductivist manner in which several observations are needed prior to hypothesis generation. Instead, while processing sensory information, the brain seems to function in a way that can be characterized as hypothetico-predictive. There is good reason in terms of human evolution why this would be so. If you were a primitive person and you look into the brush and see stripes, it would certainly be advantageous to get out of there quickly as the odds of being attacked by the tiger are high. And anyone programmed to look, look again, and look still again before generating the tiger hypothesis would most likely not survive long enough to pass on his plodding inductivist genes to the next generation. The next section will introduce key structures involved in neural signaling so that we can begin to understand what takes place at the level of neurons and neural systems during information processing and cognition.

4. KEY STRUCTURES INVOLVED IN NEURAL SIGNALING Figure 2 is a side view of the human brain showing the spinal cord, brain stem, and cerebral cortex. In general, the cortex is divided into a frontal portion containing neurons that control motor output and a rear portion that receives sensory input.

32

CHAPTER 2

The thalamus is a relay center at the top of the brain stem that transfers signals from the sense receptors to the sensory cortex. All sensory inputs, with the exception of smell, pass through one of 29 thalamic regions on the way to the cortex. One of the most important regions is the lateral geniculate nucleus, the relay station of the optic tract from the retina to the visual cortex (see Figure 3).

At the center of the brain stem from just below the thalamus down to the medulla (lowest segment of the brain stem) is the reticular formation. As we will see, the reticular formation plays a key role in neural networks by serving as a source of nonspecific arousal. Located in the inner surface of the deep cleft between the two brain hemispheres lies the hypothalamus. The hypothalamus appears to be the source of specific drive dipoles such as fear-relief and hunger-satisfaction, which also play a key role in the neural networks that will be developed.

5. NEURON SIGNALS AND LAYERS The basic unit of the functioning nervous system is the nerve cell or neuron. Although there are many types of neurons, they all share characteristics exemplified by pyramid cells found in the cerebral cortex (shown in Figure 4).

THE NEUROLOGICAL BASIS OF SELF-REGULATION

33

Pyramid cells consist of four basic parts, a cell body, and a set of dendrites, an axon or axons, and a set of terminal knobs. The dendrites and the cell body receive electrical signals from axons of other neurons. The axons, which may branch, conduct signals away from the cell body. When stimulated by incoming signals, the terminal knobs open small packets of chemical transmitter that, if released in sufficient quantity, cause the signal to pass across the gap (synapse) to the next neuron. A non-firing neuron has a slightly negative potential across its cell membrane (approximately -70mV), which is termed its resting potential. Incoming signals, which can be either excitatory or inhibitory, modify the resting potential in an additive fashion and induce what is referred to as the cell's generating potential. When the generating potential exceeds a certain threshold, a spike or action potential is generated in the cell body and travels down the axons. The action potential travels at a constant velocity with amplitude of up to about 50 Mv. Signals are emitted in bursts of varying frequency depending upon the amount of neuron depolarization. Presumably all of the information in the signal depends on burst frequency. Importantly, neurons are arranged in layers. Consider, for example, the neuron layers in the visual system. An initial layer of photoreceptors in the retina receives light. Excitation of retinal cells fires signals along the optic nerve to a layer of neurons located in the lateral geniculate nucleus (LGN). Cells of the LGN then process the signals and relay them to a third layer of cells in the visual cortex at the back of the brain. From the visual cortex, signals are transmitted back to the LGN and to additional neuron layers for further processing. The signals that are sent back to the LGN play a significant role by allowing the system to compare incoming signals with expectations acquired from prior

34

CHAPTER 2

learning. More will be said about this crucial comparison later (also see Grossberg, 1982 especially pp. 8-15 as well as several of Grossberg's and his colleagues' more recent publications available at http://cns-web.bu.edu). An excellent discussion of the neural anatomy relevant to learning and memory can also be found in Miskin & Appenzeller (1987).

6. NETWORK MODELING PRINCIPLES Table 1 (after Grossberg, 1982) lists crucial components and variables of neurons and layers of neurons as well as their physiological and psychological interpretation within neural network theory.

Consider the neuron in a collection of interacting neurons. The average generating potential of the neuron at node is signified by the stimulus or short-term memory (STM) trace. This activity can be sustained by a feedback loop. Thus STM is the property of any neuron where activity is sustained for a specific period of time. STM is not a single undetermined location in the brain into which a limited amount of information can be input and stored temporarily as has been a common hypothesis in cognitive psychology.

THE NEUROLOGICAL BASIS OF SELF-REGULATION

35

represents the signal that propagates along the axon from node to synapse knob The signal is a function of the activity at node The final extremely important neural variable is the synaptic strength, of knob is the average rate of transmitter release at the synapse. In other words, represents the ease with which signals traveling down can cause to fire. If the signals cause the knob to release a lot of transmitter (a large value for then signals are sent across the synapse and the next cell in line fires. If the signals do not cause the knob to release much transmitter (a small value for then signals will not cause to fire. Increases in represent modification of knobs that allow transmission of signals among neurons. Thus becomes the location of long-term changes in systems of neurons i.e., the long-term memory (LTM) of the system. In other words, learning can be understood as a biochemical modification of synaptic strengths. Consequently, as was the case for STM, neural network theory makes LTM a property of neuron connections rather than a single location in the brain.

6.1 Equations of Neural Activity and Learning Grossberg (1982) has proposed equations describing the basic interaction of the variables mentioned above. Of particular significance are equations describing changes in and in i.e., changes in short term memory (activity) and changes in long term memory (learning). In general, these equations, for a network with n nodes, are of the form:

Where the overdot represents a time derivative and i, j,= 1, 2,....n. The equations identify factors that drive a change in activity of and a change in rate of transmitter release at knob Equation (1) is referred to as the activity equation of because it identifies factors that cause changes in STM, while equation (2) is referred to as the learning equation because it identifies factors that cause changes in LTM. First consider equation (1), the activity equation. As mentioned, represents the initial level of activity of nodes represents a passive decay constant inherent in any dissipative system. The sign is negative indicating a drop in activity of across time due to the product of and In other words, if receives no additional input or feedback from itself, activity stops. represents inputs to the nodes from prior cells in the system mediated by their respective synaptic strengths The positive sign

36

CHAPTER

2

indicates that these signals increase the activity of cells Inputs are additive, hence their summation is called for. represents inhibitory node-node interactions of the network, hence the negative sign. Recall that inputs to neurons can be excitatory or inhibitory. Lastly, represents inputs to from sources outside the network (i.e., neurons other than those in layer Equation (2), the learning equation, identifies factors that modify the synaptic strengths of knobs represents the initial synaptic strength. is a decay constant thus is a forgetting or decay term. is the learning term as it drives increases in is the signal that has passed from node to knob The prime reflects the fact that the initial signal, may be slightly altered as it passes down represents the activity level of post-synaptic nodes that exceeds the firing threshold. Only activity above threshold can cause changes in In short, the learning term indicates that for information to be stored in LTM, two events must occur simultaneously. First, signals must be received at Second, nodes must receive inputs from other sources that cause the nodes to fire. When these two events drive activity at above a specified constant of decay, the increase, i.e., the network learns.

7. HOW DOES EXPERIENCE STRENGTHEN CONNECTIONS? Learning occurs when synaptic strengths increase, that is, when transmitter release rate increases make signal transmission from one neuron to the next easier. Hence learning is, in effect, an increase in the number of "operative" connections among neurons. Thus, in order to have a "mental structure" become more complex, transmitter release rates must increase at a number of knobs so that the signals can be easily transmitted across synapses that were previously there, but inoperative. This view reveals a sense in which innatism is correct. If one equates mental structures with already present but inoperative synapses, then mental structures are present prior to any specific experience. But the view also reveals why experience is necessary to "strengthen" some of the connections to make them operative. How does experience strengthen connections? Consider Pavlov's classical conditioning experiment in which a dog is stimulated to salivate by the sound of a bell. As you may recall, when Pavlov first rang the bell, the dog, as expected, did not salivate. However, upon repeated simultaneous presentation of food, which did initially cause salivation, and bell ringing, the ringing alone eventually caused salivation. In Pavlovian terms, the food is the unconditioned stimulus (US). Salivation upon presentation of the food is the unconditioned response (UCR). And the bell is the conditioned stimulus (CS). In general terms, Pavlov's experiment showed that when a conditioned stimulus (e.g., a bell) is repeatedly paired with an unconditioned stimulus (e.g., food), the conditioned stimulus alone will eventually evoke the unconditioned response (e.g., salivation). How can the unconditioned stimulus do this? Figure 5 shows a simple neural network capable of explaining classical conditioning. Although the network is depicted as just three cells A, B, and C, each cell represents many neurons of the type A, B and C. Initial food presentation causes cell C to fire. This creates a

THE NEUROLOGICAL BASIS OF SELF-REGULATION

37

signal down its axon that, because of prior learning (i.e., a relatively large causes the signal to be transmitted to cell B. Thus cell B fires and the dog salivates. At the outset, bellringing causes cell A to fire and send signals toward cell B. However, when the signal reaches knob its synaptic strength is not large enough to cause B to fire. So the dog does not salivate. However, when the bell and the food are paired, cell A learns to fire cell B according the learning equation. Cell A firing results in a large and the appearance of food results in a large Thus the product is sufficiently large to drive an increase in to the point at which it alone causes node to fire and evoke salivation. Food is no longer needed. The dog has learned to salivate at the ringing of a bell. The key theoretical point is that learning is driven by simultaneous activity of preand post synaptic neurons, in this case activity of cells A and B.

8. A NEURAL EXPLANATION OF LAURENT'S LEARNING

8.1 The Basic Pattern Can network principles also explain human learning? For example, can they explain how Laurent learned to flip his bottle to suck milk? Modeling such simple learning will provide a framework to understand neural events that may be involved in more advanced learning. As you recall from Chapter 1, Laurent's initial behavior consisted of lifting and sucking whether the bottle's nipple was oriented properly or not. Apparently Laurent did not notice the difference between the bottle's top and bottom. Nor did he know how to modify his behavior when the bottom was presented. In order to construct a neural model of Laurent's learning, we need to be clear on just what new behavior Laurent must acquire. At the outset Laurent knew how to flip the bottle to orient it properly for sucking provided the nipple was visible. He also knew how to bring the bottle to his mouth and

CHAPTER 2

38

to suck. What he lacked was the ability to flip the bottle prior to lifting and sucking when only the bottom was visible. How was this behavior acquired? Laurent's behavior, although relatively simple, follows a basic pattern. That pattern consists of: 1. initially successful behavior driven in part by a response to an external stimulus and in part by an internal drive, in this case hunger; 2. contradiction of the behavior when misapplied beyond the situation in which it was acquired; contradiction consists of a mismatch between what the behavior leads one to expect and what actually happens; in this case Laurent sucked glass when he expected to suck milk; Of course Laurent behavior is sensory motor, not verbal, in nature. Nevertheless, we can verbally characterize his behavior to this point in the following way: If...what I see is my bottle, (initial idea) and...I lift and suck, (behavior) then...I should suck milk. (expectation) But...I do not suck milk. Instead I am sucking glass! (what actually happens) Therefore...something is wrong, either with my initial idea or with my behavior. I cannot tell which. So I am frustrated (conclusion) 3. as shown above, the contradiction between expectation and what actually happens leads to frustration (reminiscent of Piaget's concept of disequilibrium) and, in neural modeling terms, leads to an eventual shutting down of the internal drive and to stopping the behavior; 4. nonspecific arousal now causes the one to attend more closely to the external stimulus that initially provoked the behavior; 5. attention, once aroused, allows one to notice previously ignored cues and/or relationships among the cues, which in turn allows one to couple those cues with modified behavior and to deal successfully with the new situation; in this case a new procedure and a better differentiated bottle resulted.

8.2 The Neural Network Figure 6 depicts a neural network (after Grossberg, 1982, Chapter 6) that might drive this learning. In general, represents the conditioned stimulus among possible stimuli that excites cell population in the sensory cortex. Input to has already passed through prior layers of neurons, specifically the retina and the lateral geniculate nucleus, as in this specific case represents the undifferentiated pattern of visual inputs from Laurent's bottle (i.e., either the top or the bottom). In response to sends signals to another layer of neurons in the motor cortex, (Brodmann area 4, Albus, 1981, pp. 89-90) as well as to all populations of arousal cells for specific drives (probably located in the hypothalamus, Grossman, 1967). Because in this case hunger is the drive of interest, will be generally limited to arousal of the cell populations that increase the hunger drive, and those that decrease the hunger drive, (see

THE NEUROLOGICAL BASIS OF SELF-REGULATION

39

Grossberg, pp. 259-262 for a discussion of the pairing of cue with appropriate drives). Populations and then send signals to Finally, and only when excited by signals from and by excitatory signals from fires and sends signals to M (the motor cells controlling the behavioral response). The motor cells then release the conditioned response, the lifting and sucking of the bottle.

Notice that these events cause the synaptic weights at the layer and at the layer to increase because pre- and postsynaptic activity occurs at both layers, thus conditioning the behavior of lifting and sucking to the appearance of the bottle when the child is hungry. Therefore, this network can explain the initiation of Laurent's behavior. How can it explain the behavior's termination upon satisfaction of the hunger drive?

8.3 Stopping Feeding Due to Satisfaction Intake of food gradually reduces the activity of cells, which in turn causes a "rebound" or activation of cells, which in turn inhibits activity at thereby stopping the motor response. But how does the satisfaction of hunger at generate a rebound of activity at The simplest version of the neural rebound mechanism, referred to as a dipole, is shown in Figure 7.

40

CHAPTER 2

An internally generated and persistent input, I, stimulates both the and the channels. This input will drive the rebound at when the hunger-derived input H is shut off. When Laurent is hungry, the sum of inputs I + H create a signal along (i.e., from to A smaller signal is also set along by I alone. At the synaptic knobs (the knob connecting to and (the knob connecting to transmitter is produced at a fixed rate but is used more rapidly at than at Signals emitted by exceed those emitted by Because these signals compete subtractively at and only the output from is positive, hence it produces a positive incentive motivation that drives feeding behavior. When hunger is reduced and the hunger drive stops, the network exhibits a rebound due to the relative depletion of transmitter at This occurs because input I to both and is the same but signals leaving are now stronger than those leaving (due to varying levels of transmitter). Thus, the subtractive effect causes a firing of that, due to its inhibitory effect on stops feeding behavior.

THE NEUROLOGICAL BASIS OF SELF-REGULATION

41

8.4 Stopping Feeding Behavior Due to Frustration A mechanism to stop feeding while the hunger drive persists is also needed. Again the dipole is involved. A nonspecific orienting arousal source (OA) is also required (see Figure 7). In general, unexpected feedback to the sense receptors causes a decrease in input to to and to to the point at which activity at falls below threshold and the motor behavior stops. A decrease in activity at also causes a decrease in inhibitory output to the nonspecific orienting arousal cells, OA (probably located in the reticular formation). With inhibition shut down, the orienting arousal cells fire and provoke a motor response of cue search. Simply put, unexpected events are arousing. Once the maladaptive behavior is extinguished, attention can be focused on the situation and the problem solver, Laurent in this case, is free to attend to previously ignored cues. Recall Laurent's behavior on the 30th day of Piaget's experiment. Laurent "....no longer tries to suck the glass as before, but pushes the bottle away, crying." (p. 128). Further, when the bottle is moved a little farther away,".... he looks at both ends very attentively and stops crying." (p. 128). A key question then is this: How do unexpected events cause a decrease in input to

8.5 Matching Input with Expectations: Adaptive Resonance A detailed answer to the previous question lies beyond the scope of the present chapter. In general, however, it can be shown that the suppression of specific input and the activation of nonspecific arousal depend on the layer-like configuration of neurons and feedback expectancies. Consider a pattern of sensory representations to the visual system (i.e. the retina). The retina consists of a layer of retinal cells, each with activity, at every time t due to inputs from an external source. At every time t, the input drives an activity pattern across the layer. From the retina, the activity pattern is sent to the lateral geniculate nucleus (LGN) where it excites another layer of cells and also sends inhibitory signals to the nonspecific arousal source (see Figure 8). Thus, nonspecific arousal is initially turned off by the input. Following Grossberg, the field of excitation in the LGN is be referred to as Now suppose that, due to prior experience, the activity pattern, at causes another pattern at to fire. may be the next pattern to follow in a sequence of events previously recorded and is another layer of cells, which, in this case, is in the visual cortex. constitutes an expectation of what will occur when excites cells in the LGN. Suppose further that the pattern at is now fed back to the LGN to be compared with the retinal input following This would allow the two patterns to be compared. The present is, in effect, compared with the future (i.e., the expectation). If the two patterns match, then you see what you expect to see. This allows an uninterrupted processing of input and a continued quenching of nonspecific arousal. Grossberg refers to the match of input with expectations as adaptive resonance.

42

CHAPTER

2

Following Grossberg, the field of excitation in the LGN is be referred to as Now suppose that, due to prior experience, the activity pattern, at causes another pattern at to fire. may be the next pattern to follow in a sequence of events previously recorded and is another layer of cells, which, in this case, is in the visual cortex. constitutes an expectation of what will occur when excites cells in the LGN. Suppose further that the pattern at is now fed back to the LGN to be compared with the retinal input following This would allow the two patterns to be compared. The present is, in effect, compared with the future (i.e., the expectation). If the two patterns match, then you see what you expect to see. This allows an uninterrupted processing of input and a continued quenching of nonspecific arousal. Grossberg refers to the match of input with expectations as adaptive resonance. But suppose the new input to does not match the expected pattern from Mismatch occurs and this causes activity at to be turned off, which in turn shuts off the inhibitory output to the nonspecific arousal source. This turns on nonspecific arousal and initiates an internal search for a new pattern at that will match If no match is found, new cells will be used to record the new neural sensory input to which the subject is now attending.

THE NEUROLOGICAL BASIS OF SELF-REGULATION

43

8.6 Why Are So Many Contradictions Necessary? The previous discussion can explain the shutting down of contradicted behavior even in the presence of a continued hunger drive. But why did it take so many contradictions to shut down that behavior? The answer probably lies in the fact that, on many trials, Laurent's behavior was in fact not contradicted. The behavior was successful prior to the start of Piaget's experiment. Further, it was successful on many trials during the experiment when Laurent was allowed to feed in his normal way. Thus, on these trials the synaptic strengths of and increased when fired by (the top of the bottle). On the other hand, when the behavior was contradicted, the sensory representation of the bottle's bottom active at during the rebound was conditioned to So the to (either directly to or via was smaller than when net feedback from behavior was always successful. As Piaget's experiment continued, the projections to became stronger until they finally, on the 30th day, dominated the projections and Laurent stopped lifting and sucking when the bottom was presented. At last, his incorrect behavior was extinguished and he is free to build new connections. Laurent must now learn to flip the bottle when the bottom is visible. The bottom is the important cue to be linked with flipping. According to the theory, to provoke this learning the neural activity in the cells responsible for the recognizing the bottom of the bottle must be sustained in STM while the motor act of flipping occurs. Nonspecific arousal serves as the source drive to provoke a variety of behaviors (e.g., turning and flipping the bottle), thus when Laurent hits on the act of flipping while he is either paying attention to the relevant visual cues or while they are still active in STM, the required learning can take place. Again consider Figure 7. In this case represents the excitation pattern in the sensory cortex provoked by looking at the bottle's bottom. If this pattern remains active in STM while flipping the bottle (see Grossberg, pp. 247-250 for mechanisms), the synaptic strengths of the pattern playing at the nonspecific orienting arousal center (firing due to nonspecific arousal) are strengthened. The sensory pattern from plus the nonspecific arousal provides pre and postsynaptic activity that drives increases in the This in turn fires the pathway. Thus the cells responsible for bottle flipping, receive inputs from (the bottom of the bottle) and from the orienting arousal source that both drive increases in synaptic strengths. In other words, the network allows the child to link, or condition, the sight of the bottle's bottom with the behavioral response of flipping. Of course, flipping when the bottom is seen is the behavior to be acquired. Further, when the behavior is performed, it results in the sight of the nipple, which of course had been conditioned to the act of lifting and sucking. Thus, bottle flipping becomes linked to lifting and sucking. With each repetition of the above sequence, the appropriate synaptic strengths increase until the act takes place with considerable ease. Thus, Laurent solves his problem and the network has become more complex by strengthening specific synaptic connections. As with Pavlov's dog, complexity of the neural networks (mental structures) increases. Importantly this increase has not been due

44

CHAPTER

2

to the unfolding of some innate ideas, unless one considers prewired synaptic connections as innate ideas. 9. CAN NEURAL NETWORKS EXPLAIN HIGHER LEVELS OF LEARNING? The percentage of students who successfully use advanced reasoning strategies increase gradually with age (cf., Lawson, Karplus & Adi, 1978). These advances can not be attributed solely to direct teaching because either the increases come well after direct teaching has been attempted (e.g., proportional reasoning), or they come without any direct teaching at all, as is the case of correlational reasoning (e.g., Lawson & Bealer, 1984). For the sake of simplicity, let us restrict our discussion to proportional reasoning problems because they seem to evoke the most consistent and smallest class of student responses. Let's further restrict the discussion to just one problem of proportional reasoning, the Suarez & Rhonheimer (1974) Pouring Water Task introduced in Chapter 1. The Pouring Water Task, as adapted by Lawson, Karplus & Adi (1978), requires students to predict how high water will rise when poured from one cylinder to another. As you may recall, students are first shown that water at mark 4 in a wide cylinder rises to mark 6 when poured into a narrow cylinder. They are then asked to predict how high water at mark 6 in the wide cylinder will rise when poured into the empty narrow cylinder. Responses vary but typically fall into one of four categories: 1. additive strategy, e.g., water rose from 4 to 6 (4+2=6); therefore, it will rise from 6 to 8 (6+2=8); 2. qualitative guess, e.g., the water will rise to about 10; 3. additive proportions strategy, e.g., the water will rise to 9 because the ratio is 2 to 3 and 2+2+2=6 in narrow and 3+3+3=9 in the wide; 4. proportions strategy, e.g., 2/3 = 4/6 = 6/x, x = 9.

Again, for simplicity, the discussion will be limited to just two strategies, the additive strategy and the proportions strategy as they reflect the most naive and sophisticated strategies respectively. Given the typical naive response of the child to the task is 8, by use of the additive strategy, and the typical sophisticated response of the adolescent is 9, by use of the proportions strategy, the central question becomes: How does the shift from use of the additive strategy to use of the proportions strategy during adolescence come about? The present hypothesis is that it comes about in basically the same way that Laurent learned to flip his bottle. The child responding to the task with the additive strategy is like Laurent responding to the bottle's bottom by lifting and sucking. To the naive problem solver, the Pouring Water Task presents problem cues, just as the bottle presented cues to Laurent. The difficulty is

THE NEUROLOGICAL BASIS OF SELF-REGULATION

45

that these cues set off the wrong response - the additive response. In other words, by analogy with the neural network involved in Laurent's shift in behavior, we assume that the problem cues plus some internal drive to solve the task, combine to evoke the UCR, the additive response controlled by some in the motor cortex. For children, say below age 10-11 years, responding to quantitative problems by use of addition and/or subtraction is indeed a common strategy and, in many instances, leads to success. Many children know how to multiply and divide and many can solve textbook proportions problems. Yet use of the proportions strategy (which, of course, utilizes multiplication and/or division) seldom occurs to them just as it did not occur to Laurent to flip his bottle before lifting and sucking (at least during the first 29 days). Laurent's initial behavior had been successful in the past and he had no reason to believe it would not continue to be successful. Indeed many children who use the additive strategy are quite certain that they have solved the problem correctly. How then do additive reasoners come to recognize the limitations of their thinking? And once they do, how do they learn to deploy the correct proportions strategy? The steps in that process are seen as follows: 1. indiscriminate use of the additive strategy to solve additive and multiplicative problems; 2. contradictory and unexpected (i.e. negative) feedback following use of the additive strategy when used to solve multiplicative problems; 3. contradiction eventually leads to termination of use of the additive strategy in a knee-jerk fashion; 4. initiation of nonspecific orienting arousal provoking an external search for problem cues and an internal search through memory for successful strategies that can be linked to those cues; 5. selection of cues and the discovery of a new strategy that is successful in that it receives positive feedback when used; and 6. the acquisition of an internal strategy monitoring system to check for consistency or contradiction. The system presumably facilitates the matching of problem cues with appropriate strategies in future situations. Let us consider each step in turn.

9.1 Starting and Stopping Problem-Solving Behavior A hypothesized minimal neural network (analogous to that previously derived to account for Laurent's behavior) that may account for some of the characteristics of the problem solving behavior in question is shown in Figure 9. Figure 9 assumes that some problem-solving drive (P) exists and functions to stimulate arousal cells Although the physical basis of specific drives such as hunger and fear are well known, the very existence of a "problem-solving drive" is speculative. Let represent problem cues from the Pouring Water Task, which initially evoke use of the additive strategy. Specific problem cues of the task fire cells in the sensory cortex that in turn send that pattern of activity to arousal cells, which are also being stimulated by the hypothesized

46

CHAPTER

2

problem-solving drive P to arousal cells Due to prior conditioning, this activity feeds to (also activated by which in this case represents neural activity to initiate the motor response of addition. Thus, problem cues from the Pouring Water Task are initially conditioned to additive behavior. The key cue may be that the water previously rose "2 more" marks when poured into the narrow cylinder (an absolute difference). Other cues, such as the relative difference of the water levels (narrow cylinder = 1 1/2 x the height of the wide cylinder) are ignored. Just as Laurent's feeding behavior was terminated by satisfaction of the hunger drive, the student's problem solving behavior is terminated by reduction of the problem solving drive P when a solution has been generated. When input from P stops, the tonic input I to both and to causes a rebound at This rebound then quickly inhibits activity to stop problem solving behavior.

9.2 Contradicting the Additive Strategy A student using the additive strategy to response with 8 to the Pouring Water Task fully expects that the answer is correct just as Laurent expected to get milk when he sucked the bottom of his bottle. As we saw in the case of Laurent, the unexpected feedback from obtaining an incorrect answer eventually stops the conditioned motor response in similar situations and turns on nonspecific arousal. In turn, nonspecific arousal causes a closer inspection of problem cues and a search for a more effective strategy.

THE NEUROLOGICAL BASIS OF SELF-REGULATION

47

What form can this contradiction take? Certainly missing problems on a math test could be one form. Yet that feedback normally occurs well after the act of problem solving, thus most likely would lose effectiveness in focusing student attention on the problem. More effective feedback would be to have the student actually pour the water following his prediction of eight. The water rise to mark nine would present immediate contradictory feedback that should produce the desired effect. A crucial point, however, is that a single contradiction no matter its source, is probably not sufficient to the cause of shutting down of the additive strategy. Recall that it took Laurent many trials before he stopped bringing the bottle's bottom to his mouth and sucking. A possible reason for this is that the student's use of the additive strategy does not always lead to contradiction. In many problem situations, addition/subtraction are the correct operations. Further, even if they are not correct, the student may not discover they are wrong for many days, if ever. Thus sensory task cues from additive problems to the channel linked to the additive strategy would continue to be strengthened in some situations. In situations where use of the additive strategy leads to contradictions the sensory task cues from proportions problems leads to thus the channel would be conditioned. As students who use the additive strategy meet continued contradictions the projections to would become stronger than the projections to until they eventually dominate and the student no longer responds unthinkingly with an additive strategy to quantitative problems of this sort. 9.3 Arousal and the Search for a Better Strategy Only when the unthinking use of the additive strategy has been extinguished and nonspecific arousal is sufficient, can the sort of problem inspection and strategy search occur that will lead to successful conditioning of the input to the proportions strategy. How might this occur? Again consider the example of Laurent learning to flip his bottle prior to lifting and sucking. What seems to be required in the case of proportional reasoning is to link input (multiplicative cues from proportions problems) to the motor response of the proportion strategy. In other words, input at must match feedback. This would not appear difficult as it seems to simply require that it occur to the student to use multiplication/division instead of addition/subtraction in the presence of input and nonspecific arousal (see Figure 7). But this is not the entire story. A student so conditioned may respond to additive problems with a proportions strategy if s/he is not sufficiently aware of the problem cues that suggest which strategy to use! 9.4 Feedback and Monitoring Problem-Solving Behavior How then do we solve the problem of reliably matching cues with strategies? This of course is a central question. The proposed answer is as follows. When confronted with a

48

CHAPTER 2

quantitative problem certain key words or concrete referents are conditioned to strategies (as stated above). For example, the word "twice" suggests a multiplicative relationship. The word "more" suggests an additive relationship. However, because these cues are not always reliable, what the problem solver must do is initiate the use of a strategy to determine its consequences, or probable consequences if carried out completely, and then compare those consequences with other known information about the problem situation. If this leads to an internal contradiction, then that strategy must be incorrect and another strategy must be tried. Internal contradiction means that an adaptive resonance has not been found between input and expectations. This leads to an immediate termination of the input, which in turn drives a rebound at to terminate use of that strategy and to provoke excitation of nonspecific arousal. Nonspecific arousal then provokes a search through LTM for another strategy. As mentioned, in the Pouring Water Task, use of the additive strategy leads to the prediction that water at mark 2 in the narrow cylinder should rise to mark 0 when poured into the wide cylinder. The water disappears! Of course this is impossible, therefore, the additive strategy must be wrong (i.e., it has led to contradictory feedback), i.e., If...the difference in waters levels is always 2 marks, (initial idea) and...water at mark 2 in the narrow cylinder is poured into the wide cylinder, (behavioral test) then...it should rise to mark 0 (i.e., 2 - 2 = 0). In other words, the water should disappear. (prediction) But...water does not disappear when poured from one cylinder to another (what actually happens) Therefore...the difference in water levels must not always be 2 marks. (conclusion) Or consider the following problem: John is 6 years old and his sister Linda is 8 years old. When John is twice as old as he is now, how old will Linda be? The word "twice" may suggest that you should multiply 6 x 2 = 12 to get John's age. Consequently, you should also multiply 8 x 2 = 16 to get Linda's age (many students do this following a lesson on proportions). But this of course is wrong because we all know that Linda cannot age at a rate faster than John. Therefore, if one internally monitors his/her tentative solution, an internal contradiction results that shuts down S input to and supporting the additive strategy. Hence, the additive strategy is rejected as it fails to obtain an adaptive resonance. LTM is then searched until another strategy is found that no longer generates internal contradictions. Thus, internal monitoring is utilized to match problem cues to problem strategies. This monitoring presumably takes place when students have learned a variety of solution strategies and are left on their own to match strategies with cues. To summarize, advanced problem solvers appear to have at their disposal the memory record of a variety of problem cues, a variety of problem strategies, and a general mode of operation. That general mode tells the problem solver to try the available strategies until s/he finds one that does not produce contradictions. Consequently, the key

THE NEUROLOGICAL BASIS OF SELF-REGULATION

49

difference between the additive reasoning child and the proportional reasoning adolescent is not the strategies they possess. Both types of individuals are capable of using both types of strategies. Rather the key difference appears to be that the child unthinkingly initiates a strategy and then fails to internally check its consequences for consistency with other known data (e.g., water does not disappear when poured from one container to another). On the other hand, the adolescent unthinkingly initiates a strategy and (this is new) checks its results for possible contradictions. If contradictions are found, (if an adaptive resonance is not found), a new strategy is tried until no contradictions are discovered. This key difference may arise because adolescents (at least some of them) have gradually become aware of the fallacy of automatically "jumping to conclusions" while their younger counterparts have not. Thus, a novel behavior has emerged (developed) not by direct assimilation of environmental input, nor has it developed by the maturation of innate structures. Rather, it has developed from by the novel combination of already present, but previously unlinked, problem-solving behaviors and problem cues.

10. INSTRUCTIONAL IMPLICATIONS The proposed theory of neural processing makes it clear why the normal curriculum is insufficient to provoke many students to acquire the skills needed to deal successfully with problems of the Pouring Water type. Students learn algorithmic strategies but they are seldom confronted with the diversity of problems needed to provoke the sort of close inspection of problem cues necessary to link cues with strategies and tentative results with implied consequences. In short, what is acquired in school lessons is often insufficient. This statement is reminiscent of Piaget's position regarding the role of teaching in intellectual development. Piaget long insisted that normal teaching practices are insufficient because they seldom, if ever, provoke the necessary contradictions and accommodations (cf., Piaget 1964). Unfortunately, as mentioned, Piaget's theory of psychological selfregulation is based upon evolutionary and developmental analogies rather than on neurological networks. The present theory, although most certainly too simplistic to account for the details of advanced reasoning, nevertheless, suggests neurological mechanisms that may be involved in important aspects of learning and development. Consider the child's initial use of the additive strategy in a knee-jerk fashion as an instance of the immediate assimilation and processing of input by previously acquired mental structures (strategies). This is the Piagetian state of equilibrium. The individual is satisfied by his/her response and not intellectually aroused. But suppose repeated attempts at using that strategy lead to contradiction. At the neurological level this could speculatively be interpreted as the channel being weakened and the channel being strengthened until it dominates and nonspecific-orienting arousal is turned on and searching behavior is initiated to acquire an appropriate response to solve the problem. This is the state of disequilibrium. Finally through the internal trial and error

50

CHAPTER

2

search behavior (see Grossberg, 1982, pp. 14-15) and/or a closer inspection of the phenomena, a successful behavior pattern is acquired, i.e., new neural connections are formed by increases in the synaptic strengths of the pathways from the input stimulus to the output response. This constitutes an accommodation of mental structures, the acquisition of more complex behavior, and resolution of the problem. In Piagetian terms it restores equilibrium, but at a more sophisticated, emergent level. Having suggested a sequence of events involved in the successful emergence of proportional reasoning, it becomes possible to identify why some students never acquire the ability. First, if prerequisite strategies and knowledge are not in place they cannot be utilized. By analogy, Laurent already knew how to flip his bottle. That was not the problem. Rather, the problem was to connect the flipping with the appearance of the bottom of the bottle. Likewise the problem for most adolescents is not that they do not know how to multiply and divide or have not memorized that the "product of the means equals the product of the extremes." Rather the problem is that they have failed to link the appropriate operations with the appropriate problem cues. Second, the student must be confronted with many diverse problem-solving opportunities that provide the necessary contradictions to his/her use of the additive strategy. Without feedback and contradiction the necessary arousal will not occur. Therefore, even if students are told to use "proportions" to solve the problems, they are likely to fail to do so in transfer situations because use of the old incorrect strategy has not been extinguished. The previous discussion, although related most directly to the gradual acquisition of proportional reasoning, does not necessarily preclude its direct teaching. As mentioned, with respect to the Pouring Water Task, direct contradiction of the additive strategy can be obtained simply by pouring the water from the wide to the narrow cylinder and noting the rise to 9th mark instead of the 8th mark. Other problems with similar contradictory feedback can be utilized. One would expect this type of instruction to be very effective, yet teachers and curriculum developers must continue to remind themselves of the remaining limiting factor, namely the student. No matter how potentially interesting the material may seem to the teacher, it is the student that must be aroused by the contradictory feedback to relinquish an incorrect strategy and begin the search for a new one. Sufficient arousal may be difficult to achieve in the classroom setting particularly if the problems bare little resemblance to problems of personal importance. Further, short-term direct teaching is probably insufficient to promote the development of the internal monitoring system needed to match problem cues to solution strategies in novel situations. Long-term efforts appear necessary for this sort of development. Another extremely important educational implication follows from Grossberg's learning equation. Recall that learning is understood in terms of increases in the synaptic strengths of knobs. According to the learning equation, learning occurs when the total activity exceeds a certain threshold and total activity is a function of both pre- and respectively). The level of pre-synaptic activity is postsynaptic activity (i.e., and a function of current inputs, while the level of postsynaptic activity is a function of prior learning. Thus, it follows that there are two ways of learning, i.e., of storing new information into long-term memory. The first way is to boost pre-synaptic activity to

THE NEUROLOGICAL BASIS OF SELF-REGULATION

51

such a high level that it alone reaches threshold. This could be done, for example, by reciting a list of words over and over again until they get "burned in", i.e., get memorized. I did this in a high school English class when I memorized passages from Chaucer's Beowulf - passages that to me were meaningless. Nevertheless, I can still recite some of those passages today. Another way to boost pre-synaptic activity is to emotionally boost overall arousal by, for example, yelling "fire" while sitting in a packed movie theater. The emotional boost also will "burn in" memories. The second way to learn is to connect the new input with something that is already known. The new input boosts the pre-synaptic activity, while the prior learning boosts the post-synaptic activity. So together they reach threshold and cause a change in transmitter release rate. This sort of learning can take place without such a massive amount of effort spent in boosting the new input. Further, the new learning is not meaningless because it is connected to what one already knows. So learning is easier and it is meaningful. Further, like a folder that you file in the correct place in a filing cabinet, instead of piling it carelessly on a shelf where it gets buried under subsequent folders, the new knowledge can be easily retrieved and used in the future. Consequently, it is far more effective when one teaches in ways that take what students already know into account and build on, connect with, that knowledge. Without making such connections students will not know how the new knowledge fits with, or perhaps does not fit with, prior conceptions. Thus, little long-term retention occurs and/or students may acquire conflicting conceptions and not even know it (e.g., Lawson & Thompson, 1988). More will be said about this very important aspect of learning in Chapter 5 when the usefulness of analogies is discussed. But for now, consider the text passages that appear in Tables 2 and 3 (from Musheno & Lawson, 1999). Take a few minutes to read each passage before reading on.

Does Cooperation Ever Replace Competition in Nature? Organisms compete for food, water, and space, and defend themselves from others who might want to make a meal of them. Is life always competitive or do species ever work together? Consider two examples: In the lowlands of Mexico and Central America, the bull's horn acacia tree grows. To protect itself from being eaten, the tree grows large thorns at the base of its leaves. At the very tip of each leaflet, the tree produces small orange bead-like structures, which are filled with oils and proteins. Scientists could find no purpose for the orange beads until they made an interesting observation. They found that a certain type of ant uses the acacia tree for its home. The ants, which live in the thorns of the tree, use the mysterious orange beads for food. The ants do not harm the tree, but they do aggressively attack anything that touches it. They attack other insects that land on the leaves or branches and if a large animal even brushes

52

CHAPTER

2

against the tree, they swarm and attack with painful, burning bites. The ants even chew up and destroy plants that grow near their tree. With the help of the ants, animals eat the acacia's tender leaves and neighboring plants quickly outgrow the damaged trees. These particular ants are found only in acacia trees. Here, the acacia tree and ants depend on each other. Both benefit; neither is harmed. Teaming up gives both an advantage. This kind of cooperation is known as mutualism. Is the next example also mutualism? In Africa, a bird known as the oxpecker eats ticks as the main part of its diet. But the oxpecker has a very interesting manner of collecting its meals. Each bird will choose a large grazing animal, such as a zebra, and set up house on the zebra's back. The bird picks off all the ticks it can find, and the zebra allows the oxpecker to hitch a ride as long as it chooses. In this relationship, the bird has a steady food supply, and the zebra is kept tick free. In both examples, the species have a close, long-term, cooperative relationship. Thus they are both examples of mutualism. Consider another example: In Tanzania, a heron-like bird called the cattle egret follows cape buffaloes and other large grass eating mammals. The birds gather at the buffaloes' feet, sometimes even perching on the grazers' back. As the buffaloes walk and graze, they scare up small mice and insects, which become the egrets' food supply. Egrets that follow the buffaloes find a better food supply than they could on their own. The buffalos do not benefit from the egrets' presence, but do not seem to be bothered by the egrets, either. The egret and buffalo have a close, longterm relationship. However, in this case only the egret benefits. The buffalo is not affected. This type of association, which benefits one species and does not affect the other, is called commensalism. Does the next example represent mutualism, commensalism, or something different? Mistletoe, the leafy green plant many Americans traditionally hang in doorways during the Christmas season, does not grow on the ground like most plants. Mistletoe grows only on the branches of trees such as oaks, or mesquite trees here in Arizona. The mistletoe has a special type of root that burrows into the tree and taps into the tree's sap supply. The sap provides nutrition for the mistletoe, which can then grow larger, sinking new "roots" into the three branches as its need for food grows. As the mesquite tree gives up more of its sap to support the mistletoe, it will be harmed because it loses valuable water and nutrients. Again this is example shows a close, long-term relationship between two species. Here, the mistletoe benefits, but the mesquite tree is harmed. When one species benefits and the other is harmed, the relationship is known as parasitism. In this example, the mistletoe is the parasite. Mutualism, commensalism and parasitism all involve close, long-term relationships between two species. The relationship can be between plants, between animals, or between plants and animals. Collectively, the close, long-term relationships are called symbiosis. This word comes from the Greek language: bios means life and sym means together, so the word symbiosis translates into life together.

THE NEUROLOGICAL BASIS OF SELF-REGULATION

Symbiosis Symbiosis is a term that means a close, long-term relationship between organisms of two different species. The relationship can be between plants, between animals, or between plants and animals. The word "symbiosis" word comes from the Greek language: bios means life and sym means together, so the word symbiosis translates into life together. In nature, relationships between species are usually competitive, with plants and animals battling for food, water and space to live, as well as defending themselves from other species that might want to make a meal of them. Symbiosis represents a different, noncompetitive type of relationship between two species, which involves cooperation and dependence. it is found in three distinct forms called mutualism, commensalism and parasitism. In mutualism, the close, long-term relationship is beneficial to both species. In commensalism, the relationship benefits one species and the other species is neither harmed nor benefits. In the third form, parasitism, one species benefits ate the expense of the other species, which is harmed in the process. A good example of mutualism between a plant and an animal species can be found in the lowlands of Mexico and Central America, where the bull's horn acacia tree grows. To help protect itself from being eaten, the tree grows large thorns at the base of its leaves. At the very tip of each leaflet, the tree produces small orange bead-like structures, which are filled with oils and proteins. Scientists could find no purpose for the orange beads until they made an interesting observation. They found that a certain type of ant uses the acacia tree for its home. The ants, which live in the thorns of the tree, use the mysterious orange beads for food. The ants do not harm the tree, but they do aggressively attack anything that touches it. They attack other insects that land on the leaves or branches and if a large animal even brushes against the tree, they swarm and attack with painful, burning bites. The ants even chew up and destroy plants that grow near their tree. With the help of the ants, animals eat the acacia's tender leaves and neighboring plants quickly outgrow the damaged trees. These particular ants are found only in acacia trees. In another example of mutualism, in this case between two species of animals, an African bird known as the oxpecker eats ticks as the main part of its diet. But the oxpecker has a very interesting manner of collecting its meals. Each bird will choose a large grazing animal, such as a zebra, and set up house on the zebra's back. The bird picks off all the ticks it can find, and the zebra allows the oxpecker to hitch a ride as long as it chooses. In this relationship, the bird has a steady food supply, and the zebra is kept tick free. Commensalism is much more rare than mutualism or parasitism as it is hard to find cases where one of the species is not affected at all by the relationship. One good example of commensalism, again between two species of animals, is found in Tanzania, where a heronlike bird called the cattle egret follows cape buffaloes and other large grass-eating mammals. The birds gather at the buffaloes' feet, sometimes even perching on the grazer's back. As the buffaloes walk and graze, they scare up small mice and insects, which become the egret's food supply. Egrets that follow the buffaloes find a better food supply than they could on their own. The buffalos do not benefit from the egrets' presence, but do not seem to be bothered by the egrets, either.

53

54

CHAPTER

2

Parasitism is the final form of symbiosis. There are many examples of this type of relationship to be found in nature. For example, mistletoe, the leafy green plant many Americans traditionally hang in doorways during the Christmas season, does not grow on the ground like most plants. Mistletoe grows only on the branches of trees such as oaks, or mesquite trees here in Arizona. The mistletoe has a special type of root that burrows into the tree and taps into the tree's sap supply. The sap provides nutrition for the mistletoe, which can then grow larger, sinking new "roots" into the three branches as its need for food grows. As the mesquite tree gives up more of its sap to support the mistletoe, it will be harmed because it loses valuable water and nutrients.

As you found out, each passage introduces four new biological terms: symbiosis, mutualism, commensalism, and parasitism. The passage in Table 2 introduces the examples first and the new terms second (i.e., in a "learning cycle" format). Also the new terms are introduced in a "bottom-up" manner. In other words, in terms of the conceptual hierarchy, the less inclusive (lower-order) concepts of mutualism, commensalism and parasitism are introduced before the more inclusive "higherorder" symbiosis concept. On the other hand, the passage in Table 3 introduces the new terms in a more "traditional" top-down manner with symbiosis coming first. Also notice that the new terms are introduced prior to the examples (i.e., terms first, examples second). According to what we have learned about what it takes to provoke learning (i.e., to increase the synaptic strengths of knobs), which passage should work best in terms of concept construction and retention? In theory, the learning cycle passage should work best. Presumably the level of pre-synaptic activity provoked by both passages would be the same. But the relevant post-synaptic activity should be higher for students reading the learning cycle passage. This is because when the new terms appear for students reading that passage, they have just read about the phenomena to which the new terms are supposed to be "linked." So thanks to this just-activated, and still active, post-synaptic activity, the combination of pre- and post-synaptic activity reaches threshold and the relevant synaptic strengths increase. Therefore, learning occurs as described by Grossberg's learning equation. However, for students reading the traditional passage, the terms come before the examples. Thus, the pre-synaptic activity provoked by the new terms is not matched at the correct time by the relevant post-synaptic activity provoked by the examples. Consequently, learning does not easily take place. In other words, when introduced, a new term has no where to "attach." Hence, when the activity boosted by reading a new term decays, as described by Grossberg's activity equation, the new term has not "attached" and is forgotten. In fact, prior to providing the reader with a relevant example, the traditional passage introduces additional new terms that also have no "points of attachment." As expected, Musheno & Lawson (1999) found that ninth and tenth grade students who read the learning cycle passage scored significantly higher on a posttest of concept comprehension than those who read the traditional passage. More

THE NEUROLOGICAL BASIS OF SELF-REGULATION

55

generally, Grossberg's activity and learning equations imply that all learning contexts (e.g., labs, lectures, discussions) that employ the learning cycle approach should be more effective than "traditional" term-first, top-down approaches (i.e., Lawson, Abraham & Renner, 1989). For example, who among us has not suffered through the occasional lecture in which the speaker strung together several unfamiliar words, that although easy to hear, were, nevertheless, meaningless. Consequently, we quickly become "lost" - some of us even fall asleep. The problem here is not a lack of presynaptic activity. Instead, the problem is a lack of post-synaptic activity, thus a loss of attention, comprehension, learning and retention.

This page intentionally left blank

CHAPTER 3

BRAIN MATURATION, INTELLECTUAL DEVELOPMENT AND DESCRIPTIVE CONCEPT CONSTRUCTION

1. INTRODUCTION Thus far we have found the pattern of hypothetico-predictive reasoning at work in our attempts to draw in a mirror, in the behavior of Piaget's son Laurent learning to orient his bottle to suck milk, in the case of the unlit barbecue, in both visual and auditory information processing, and in the solution of a proportions problem by adolescents. Is the same pattern at work in students' reasoning during descriptive concept construction? Consider for example the creatures called Mellinarks in the first row of Figure 7. Why do you suppose these are Mellinarks while the creatures in the second row are not Mellinarks? In other words, what makes a Mellinark a Mellinark? Can you use the information in the figure to find out? If so, which creatures in row three are Mellinarks? How do you know? In other words, how do you define a Mellinark and how did you arrive at that definition? What were the steps in your reasoning? Take a few minutes to try to answer these questions before reading on. To gain insight into the reasoning used by students to solve the Mellinark Task, several students tried the task and told us about their reasoning. Consider, for example, the following remarks of a student who identified creatures one, two, and six in row three as Mellinarks (Lawson, McElrath, Burton, James, Doyle, Woodward, Kellerman & Snyder, 1991, p. 967): Number one, two, and six are Mellinarks. OK, how did you figure that out? Um. Well, the first thing I started looking for was just overall shape, whether it's straight, looks like a dumbbell, but this doesn't really work, because some of these (row two) are similar in overall body shape. So I ruled that out. Well, then I said, all of these are spotted (row one). But some of these (row two) are spotted and these aren't Mellinarks, so that can't be the only thing. So I looked back at these (row one) and noticed that they all have a tail. But some of these have a tail (row two), so that can't be the only thing either. And so then I was sort of confused and had to look back, and think about what else it was. Then I saw the big dot. So all of these (row one) have all three things, but none of these (row two) have all three.

57

58

CHAPTER 3

According to the student, she first generated the idea that overall shape is a critical feature. But as she tells us, this idea was quickly rejected because some of the creatures in row two are similar in overall shape. Thus, at the outset, the student may have reasoned like this: If...overall shape is a critical feature of Mellinarks, (descriptive hypothesis) and...I look closely at the non-Mellinarks in row two, (behavioral test) then...none should be similar in overall shape to the Mellinarks in row one. (prediction) But...some of the non-Mellinarks in row two are similar in overall shape, (observed result) Therefore..."I ruled that out," i.e., I concluded that my initial idea was wrong. (conclusion) Of course this is the same pattern of reasoning that we have seen before. Some logicians call this pattern "reasoning to a contradiction" or "reductio absurdum" (e.g., Ambrose & Lazerowitz, 1948). And as we can see in the remainder of the student's comments, the pattern appears to have been recycled until all contradictions were eliminated. So after rejecting her initial descriptive hypothesis, the student seems to have quickly generated others (e.g., spots are the key feature, a tail is the key feature) and presumably tested them in the same fashion until she eventually found a combination of features (spots, tail, big dot) that led to predictions that were not contradicted, i.e., If...Mellinarks are creatures that have spots, a tail, and one big dot, (descriptive hypothesis) and...I check out all the creatures in rows one and two, (test) then...all those in row one should have all three "things" and none in row two should have all three "things." (prediction) And...this is what I see. (observed result) and six in row three have all three "things" so they are Mellinarks). (conclusion) Did you also conclude that creatures one, two, and six of row three are Mellinarks? If so, did your reasoning look something like the above? How do you suppose a sample of high school students would do on a series of Mellinark-type tasks? Would they also use this reasoning pattern? Or would they use something else and run into difficulties? To find out, Lawson, et al. (1991) administered a series of Mellinark-type tasks to 314 high school students. Interestingly, not only did many students experience difficulties, their performance was highly correlated with performance on a measure of scientific and mathematical reasoning (i.e., developmental level). Difficulties experienced by students who presumably failed to employ cycles of hypothetico-predictive reasoning to solve the tasks were exemplified by the following discussion with a student following her failed attempt:

BRAIN MATURATION AND DESCRIPTIVE CONCEPT CONSTRUCTION

59

Suppose I define a Mellinark as being a creature with a tail. How could I test that idea? Is there any information here that would tell me if that idea is right or wrong? ...Um...you could um...huh...a...just look to see if the other creatures have the same tails...or, I mean...you know...characteristics of the creatures...with the tails and the points and the dots and stuff to see if they are...you know...all the same or close to...and then...um...heh...I don't know...heh. OK, let's look at the second row. We know that none of these are Mellinarks. So what would you expect about these with regard to tails? I mean, if it's true that Mellinarks are creatures with tails then what would you expect to find in row two with regard to tails? Um...they would a...they would be some different kind of creature with tails...I don't know...they would um...I don't know...they would just...they don't have the dots on `em. And then...um...they are more... 1 don't know. OK. Let's go back. Once again, I'm going to say that Mellinarks are creatures with tails and I look down here (row two) and I see that this non-Mellinark has a tail. See that tail right there? Yeah And I know that is not a Mellinark. So I would conclude from that my definition must be wrong. Yeah...well they could have classified 'em wrong. It could have been a mistake. These would have been up with the other Mellinarks.

Although this sort of response and the quantitative data reported by Lawson et al. (1991) reveal clear difficulties by many high school students, a question remains as to the cause(s) of the difficulties. Perhaps the difficulties stem from students' lack of hypothetico-predictive reasoning skill. Suppose like Piaget (e.g., Piaget, 1964), we assume that such reasoning skill is the product of intellectual development (i.e., the product of physical and social experience, neural maturation and self-regulation). If this is true, then brief verbal training in the use of such reasoning should not be successful in provoking students to solve Mellinark-type tasks. In other words, the training should fail because, in theory, the necessary reasoning skill results from the long-term process of intellectual development, not from short-term training. Consequently, research was initiated in which six Mellinark-type tasks were constructed and a brief verbal training session was used to point out potentially relevant features (i.e., provide descriptive hypotheses to be tested) and to explain to students how to use cycles of If/then/Therefore reasoning to test those features and solve the tasks. More specifically, the reasoning guiding the research can be stated as follows: If...the difficulties experienced high school students are caused by lack developmentally derived, hypothetico-predictive reasoning skill needed to construct descriptive concepts, (developmental hypothesis)

60

CHAPTER

3

and...students are given brief verbal training in how to use such reasoning to solve a series of Mellinark-type tasks, (planned test) then...when given an additional non-trained task, they should fail, (prediction) 2. METHOD

2.1 Research Design Prior to subject selection, a few pilot training sessions were conducted. Student responses led us to suspect that at least some eighth grade students (12-14 years of age) would respond successfully. Therefore, the first training sessions were conducted with eighth graders. If the eighth graders were successful, then a younger sample of students would be chosen to see if they would also be successful, and so on until a sample was found that did not succeed. On the other hand, if the eighth graders did not respond successfully, then an older sample would be chosen and so on until, if possible, a sample was found that was successful. 2.2 Subjects Subjects (Ss) were 175 students (88 males and 87 females) enrolled in two elementary schools and junior high school in a suburban community in the southwest USA. Grades and student ages were as follows: kindergarten (n = 70, 5.3 to 7.0 years, mean = 6.4); grade 1 (n = 30, 6.8 to 7.9 years, mean = 7.5); grade 2 (n = 30, 7.9 to 8.9 years, mean = 8.4); grade 4 (n = 15, 8.4 to 10.3 years, mean = 9.4.); grade 6 (n = 15, 10.4 to 11.9, mean = 11.5); grade 8 (n= 15, 12.4 to 14.4 years, mean = 13.4). 2.3

Brief Verbal Training

Ss were individually trained in quiet locations near their classrooms. One goal of the training was to determine the extent to which Ss could utilize the If/then/Therefore reasoning pattern presumably necessary for successful concept construction. The reasoning pattern was introduced repeatedly during the training when Ss experienced difficulty. Another intent was to reveal the relevant task features: 1) the nature of the creature's sides, 2) the presence of little spots, 3) tails, 4) a big spot, or 5) some combination of the above. The cumulative effect of the training was evaluated on the seventh and final task - the Mellinark Task. Thus, no training was given on the Mellinark Task but was given, if necessary, on some or all of the preceding tasks. Each training session took approximately 15-20 minutes.

BRAIN MATURATION AND DESCRIPTIVE CONCEPT CONSTRUCTION

61

2.4 Descriptive Concept Construction Tasks Seven descriptive concept construction tasks patterned after the "creature cards" of the Elementary Science Study (1974) were developed. Each task consisted of three rows of figures (creatures) drawn on an 8 1/2 x 11-inch sheet of paper. The verbal introduction given to each student as s/he was shown the first task went as follows: The figures that I have drawn in the first row are all called Shlooms because they have something(s) in common. The figures in the second row are not Shlooms because they do not have that something(s). Based on this information, try to figure out which of the figures in the third row are Shlooms. Take a few minutes at this time to solve each task in Figures 1-6 to obtain a sense of the reasoning necessary for success

62

CHAPTER

3

CHAPTER

3

63

2.1 Specific Task Training Initially many Ss matched creatures based upon overall shape. For example, on Task 1 many Ss identified creatures one and three in the third row as Shlooms "because they look like creatures one and two of row one." And creature number two of row three was identified as a non-Shloom "because it looks like creature four from row two." Typically, Ss using this matching strategy did not know whether creatures four and five in row three were Shlooms. Many unsuccessful Ss continued to utilize this matching strategy on subsequent tasks even after the relevant feature(s) and the correct strategy were provided. More specifically, training on Task 1 (if necessary) proceeded by experimenter statements as follows: Notice that all of the creatures in row one have curvy sides. Notice also that none of the creatures in row two have curvy sides. Instead their sides are straight. So if we say that creatures with curvy sides are Shlooms, then creatures one, three, and five in row three must be Shlooms.

64

CHAPTER 3

Hence, Ss were alerted to the fact that they should pay attention to the nature of the sides (i.e., curvy or straight). Task 1 was not used to introduce the If/then/Therefore reasoning pattern. Consequently when Task 2 was presented, Ss would do one of four things:

1. persevere with the matching strategy (e.g., creature two in row three is a Thomp because it looks like creature four in row one, and creature four in row three is a Thomp because it looks like creature three in row one); 2. persevere with the idea that a curvy side is relevant and conclude that creatures one and four (the ones with the curvy sides) are Thomps; 3. notice the general abundance of spots on the creatures in row one and immediately conclude that Thomps are creatures with spots. Although this third approach leads to a successful identification of creatures one, three and four in row three as Thomps, it does not constitute totally effective reasoning because other possibly relevant features have not been eliminated. Thus, Ss using this strategy obtained the correct answer by guessing. Provided that their initial hypothesis was correct, they were successful. However, if their initial hypothesis was incorrect they were unsuccessful because they did not employ the reasoning pattern necessary to test and reject it; 4. use hypothetico-predictive reasoning to, for example, a) reject the idea that type of sides is relevant (because both types of sides are present in rows one and two), b) generate the alternative idea that the presence or absence of spots is relevant, c) confirm this idea by noting that all of the Thomps in row one, but none of the non-Thomps in row two have spots, and d) therefore conclude that creatures one, three and four of row three are Thomps. If an S did 1) or 2) above s/he was corrected by the experimenter pointing out the relevant features of the creatures and verbally presenting the argument embodied in 4) above as follows: The Slooms had curvy sides so it is reasonable to think that the Thomps may also have curvy sides. But if curvy sides were the key feature, then all of the creatures in row one should be curvy. But notice that these two creatures (numbers two and four) have straight sides and they are Thomps. So this means that something other than curvy sides must be important. Notice also that if curvy sides were the key feature, then none of the creatures in row two should have curvy sides. But these two creatures have curvy sides (numbers two and five in row two) and they are not Thomps. So again there must be something other than curvy sides that is important to be a Thomp.

This verbal argument, of course, amounts to training and assumes that Ss capable of such hypothetico-predictive reasoning will assimilate the verbal training and will apply the reasoning to solve subsequent tasks (cf., Lawson, 1987). Whereas Ss incapable of such reasoning will not assimilate the words and should persevere with their initially incorrect approach, i.e., 1), 2), or 3) above. Of course, it was difficult to tell when an S was simply guessing - approach 3) above - or was, in fact, using the reasoning of

BRAIN MATURATION AND DESCRIPTIVE CONCEPT CONSTRUCTION

65

approach 4). Consequently, whenever an S obtained the correct answer, the reasoning pattern was verbally presented whether the S verbalized it or not. The training continued through the first six tasks by repetition of this verbal presentation when necessary. Thus, by the time Ss reached the seventh task, they may have heard a presentation of the reasoning pattern on five separate occasions (Tasks 26). Ss had also been presented all of the relevant features. Finally, the Mellinark Task, Task 7 was given with no coaching as a final assessment of the Ss' ability to use the reasoning pattern to construct the descriptive concept of Mellinark. 2.2 Scoring Performance on each task was recorded by noting which creatures in row three were identified as Shlooms, Thomps, Bloops, etc. prior to training on that task. Ss were considered successful on the Mellinark Task if they identified creature one, two and six in row three as Mellinarks. 3. GENERAL RESULTS, AN INITIAL CONCLUSION AND KEY QUESTIONS RAISED All 15 eighth graders immediately understood the training and successfully identified creatures one, two, and six in row three as Mellinarks. The sixth graders were equally successful as all 15 showed no difficulty and all correctly identified the Mellinarks in row three. The fourth graders also showed little difficulty and all 15 were successful. The second graders exhibited some difficulties (discussed in more detail below). Nevertheless, the first five were successful on the Mellinark Task. The sixth student was unsuccessful as he identified creatures one, two, four and six as Mellinarks. Creature four was incorrectly identified as a Mellinark "because it looks like Mellinark 4 in the first row." The remaining 24-second graders were successful. Therefore, the results thus far clearly contradict the studies' working hypothesis that older students' difficulties stem from a lack of developmentally-derived, hypothetico-predictive reasoning skill needed to construct descriptive concepts. Although most of the kindergartners (27/30) easily identified creature features, none appeared to understand the reasoning and none (0/30) solved the Mellinark Task. Needless to say, the success of virtually all of the older Ss coupled with the failure of all of the kindergartners is striking and prompted the selection and training of the sample of first graders of intermediate age. Approximately one half (14/30) of the first graders were successful on the Mellinark Task. Figure 8 displays Mellinark Task results as a function of age in months for the kindergarten, first and second graders. The solid dots represent successful performance. The open dots represent unsuccessful performance. The relationship between age and success is dramatic. None of the 30 Ss younger than 84 months (seven years) were successful. Fourteen of 30 of the Ss age 84 to 95 months (the seven-year-olds) were

66

CHAPTER 3

successful, predominantly the older ones, and virtually all of the Ss (29/30) from age 96 to 107 months (the eight-year-olds) were successful.

Two aspects of these results are striking. First, many Ss much younger than those who took part in the Lawson et al. (1991) study were easily trained to solve Mellinarktype tasks. Second, the positive effect of the training dropped dramatically at precisely age seven. Age seven is of considerable interest because it is precisely at this age that many previous investigators have found profound advances in intellectual development (e.g., Cole & Cole, 1989). Indeed, Piaget cites age seven as the transition age between the preoperational and concrete operational stages of development (e.g., Piaget & Inhelder, 1969, p. 96). Thus, we are left with two results in need of explanation. Why, given that Ss in second grade and up appear able to use the needed hypotheticopredictive reasoning, did many of the high school students in the Lawson et al. (1991)

BRAIN MATURATION AND DESCRIPTIVE CONCEPT CONSTRUCTION

67

study experience difficulties? And what caused such an abrupt drop in performance at age seven? Let's consider the specific tasks results in greater detail to see if they will help us answer these questions. 4. SPECIFIC TASK RESULTS Table 1 shows the kindergarten, first and second graders performance on each of the seven tasks. The numbers represent the percentage of Ss at each grade that, prior to training on that task, was successful at identifying the correct creatures in row three for each task. The percentages not only reveal a clear relationship between age and performance on all tasks, but also show that some of the six-year-olds were successful on some of the one-feature tasks (i.e., Tasks 1-4).

A finding that does not show up in Table 1 or in Figure 8 is the younger Ss' clear preference for the matching strategy. Indeed for the six-year-olds on the one-feature tasks, matching led to some success (7% on Task 1 to 40% on Task 2). The likelihood of successful matching/guessing the correct features on Tasks 5-7 was, of course, much less because these tasks involved combinations of features. Note that success for the six-year-olds dropped to 0% on Tasks 5 and 7. One six-year-old did select the correct creatures on Task 6 and then on Task 7 guessed that Mellinarks were creatures that were curvy and had a tail. This led her to incorrectly conclude that creatures one, two, four and five of row three were Mellinarks. When asked about the possible relevance of creature four in row two (a non-Mellinark that is curvy and has a tail) she was unable to use this information to conclude that her initial idea must be wrong. Indeed, it is precisely this conclusion that none of the unsuccessful Ss drew. The point is that the use of hypothetico-predictive reasoning appears necessary for drawing such a conclusion (e.g., If...Mellinarks are curvy creatures with tails, and...I check out the non-Mellinarks in row two, then...none of them should be curvy and have a tail. But... creature four in

68

CHAPTER

3

row two is curvy and has a tail. Therefore...my curvy-creatures-with-a-tail idea must be wrong). Thus, it appears that the younger students failed because they did not use this reasoning pattern and the older Ss succeeded because they did. Therefore, the hypothesis that the difficulties of the initial sample of high school students stem from a lack of hypothetico-predictive reasoning skill needed to construct descriptive concepts is not supported. Indeed, it seems that virtually all students all the way down to the second grade could use hypothetico-predictive reasoning to construct descriptive concepts once that reasoning pattern had been briefly introduced. For example, when an eight-year-old was questioned about his correct answer on Task 6 that creatures one, three, and four of row three were Gloms, he remarked: "It couldn't be strings because these guys (row two numbers one and three) have strings and it couldn't be straight sides because of this one (number two row one)." Then, when he proceeded to the final task, Task 7, he used hypothetico-predictive reasoning to check his ideas: "I think its big dot, little dots, and tail...Oh wait! (he looks at the second row)...OK, none of them in the second row have all these so it's one, two and six." 4.1 Why Did the Kindergartners Fail ? Given that virtually all Ss from kindergarten to eighth grade initiated the Mellinark task with incorrect/incomplete hypotheses (e.g., Mellinarks are creatures with tails), the central question becomes: Why could the older Ss successfully use hypotheticopredictive reasoning to reject/modify their initial hypotheses, while the kindergartners could not? At least three possibilities come to mind:

1. Perhaps kindergartners are unable to generate combinations of features to be tested. In other words, perhaps they are unable to form conjunctive concepts.

2. Perhaps kindergartners do not yet understand the "logic" of falsification, thus when contradictory evidence is gathered, it makes no "cognitive" impact.

3. Perhaps once an initial idea has been generated, it is held so firmly that kindergartners are unable to entertain alternative possibilities. Can Kindergarteners Form Conjunctive Concepts? Let's first consider the hypothesis that the kindergartners failed because they were unable to form conjunctive concepts (e.g., perhaps a Mellinark is a creature with a tail and a dot). If this is true, then they should have been successful on the one-feature tasks (i.e., Tasks 1-4) and they should have failed the two and three feature tasks (i.e., Tasks 5-7). Notice in Table 1 that the kindergartners did show some success on Tasks 1-4. Also notice the substantial decrease in success from Task 4 (the last one-feature task) to Task 5 (the first twofeature task), a decrease from 33% to 0%. Further, the percentages went up substantially for the seven and eight-year-olds on Task 6 after those that failed Task 5 received training, but the six-year-olds' performance on Task 6 did not go up. On Task

BRAIN MATURATION AND DESCRIPTIVE CONCEPT CONSTRUCTION

69

6, 40% of the seven-year-olds were successful on this two-feature task, 50% of eightyear-olds were successful but only one of the six-year-olds (3%) was successful. The percentages increased again on Task 7 (the only three-feature task) for the seven and eight-year-olds to 47% and 97% respectively but not for the six-year-olds (0%). Thus, it appears that task complexity in terms of number of relevant features was an initial source of difficulty for many Ss. And after training, task complexity may have continued to be a source of difficulty for the younger Ss, but not for the older Ss. Is the ability to combine features actually limiting performance of the kindergartners? A closer inspection of the data for the six-year-olds reveals that 9 of them (33%) did in fact combine features on Tasks 6 and 7. For example, one six-yearold concluded that creature number three in row three was a Glom, "Because it has little dots, one big dot and a string (i.e., a tail) like creature number five in row one." Thus, for her, as well as several of her peers, the problem was not that she could not generate and combine features, but that she failed to test these combinations once generated. Thus, the conclusion appears to be that the primary factor limiting the kindergartners' performance was not their inability to generate features or combinations of features (i.e., to form conjunctive concepts), but was their failure to test the combinations once generated. As a further check on this tentative conclusion, another sample of 15 kindergarten Ss was selected and individually administered the seven tasks in a more direct manner. Instead of requiring that Ss generate and test their own ideas, they were told precisely what the key feature(s) were and they were then merely asked to select the correct creatures from row three. For example, the verbal instructions for Task 1 proceeded as follows: These creatures (row one) are calls Shlooms because they all have curvy sides (the curvy sides were pointed out). Notice that none of these in row two have curvy sides. All their sides are straight, so they are not Shlooms. Which of the creatures in row three do you think are Shlooms?

The verbal instructions for Tasks 5, 6 and 7 (the two and three feature tasks) were slightly more complicated. For example, for the Trugs Task the following remarks were also included: So Trugs are creatures with straight sides and little dots. Notice that none of these in row two are Trugs because none of them have both straight sides and little dots. The first one has little dots, but no straight sides, so it's not a Trug. The fifth one has straight sides, but no little dots so it's also not a Trug. So you have to have both straight sides and little dots to be a Trug. Now you see if you can pick out the Trugs in row three.

Instructions for the Mellinark Task were similar except that Ss were shown the three features that had to be combined to make a Mellinark. Success rates on the one feature tasks (Tasks 1-4) were 93.3%, 100.0%, 93.3% and 93.3% respectively. Success rates on the two feature tasks (Tasks 5 and 6) and the one three-feature task (Task 7) were 46.6%, 73.3% and 66.6% respectively. These results indicate that these five and six-year-olds were generally, but not completely, successful

70

CHAPTER 3

at forming conjunctive concepts. Thus, again it appears that the failure of the six-yearolds in the initial sample to solve the Mellinark Task (i.e., 0% success rate) is probably not due to an inability to form conjunctive concepts (i.e., note the 66.6% success rate on the Mellinark Task when five-year-olds were given direct instruction). Although a few five-year-olds exhibited difficulties such as these, the important point is that over all, the clear majority was able to form conjunctive concepts. Therefore, the hypothesis that they failed due to an inability to form conjuctive concepts is not supported. Do Kindergartners Understand the "Logic" of Falsification? The second hypothesis for the kindergartners' failure proposes that they do not yet understand the "logic" of falsification, thus when contradictory evidence is gathered, it makes no "cognitive" impact. In this sense Piaget might be correct in claiming that the shift from the preoperational stage to the concrete operational stage involves the acquisition of new "logical" operations. To test this hypothesis an additional sample of kindergartners was administered a logic-of-falsification task. If the lack-of-logic hypothesis is correct, then the kindergartners should fail the task. During the task, Ss were shown eight cards with either a triangle or a square on one side and either green dots or blue dots on the other side (e.g., Lawson, 1990). They were then told the following conditional rule: If a card has a triangle on one side (p), then it has green dots on the other side (q), i.e., Ss were told to state whether or not each card, once turned over to reveal the other side, broke the rule. The cards, in order of presentation were: a) b) c) d) e) f) g) h)

triangle then green dots (i.e., p then q) green dots then triangle (i.e., q then p) square then green dots (i.e., not p then q) green dots then square (i.e., q then not p) triangle then blue dots (i.e., p then not q) blue dots then triangle (i.e., not q then p) square then blue dots (i.e., not p then not q) blue dots then square (i.e., not q then not p)

The percentage of Ss who thought that the respective cards broke the rule were: a. 16%, b. 12%, c. 44%, d. 56%, e. 88%, f. 73%, g. 48%, and h. 44%. None of the Ss responded correctly to all cards (i.e., only cards e and f logically break the rule), but most of them did state that cards e and f broke the rule (i.e., 88% and 73% respectively). In other words, most of the Ss understood that the rule had been broken (i.e., falsified) when p and not q occurred and when not q and p occurred. Therefore, the lack-of-logic hypothesis is not supported. The fact that many Ss thought that cards other than e and f broke the rule indicates some confusion on their part. However, this confusion does not appear to be the reason for failure on the concept construction tasks because similar confusion has been found on this task even among high school and college Ss who would have no trouble responding successfully to the brief instruction on the tasks (Lawson, 1990). This

BRAIN MATURATION AND DESCRIPTIVE CONCEPT CONSTRUCTION

71

means that the failure of the younger Ss on the concept construction tasks appears not to be due to their inability to recognize contradictory evidence when directly presented. In other words, the six-year-olds' failure is not due to a lack of logic, or due to a failure to form conjunctive concepts.1 Are Kindergartners Unable to Entertain Alternative Possibilities? The third hypothesis listed above suggests that the kindergartners' failure was due to the fact that they held so firmly to their initial ideas that they were unable to entertain alternative possibilities. This sort of failure represents a "perseveration" error i.e., the S perseveres with a previous idea in spite of the presentation of contradictory evidence. When administered the Wisconsin Card Sorting Task, perseveration errors occur among young children (below seven years in age) and among adults with frontal lobe brain damage. Perseveration errors on the Wisconsin Card Sorting Task occur when Ss fail to shift from, say, a previously successful sorting of cards based upon color, to another feature (e.g., shape) even when the experimenter repeatedly tells the S that the selection is in error. Perseveration errors continue in the face of contradictory evidence. In a sense, contradictory evidence has no impact on the Ss' reasoning consequently they do not generate and test other ideas. In other words, they do not employ the necessary hypothetico-predictive reasoning for task success. Dempster (1992) reviewed a considerable amount of research that implicates children's failure to suppress misleading or irrelevant information as a major sort of difficulty in performance on a variety of interference sensitive tasks such as the Wisconsin Card Sorting Task, measures of field independence, conservation tasks, selective attention tasks, and the Brown-Peterson task. Dempster's review provides considerable support for two points crucial to a possible explanation for the present results. First, research by Luria (1973) and several associates is cited in which Luria concludes:

1 Another hypothesis for the difference in performance between the six and eight-year-olds deserves mention. According to Pascual-Leone (1969, 1970), mental capacity increases with age. Presumably sixyear-olds have a mental capacity of 2 units (i.e., they can simultaneously process 2 discrete units of information). By the time a child is eight years old his/her mental capacity has increased to 3 units. This increase is presumed to be independent of factors such as degree of field independence (Globerson, 1985) and social class (Globerson, 1983). If the reasoning involved in solving the concept acquisition tasks requires the child to simultaneously process 3 units of information (i.e., 1. If a tail makes a creature a Mellinark, and 2, this creature [creature one in row two] is not a Mellinark, but it has a tail, then 3. The presence of a tail is not sufficient to make a Mellinark.), and if our six-year-olds only have a mental capacity of 2 units, then we have a "lack of sufficient mental capacity" explanation for their failure. The problem with this explanation is that it should also hold for the logically similar evaluation task (i.e., 1. If a card has a triangle on one side, then it has green dots on the other side, and 2. I turn over the triangle card and find blue dots, so a card exists with a triangle and blue dots. Therefore 3. The rule has been broken). In both situations, the logic involves these steps (i.e., 1. 2. p and not q. 3. not not q.). The fact that most of the six-year-olds who took the evaluation task were able to generate this three-step argument argues against the mental capacity explanation.

72

CHAPTER

3

..it must also be noted that the prefrontal regions of the cortex do not mature until very late in ontogeny, and not until the child has reached the age of four to seven years do they become prepared for action. ...the rate of increase in area of the frontal regions of the brain rises sharply by the age of three and a half to four years, and this is followed by a second jump towards the age of seven to eight, (pp. 87-88)

Second, adult patients with frontal lobe damage make significantly more errors and make significantly fewer shifts (i.e., greater numbers of perserverative errors) on the Wisconsin Card Sorting Task than do adult patients with damage to other parts of the brain. As Dempster points out, a comparison of the mean number of perserverative errors of adult patients with frontal lesions (Heaton, 1981) with normal six-year-old children reveals that they perform in a similar manner (Chelune & Baer, 1986). Hence, the second graders' success and the kindergartners' failure on the present tasks could be due to degree of frontal lobe maturation. In other words, the frontal lobes may play a key role in successful task performance; and the frontal lobes are not sufficiently operational until seven to eight years of age. The frontal lobes are the seat of several of the brains "higher" executive functions such as extracting information from other brain systems and anticipating, selecting goals, experimenting and monitoring information to produce novel responses (cf., Stuss & Benson, 1986). Thus, if it can be demonstrated that the present tasks involve similar cognitive demands (i.e., like those of the Wisconsin Card Sorting Task - the WCST), then this frontal-lobes hypothesis will have gained support. Levine & Pruiett (1989) provide a detailed neural network and computer simulation of frontal lobe function on the WCST. Can this network also be applied to the present tasks? 5.

THE LEVINE-PRUIETT NEURAL NETWORK

Figure 9 depicts the neural network, isomorphic to the Levine and Prueitt network that may be operative in the present concept construction tasks. Task 3, the Bloops Task, has been selected as the example task. The network includes a field of nodes referred to as that codes input features. The features in the WCST are color (red, yellow, blue, green), shape (circle, square, triangle, cross) and number of figures (1,2,3,4). In the Bloops Task the features that must be coded are number of tails (0 or 1), number of spots (0 or many), and type of border (straight or curvy). Nodes in field code the template cards in the Levine and Pruiett network. The template cards in the WCST show one red triangle, two green stars, three yellow crosses, and four blue circles. The template cards serve as sources of ideas about what the relevant feature might be upon which to base the sorting of the response cards (e.g., sort by the color red, sort by the shape circle). The figures in row one of the Bloops Task serve the same role in that they contain the relevant features that can be induced as the basis for sorting the creatures in row three into categories of Bloops and non-Bloops (e.g., It's a Bloop if it has one tail; It's a Bloop if it has spots; It's a Bloop if it has straight sides). Thus, possible categories at on the Bloops Task are groups of, say, all creatures with a tail, all creatures with spots, all creatures with straight sides.

BRAIN MATURATION AND DESCRIPTIVE CONCEPT CONSTRUCTION

73

The network also includes a habit node and a bias node as shown in the figure. These nodes correspond to each of the subfields in Habit nodes detect how often prior classifications have correctly and incorrectly been made. On the WCST this means, for instance, how many times a sorting based on color has been reinforced by a "correct" or "incorrect" response from the examiner. In the present series of concept acquisition tasks the habit node detects how many times a prior classification has been made based upon say, type of border, as in Task 1, or presence of spots as in Task 2. In other words, if, for example, the presence of spots has been the relevant feature on previous tasks, then the "habit" of classifying based upon this feature is strengthened. It should be noted that most of the Ss in the present study began Task 1 using the matching strategy based on overall shape presumably because shape matching had been reinforced numerous times in their pasts. Of considerable importance is the fact that many of the younger Ss persevered with this shape matching strategy throughout the interview, while all of the many eight-year-olds who initially considered only shape were able to give it up. The bias nodes are affected both by activity in the habit nodes and by reinforcement. In the WCST, the experimenter gives positive or negative reinforcement as he/she responds to the S's sorting with the statement of "right" or "wrong." Reinforcement on the concept acquisition tasks comes in the form of the creatures in row two and from the experimenter when he/she suggests alternative strategies for task solution. Suppose, for example, that an S, armed with the idea that the presence of spots is a relevant feature based upon his/her previous experience with Task 2, inspects the creatures in row one and notes that the first, third and fourth Bloops have spots. The presence of these three spotted Bloops then reinforces the idea that the presence of spots is the relevant criterion. Of course, the first row also contains negative reinforcement in the form of creatures two and five that do not have spots. Nevertheless, if the positive reinforcement signal is too great, or if negative signal is too weak, the habit will prevail (i.e., the S exhibits persrveration errors as he/she fails to switch from previous ways of classifying the creatures). Note also that row two contains creatures that may serve as positive reinforcement (unspotted creatures two and three) or negative reinforcement (spotted creatures one and four). The Zij's and Zji's between and represent synaptic strengths of the neuron connections between the two nodes (i.e., in both directions). These are large when node (e.g., the creatures that one is attending to, such as creature one of row one in the Bloops Task with spots) contains a feature that is active at (e.g., the presence of spots is the key feature). Attentional gating from bias nodes increases some to signals. If, for instance, the "It's a Bloop if it has spots" bias is high and the "It's a Bloop if it has a tail" bias is low, then attending to creature one of row one that contains spots and one tail will excite the "It's a Bloop if it has spots" node at more than it will excite the "It's a Bloop if it has a tail" node. When a creature is paid attention to, the proposal category whose activity is largest in response to the input creature is chosen as the one matched. A match signal corresponding to the shared feature(s) is sent to the habit and bias nodes. These signals either increase or decrease the activity of the bias node

74

CHAPTER

3

depending upon whether the creature is in row one (is a Bloop) or in row two (not a Bloop). In other words, if one initiates the idea that the presence of spots is the relevant feature and attends to creature one of row one that has many spots and is a Bloop, then signals to the habit and bias nodes increase. On the other hand, if one attends to creature one of row two that has many spots but is not a Bloop, then the signals decrease.

Additional details of the network, including equations that the various signals obey can be found in Levine & Prueitt (1989). For our purposes the one remaining key variable is reinforcement R that activates the bias nodes. As shown in Figure 9, this reinforcement can take on the value or where is parameter assumed to be relatively high in normal adults and relatively low in adults with frontal lobe damage. This is to say that the reinforcement arrow (either + or -) from the reinforcement locus to the bias node corresponds to the role of the frontal lobes in task performance. Thus

BRAIN MATURATION AND DESCRIPTIVE CONCEPT CONSTRUCTION

75

in the present study the value for our six-year-olds is assumed to be relatively low because their frontal lobes are not yet sufficiently operational. Whereas the value for the eight-year-olds is relatively high because their frontal lobes are assumed to be operational. In brief, the failure of adults with frontal lobe damage to shift from sorting cards on the WCST based upon, say, a color criterion to a shape criterion is explained by the failure of the reinforcement locus in the frontal lobes to send sufficiently strong signals (either + or -) to the bias node to sufficiently alter the activity of the bias node. Without sufficiently strong signals the currently active bias will continue to control behavior. It is possible that the six-year-olds in the present study failed to shift their classification criteria for the same reason. Levine & Pruiett (1989) cite a number of experimental and anatomical findings (e.g., Mishkin, Malamut & Bachevalier, 1984; Mishkin & Appenzeller, 1987; Ulinski, 1980; Nauta, 1971) in support of the distinctions made in their neural network. They also report results of a simulation of normal and frontally damaged persons on the WCST in which was the only parameter altered. For normal persons was set at 4. To simulate frontal damage was set at 1.5. Results of the simulations were nearly identical to previously reported results with actual normal and frontally damaged persons. Therefore, the results provide support for the accuracy of their network and, by inference, for the network presented in Figure 9. 6. CONCLUSIONS The basic argument advanced is that the ability to evaluate evidence that is either supportive of or contradictory to proposals regarding the relevant features of objects encountered in one's environment is central to the process of descriptive concept construction. Further, it may be that it is not until seven years of age that the frontal lobes are mature enough to attend to contradictory evidence with sufficient regard to prompt the evaluation and possible alteration of one's initial ideas. In other words, hypothetico-predictive arguments in descriptive contexts carry little or no force when the child initially believes that tails are the key feature. However, when the frontal lobes mature sufficiently to allow contradictory evidence to be attended to and evaluated, a powerful pattern of verbal hypothetico-predictive argumentation becomes available to the child, a pattern that could well warrant the designation as a new stage of intellectual development because it allows for the personal construction of descriptive concepts. The tentative conclusion then is that the stage of intellectual development, which beings at seven years of age (Piaget called it concrete operational), involves use of a verbally-mediated, hypothetico-predictive reasoning pattern to test the relevance of alternative features of objects, events, and situations in the child's environment to construct descriptive concepts. Reasoning at this stage is initiated with what the child directly perceives in his/her environment, e.g., the child is able to actually see the tiny spots, tails, etc. on the creatures in the Mellinark Task. In this sense the representations

76

CHAPTER 3

the child uses to initiate reasoning are empirical in origin and the concepts that are proposed and tested are descriptive in nature. Of course later in life, particularly in science, many entities and processes are proposed and tested that are explanatory in nature. For example, it is well known that adult salmon return to the stream of their birth to spawn. This observation raises a very interesting causal question. Namely: How do salmon locate the stream of their birth prior to spawning? (i.e., What causes salmon to end up in their home stream?) Because the salmon will not tell you how they do it, nor can one find the answer by merely watching salmon as they head upstream, answering a causal question of this sort requires that one generate and test alternative causal, as opposed to descriptive, hypotheses. Causal hypothesis generation requires the use of analogy (borrowing explanations) as opposed to direct observation (Hanson, 1958; pp. 8S-86 refers to the process as abduction, i.e., abducting/stealing/borrowing ideas from one context for use in another context). Regardless of how causal hypotheses are generated, once generated, they must be tested using the same hypothetico-predictive reasoning pattern, which in this case might go something like this: If...salmon navigate by using their eyes in a way analogous to the way humans often navigate, (sight hypothesis) and...some returning salmon are blindfolded, (planned test) then...they should not be as successful at finding their home stream as non-blindfolded salmon. (prediction) But... both groups of salmon are equally successful. (observed result) Therefore...the sight hypothesis is not supported. We need to generate and test another causal hypothesis. (conclusion) Thus, we have identified at least two levels of hypothetico-predictive reasoning. On the lower level, reasoning is initiated by empirical representations, by the direct perception of environmental stimuli. This level of reasoning is used to test descriptive hypotheses and to construct descriptive concepts. On the higher level, reasoning is initiated by abductively generated hypothetical representations, by analogies, and is used to test causal hypotheses and presumably to construct causal concepts (more will said about this in subsequent chapters, particularly in Chapter 8). Having differentiated at least two levels of hypothetico-predictive reasoning, we may finally be in a position to explain why Lawson et al. (1991) found such a high correlation between high school students' performance on a test of scientific/mathematical reasoning and performance on the Mellinark-type tasks. As mentioned, the problem for the unsuccessful high school students was not that they lacked skill in use of the lower-level reasoning needed to test descriptive hypotheses. We know this because students all the way down to second grade were easily prompted to use the lower-level reasoning to solve the descriptive tasks. Instead the problem for the high school students seems to have been that some lack skill in use of higher-level reasoning to test alternative problem-solving strategies (e.g., a matching strategy versus

BRAIN MATURATION AND DESCRIPTIVE CONCEPT CONSTRUCTION

77

use the lower-order, hypothetico-predictive reasoning). In other words, successful performance on the creature card tasks, when left on your own as the high school students were, appears to require that one try out and test a number of abductivelygenerated strategies. Thus, if students lack skill in this higher-level reasoning, they will have difficulty in solving the tasks whenever their first "hypothesis" about what strategy the task calls for is wrong. In support of this tentative explanation, consider the remarks of a third student cited in Lawson et al. (1991, pp. 965-966). This student initially generated the matching strategy, found it unsatisfactory, but was unable, on her own, to reject it and derive a successful strategy: To me this is mind-boggling. I don't relate much to this. I'll say number four is a Mellinark...number three...number one is not a Mellinark. There is no rhyme or reason to this to me, absolutely none. Well let's just take them on at a time. You said four is a Mellinark. I guess because it compares to this (number four row one). And that's the only reason, the circle fits in the middle, and this (number three, row three) relates because it's a rounded figure...and some of these (row one) are, but some of these (row two) aren't. This (number one, row three) is more of a jagged effect, so I would say it's not a Mellinark. These are more straight line. This has a tail on it. I can't even relate to that. I can't figure out what you are getting at because you see some of both ideas in both of them. Because I can't reason on it, I don't like guessing either. Well, some people have looked at it this way. Say, for example, that all of these (row one) have tails. If a Mellinark is a creature with a tail, then you would expect that none of them in row two would have a tail, but some of them do. So the idea is that a Mellinark is just a creature with a tail must be wrong. Uh huh.

So there must be some other reason for being a Mellinark. Yeah, that's what I was looking for - some similar point. If they were all more of a rounder effect, and they were more of a jagged effect or straight lines. But I could not see that -I could not see what you were getting at. Well, suppose you look for combinations of features. For example, these all have tails and a big dot. Well, that's true. Maybe the big dot plus a tail is what the Mellinark is. Ah! OK, that makes a little more sense. OK, go with that idea for a minute. Does that pan out? Yeah, I think it does - you get your dot, tail and your Mellinark...or your dots. Is that what you are saying? Your dots, with the big dot and with the tail. Because you don't

78

CHAPTER

3

see all three on any of these (row two) that I can see. OK...so if you put all three combinations, then I would say one, two, and six (row three). So you had to give me that idea, but after I looked I thought, ah! Heh! heh! heh! But I don't think I could sit here and figure that out. OK.

This response implies that the older, untrained students can identify task features and can use the necessary hypothetico-predictive reasoning to test these features. But they cannot use hypothetico-predictive reasoning to generate and test alternative problem-solving strategies. Thus, just like kindergarten students who perseverate on incorrect task features, many high school students perseverate on an initially generated and incorrect strategy. In conclusion, the creature card tasks appear to require use of two levels of hypothetico-predictive reasoning for solution. Use of the higher-level reasoning appears necessary when students must solve the tasks on their own and when their initial problem-solving strategy is in error and must be rejected. However, only the lowerlevel reasoning is necessary when the correct strategy is provided through brief training. The Lawson et al. (1991) results, coupled with the present results, imply that many high school students are not skilled in use of the higher-level reasoning, whereas virtually all elementary school students are skilled in use of the lower-level reasoning, reasoning that appears to emerge at age seven as a consequence of the acquisition of language and the maturation of the brain's frontal lobes. Of course the possibility exists that another spurt of brain maturation is necessary for use of the higher-level reasoning (see Chapters 4 and 5). 7.

INSTRUCTIONAL IMPLICATIONS

At this point, only tentative instructional implications can be drawn. One might suspect, however, that classroom introduction of several creature task tasks, followed by discussion of the reasoning pattern used to solve them might be an effective way to help unskilled junior high school and high school students begin to understand and use (via analogy) the same pattern of reasoning employed at the higher level to test causal hypotheses and problem-solving strategies. Effective instruction along these lines would seem to require that the teacher clearly point out how the reasoning pattern in both situations is the same but that reasoning in the two situations is initiated by different sorts of ideas (i.e., observationally-generated descriptive hypotheses versus abductively-generated causal hypotheses/strategies). The intended result of such instruction would be that older students would become more conscious of the use of hypothetico-predictive reasoning at this higher level. Such increased consciousness should pay off in terms of increased skill in testing causal hypotheses, in testing alternative problem-solving strategies and presumably in increased understanding of higher-level scientific and mathematical concepts.

CHAPTER 4 BRAIN MATURATION, INTELLECTUAL DEVELOPMENT AND THEORETICAL CONCEPT CONSTRUCTION

1. INTRODUCTION

The development of hypothetico-predictive reasoning skill used to construct descriptive concepts appears to be linked to frontal lobe maturation at age seven (see Chapter 3). Likewise, the development of higher-level, hypothetico-predictive reasoning, which presumably is used to construct theoretical concepts, may also be linked to further maturation of the brain's frontal lobes during early adolescence. In theory, the construction of theoretical concepts involves higher-level, hypotheticopredictive reasoning when such reasoning is used to construct arguments to reject previously constructed misconceptions and accept more appropriate theoretical conceptions. In other words, such reasoning skill is needed to undergo the necessary conceptual change. This chapter will discuss research designed to test the hypothesis that frontal lobe maturation during early adolescence influences the development of higher-level, hypothetico-predictive reasoning skill and that the development of such reasoning skill influences one's ability to construct theoretical concepts. 2. RELATED RESEARCH ON BRAIN MATURATION

Based on measured increases in brain weight and skull circumference, Epstein (1974a; 1974b; 1978) concluded that brain growth during childhood and adolescence occurs in a series of plateaus and spurts. With respect to early adolescence, Epstein & Toepfer (1978) state... "in perhaps 85% of all youngsters between ages 12 and 14, the brain virtually ceases to grow" (p. 657). According to Epstein and Toepfer, the early adolescent plateau, which coincides with the onset of puberty, is followed by a spurt from age 14 to 16. The plateau and subsequent spurt appear to be related to learning ability. For example, Epstein & Toepfer cite data establishing a peak in fluid intelligence around age 11 (presumably when the brain is growing) followed by dip around age 13 to 13.5 (presumably when the brain has stopped growing). Further, they claim that overall brain growth coincides with the four classical stages of Piaget's developmental theory (i.e., sensory-motor, preoperational, concrete operational, and formal operational). In their words, "These brain growth periods may turn out to be the biological basis of the Piaget stages" (p. 657). More recent

79

80

CHAPTER 4

electroencephalographic data reported by Hudspeth & Pribram (1990) tend to corroborate the link between developmental stages and brain growth. Interestingly, these data show five cycles (i.e., spurts and plateaus) over the first 21 years of postnatal development with the last starting at about 17 years of age suggesting the possibility of a fifth developmental stage (see Chapters 7, 8 and 10). Although the maximum number of neurons is probably present at birth, existing neurons in the frontal lobes continue to grow throughout adolescence and perhaps even into early adulthood (Schadè & Van Groenigen, 1961). More specifically, Blinkov & Glezer (1968) found that pyramidal neurons (see Chapter 2) in the frontal lobes increase more in length and width during adolescence than do neurons in the pre-motor and sensory-motor areas. Dendrites of the frontal pyramidal neurons also continue to grow after birth. Dendrites, which are relatively rudimentary in newborns, continue to grow throughout the teenage years resulting in increases in total dendrite length and in number of branches (Schadé & Van Groenigen, 1961). Increases in frontal lobe neuron myelinization also continue during the teenage years. In contrast, myelinization of the sensory-motor cortex is mostly complete by age two (Yakoblev & Lecours, 1967). Also, spurts of electroencephalographic activity during adolescence are centered in the frontal lobes (Thatcher et al., 1987). Therefore, it seems reasonable to suspect that the age 14 to 16 brain growth spurt occurs primarily in the frontal lobes. Research has yet to establish a clear link between the apparent age 14 - 16 brain growth spurt and frontal lobe activity. Nevertheless, published data on children's and adolescents' ability to inhibit previously relevant, but currently irrelevant, cues to correctly sort cards in the Wisconsin Card Sorting Task (i.e., Heaton, Chelune, Tally, Kay & Curtiss, 1993) are suggestive of such a link. Several neurological studies, many dealing with patients with frontal lobe damage, have established the Wisconsin Card Sorting Task as a valid measure of frontal lobe activity (e.g., Knight & Grabowecky, 1995; Luria, 1980; Milner, 1963; Milner, 1964; Shimamura, Gershberg, Jurica, Mangels & Knight, 1992; Weinberger, Berman & Illowsky, 1988; Weinberger, Berman & Zec, 1986). Analysis of the Heaton et al. data shows that inhibiting ability (i.e., one's ability to disregard/inhibit potentially misleading cues), as measured by the Wisconsin Card Sorting Task, increases with age with the exception of a rather pronounced performance dip from age 10 to about 13 years - a time period that coincides with the onset of puberty (Cole & Cole, 1989). Could this dip be caused by a lack of frontal lobe growth during this age period? Could the dip be linked to other cognitive abilities that are also centered in the frontal lobes, such one's ability to plan a series of moves to reach a goal, one's ability to find a simple pattern embedded in a complex background, and one's ability to mentally coordinate separate bits of information? Assuming that the apparent age 12-14 plateau and age 14-16 spurt can be linked to such frontal lobe activities, can they also be linked to students' reasoning skill and to their ability to construct scientific and mathematical concepts? Previous studies are suggestive of such links. For example, Lawson, Karplus & Adi (1978) found

BRAIN MATURATION AND THEORETICAL CONCEPT CONSTRUCTION

81

little or no difference between sixth graders (mean age = 12.9 years) and eighth graders (mean age = 14.3 years) use of proportional and probabilistic reasoning. But they found huge advances in the use of proportional and probabilistic reasoning from the eighth graders to tenth graders (mean age 16.1 years). Also in a sample of 6,130 Korean students, Hwang, Park & Kim (1989) found generally similar performances on measures of proportional, combinatorial, probabilistic and correlational reasoning among 12, 13 and 14-year-olds (i.e., an average of only 3.8% increase in the number of successful responses across this age span). However, they found substantial performance increases by the 15-year-olds (i.e., an average of 15.2% increase in the number of successful responses). Further, several studies have established a clear link between reasoning skill and concept learning (e.g., Baker, 1994; Choi & Hur, 1987; Johnson & Lawson, 1998; Kim & Kwon, 1994; Lawson & Renner, 1975; Lawson, 1985; Robinson & Niaz, 1991; Ward & Herron, 1980). Analysis of the Heaton et al. data and these education studies suggest that the early adolescent brain growth plateau and spurt may impact several important cognitive abilities and what students may or may not learn as a consequence of instruction. Frontal lobe maturation during early adolescence is accompanied by increases in neuron myelination. Increased myelination increases signal transmission rate. Thus, it seems reasonable to suspect that increased signal transmission rate in turn increases the amount of information that can be processed during any time period before signal decay causes a loss of that information (see Grossberg's activity equation introduced in Chapter 2). Hence, one's ability to mentally represent information (i.e., one's representing ability) can be expected to increase during early adolescence. Representing ability presumably includes one's ability to disembed relevant task information from background noise, one's ability to plan a series of steps to reach a goal, and one's working memory. In the context of theoretical concept construction, the ability to represent task-relevant information presumably is crucial. Further, increased signal transmission rate due to increased myelinization can be expected to increase signal frequency, hence signal strength. If increased myelination occurs in the axons that transmit signals from the frontal lobes responsible for the positive and negative reinforcement to bias nodes (as depicted in the Levine-Pruiett neural network introduced in Chapter 3), then increases in one's ability to inhibit taskirrelevant information can also be expected to increase during early adolescence. In the context of conceptual change, task-irrelevant information represents prior misconceptions that must be inhibited prior to engaging in internal and/or external hypothetico-predictive arguments that may cause the misconceptions to be rejected. In other words, if a person is so certain that their prior conceptions are correct, they may be unwilling/unable to subject them to hypothetico-predictive tests, hence will not undergo conceptual change. On the other hand, once a new conception is seen as at least plausible then the student is in a position to engage in hypothetico-predictive argumentation that may result in conceptual change. Figure 1 summarizes the key theoretical relationships just described.

82

CHAPTER

4

2.1 Research Design and Predictions

As a test of the theoretical relationships summarized by Figure 1, an identical series of 14 inquiry lessons was taught to eight groups of students ranging in age from 13.1 to 16.9 years - an age range in which growth of the frontal lobes presumably plateaus and then spurts. Prior to instruction, measures associated with frontal lobe activity (i.e., inhibiting, planning, and disembedding abilities and mental capacity) were administered to all students, as was a test of scientific reasoning skill. A test of theoretical concepts understanding (i.e., air pressure concepts derived from kinetic-molecular theory) was administered before and after instruction. The following argument summarizes the alternative hypotheses tested and their predicted results: If...frontal lobe maturation during early adolescence influences the development of higher-order reasoning skill and the development of higher-order reasoning skill influences one's ability to construct theoretical concepts, (frontal-lobe-maturation hypothesis) and...frontal lobe activities and reasoning skill are measured in students ranging in age from 13.1 to 16.9 years and the students are taught a series of identical lessons involving theoretical concepts, (planned test) then...the measures should show performance plateaus among the 13 and the 14year-old students that should be followed by performance spurts among the older students. Further, instruction should be equally ineffective among the 13 and 14 year-olds but should become increasingly effective among the 15 and 16-year-olds. (predictions) On the other hand,

BRAIN MATURATION AND THEORETICAL CONCEPT CONSTRUCTION

83

if...increases in reasoning skill and learning ability depend only on environmental influences (e.g., increases in declarative knowledge due to schooling or simply to increases in general life experiences), which presumably increase linearly with age, (experience hypothesis) then...no performance plateaus and/or spurts should be found and instruction should be increasingly effective across age in a linear fashion. (predictions) 3. METHOD

3.1 Sample

Two hundred six volunteer students (107 females and 99 males) ranging from 13.1 to 16.9 years of age from two junior high schools and two senior high schools in Korea participated in the study. One junior and one senior high school were located in city of approximately 100,000 people. The other junior and senior high schools were located in a city of approximately two million people. Each student was enrolled in one of eight all male or all female eighth-grade through eleventh-grade science classes. 3.2 Instruments

Inhibiting Ability. The individually administered Wisconsin Card Sorting Task WCST (Heaton et al., 1993) was used to measure inhibiting ability. Testing of each student took about 10 minutes. The WCST consists of four stimulus cards and 128 response cards (see Figure 2). The first stimulus card shows one red triangle. The second shows two green stars. The third shows three yellow crosses. And the fourth shows four blue circles. The 128 response cards have different shapes (crosses, circles, triangles, or stars), colors (red, yellow, blue, or green) and number of figures (one, two, three, or four). The student is given the 128 response cards and asked to match each card to one of the four stimulus cards. After each attempted match, the student is told whether the match is correct or incorrect, but not told the matching principle (i.e., match by color, match by shape, match by number). More specifically, the first matching principle was match by color. All other attempted matches were called incorrect. Once the student made ten consecutive correct color matches, the sorting principle was secretly shifted to shape. If the student continued to incorrectly match by color in spite of negative feedback from the interviewer, he/she is said to have committed a perseveration error (i.e., an incorrect response in card sorting in the face of negative feedback). After ten consecutive correct responses to shape, the principle was shifted to number and then back to color. This procedure continued until the student successfully completed six matching categories or until all 128 cards had been used. Because this test was quite

84

CHAPTER 4

time consuming, five interviewers were used to administer the test. Interviewer training included verbal explanations and practical examples on presenting the test directions, on recording student responses, on giving feedback, and on making appropriate category shifts. The training session lasted about two hours. Inter-rater reliability 0.93 based on records of sample student responses.

Scoring. The number of perseveration errors for each category was summed to obtain a total number for each student. Data analyses were then run using these numbers. Note however that inhibiting ability is inversely correlated with the number of perseveration errors. Thus, students who make fewer perseveration errors are assumed to have more inhibiting ability. Planning Ability. Planning ability was assessed by the individually administered Tower of London Test. Testing of each student took about 20 minutes. The test requires planning in terms of means-ends analysis to successively solve a set of increasingly difficult tasks (Krikorian, Bartok, & Gay, 1994; Shallice, 1982). To solve each task, students must plan and execute a series of moves with success being defined in terms of task completion within a minimum number of moves. Test materials consist of a board with three vertical wooden sticks of varying heights and three moveable balls. The balls, colored red, green, and blue, can be slid up and down the sticks. The first stick can hold all three balls. The second stick can hold two balls. And the third stick could hold just one ball. From the initial ball positions, the student is asked to move one ball at a time from stick to stick, in a prescribed number of moves to achieve a certain predetermined goal (e.g., order the balls, green over blue over red on the long stick in five moves). The test requires students to plan a series of sub-goals as they must not only anticipate and visualize the end goal, but each step to that goal must also be mapped in the proper sequence. Krikorian et al. (1994) developed a set of tasks appropriate for students in grades one through eight. Because the present study tested students in grades eight through

BRAIN MATURATION AND THEORETICAL CONCEPT CONSTRUCTION

85

eleven, the Krikorian et al. test was modified to include five additional tasks of increasing difficulty for a total of 12 tasks, two of which were practice. Each student was tested individually by one of five trained interviewers. Training included verbal explanations and practice on presenting test directions, on recording student responses, on checking time limits, and on giving feedback. The training session took about two hours. Inter-rater reliability was 0.95 for a sample of student responses. Scoring. The easiest of the scored tasks required four moves and the most difficult required seven. Three trials were allowed for each task. Students were given one minute to reach the goal position per trial. Three points were awarded if the goal position was achieved in the prescribed number of moves and within the time limit on the first trial. Two points were awarded for a successful performance on the second trial. And one point was awarded for a successful performance on the third trial. If the student failed all three trials, a score of 0 was awarded. A student's total score was the sum of points earned on all 10 tasks. Thus a maximum of 30 points was possible. In a pilot test of 30 9th-grade students, a Chronbach reliability coefficient of 0.61 was obtained. Disembedding Ability. The group administered Group Embedded Figures Test (Dumsha, Minard & McWilliams, 1973; Thompson, Pitts & Gipe, 1983; Witkin, Moore, Goodenough & Cox, 1977; Witkin, Oltman, Raskin & Karp, 1971) was used to assess disembedding ability. The test requires students to locate and outline simple figures concealed in complex and potentially misleading backgrounds. Disembedding ability improves with age during childhood and adolescence, but one's ability relative to one's peers remains relatively constant across age (Witkin, et al. 1971; Witkin, et al. 1977). The Korean version of the Group Embedded Figures Test used in the present study consists of 16 figures in each of two sections (Jeon & Jang, 1995). Students were given 10 minutes for each section. Ahn (1995) reported a Cronbach's reliability coefficient of 0.70 when the test was used with a sample of Korean secondary students similar to those in the present study. Mental Capacity. The group administered Figural Intersection Test developed by Pascual-Leone & Smith (1969) was used to assess mental capacity. The test took about 15 minutes to complete. Mental capacity is defined by Pascual-Leone (1970) as the size of one's central computing space or working memory. According to Pascual-Leone, mental capacity increases from e + 1 at three years of age to about e + 7 at 15 years; where e represents the mental effort or energy required to attend to specific easily understood and remembered questions posed by given tasks and the number represents the maximum number of "schemes" that can be successfully coordinated at a given time to solve the task. The Figural Intersection Test has been used to assess the mental capacity of students in various studies (e.g., de Ribaupierre & Pascual-Leone, 1979; Globerson, 1983; Niaz & Lawson, 1985; Pascual-Leone, 1970; Pascual-Leone & Ijaz, 1989). Scoring. The test used in the present study consists of 32 items with from two to eight overlapping figures. For each item, the student is asked to mark a point indicating the area of intersection of the overlapping figures. No time limit is given

86

CHAPTER 4

to complete the test. A maximum score of 32 points was possible. A Cronbach's reliability coefficient of 0.88 was obtained in a sample of Korean secondary school students similar to those of the present study was 0.88 (Ahn, 1995). Validity of the above described instruments as measures of frontal lobe activity have been established primarily through multiple reports of frontal lobe damage leading to striking deficits in performance on these and similar instruments: inhibiting ability (e.g., Milner, 1963; 1964; Weinberger, Berman & Illowski, 1988; Weinberger, Berman & Zec, 1986); planning ability (e.g., Baker et al., 1996; Black & Strub, 1976; Fuster, 1989; Luria & Tsvetkova, 1964; Luria, 1973; Stuss & Benson, 1986); dissembedding ability (Cicerone et al., 1983; Dempster, 1992; Knight & Grabowecky, 1995; Kolb & Whishaw, 1996; Teuber, 1972); working memory (e.g., Baur & Fuster, 1976; Fuster, 1973; Goldman-Rakic, 1990; GoldmanRakic & Friedman, 1991; McCarthy et al., 1995). Reasoning Skill. A 14-item group administered test was used to assess reasoning skill. The test took about 50 minutes to complete. The test is a modified version of Lawson's Classroom Test of Scientific Reasoning (Lawson, 1978; 1987; 1992). The modified test contains 8 of the original 12 items. The original items were based on Piagetian tasks and involve the identification and control of variables, and proportional, probabilistic, correlational and combinatorial reasoning (Inhelder & Piaget, 1958; Karplus & Lavatelli, 1969; Piaget & Inhelder, 1962; Suarez & Rhonheimer, 1974). Two of the additional items on the modified test involve proportional and combinatorial reasoning and came from Lawson, Carlson, Sullivan, Wilcox & Wollman (1976). The four remaining items came from Lawson, Clark, Cramer-Meldrum, Falconer, Sequist & Kwon (2000). Two of these involve water rise in an inverted cylinder after the cylinder had been placed over a burning candle sitting in water. The other two involve changes in the appearance of red onion cells when bathed in salt water. These four items require students to use hypotheticodeductive reasoning to reject hypotheses involving theoretical entities. For example, the burning-candle items ask students to propose an experiment to test and allow one to reject the hypothesis that water rises in the inverted cylinder because the carbon dioxide produced by the flame rapidly dissolves in the water. Scoring. All items required students to respond to a question or make a prediction in writing and to either explain how they obtained their answer, or in the case of quantitative problems, to show their calculations. Items were judged correct (a score of 1) if the correct answer plus an adequate explanation or set of calculations was present. Incorrect answers were scored 0. A Cronbach's reliability coefficient of 0.75 was obtained in a pilot study of 37 10th-grade students. Validity of the test has been established through numerous studies (e.g., Lawson, 1978; 1979; 1980a; 1980b; 1982; 1983; Lawson & Weser, 1990). Test of Air Pressure Concepts. The researchers constructed a group-administered test to assess students' understanding of air pressure concepts. The test was administered before and after instruction. The test, which took about 20 minutes to complete, consists of six short-answer essay items concerning the causes of: 1) a

BRAIN MATURATION AND THEORETICAL CONCEPT CONSTRUCTION

87

milk shake rising up a straw when you "suck," 2) water rising in a cylinder inverted over a burning candle sitting in a pan of water, 3) a collapsing soda can submerged in cool water, 4) a peeled, hard-boiled egg entering a bottle that previously contained a burning piece of paper, 5) a rising hot air balloon and, 6) air entering your lungs. For example, Item 1 read: When drinking a milk shake with a straw, you can "suck" the milk shake into your mouth through the straw. How does "sucking" on the straw cause the milk shake to move up the straw? And Item 5 read: When you heat a hotair balloon from below, the balloon rises. Explain why heating causes the balloon to rise. Scoring. Correct written responses were awarded 2 points each for a total of 12 possible points. Partially correct responses were awarded 1 point. Incorrect responses received 0 points. Content validity and item clarity were established through content-expert analysis prior to administration. A Cronbach's reliability coefficient of 0.69 was obtained in a pilot study of 37 l0th-grade students.

3.3 Instructional Treatment

Instructional treatment consisted of 14 two-hour, inquiry-based lessons using the learning cycle method of instruction (Lawson, Abraham & Renner, 1989). The same instructor (Yong-Ju Kwon) taught all lessons, Lesson 1 introduced students to the hypothetico-predictive pattern of scientific research (i.e., causal question alternative hypotheses planned tests predicted results actual tests observed results conclusion), through use of examples of prior scientific research. Once the research pattern was introduced, students were challenged to apply the pattern in the context of earthworm responses to various stimuli.

88

CHAPTER 4

Lessons 2-4 provided students with an opportunity to apply hypotheticopredictive reasoning to generate and test hypotheses about why empty soda cans collapse when submerged in cool water. Following the test of several studentgenerated hypotheses, the instructor introduced relevant postulates of kineticmolecular theory to explain the cause of greater air pressure outside the can, thus its collapse. Students were then challenged to apply the introduced concepts to predict and explain what will happen to air-filled balloons when cooled. During lessons 5-7 students explored what happens when burning pieces of paper are dropped into bottles and then peeled hard-boiled eggs are placed on the bottle openings. Based on their observations, students raised causal questions (e.g., What causes the eggs to move into the bottles?) and then generated and tested alternative hypotheses. The relevant postulates of kinetic-molecular theory were applied to explain the phenomenon. Students were then challenged to apply the theory to remove the eggs from the bottles and to explain what they did and why it worked. Lessons 8-10 allowed students to explore what happens when an inverted cylinder is placed over a burning candle sitting upright in a pan of water. Students generated and tested several hypotheses in response to the question: What causes water to rise in the inverted cylinder? Again following student hypothesis testing, relevant concepts of kinetic-molecular theory were applied to derive an explanation consistent with the students' observations. During lessons 11-12 students explored the causes of liquids (e.g., milk shakes) moving up straws when students "sucked" on the straws. After again using air pressure concepts derived from kinetic-molecular theory to explain liquid movement, students were challenged to explain how syringes can be used to "draw" blood samples. Lessons 13-14 challenged students to explore and explain how air passes into and out of one's lungs during breathing. Again relevant air pressure concepts were employed. 4. RESULTS

4.1 Frontal Lobe Activity Across Age Figure 3 shows student performance on the four measures of frontal lobe activity across student age groups. As shown at the upper left, inhibiting ability decreased from age group 13 to 14 and then improved linearly from age group 14 to 16. Overall group differences were statistically significant p < 0.01). To determine which specific age groups differed in inhibiting ability, a post hoc test (Tukey's test) was conducted. The test showed that the difference between age groups 14 and 16 was statistically significant (p < 0.01). Planning ability, shown at the upper right, decreased from age group 13 to 14, then improved dramatically in

BRAIN MATURATION AND THEORETICAL CONCEPT CONSTRUCTION

89

age group 15, and then only slightly in age group 16. Overall improvements with age were not statistically significant p > 0.25). The lower left shows that disembedding ability increased in a generally linear, but not significant, fashion across all age groups p > 0.10). Finally, the lower right shows that mental capacity decreased from age group 13 to 14 and then increased linearly from age group 14 to 16. Overall group differences were statistically significant 4.06, p < 0.01). The post hoc Tukey's test showed that mental capacity differences between ages 14 and 16, and 13 and 16 were statistically significant (p < 0.01).

90

CHAPTER 4

4.2 Reasoning Skill Across Age As shown in Figure 4, reasoning skill increased across age. A slight increase in rate of improvement can be seen after age 14. Overall age-group improvements were statistically significant p < 0.01). Tukey's test revealed statistically significant differences between ages 13 and 15, 13 and 16, 14 and 15, and 14 and 16 (p < 0.05), but not between age 13 and 14.

4.3 Predicting Reasoning Skill Table 2a shows the results of a stepwise multiple regression analysis used to determine which of the frontal lobe variables and age best predicts reasoning skill. Collectively, the variables explained 56.1 % of the variance in reasoning skill = 30.63, p < 0.001). As shown, inhibiting ability explained the largest percent of total variance (29.3 %) followed by planning ability (14.9 %), age (8.8%), disembedding ability (2.1%), and mental capacity (1.0 %).

BRAIN MATURATION AND THEORETICAL CONCEPT CONSTRUCTION

91

4.4 Theoretical Concept Construction Across Age Figure 5 shows student performance on the test of air pressure concepts across age groups. Pretest mean scores, posttest mean scores, and mean gain scores (i.e., posttest minus pretest scores) are shown. As you can see, both pretest and posttest mean scores improved with age. Both main effects were statistically significant p < 0.001 and p < 0.001, respectively). Age-wise

92

CHAPTER 4

improvement in mean gain scores was also statistically significant p< 0.01). The gain scores for the 13 and 14-year-old groups were nearly identical (3.5 and 3.6 points respectively), while the 15-year-olds showed somewhat greater gains (4.5 points) and the 16-year-olds showed still greater gains (5.3 points). Tukey's test showed that the gains between ages 13 and 16, and 14 and 16 were statistically significant (p < 0.05). Importantly, the difference between age 13 and age 14 gains was not statistically significant.

4.5 Predicting Concept Gains and Posttest Performance Table 2b shows the results of a stepwise multiple regression analysis used to determine which of the frontal lobe measures, age, reasoning skill, and concept pretest scores (prior knowledge) were significant predictors of concept gains. As shown, inhibiting ability, reasoning skill, concept pretest, age and planning ability significantly explained 42.9% of the variance in concept gains p< 0.001). Specifically, inhibiting ability was the best single predictor explaining 28.1% of the variance. Reasoning skill, concept pretest, age and planning ability explained 6.9%, 5.4%, 1.4% and 1.1% of the respective unique variance. Table 2c shows

BRAIN MATURATION AND THEORETICAL CONCEPT CONSTRUCTION

93

results of stepwise multiple regression analysis in which the frontal lobe measures, age, reasoning skill, and concept pretest score (prior knowledge), were used to predict concept posttest performance. As shown, reasoning skill, inhibiting ability, concept pretest, age and planning ability explained 70.7% the variance on concept posttest performance p < 0.001). The predictor variables explained 53.3%, 11.9%, 4.2%, 0.7% and 0.6% of the variance respectively. Respective standardized partial-regression coefficients were 0.26, 0.42, 0.25, 0.11 and 0.09. Each of the respective variables explained 7.0%, 17.7%, 6.1%, 1.1%, and 8.3% of the unique variance. 4.6 Inter-correlations Among Study Variables Table 3 shows Pearson product-moment correlation coefficients among the study variables. As you can see, all variables correlated significantly with reasoning skill with coefficients ranging from 0.36 for disembedding ability to 0.73 for the concepts posttest. The correlation of reasoning skill with concept pretest was 0.57 and with concept gains was 0.51. The four frontal lobe measures showed positive and significant correlations with reasoning skill, with concept gains, and with concept posttest scores. Inhibiting and planning ability showed the highest correlations with reasoning skill (0.54); while inhibiting ability showed the highest correlation with concept gains (0.53) and with concept posttest scores (0.55). Intercorrelations among the frontal lobe measures were low to moderate (0.20, NS to 0.35, p < 0.01).

94

4.7

CHAPTER 4

Common Components of Study Variables

Table 4 shows the results of a principal components analysis of all study variables. The analysis was conducted with varimax rotation extracting eigenvalues greater than one. Two principal components were extracted accounting for 29.5% and 27.2% of the variance respectively. Inhibiting ability loaded most strongly on component 2 (0.75), while the other frontal lobe measures loaded moderately on both components. Age loaded primarily on component 1 (0.50). Reasoning skill loaded moderately on both components (0.70 on component 1 and 0.53 on component 2). Concept pretest loaded heavily on component 1 (0.92), while concept gains loaded more strongly on component 2 (0.92). Concept posttest loaded moderately on both components (0.66 on component 1 and 0.63 on component 2).

5. DISCUSSION Figure 3 shows that inhibiting ability and mental capacity decreased from age 13 to 14 and then showed the predicted increases at ages 15 and 16 based on the frontallobe-maturation hypothesis. The pattern for planning ability is also as predicted with the exception of the plateau between ages 15 and 16. The disembedding ability pattern is not the predicted one based on the frontal-lobe-maturation hypothesis. But notice that neither is the pattern the linear one predicted by the experience hypothesis. Whether or not the apparent increase in rate of disembedding improvement seen after age 15 is real, or merely an artifact of the present sample, is an issue that remains for future research. Nevertheless, these results in large part support the hypothesis that these cognitive abilities are influenced by frontal lobe maturation.

BRAIN MATURATION AND THEORETICAL CONCEPT CONSTRUCTION

95

Figure 4 indicates that reasoning skill increases with age with the rate of increase accelerating after age 14. As mentioned, the difference between the 13 and 14-yearolds' scores was not statistically significant. This improvement pattern, which appears to be a "hybrid" between the predicted linear experiential pattern and the predicted plateau/spurt maturational pattern, is consistent with the view that reasoning improvements are a product of both neurological maturation and experience (physical and social). Finding evidence that both neurological maturation and experience play a role in the development of reasoning skill is consistent with developmental theory. For example, with regard to the development of adolescent thought, Inhelder & Piaget (1958) stated: "...this structure formation depends on three principal factors: maturation of the nervous system, experience acquired in interaction with the physical environment, and the influence of the social milieu" (p. 243). Figure 5, which indicates student performance on the concept pre and posttests, and concept gains, reveals the predicted improvements with age. Importantly, the amount of learning as evidenced by gains shows the predicted plateau and spurt pattern as gains of the 13 and 14-year-olds were virtually identical (3.5 and 3.6 respectively). The failure of the 14-year-olds to outperform the 13-year-olds is similar to the result reported by Choi & Hur (1987) who administered a test of biology, chemistry and physics concepts to students in grades 7, 8 and 9 and found that performance dropped from 7th grade (mean age = 12.9) to 8th grade (mean age 13.9) and then improved slightly among the 9th graders (mean age 14.8). The multiple regression analyses shown in Tables 2b and 2c indicate that concept gains are best predicted by inhibiting ability and by reasoning skill, while concept posttest scores are best predicted by reasoning skill. Therefore, the hypothesis that theoretical concept construction is in part dependent upon frontal lobe maturation is supported. The results also add to the growing list of studies, some of which were cited in the introduction, that have found reasoning skill to be a strong predictor of concept construction/change. The generally positive inter-correlations among the study variables (Table 3), as well as the results of the principal components analysis (Table 4), suggest that the study variables can be reduced to a smaller number of cognitive parameters. Note in Table 4 that inhibiting ability loaded primarily on component 2 while planning ability and mental capacity loaded more strongly on component 1. Disembedding ability loaded moderately on both components. Thus, as hypothesized, it appears that the frontal lobes may be involved in executing two primary functions - an inhibiting function and a representing function. The fact that reasoning skill loaded moderately on both components suggests that reasoning involves both the inhibiting and representing functions. In addition, concept pretest scores loaded heavily on the representing component, while posttest scores loaded moderately on both the representing and inhibiting component. Gains loaded heavily the inhibiting component. This suggests that students who made substantial gains did so primarily because they were able to inhibit irrelevant information.

96

CHAPTER 4

One does not have to look far to identify two "misconceptions" that need to be inhibited to successfully conceptualize the causes of air-pressure changes. The first is the "suction" misconception and the second is that air lacks weight. Viewed in this way, the key instructional question becomes one of how to overcome these sorts of misconceptions. Lessons 8-10 dealt with burning candles. The burning candle phenomenon is interesting because it causes many students to invoke still another misconception, namely the idea that combustion "eats" or "consumes" oxygen. When students place an inverted cylinder over a burning candle sitting in a pan of water, they see that the flame quickly goes out and the water rushes up into the cylinder. Thus, an interesting question is raised: Why does water rise in the cylinder? The most common student hypothesis is that the flame burns up the oxygen and this "lack-of-oxygen" sucks the water up. During instruction students tested this hypothesis along with several alternatives. Testing these alternative hypotheses requires use of some rather sophisticated hypothetico-predictive reasoning. For example, to pit the oxygenconsumption hypothesis against an air-expansion-and-escape hypothesis, one can use the following argument: If...water is sucked up because oxygen is consumed, and...water rise with one, two, and three candles is measured, then...the height of water rise should be the same regardless of the number of burning candles. This result is expected because there is only so much oxygen in the cylinder. So more candles will burn up the oxygen faster; but they will not burn up more oxygen. On the other hand, if...the air-expansion-and-escape hypothesis is correct, then...more candles should cause more water to rise because more candles will heat more air, thus more will escape, which in turn will be replaced by more water when the remaining air cools and contracts. Once students carry out the experiment and find that more candles produce more water rise, the oxygen-consumption hypothesis is contradicted and the air-expansionand-escape hypothesis is supported. So what does it take to get students to reject incorrect hypotheses (some complete with misconceptions) and accept scientifically correct hypotheses? Based on this analysis, it would seem that students have to initially suspend (i.e., inhibit) their initial incorrect beliefs. In other words, they have to be willing to admit that their initial ideas might be wrong and then be willing to test them. They must then mentally represent some rather abstract/imaginary entities (i.e., moving and colliding molecules) and then understand (assimilate) hypothetico-predictive arguments of the If/then/Therefore form. In other words, they have to inhibit taskirrelevant information, represent task-relevant information and use cycles of hypothetico-predictive reasoning.

BRAIN MATURATION AND THEORETICAL CONCEPT CONSTRUCTION

97

6. CONCLUSIONS AND INSTRUCTIONAL IMPLICATIONS In conclusion, the present results provide support for the hypothesis that an early adolescent brain growth plateau and spurt influences students' higher-level reasoning skill and their ability to construct theoretical science concepts. In short, maturation of the frontal lobes during early adolescence appears to be linked to students' abilities to inhibit task-irrelevant information and mentally represent task-relevant information, which along with both physical and social experience influences reasoning skill and students' ability to reject intuitively derived scientific misconceptions and accept scientific, but sometimes counter-intuitive, theoretical conceptions. This conclusion is similar to that discussed in Chapter 3 in which an earlier brain growth spurt at age seven was linked to students' ability to construct descriptive concepts. Perhaps this is a good time to recall Bruner's famous dictum that "...any subject can be taught effectively in some intellectually honest form to any child at any stage of development" (Bruner, 1963, p. 33). At first blush, the present results and conclusion seem to contradict this view. But note Bruner's key phrase "in some intellectually honest form." If unlike the theoretical concept of air pressure that was taught in the present study, we define air pressure as the force felt at one end of a straw when someone else blows in the other end, or as the force created by the moving blades of an electric fan, then the concept of air pressure (in this less abstract but still intellectually honest form) becomes accessible to students at younger ages. Thus, no contradiction with Bruner's position need exist. Indeed, consider Bruner's follow up statement: What is most important for teaching basic concepts is that the child be helped to pass progressively from concrete thinking to the utilization of more conceptually adequate modes of thought. But it is futile to attempt this by presenting formal explanations based on logic that is distant from the child's manner of thinking and sterile in its implications for him. (p. 38)

An approach to progressively moving from concrete/descriptive reasoning to more abstract modes of thought that we take in a college-level biology course is to first provide students with opportunities to generate and test causal hypotheses in several familiar contexts and to carefully sequence those contexts so that they progress from the familiar and observable to the less familiar and theoretical. Preliminary results suggest that this approach produces less frustration and more understanding. We should perhaps also mention that these college students are all age 18 and older. Hence, they presumably have all undergone the fifth and apparently final brain growth spurt by age 18. The extent to which this final growth spurt may influence reasoning skill and theoretical concept construction/change is a question that remains for future research. However, we should point out that even the 16 year-olds in the present study struggled with the theoretical concepts introduced. In fact, their average score on the concepts posttest was only 68%. Given that the students experienced at least 26 hours of instruction devoted to teaching those concepts, this can hardly be considered a success.

98

CHAPTER 4

Chapters 7, 8 and 10 will present data suggestive of a fifth stage of intellectual development. The data also suggest that fifth stage reasoning may be involved in theoretical concept construction. Therefore, the practice of introducing theoretical concepts "prematurely" is called into question. The point is that a teacher may tell young students that theoretical constructs such as atoms exist, and that these atoms have weight, can push down on surfaces, such as water, and so on. Perhaps some of the young students will even believe the teacher - based on faith. However, if instruction about atoms is scientific in the sense that it includes the reasons (i.e., evidence and arguments) for why scientists believe atoms exist and behave as they do, then students must be "developmentally ready" for such instruction. Being "developmentally ready" may mean being 18 years of age or older!

CHAPTER 5 CREATIVE THINKING, ANALOGY AND A NEURAL MODEL OF ANALOGICAL REASONING

1. INTRODUCTION

According to Webster, to create means "to bring into existence; cause to be; evolve from one's own thoughts or imagination" (Merriam-Webster, 1986). Scientific creation has been described in terms of sequential phases of preparation, incubation, illumination and F (Wallas, 1926; Sternberg & Davidson, 1995). During the creative process, the conscious mind mulls over a question or problem only to give up and turn it over to the subconscious. The subconscious then operates until it somehow produces a novel combination of ideas that spontaneously erupt into consciousness to produce the tentative answer or solution. From here the conscious mind guides a more critical testing of the novel idea to discover whether or not its value is real or illusionary (cf., Amsler, 1987; Boden, 1994; Koestler, 1964; McKellar, 1957; Wallace & Gruber, 1989). Consider for example, Koestler's (1964) version of the often-told story of Archimedes and the golden crown. As Koestler tells the story, Hiero was given a crown, allegedly made of pure gold. He suspected the crown was adulterated with silver but he did not know how to tell for certain. So he asked Archimedes. Archimedes knew the specific weights of gold and silver - their weights per unit volume. Thus, if he could measure the crown's volume, he could determine whether it was made of pure gold. But he did not know how to measure the volume of such an irregularly shaped object. Clearly he could not melt down the crown and measure the resulting liquid. Nor could he pound it into a measurable rectangular shape. With these easy solutions blocked, Archimedes had a problem. Using Wallas' terminology, Archimedes was engaged in the preparation phase of creative thought. Having hit numerous dead ends, Archimedes put the problem aside. Nevertheless, his mind was well prepared for progress as several blind alleys had been tried and rejected. In a sense Archimedes now shunted the problem to his subconscious to let it incubate. The next phase, illumination, presumably began while Archimedes was about to take a bath. While lowering himself into the tub, he noticed the water level rise. And in a flash it occurred to him that the water rise was an indirect measure of his bodies' volume. Thus, presumably at that moment, Archimedes "saw" how he could also measure the crown's volume - simply by immersing it in water. And once he knew its volume, he could calculate its specific weight to know if it were made of pure gold. Eureka! Archimedes had the solution. 99

100

CHAPTER 5

In Koestler's view, Archimedes' creative act can be understood essentially as one of joining two planes of previously unconnected thought to reach a target solution T. For example, Figure 1 depicts the plane of thought that contains the starting point S and several thought paths that have unsuccessfully sought the target. Thus presents the habitual rules that Archimedes used to measure volumes, weights, to determine the nature of materials, and so on. But as you can see, the target T is not contained on Instead, it is located on - the thought plane associated with taking a bath. Thus no amount of thinking on can reach T. Archimedes needs to shift his thinking from to To do this he needs a link L. As Koestler points out, the link may have been verbal (for example, the sentence: rise in water level in the tub equals melting down of my body); or it may have been visual in which the water-level rise was seen to correspond to body volume and hence crown volume. Either way, the key notion is that both planes of thought must be active in Archimedes' mind - albeit not both on the conscious level - for the link to occur and for him to consciously "see" the solution. Once illumination occurs, verification can take place. To do this, Archimedes presumably thought through the steps of his newly created path from S to T to satisfy himself that no crucial steps had been left out - that the path really led to T. Another aspect of the verification phase is to actually put the new strategy to work to discover if Hiero's crown had in fact been adulterated. The following summarizes the key argument: If...the crown is made of pure gold, (pure-gold hypothesis) and...the crown is immersed in water and the displaced water is measured, (planned test) then...the crown should displace the same volume of water as displaced by a known sample of pure gold of equal weight. (prediction) On the other hand, if...the crown has been adulterated by silver or by some other less dense metal, (adulterated hypothesis) then...it should displace a greater volume of water than displaced by a known sample of pure gold of equal weight. (prediction) Notice how the preparation, incubation and illumination phases of Archimedes' thinking were creative in the sense that they brought into existence a new piece of procedural knowledge (i.e., a procedure for measuring the volume of irregularlyshaped objects). On the other hand, the verification phase of his thinking can be characterized as critical in the sense that once Archimedes created the new procedure, he used it to analyze the metals in Hiero's crown. This critical thinking produced a new piece of declarative knowledge (i.e., the crown was not pure gold).

CREATIVE THINKING

101

CHAPTER 5

102

1.1 Linking Thought Planes At the heart of this model of creative and critical thinking lies the linking of two or more previously disconnected "planes" of thought. Consequently, the issue of how these planes are linked becomes of central importance. To see how thought planes might be linked, let's turn to the research of two biologists. As told by Beveridge (1950), while his family had left for a day at the circus one afternoon in 1890, Elie Mechnikoff half-heartedly watched some transparent starfish larvae as he tossed a few rose thorns among them. To his surprise, Mechnikoff noticed that the thorns were quickly surrounded and dissolved by the larvae. The thorns were being swallowed and digested. This reminded him of what happens when a splinter infects a finger. The splinter becomes surrounded by pus, which, Mechnikoff surmised, attacks and eats the splinter. Thus, Mechnikoffs observation of the swarming larvae struck him as analogous to human cells swarming around a splinter. In this way the use of an analogy helped Mechnikoff "discover" the bodies' main defense mechanism - namely mobile white blood cells (phagocytes) that swarm around and engulf invading microbes. Mechnikoff s use of analogy is common in the history of science. For example, can Charles Darwin's invention of natural selection theory also be traced to an analogy? Consider Darwin's words: It seemed to me probable that a careful study of domesticated animals and cultivated plants would offer the best chance of making out this obscure problem. Nor have I been disappointed; in this and all other perplexing cases I have invariably found that our knowledge, imperfect though it be, of variation under domestication, afforded the best and safest clue. (Darwin, 1898, p. 4)

Armed with this clue, Darwin tried to put the evolutionary puzzle pieces together. His attempt involved several unsuccessful trials until September of 1838 when he read Thomas Malthus' Essay on Population and wrote, "I came to the conclusion that selection was the principle of change from the study of domesticated productions; and then reading Malthus, I saw at once how to apply this principle" (quoted in Green, 1958, pp. 257-258). Gruber & Barrett (1974) point out, Darwin had read Malthus before, but it was not until this reading that he became conscious of the analogical link between "artificial" selection and evolutionary change. Now that the link had been established, Darwin began marshalling the evidence favoring his new theory of "natural" selection. Other examples of the use of analogy are numerous in the history of science. Kepler borrowed the idea of the ellipse from Appolonious to describe planetary orbits. Kekulè borrowed the idea of snakes eating their tails (in a dream) to create a molecular structure for benzene, and Coulomb borrowed Newton's ideas of gravitational attraction to describe the electrical forces that exist at the level of subatomic particles. As mentioned in Chapter 1, the use of analogy - the act of borrowing old ideas and applying them in new situations to invent new insights and explanations - is sometimes called analogical reasoning, or analogical transfer (cf.,

CREATIVE THINKING

103

Biela, 1993; Boden, 1994; Bruner, 1962; Dreistadt, 1968; Fauconnier & Turner, 2002; Finke, Ward & Smith, 1992; Gentner, 1989; Hestenes, 1992; Hoffman, 1980; Hofstadter, 1981; Hofstadter, 1995; Holland, Holyoak, Nisbett & Thagard, 1986; Johnson, 1987; Koestler, 1964; Wong, 1993). Thus, often (always?) an analogy provides the link - the L - between the thought planes so that the thinker can pass to the second plane and arrive at the target. 2. WHY DO ANALOGIES PLAY SUCH A KEY ROLE IN SCIENCE AND IN LEARNING?

This chapter extends the basic neural modeling principles introduced in Chapter 2 at this point to provide a foundation upon which a theory of analogical insight at the neural level can be constructed. The intent is to provide a framework in which we can begin to understand how analogical insight plays such a key role in creative thought and in learning. The present position is rather complex and will be presented in steps. First, a central question regarding human memory will be clarified. Second, basic neural network principles will be reviewed to provide a framework for answering the questions at the neural level. Third, the network principles will be extended to explain why analogies play such a central role. Both visual and verbal analogies will be modeled. Instructional implications will follow. 3. THE CENTRAL QUESTION

The central question is this: Why do some experiences find their way into longterm memory while others do not? The brief answer to this question is that the crucial element in transferring experiences to long-term memory is the brain's ability to find past experiences that are enough like the present ones to allow their assimilation. If such analogous experiences can be found, then assimilation and retention will occur. If not, then the new experiences will be forgotten. Consider a recent experience that will more sharply delimit the question. During a visit to a Japanese elementary school, I observed a teacher and his students as they discussed the results of an experiment investigating seed growth. The teacher organized the students' comments in words, symbols (some English and some Japanese) and diagrams on the board. The students were very enthusiastic and the teacher wrote very clearly. The experiment was familiar, but my inability to understand spoken or written Japanese made it difficult to understand much of what was said. At the lesson's conclusion, we adjourned to the school principal's office for a traditional cup of tea. At that time it occurred to me that I had observed a very good lesson and should attempt to make a few notes, including a record of what the teacher had written on the board. Predictably I was able to reconstruct some, but not all, of what had been written. Interestingly, recalling the relative position of the

104

CHAPTER 5

major items on the board was easy. The diagram of the seeds and their container, the numbers 1 and 2, the letters A and B, and the question mark were all easily recalled. But recall of the shapes of the Japanese/Chinese symbols and words was impossible. To be more specific, a symbol shaped like this "A" was recalled, but a symbol shaped like this was not. Why? You may be saying to yourself that this is not the least bit surprising. Familiar English language symbols were recalled while unfamiliar foreign language symbols were not. Because the observer does not speak or write in Japanese, this is entirely predictable. Agreed! This can easily be predicted based upon past experiences we have all had trying to remember familiar and unfamiliar items. But how can this be explained at the neural level? After all, all of the stimuli on the board were clear and all could have easily been copied at the time. The question then is why does one remember items that are familiar and forget items that are not? What precisely does "familiar" mean in neurological terms? And how does familiarity facilitate transfer into long-term memory? 4. ADAPTIVE RESONANCE: MATCHING INPUT WITH EXPECTATIONS. As described in Chapter 2, the brain is able to process a continuous stream of changing stimuli and constantly modify behavior accordingly. This implies that a mechanism exists to match input with expectations from prior experience and to select alternative expectations when a mismatch occurs. Grossberg's mechanism for this, called adaptive resonance, was presented in Chapter 2 and is reproduced below in Figure 2. Let's briefly review the process by again considering visual processing. As described, due to prior experience a pattern of activity, plays at and causes a firing of pattern at where could be a single neuron. then excites a pattern P on The pattern P is compared with the retinal input following Thus, P is the expectation. P will be in a static scene and the pattern to follow in a temporal sequence. If the two patterns match, then you see what you expect to see. This allows an uninterrupted processing of input and a continued quenching of nonspecific arousal. Importantly one is only aware of patterns that enter the matched/resonant state. Unless resonance occurs, coding in long-term memory (LTM) is not likely to take place. This is because only in the resonant state is there both pre and post synaptic excitation of the cells at (see Grossberg's learning equation). Now suppose the new input to does not match the expected pattern P from Mismatch occurs and this causes activity at to be turned off by lateral inhibition, which in turn shuts off the inhibitory output to the nonspecific arousal source. This turns on nonspecific arousal and initiates an internal search for a new pattern at that will match

CREATIVE THINKING

105

Such a series of events explains how information is processed across time. The important point is that stimuli are considered "familiar" if a memory record of them exists at such that the pattern of excitation sent back to matches the incoming pattern. If they do not match, the incoming stimuli are unfamiliar and orienting arousal is turned on to allow an unconscious search for another pattern. If no such match is obtained, (as in the case of looking at an unfamiliar Japanese symbol) then no coding in LTM will take place unless attention is directed more closely at the object in question. Directing careful attention at the unfamiliar object many boost pre-synaptic activity to a high enough level to compensate for the relatively low postsynaptic activity and eventually allow a recording of the sensory input into a set of previously uncommitted cells. Adaptive resonance and Grossberg's learning equation explain how input patterns find their way into LTM. This chapter extends Grossberg's theory at this point. In general, the theory of analogical operations proposed describes specific neural processes that greatly facilitate coding of new experiences in LTM. However, prior to discussing of the role that analogies play, we need to take a closer look at the way slabs of neurons function to recall and reproduce patterns.

106

CHAPTER 5

4.1 Outstars and Instars Grossberg proposes outstars as the underlying neural mechanism for reproduction and recall of patterns. An outstar is a neuron whose cell body lies in one slab of interconnected neurons with a set of synaptic knobs that connect it to a set of cell bodies embedded in a lower slab of neurons (see Figure 3). In theory, outstars are the fundamental functional unit able to learn and reproduce a pattern (a concept). Understanding how outstars accomplish this is central to understanding how analogies enhance learning.

The outstar shown in Figure 3 is actively firing impulses down its axons to a lower slab of neurons that is simultaneously receiving a pattern of input from a still lower slab of neurons, or perhaps from the environment (e.g., a pattern of visual input on the retina). In the figure, the darkened neurons on the input slab represent active neurons, the more the cell body is darkened the more active it is (i.e., the more input it is receiving hence the more frequently it is firing). When the outstar is firing and the signals from the outstar are reaching the input slab at the same time that the pattern on the lower slab of neurons is firing, the synaptic strengths will grow according to the learning equation. A very important consequence of this change in synaptic strengths is that when the pattern of activity on the input slab is gone, the outstar can reproduce the pattern whenever it fires again. When the outstar fires repeatedly, synapses with high synaptic strength will cause their associated cells

CREATIVE THINKING

107

on the original input slab to become very active, and cells with low synaptic strength will be less active, just as they were when the input slab was first being sampled by the outstar. In this manner the pattern will reappear (see Figure 4).

Slabs of neurons are not only connected via axons from higher slabs, as depicted in Figures 3 and 4, the neuron cell bodies on the input slab also have axons that connect them to the cell bodies of higher slabs. As depicted in Figure 5, a pattern of activity on a lower slab is mirrored by the rate of transmitter release in the synapses leading to the active cell bodies on the higher slab. Thus, when the pattern is active on the lower slab and when the cell body on the higher slab (the outstar) is active, these synaptic strengths will increase in a fashion that mirrors that pattern of activity on the lower slab. Consequently, if the pattern appears again, the outstar will fire. In this sense the outstar has "remembered" the pattern. Importantly, a sufficient period of time is needed for the outstar (the neuron on the higher slab) to learn the pattern. We shall see later that analogy plays a key role by reducing this period of time thus making learning likely when it would otherwise not occur.

108

CHAPTER 5

The activity depicted in Figure 5 is of such functional importance that Grossberg has given it a name, the instar. The instar is actually the set of synaptic weights associated with the synaptic knobs connected to a neuron. If a pattern fires a neuron repeatedly, then that pattern will reappear as part of the instar of that neuron. To summarize, the synaptic strengths of outstars align themselves to an input. Outstars are then able to reproduce the input. If a collection of outstars are not aligned to an input, then that input cannot be reproduced unless presented again. Thus, it will not be remembered. The important point is this. If outstars are not present, then a pattern cannot be reproduced, thus not remembered. In the initial example of the Japanese classroom, the Japanese symbols could not be reproduced because outstars necessary to reproduce them did not exist. In short, outstars must be present for recall to occur. Having said this one must keep in mind that input patterns, such as those on the retina are never exactly the same. We do not look the same when we awake as we remember looking before going to bed, but we do "recognize" ourselves nevertheless. Grossberg's theory of adaptive resonance shows how this can be accomplished. It is a method by which slabs of neurons can interact with each other to find a "best fit." Suppose that slab 1 is presented with an image. That image will have several features, i.e., it will consist of several patterns. Each pattern (or feature)

CREATIVE THINKING

109

that has been learned will trigger outstars in slab 2. Outstars triggered in slab 2 will in turn fire back on slab 1. Patterns that have been correctly triggered will reproduce the pattern that triggered them. If all is correct, or close enough, then a best fit has been found. If a pattern does not match, then a search for different outstars associated with a different pattern begins. Grossberg's theory of adaptive resonance includes a detailed description of this search for a best fit. 4.2 Outstars as a Mechanism for Chunking Prior to discussing of the role of analogy in facilitating learning one more neurological mechanism needs to be in place. That mechanism deals with the wellknown psychological phenomenon of chunking. Chunking has an interesting place in the literature of psychology. Miller's magic number 7, plus or minus 2, refers to the fact that it is almost universally true that people can recall only seven unrelated units of data, if they do not resort to various memory tricks or aids (Miller, 1956). This may explain why telephone numbers are seven digits long. Clearly, however, we all form concepts that contain far more information than seven "units." Thus, a mental process must occur in which previously unrelated units of input are grouped or "chunked" together to produce higher-order chunks (units of thought/concepts). This implied process is known as chunking (Simon, 1974). Consider for example, the term ecosystem. As you may know, an ecosystem consists of a biological community plus its abiotic (non-living) environmental components. In turn, a biological community consists of producers, consumers, and decomposers; while the abiotic components consist of factors such a amount of rainfall, temperature, substrate type, and so on. Each of these subcomponents can in turn be further subdivided. Producers, for example might include grasses, bushes, Pine trees, and the like. Thus, the term ecosystem subsumes a far greater number of discrete units or chunks than seven. The term ecosystem itself is a concept. Thus, for those who "understand" the term, it occupies but one chunk in long-term memory. The result of chunking (i.e., of higher-order concept formation) is extremely important. Chunking reduces the load on mental capacity and simultaneously opens up additional mental capacity that can then be occupied by additional concepts. This in turn allows one to construct still more complex and inclusive concepts (i.e., concepts that subsume greater numbers of subordinate concepts). To turn back to the Mellinarks introduced in Chapter 3, once we all know what a Mellinark is, we no longer have to refer to them as "creatures within an enclosed membrane that may be curved or straight, with one large dot and several smaller dots inside and with one tail." Use of the term Mellinark to subsume all of this information greatly facilitates thinking and communication when both parties have constructed the concept. Grossberg hypothesizes that outstars are the anatomical/functional unit that makes chunking (i.e., concept formation) possible. Outstars sampling a lower slab can group a set of neurons that are firing at the same time. To do this they must

110

CHAPTER 5

merely fire at a rate high enough to allow the synaptic strengths at its synapses to mirror the activity of the neurons being grouped (or chunked). For adaptive resonance to occur the neurons being chunked must fire outstars. In this sense, the purpose of outstars is to form a chunk, and later, to identify and reproduce the chunk once formed. An architecture called On-Center, Off-Surround (OCOS) plays an important part in chunking. OCOS is sometimes referred to as winner-take-all architecture. In an OCOS architecture active cells excite nearby cells and inhibit those that are farther away. Because OCOS cells excite nearby cells, cells close together will excite each other. "Hot spots" of active cells close together result and then inhibit cells further away. The cells within the hot spots sample the lower slab and become outstars that learn the pattern that is active on that lower slab. Thus, the cells in a pattern in the lower slab become the cells that will excite a hot spot on the higher slab, and the cells in the hot spot become outstars that learn the pattern. Chunking can be either temporal or spatial. For example, a spoken word is the sequential chunk of neural activity needed to produce the word. A heard word is the sequential pattern of sounds that have been identified as that word. The OCOS architecture can force a winner (a hot spot) on the higher sampling slab and thus force chunking to occur in either the spatial or the temporal case. If outstars are indeed the biological mechanism that is the basis for chunking, then Miller's magic number 7 must have some physical relationship to the outstar architecture. What might this be? There are probably physical limits associated with the activity of cells, their rates of decay, and the spread of axonal trees. This is speculation but only so many hot spots can exist on a slab so some limit must exist, and an excited neuron can continue to fire for only a certain length of time. Constraints such as these should force a physical limit on the size of a chunk. Therefore, the brain contains outstars that form chunks. Someone who "understands" the term ecosystem has formed an ecosystem chuck - has a set of ecosystem outstars. In other words, that person has an ensemble of cells somewhere in his/her brain that fire when the term ecosystem is heard, is read, is written, and so on. Recent research with monkeys by Wallis, Anderson & Miller (2001) has shown that abstract rules reside in single neurons, in this case in neurons located in the prefrontal cortex. Echoing the point made above about the importance of chunking, Wallis et al. stated: The capacity for abstraction is an important component of cognition; it frees an organism from specific associations and gives it the ability to generalize and develop overarching concepts and principles, (p. 956)

The finding that abstract concepts and principles/rules reside in single neurons, or in ensembles of neurons, thanks to chunking is important and perhaps surprising. The next section will discuss the neural basis for analogy and how analogies help in the construction of chunks.

CREATIVE THINKING

111

5. THE NEURAL BASIS FOR ANALOGY

An analogy consists of objects, events or situations that share features (or patterns) in common, that is, they are in one or more ways similar. Shared features have a significant neural impact. Presumably similar features have a similar impact. The heart of the argument will be the claim that chunks with shared, or similar, features reinforce each other, and do so in a very significant manner, by forming feedback loops. Mathematically it can be shown that these feedback loops cause the activity of the sampling outstars (i.e., the cells that are sampling the new to-be-learned patterns), to grow exponentially as the feedback loop is forming. Such a rapid increase in cell activity is significant for two reasons. First, it causes rapid sampling and rapid sampling means fast learning (or just learning period, as slow learning and no learning are often synonymous). Second, exponential growth of activity is very important because cells on an OCOS slab compete with each other and those that become active first quench less active cells. The following example will be used to explicate these points. 5.1 Analogies Facilitate Learning

When I was a seventh grader, my math teacher introduced the word perpendicular and the symbol to refer to two lines that intersect at a 90 degree angle. The teacher wanted us to remember the word and the symbol and of course the meaning. So when he introduced the word and the symbol, he also introduced the words pup-in-da-cooler. Presumably he intuitively believed that introduction of these similar sounding words and the images they would evoke in our minds would aid recall. The words not only brought out a few laughs from the students, they also worked extremely well. To this day, I cannot think of the word perpendicular or the symbol without pup-in-da-cooler following close behind. The words perpendicular and pup-in-da-cooler are very similar. The letters are similar, of course, and so are the chunks. We shall focus on each of these facts as they make the example analogous to analogies that share similarities at different levels. We assume that the word pup is an already acquired chunk in LTM, and the word perp represents a to-be-learned chunk. We will explain why having pup as an active chunk in LTM will speed the learning of perp. The example will similarly show that pup-in-da-cooler speeds the learning of perp-in-dic-ular because they share common features. Basic auditory features (or patterns) are called phonemes. However, it will simplify the discussion to assume that letters are the basic auditory patterns, the phonemes. One must merely replace the letter with phoneme to provide a more technically correct version of the following discussion. In brief, when perpendicular is spoken, much of the neural activity present in the STM of the words pup-in-dacooler remains active because the two words sound the same. The shared features

112

CHAPTER 5

remain active and cause chunking to occur, which makes it possible to quickly learn the word perpendicular. How do shared features cause chunking of new input to occur? Consider Figure 6. The word pup is heard. As shown, this presents input to slab 1. In turn, this input activates the chunk for pup in LTM on slab 2. At the same time, the sound perp creates activity on slab 1 as well as a hot spot of activity on slab 2. Thus, we have an outstar representing the chunk pup feeding the beginning and ending letters p that remain active on slab 1. These letters begin to form a portion of an instar connected to the hot spot on slab 2. The hot spot will chunk perp and will create a feedback loop from pup to perp and back again (see Figure 7). This feedback loop will greatly increase the activity of the neuron perp. This increased activity will then make it much easier for the chunk (the outstar) perp to form.

CREATIVE THINKING

113

Neurons on slab 2 chunk each of the syllables pup, in, da, coo, and ler. There is also a still higher slab 3. And on slab 3 there is a neuron chunking the five syllables pup-in-da-coo-ler, At the same time on slab 2, feedback loops are causing (aiding) the formation of the chunks perp, in, di, cu, ler. Also on slab 3, a neuron is beginning to chunk the syllables perp-in-di-cu-ler. Multiple feedback loops are forming between these neurons on slab 3, thus speeding the chunking of the word perpendicular (see Figure 8).

114

CHAPTER 5

5.2 An Emergent, Self-Organizing System How the symbol is learned has not yet been explained. This section will do so and show that the shared features that exist between pup-in-da-cooler and perpendicular are responsible for the creation of an emergent neural control system that greatly increases the speed at which is learned. The section begins with two alternative configurations to the emergent neural control system. Then the control system itself will be introduced. Why the neural control system is such an improvement over the alternatives, and why it greatly increases the rate of learning will be explained. This will be followed by a mathematical demonstration that the control system induces an exponential learning rate. Figure 9 depicts the first alternative. Here perp represents the word perpendicular to be associated with the recall of A and C each represent a neuron (i.e., in the OCOS architecture a small group of neurons that mutually excite each other). A is the neuron, or group of neurons, that are active in the auditory neural subsystem when the word perpendicular is spoken. This group of neurons either chunks or will chunk the word. C is a neuron that will sample the area of the visual system that contains the symbol C is the neuron that will chunk the symbol if the learning is successful.

Excitation of neurons A and C results in the association of the word perpendicular with the symbol In turn, the word perpendicular will cause the recall of the symbol. The activity of A can be considered chunking enhancement. This is because C is a sampling cell and its activity results in the formation of a chunk, a set of features that are grouped together. Activity of A will help increase the sampling rate of C, thus, the ability of C to chunk. The problem with this configuration is that the activity of cell C is dependent solely of the activity of A. Thus, unless A is extremely active, or repeated many times, the learning that cell C is attempting will not take place.

CREATIVE THINKING

115

Figure 10 shows an extension of Figure 9. In this configuration two words pup and perp activate the neuron C. Thus, C will be excited twice as much as in the previous case This configuration is an improvement over that shown in Figure 9, but still does not allow for large scale boosts in neural activity.

Figure 11 shows an emergent self-organizing neural control system that can cause large scale boosts in neural activity. In fact, it can cause the sampling rate of C to increase exponentially. As shown, neurons A and B form a feedback loop. This feedback loop is powerful because the sampling rate of C will initially grow exponentially. Presumably this is the neural mechanism that an analogy produces. Because neurons A and B of the control structure form a feedback loop, as A and B fire, each will increase the rate at which the other fires. A increases the firing rate of B and B increases the firing rate of A. Thus, the sampling rate of C will initially grow exponentially.

116

CHAPTER 5

In the architecture presented in Figure 11, the signal down the axon leaving A travels to both B and C. Thus, In the same fashion Thus, an increase in and will also result in an increase in and The signals to C from A and B are a by-product of this architecture. The feedback loop from A to B and back again to A emerges when the organism is presented with data that cause A and B to fire at the same time. As a by-product, other regions are also flooded with neural excitation. The neurons chunking pup and perp are such an A and B. If the region they flood is a winner-take-all region, then a C will emerge, will become strongly excited, and will learn the symbol Perp will be associated with and if C's axonal tree also reaches the auditory cortex, then will be associated with perp. 5.3 The Control System Drives the Learning of the Symbol

The control system drives the learning. In other words, the control system determines the rate at which learning occurs. To understand why the analogy controls the learning rate, notice in the sampling rate equation (equation [5] in the appendix) that, even if is small, if is large, then d/dt the sampling rate of C, will also be large. This is interesting because will be large if the association between A and B is strong. Thus, the analogy, the signals between A and B, drive the learning of the symbol The shared features within the input data pup-in-da-cooler and perpendicular cause the control system (the neurons A and B and the feedback loop they form) to arise. The letter A represents the neuron chunking the word pup-in-da-cooler. B represents the neuron chunking perpendicular. The system arose because the shared features caused the chunking to occur. As mentioned, a major reason chunking occurred was because the shared features caused an exponential growth in neural activity. This rapid rise in activity allowed the chunks to form. Thus, the input data, the neural ability to chunk and the exponential growth associated with feedback causes the control system to emerge. In this sense, the analogy caused the control system to arise. 6. SUMMARY

The two examples, forgetting the Japanese symbol and learning the word perpendicular and its mathematical symbol, have natural explanations within a hierarchical neural network. The explanation for the first example used a hierarchical network with two slabs. The second example used a hierarchical network with three slabs. The first network explained why the Japanese symbol could not easily be recalled. The first slab of this network was a slab of neurons activated by line segments tilted (or oriented) in a specific direction. The second slab consisted of

CREATIVE THINKING

117

cells (outstars) that chunked neurons in the first slab. If there is a neuron on the second slab that has chunked the neurons on the first slab activated by the Japanese symbol, then that symbol can be recalled by activating that neuron. If no neuron has chunked the Japanese symbol, it cannot be recalled unless pre-synaptic activity associated with the symbol receives a considerable boost. The second example was presented in Figure 7. The first slab of the three-slab network consisted of cells activated by phonemes, sounds that are building blocks of speech much as oriented lines can be used as building blocks for line images. The second slab chunks neurons active on the first slab. The third slab chunks neurons active on the second slab. Chunks on slab 2 become syllables such as pup and perp. Chunks on slab 3 become words such as pupindacooler and perpendicular. The second example demonstrated that similar activity on the first slab (activity such as that created by the p sounds in the words pup and perp) creates feedback loops between elements on the second slab (between the neurons chunking pup and perp). Similar activity on the second slab (in and ler appear in both pupindacooler and perpendicular) can create feedback loops between neurons on the third slab. Each of these feedback loops greatly increases the neural postsynaptic activity, thus increases the ability to chunk and therefore to learn. In addition, the neurons on slab 3 become the emergent neural control system. 7. INSTRUCTIONAL IMPLICATIONS

How can our knowledge of the role of analogy help learners recall information such as the Japanese symbol To the extent that the brain is a hierarchical neural network, and if instars and outstars play the important role that we suppose, then the proposed neural mechanisms (the emergent feedback loops and the resultant neural control system) give a neurological explanation of how and why analogous data increases learning. The proposed neurological explanation implies that the search for an analogy greatly facilitates learning. How, for example, could an analogy be used to help one learn a symbol such as the Japanese symbol Obviously, the correct approach is to try to imagine something like the symbol. For example, the symbol might remind you of a tripod with an equals sign. Activation of these similar images already stored in LTM greatly increases postsynaptic neural activity; thus, according the Grossberg's learning equation, allows for storage of the new input in LTM. Of course, one may not be able to generate a satisfactory analogy, image, or set of images, in which case one would have to resort to the more tedious task of describing the symbol i.e., it has three vertical lines attached to a horizontal line, etc. Provided patterns for these terms exist in memory at this procedure will work, but it requires considerable effort to describe all the relevant variables. This effort is in fact a method for maintaining relevant portions of the image in STM so that chunking can occur. We have a neurological account of why a picture is worth a thousand words.

118

CHAPTER 5

The images are far superior because the relevant features are already linked in the analogous image. The pup-in-da-cooler example also demonstrated how analogy/similarity speeds learning by incorporating relevant features shared by new ideas with those already known. In the same manner, the use of analogy can presumably help learners comprehend non-observable theoretical concepts such as the biological concept of natural selection from Darwinian theory. The key insight for Darwin occurred when he "saw" the inherent analogy between the familiar (to him) artificial selection and the unfamiliar processes that presumably occurs hi nature. Learners may not be familiar with the process of artificial selection, but they can participate in classroom simulations of the process (e.g., Stebbins & Allen, 1975) to provide such familiarity. Consequently, when the process of natural selection is introduced as the mechanism of organic charge, which is analogous to the simulated process, the appropriate feedback loops between the familiar and unfamiliar will form and the desired learning will take place. In short, the present theory argues that analogical operations are basic to learning and the retention of what is learned. Hence, an active topic for educational research should be the identification of specific analogies for specific concepts and the exploration and evaluation of then- limitations and most effective use. The next chapter will provide an example of just such research.

CHAPTER 6

THE ROLE OF ANALOGIES AND REASONING SKILL IN THEORETICAL CONCEPT CONSTRUCTION AND CHANGE

1. INTRODUCTION This chapter describes an experiment designed to address two related instructional questions: (1) What factors facilitate the construction of theoretical concepts? (2) What factors enable students to discard scientifically inappropriate explanations (misconceptions) in favor of more scientifically appropriate ones? Answers will be sought in the context of introductory college biology and will concern the concepts of molecular polarity, bonding and diffusion. Such concepts are defined as theoretical, as opposed to descriptive, because they relate to imagined, unseen entities and processes that have been hypothesized to exist on the atomic and molecular levels to explain observable phenomena such as the spread of blue dye in water, but not in oil, or the detection of an odor at the opposite end of a room. Two hypotheses will be tested. Based on the theoretical rationale advanced in Chapter 5, the first proposes that analogies assist in theoretical concept construction. In brief, concept construction requires that students "disembed" patterns from experience. However, patterns that must be disembedded for theoretical concepts, by definition, cannot be directly experienced. For example, one cannot see molecules colliding with and sticking on to or bouncing off of each other. Therefore, analogous observational-level experiences that embody the patterns should help students experience and disembed the theoretical patterns. The use of analogies as instructional aids has been of increasing interest and the subject of a small, but growing, number of studies (e.g., Brown & Clement, 1989; Clement, 1989; Gabel & Samuel, 1986; Halpern, Hansen & Riefo, 1990; Flick, 1991; Friedel, Gabel & Samual, 1990; Dupin, 1989; Gilbert, 1989; Jardine & Morgan, 1987; Klauer, 1989; Stavy, 1991; Webb, 1985; Simons, 1984). Some of these studies have provided support for the foregoing analogy hypothesis, yet others have not. In a literature review, Duit (1990) summarized the studies as follows: The studies on analogical reasoning available so far reveal failure nearly as often as success. When summarizing these findings it can be stated that analogies may be of help in the learning process - if analogical reasoning really happens. (p. 27)

119

120

CHAPTER

6

Duit speculates that two conditions are necessary for successful analogical transfer. First, the analogue domain should be familiar to students, and second, the analogue should be in a domain in which the students do not hold misconceptions. Following Duit's first condition, the present study will employ a familiar analogue domain. However, the study will not follow Duit's second condition. Instead, it will employ a domain in which misconceptions are likely to occur so that a second hypothesis can be tested. That second hypothesis proposes that a change from the use of an inappropriate or incomplete theoretical concept to explain an event, to use of a more appropriate and complete set of theoretical concepts, is dependent in part on the higher-level, hypothetico-predictive reasoning skill introduced and discussed in Chapter 4. Such reasoning skill is seen as necessary to decide which of two or more theoretical concepts should be used to explain a specific phenomenon. For example, to explain the spread of dye in water, two alternative hypotheses (based on different sets of concepts) may come to mind. Perhaps the dye spreads because the water and dye molecules form molecular bonds due to their polarity (one set of concepts). Or perhaps the dye spreads due to random collisions with water molecules that result in a net motion from an area of high dye concentration to areas of low dye concentration (another set of concepts). Which, if either, or both, of these hypotheses is correct? To decide, a student might employ hypothetico-predictive reasoning such as the following: If...the dye spreads solely because the dye and water molecules are polar molecules thus form molecular bonds, (polar-molecules hypothesis) and...some dye is gently dropped into an unshaken container of water, (planned test) then...the dye should not spread - presumably because in this case there is insufficient motion to distribute the dye molecules among the water molecules. (prediction) But...the dye does spread. (observed result) Therefore...the polar-molecules hypothesis is not supported. (conclusion) However, if...the dye spreads due to random molecular collisions with water molecules, (random-motion hypothesis) then...the dye should spread - presumably because there are random molecular collisions that distribute the dye molecules among the water molecules. (prediction) And...the dye does spread. (observed result) Therefore...the random-motion hypothesis is supported. (conclusion) The hypothesis that hypothetico-predictive reasoning skill is involved in theoretical concept construction and conceptual change has been tested on at least three previous occasions. Lawson & Thompson (1988) found some support for the hypothesis as reasoning skill was significantly related to the number of

THE ROLE OF ANALOGIES

121

misconceptions that seventh grade students held following instruction on genetics and natural selection. That study, however, did not measure pre- to post-instruction change. Lawson & Weser (1990) did measure pre- to post-instruction change among college students and found that less-skilled reasoners were initially more likely to hold a variety of non-scientific beliefs about life (e.g., special creation, vitalism, orthogenesis) and were less likely to change some, but not all, of those beliefs. In the third study, Lawson & Worsnop (1992) found that the more skilled reasoners in a sample of high school students were less likely to hold pre-instruction misconceptions regarding evolution and special creation. But reasoning skill was not related to change in beliefs. The Lawson & Weser (1990) and the Lawson & Worsnop (1992) studies investigated conceptual change in the potentially emotionally charged context of evolution. Thus, the extent to which some students were emotionally committed to special creation may have contributed to their lack of conceptual change to evolution and to the failure of the results to more clearly support the hypothesis. Consequently, the present study attempts to test the reasoning-skill hypothesis in a non-emotionally charged context that may allow for a better test of the hypothesis. Students were first taught two theoretical concepts (molecular polarity and bonding) in the context of blue dye mixing with water, but not with oil, when all three were shaken in a container. The students were then tested in a potentially misleading context in which they could be expected to misapply these concepts. This misleading context asked students to explain the gradual spread of blue dye in a container of standing water - a context that also requires use of the diffusion concept. Hence, the exclusive use of the concepts of molecular polarity and bonding in this context (omitting mention of diffusion) represents a type of scientific "misconception." Here a misconception is defined as a concept, or set of concepts, that scientific research indicates is an inappropriate or incomplete explanation for a particular phenomenon. This definition does not imply that the concept(s) may not be appropriate to explain some other phenomena. Students were then taught another theoretical concept (diffusion) and were retested in the same context to see which students, if any, changed from the exclusive use of the bonding explanation to the additional and more scientifically appropriate use of the diffusion concept to explain the spread of the blue dye in the container of standing water. The analogies and reasoning-skill hypotheses led to the prediction that students introduced to the familiar physical analogies, and those who are more skilled reasoners would be more likely to undergo conceptual change and correctly apply the diffusion concept, i.e.: If...analogical and higher-level, hypothetico-predictive reasoning are utilized in theoretical concept construction and conceptual change, (analogies and reasoning-skill hypotheses) and...students of differing reasoning levels are (a) taught two theoretical concepts; (b) are initially tested in a context in which they misapply the concepts; (c) taught another

122

CHAPTER

6

theoretical concept with and without the use of physical analogies, and (d) retested, (planned test) then...(1)the more skilled reasoners and the students instructed with physical analogies should exhibit fewer misconceptions on the retest; and (2) the more skilled reasoners should be more likely to undergo conceptual change. (prediction) 2. METHOD

2.1 Subjects Subjects (Ss) were 77 students, ranging in age from 18.1 to 44.8 years (X=31.9 years), enrolled in four laboratory sections and two lecture sections of an introductory non-majors biology course at a large, suburban community college. 2.2 Reasoning Skill Reasoning skill (developmental level) was assessed by use of the Classroom Test of Scientific Reasoning (Lawson, 1978; Lawson, 1987). The test includes twelve items involving conservation of weight, volume displacement, control of variables, and proportional, probabilistic, combinatorial and correlational reasoning posed in a multiple-choice format using diagrams to illustrate problem contexts. Split-half reliability of the test was 0.55 for the present sample. Ss who scored from 0-4 were classified at the lower level corresponding generally to Piaget's concrete operational stage and to the use of hypotheticopredictive reasoning to test descriptive hypotheses as discussed in Chapter 3, e.g.: If...overall shape is a critical feature of Mellinarks, (descriptive hypothesis) and...I look closely at the non-Mellinarks in row two, (proposed test) then...none should be similar in overall shape to the Mellinarks in row one. (prediction) But...some of the non-Mellinarks in row two are similar in overall shape. (observed result) Therefore..."I ruled that out," i.e., I concluded that my initial idea was wrong. (conclusion) Because reasoning at this level is presumably preceded by two still lower levels (i.e., the sensory-motor and preoperational stages within Piagetian theory), this lower level will be designated as Level 3. Ss who scored from 5-8 were classified as transitional reasoners and those who scored from 9-12 were classified at the higher level, designated Level 4, a level that corresponds generally to Piaget's formal

THE ROLE OF ANALOGIES

123

operational stage (e.g., Inhelder & Piaget, 1958) and to use of hypothetico-predictive reasoning to successfully test causal hypotheses, e.g.: If...differences in swing speeds are caused by differences in the amount of weight hanging on pendulums, (causal hypothesis) and...the weights of two pendulums are varied, while holding other possible causes constant, (proposed test) then...pendulum swing speed should vary. (prediction) But...when the proposed test is carried out the swing speed does not vary. (observed result) Therefore...differences in swing speeds are probably not caused by weight differences, i.e., the weight hypothesis is probably wrong. (conclusion) Note that because the study involves college students, all over 18 years in age and all who have presumably undergone the final brain growth spurt discussed in Chapter 4, the word "level," as opposed to the word "stage," is used to characterize reasoning differences. 2.3 Experimental Design A modified Solomon four-group design was employed (Campbell & Stanley, 1966) that included initial instruction of all Ss during a lecture/demonstration session. The intent of this initial instruction was to introduce the terms “molecular polarity” and “bonding” in a way such that Ss would associate the terms with the spread of blue dye in water. This association was expected to lead Ss to attempt to apply the concepts to explain a perceptually similar but conceptually different phenomenon, hence render their exclusive use a misconception. Following this bonding instruction, one half of the Ss in each of the four laboratory sections were randomly administered a Dye Question concerning the spread of blue dye in standing water (see below). Two laboratory sections then became the experimental groups (the analogy groups) that received instruction on the diffusion concept utilizing one verbal analogy and two physical analogies. The remaining two sections became control groups that were given identical instruction minus the two physical analogies. Following these treatments, all Ss were readministered the Dye Question and a Diffusion Question (see below) in a counterbalanced order. Thus, the four groups were: Analogy Group 1 (n=15) - bonding instruction Dye Question diffusion instruction using one verbal and two physical analogies Dye Question Diffusion Question Analogy Group 2 (n=17) - bonding instruction diffusion instruction using one verbal and two physical analogies. Diffusion Question Dye Question

124

CHAPTER 6

Control Group 1 (n=23) - bonding instruction Dye Question diffusion instruction using one verbal but no physical analogies Dye Question Diffusion Question Control Group 2 (n=22) - bonding instruction diffusion instruction using one verbal but no physical analogies Diffusion Question Dye Question 2.4 Bonding Instruction During a lecture/demonstration session, all Ss were shown a bottle containing layers of oil and water to which some blue dye was added. The instructor then shook the bottle and pointed out that the blue dye remained throughout the water layer, but not throughout the oil layer. To explain this result, Ss were told that the water and dye molecules were polar molecules (i.e., contained segments that were positively or negatively charged), but that the oil molecules were not, hence the dye bonded (formed molecular connections) with the water molecules but not with the oil molecules. Therefore, the dye remained spread throughout the water layer but not the oil layer. 2.5 Dye Question The following Dye Question (after Westbrook & Marek, 1991) was randomly administered to one half of the analogy and control group Ss after the initial bonding instruction, but prior to instruction on the diffusion concept: A large container is full of clear water. Several drops of a dark blue dye are dropped on the surface of the water. The dye begins to spread throughout the water. Eventually the water in the container changes from clear to light blue. In a paragraph, explain why the dark blue dye spreads to change the color of the water to a uniform light blue. If possible, give your explanation in terms of interacting molecules.

2.6 Diffusion Instruction The term diffusion was introduced to all four groups during laboratory sessions. The same instructor taught all sessions. Ss first observed a change in the appearance of red onion cells exposed to various concentrations of salt water. They then advanced alternative hypotheses (i.e., explanations) for the reduction or expansion of the onion cells' boundaries. By making model cells with dialysis tubing, Ss investigated factors that affected the movement of molecules in and out of cells and attempted to test their alternative hypotheses. The model cells were filled and suspended in solutions of different-sized

THE ROLE OF ANALOGIES

125

molecules (starch, glucose and water) in varying concentrations. Molecular movement into or out of the model cells was measured by weight change of the model cells. Based on their alternative hypotheses and experimental designs, students generated predicted results. Students then compared predicted and observed weight changes to test their hypotheses. During the ensuing discussion, the instructor introduced the term “diffusion” to refer to the process by which the molecules moved. Diffusion was defined as the net movement of molecules from an area of high molecular concentration to areas of low concentration due to the collisions that result from the mixing of two or more types of randomly moving molecules. The diffusion of water molecules through a cell membrane (a special case of diffusion known as osmosis) was discussed and was likened to Mexican jumping beans moving through holes in a wire cage. The movement of perfume molecules through air was mentioned as another example of diffusion. Hence, all Ss were provided with two phenomena that could be explained in part by molecular diffusion, one with a verbal analogy, and one with a familiar example. At this point, both analogy groups were presented with two physical analogies for the diffusion process. For the first analogy, Ss placed equal amounts of large and small marbles in a jar in two layers, put on the lid and then shook the jar for one minute. For the second analogy, Ss repeated the procedure with large beans and millet. For both analogies, Ss observed that after shaking the different-sized objects were evenly distributed throughout the jar, presumably like the different types of molecules involved in the onion and model cell experiments. Total instructional time for all four groups was three hours. Time not spent on the physical analogies by the control groups was spent in additional experimentation and discussion. 2.7 Diffusion Question

To assess their understanding of the term diffusion, all Ss responded to the following Diffusion Question within seven days of the diffusion instruction: Explain what is meant by the term diffusion. Provide an example.

The Dye Question was also administered at this time. 2.8 Scoring

Diffusion Question responses, as well as both initial and retest Dye Question responses, were classified into the following categories (after Westbrook & Marek, 1991):

1. blank, irrelevant remarks or use of given terms without explanation (e.g., "Once you take away the water the cells get smaller. You put water in again and the cells will get back to normal size." "The molecules in the blue dye spread

126

2.

3.

4.

5.

6.

CHAPTER

6

throughout the water. Therefore causing the water to turn blue." "The dye was diffused through the water.") misconception, explanation based upon various concepts not related to the diffusion concept (e.g., "The molecules from both substances are small, uncharged and polar which allows them to pass." "The molecules of the dark blue dye were polar and took in clear water which made them expand and have a shade of light blue." "The dye is able to enter the water molecules.") partially correct conception plus misconception: some notion of the diffusion process but combined with other causes and/or non-molecular level objects (e.g., "Diffusion: the movement of an organism from an area of high concentration to an area of low concentration." "This process is one type of diffusion. The molecules of dark blue dye spread out and in the water and hook on to the molecules of water. The molecules of blue dye are distributed evenly throughout the water until the ratio of blue dye molecules to water molecules is equal in an area of the container.") descriptive conception: some notion of the diffusion process but no mention of molecules (e.g., "Diffusion is the movement of a substance from an area of higher concentration to a lower concentration." "The dye will not stay concentrated in one spot, they will diffuse throughout the water. Just like if you sprayed perfume in a corner of a room, eventually the whole room would smell like perfume.") partial theoretical conception: some notion of molecules moving from area of high molecular concentration to low (e.g., "Diffusion = movement of molecules from an area of higher concentration to the area of lower concentration." "Random movement of the molecules of dark blue dye. The molecules continually move through the water until they have dispersed themselves evenly." "The color appears to be relatively even light blue because the dye molecules disperse randomly throughout the water molecules. This is the same principle as shaking little marbles with big marbles.") complete theoretical conception: molecules move from area of high molecular concentration to low due to collisions of randomly moving molecules (e.g., "Diffusion causes the water to turn blue. The dye is more concentrated and moves from that higher concentration to the lower concentration as the molecules randomly diffuse by bouncing off one another. This continues until the concentration equalizes throughout. Thus the lighter color." "When gases or liquid move randomly from an area of higher concentration to an area of lower concentration, such as perfume odor when someone enters a room. The diffusion continues until the concentrations equalize, if there are no other limitations. This random movement happens as the molecules mix by bouncing off one another.")

Four raters independently scored each response using the above criteria and examples. The raters had not participated in the instruction, thus had no knowledge of Ss' identity. Further, the order in which the responses were scored was randomized

THE ROLE OF ANALOGIES

127

with respect to group membership. Inter-rater agreement was 70% for the Dye Question and 71% for the Diffusion Question. Disagreements were resolved through discussion among the raters. 3. RESULTS AND DISCUSSION

3.1 Reasoning Skill (Developmental Level)

Mean score on the Classroom Test of Scientific Reasoning was 6.5, SD=2.2. Eleven Ss (15%) scored from 0-4 and were classified as Level 3 reasoners. Fortyeight Ss (65%) scored from 5-8 and were classified as transitional reasoners, while 15 Ss (20%) scored from 9-12 and were classified as Level 4 reasoners. 3.2 Test-Retest and Order Effect

A comparison of Dye Question scores of Ss who took the initial Dye Question, with those who did not, revealed no significant difference on the Dye Question p=0.18) and on the Diffusion Question p=0.62). In other words, taking the initial Dye Question did not have a significant effect on performance on either question following diffusion instruction, A comparison of scores of Ss who responded to the Dye Question first with those who responded to the Diffusion Question first also revealed no significant differences on the Dye Question p=0.19) or on the Diffusion Question p=0.78). 3.3 Combined Group Responses

Table 1 shows the number and percentage of question responses in each category for the combined analogy and control groups. Of the 35 Ss who took the initial Dye Question, 33 (94%) responded in category one (i.e., with either a blank, irrelevant remarks, or use of terms only with no explanation), or in category two (i.e., a misconception). This level of response is poorer that obtained by Westbrook & Marek (1991) who found 61% of their college sample exhibited misconceptions. The relatively poor performance of the present sample most likely reflects the effect of the bonding instruction, which was to provoke most Ss to respond in category two with the bonding "misconception" (see below). Forty two percent (31/74) of the Dye Question responses following diffusion instruction were classified in category one or two. The remaining 58% of the Ss invoked at least a partially correct conception of diffusion to explain the dye spread. However, only 4 Ss (5%) invoked a complete theoretical conception of diffusion (category six). Responses to the Diffusion Question revealed substantially less category one and two responses (17%) and substantially more category three through six responses.

128

CHAPTER 6

This indicates that, following diffusion instruction, several of the Ss understood the diffusion concept well enough to explain it when directly asked to do so (the Diffusion Question), but that they did not invoke the concept of diffusion to explain why the blue dye spread (the Dye Question). Instead many continued to invoke alternative explanations such as chemical bonding or molecular break up.

3.4 Effect of Bonding and Diffusion Instruction on Dye Question Responses Table 2 lists responses to the initial and retest Dye Questions categorized into the type of alternative hypothesis (or combination of alternative hypotheses) that Ss generated to explain the dye spread. Note that some Ss may have generated more than one hypothesis therefore the number of alternative hypotheses generated is greater than the number of Ss. As shown, only 2/50 (4%) of the hypotheses that were generated on the initial test (following bonding instruction but prior to diffusion instruction), referred to the process of diffusion. By far the most frequent hypothesis (24/50=48%) was that some sort of bonding of the dye and water molecules was taking place. Therefore, the bonding instruction appears to have been very successful at provoking Ss to apply the concepts of molecular polarity and bonding in an attempt to explain the spread of blue dye in standing water. The next most frequent hypothesis was that the dye molecules were breaking up, off, or down (7/50=14%). Dye Question responses following diffusion instruction revealed a considerably greater percentage of diffusion related hypotheses (43/111=39%). However, a substantial percentage of alternatives to diffusion were still being proposed. Again the most frequent alternatives were that some sort of bonding was occurring

THE ROLE OF ANALOGIES

129

(20/111=18%) or that the dye molecules were breaking apart (9/111=8%). The anthropomorphic hypothesis that the dye molecules move "because they want to" or "try to" was also mentioned nine times (8%).

3.5 Analogy and Control Group Comparisons

Mean scores of the analogy and control group Ss who took the initial Dye Question were 2.00 and 2.04 respectively. This difference was not statistically significant p=0.78). Mean retest Dye Question scores of the respective groups were 3.25 and 3.04. This difference was also not statistically significant p=0.51). Mean posttest Diffusion Question scores for the respective

130

CHAPTER

6

groups were 4.09 and 3.31. This difference was statistically significant p=0.007), indicating better performance by the analogy group. Figure 1 shows the percentage of experimental and control group responses in each of the six categories on the Diffusion Question. The most obvious group differences can be seen at either end of the scale. At the bottom end, 6% percent of the analogy group responses were in categories one and two compared to 29% of control group responses. At the top end, 40% of the analogy group responses were in categories five and six compared to only 17% of those of the control group.

THE ROLE OF ANALOGIES

131

3.6 Reasoning Skill and Performance on the Dye and Diffusion Questions Table 3 lists mean scores and standard deviations of the Level 3, transitional and Level 4 Ss (combined experimental and control groups) on the three questions. As shown, mean scores of the Level 4 Ss are higher than those of the transitional Ss for all three questions. Similarly, mean scores of the transitional Ss are higher than those of the Level 3 Ss for all three questions. However, group differences reached statistical significance (p<0.05) only on the retest Dye Question p=0.03).

The fact that reasoning skill was not significantly related to performance on the initial Dye Question is similar to the Westbrook & Marek (1991) results, but not similar to those reported by Lawson & Weser (1990). Lawson & Weser found Level 3 college students more likely than their Level 4 classmates to hold beliefs in biological misconceptions such as creationism, orthogenesis, the soul, nonreductionism, vitalism, and teleology. Why was reasoning skill significantly related to performance on the retest Dye Question but not to the other two questions? Let us first consider the retest Dye Question and the Diffusion Question. It seems likely that the retest Dye Question was intellectually more challenging than the Diffusion Question because a high level response to the Diffusion Question could have resulted largely by memorization, an intellectual activity requiring no reasoning. On the other hand, a high level response to the retest Dye Question required Ss to not only explicate the process of diffusion, but to also apply it to explain an event i.e., the spread of blue dye in standing water. According to the reasoning- skill hypothesis, successful use of the diffusion concept to explain the dye spread, especially following explicit instruction on two competing explanations (molecular bonding versus diffusion), required Ss to use hypotheticopredictive reasoning to reject exclusive use of the bonding hypothesis and accept the more appropriate diffusion hypothesis. Thus, the fact that reasoning skill did correlate more highly with the retest Dye Question performance than with

132

CHAPTER

6

performance on the less demanding Diffusion Question supports the reasoning-skill hypothesis. The fact that reasoning skill correlated more highly with the retest Dye Question than with the initial Dye Question also supports the reasoning-skill hypothesis because competing hypotheses were much more likely to exist in the students' minds when they responded to the retest Dye Question (following bonding and diffusion instruction), than when they responded to the initial Dye Question (following only bonding instruction). When Ss were asked to explain the dye spread on the initial Dye Question it seems reasonable to assume that little doubt existed in most students' minds that their task was to recall the teacher's explanation concerning molecular polarity and bonding and apply it in this context (a context very similar to the one in which the concepts of molecular polarity and bonding were introduced). In support of this assumption, consider the following student responses: "Yes I know this was discussed in class earlier in the semester but I can't remember the exact words to use in order to describe the reaction...perhaps the molecules of dye are attracted to each molecule of hydrogen." "You probably expect me to remember the name of the process but I don't. However I can explain it. The blue dye & water both have the same base so they are compatible. The dye will distribute evenly throughout the water. If the blue dye was placed in oil base the dye would not distribute." As a further test of the reasoning-skill hypothesis, we considered only those Ss who responded at level two (misconception) on the initial Dye Question to see who among them changed to a diffusion explanation on the retest Dye Question (the correct conception). The reasoning-skill hypothesis predicts that Level 4 Ss should be more likely to change to use of the diffusion explanation than the transitional Ss, who in turn should be more likely to change than the Level 3 Ss. The relevant data are shown in Table 4.

THE ROLE OF ANALOGIES

133

Although the numbers of Ss are small, the results in Table 4 are essentially as predicted. None of the six Level 3 Ss (0%) changed from use of a misconception (something other than the diffusion explanation on the initial Dye Question) to the correct diffusion explanation, compared to four of the 21 transitional Ss (19%) and compared to two of the five Level 4 Ss (40%). In terms of category change, the Level 3 Ss showed no gain. The transitional Ss gained an average of 0.82 categories; and the Level 4 Ss gained an average of 1.33 categories. Finally, in terms of percentage of Ss who gained at least one category from the initial test to the retest, 0% of the Level 3 Ss gained at least one category compared to 48% of the transitional Ss and 67% of the Level 4 Ss. 4. CONCLUSIONS AND INSTRUCTIONAL IMPLICATIONS

Hypothetico-predictive reasoning skill is, in theory, related to conceptual change because such change presumably occurs when alternative conceptions exist and a decision concerning which conceptions to apply must be made. A conceptual change has occurred when a person who first applies inappropriate or incomplete concepts (e.g., molecular polarity and bonding) to explain a specific phenomenon, such as the gradual spread of dye in standing water, later applies a more appropriate concept (i.e., diffusion) to that same phenomenon. Similarly, when a child first explains the rise of soda up a straw by use of the concept of suction and later rejects suction in favor of an explanation based upon differences in air pressures on the surface of the soda inside and outside the straw, a conceptual change has occurred. Results of the present study support the hypothesis that physical analogies assist in conceptual change by clarifying the nature of new theoretical concepts, but that successful application of the new concepts involves higher-level, hypotheticopredictive reasoning skill. In the context of college genetics instruction, Baker & Lawson (2001) also found analogies helpful in teaching theoretical concepts and that successful application was linked to reasoning skill. Given that a goal of science education is to enable students to successfully apply theoretical concepts to novel situations, the present results imply that instruction should not only be designed to help students acquire concepts, but also to help them develop skill in utilizing higher-level, hypothetico-predictive reasoning to evaluate situations in which those concepts may or may not be successfully applied. The fact that less than 50% of the Level 4 students, and less than 15% of the transitional and Level 3 students in the present study "changed their minds" from use of the incomplete bonding explanation to use of the more complete diffusion explanation, is not too surprising when one considers that these alternative explanations were never explicitly contrasted and/or tested during the instructional phases of this study. In terms of the development of reasoning skills, this was unfortunate because considerable evidence, much of which is reviewed by Lawson, Abraham & Renner (1989), indicates that explicitly generating and testing alternative

134

CHAPTER

6

hypotheses in the classroom/laboratory setting is an effective means of provoking such development, particularly among college students. Research discussed in Chapters 7 and 8 may also help explain the less than perfect performance of the Level 4 students. That research suggests that there may in fact be a fifth stage in intellectual development and that fifth-stage reasoning may aid in the successful construction and application of theoretical concepts. Accordingly, perhaps some of the students classified as Level 4 students in the present study had in fact developed Stage 5 reasoning skill (the successful ones) and some of those Level 4 students had not yet developed Stage 5 reasoning skill (the unsuccessful ones).

CHAPTER 7

INTELLECTUAL DEVELOPMENT DURING THE COLLEGE YEARS: IS THERE A FIFTH STAGE?

1. INTRODUCTION

Following a review of several years of research into problem solving, Perkins & Salomon (1989) concluded that, although expert performance manifests itself in contextual ways, general cognitive skills (i.e., "habits of mind") exist. These general cognitive skills reveal themselves primarily as strategies of looking for counter examples to test causal knowledge claims. Although Perkins and Salomon discuss such strategies as thinking tools of the philosopher, scientists recognize them as components of a scientific method that has as its core the generation and test of alternative causal hypotheses (cf., Baker & Allen, 1977; Burmester, 1952; Carey, 1998; Chamberlain, 1965; Lawson, 1995; Lewis, 1988; Moore, 1993; Platt, 1964). Essentially, this method embodies a set of generally applicable questions that must be raised and satisfactorily answered prior to drawing a firm conclusion about the relative truth or falsity of any particular causal claim. The set of questions reads more or less like this: 1. What is the central causal question in this particular context? 2. In addition to the proposed cause, what alternative causes (i.e., explanations/hypotheses/theories) are possible? 3. How can each possibility be tested? 4. What specific predictions follow from each possibility and its proposed test? 5. How does the evidence (either circumstantial, correlational or experimental), once gathered, match the predictions? 6. What conclusions can be drawn based on the obtained degree of match?

Of course the development of reasoning patterns associated with these questions has been the subject of a long line of research within developmental psychology and within science education (for reviews see Lawson, 1985 and Lawson, 1992a; and for more recent research within science education see for example Cavallo, 1996; Germann, 1994; Germann & Aram, 1996; Hurst & Milkent, 1996; Johnson & Lawson, 1998; Keys, 1994; Kuhn, 1989; Lawson, 1992b; Lawson & Thompson, 1988; Lawson & Worsnop, 1992; Noh & Scharmann, 1997; Shayer & Adey, 1993; Westbrook & Rogers, 1994; Wong, 1993; Zohar, Weinberger & Tamir, 1994). The general conclusion of such research is that reasoning patterns (the exact nature of which is yet to be determined) do develop across adolescence, at least in some 135

136

CHAPTER

7

students, and play an important role in the ability to do science and to construct science concepts. Research has also documented that improvements in reasoning as a consequence of instruction, although difficult to obtain, are possible and are of general use. Dramatic evidence of this was obtained by Shayer & Adey (1993) who found that three years after the end of a two-year science program designed to promote formal operational thinking positive effects were seen on the British National examinations not only in science, but also in mathematics and in English. Consequently, one of the goals of our department's introductory non-majors' biology course, The Living World, is to help students develop general causal hypothesis-testing skill by encouraging them to raise and answer the previously listed set of questions during a series of lab and field activities. Additionally, the course lectures present several episodes that explicate how the questions have been asked and answered by biologists while conducting past research. In other words, the course attempts to teach general cognitive skills essentially in the way described as the "high road" by Perkins and Salomon, which is say that the course encourages the "deliberate and mindful abstraction" of the question-asking and question-answering skills from a variety of domain-specific contexts. During a recent semester, the quizzes listed in Table 1 were administered as part of an effort to assess the extent to which students were acquiring general, causal hypothesis-testing skill. The quizzes were administered in lab sections following investigations in which students generated and tested the alternative causal hypotheses listed. Notice that each quiz asks the same questions about testing alternative causal hypotheses. More specifically, each quiz was designed to assess the extent to which students could generate hypothetico-predictive arguments, complete with evidence that would allow rejection of the alternative causal hypotheses. For example, consider the following argument and evidence that leads to the rejection of the weight hypothesis on the Pendulum Quiz - a quiz patterned after Inhelder & Piaget's classic pendulum task (Inhelder & Piaget, 1958, pp. 67-79): If...differences in swing speeds are caused by differences in the amount of weight hanging on pendulums, (weight hypothesis) and...the weights of two pendulums are varied, while holding other possible causes constant, (proposed test) then...pendulum swing speed should vary. (prediction) But...suppose that the proposed test is actually carried out and the swing speed does not vary. (observed result) Therefore...we would conclude that differences in swing speeds are probably not caused by weight differences, i.e., the weight hypothesis is probably wrong. (conclusion) Importantly, the quizzes were administered in the order listed. This means that if students were in fact acquiring general, causal hypothesis-testing skill during the

INTELLECTUAL DEVELOPMENT DURING THE COLLEGE YEARS

137

semester, then performance should improve from quiz to quiz. Consequently, we were surprised to find that most students responded successfully on the Pendulum

Pendulum Quiz A swinging string with a weight on the end is called a pendulum. What causes pendulums to swing fast or slow? Hypothesis 1:A change in the amount of weight hanging on the end of the string will cause a difference in the swing speed - the lighter the weight, the faster the swing. Hypothesis 2:A change in the length of string will cause a difference in the swing speed - the shorter the string, the faster the swing. How could you test these hypotheses? 1. Describe your experiment. 2. What are the predicted results of your experiment (assuming that the hypotheses are correct)? 3. What result would show that hypothesis 1 is probably wrong? 4. What result would show that hypothesis 2 is probably wrong? Mealworm Quiz A student recently placed some mealworms in a rectangular box to observe their behavior. She noticed that the mealworms tended to group at the right end of the box. She also noticed that the right end had some leaves in it and that the box was darker at that end. She wondered what caused them to group at the right end. Hypothesis 1:They went to the right end because it had leaves in it. Hypothesis 2:They went to the right end because it was darker than the left end. How could you test these hypotheses? 1. Describe your experiment. 2. What are the predicted results (assuming that the hypotheses are correct)? 3. What result would show that hypothesis 1. is probably wrong? 4. What result would show that hypothesis 2 is probably wrong? "A" Mountain Quiz A recent survey of organisms on "A" Mountain revealed more grass on the north-facing slope than on the south-facing slope. In response to the causal question, "Why is there more grass on the north-facing slope?" a student generated the following hypotheses: Hypothesis 1:Lack of moisture in the soil on the south-facing slope keeps grass from growing there (i.e., north is better shaded from the sun's drying rays).

138

CHAPTER

7

Hypothesis 2:The sunlight itself is too intense for good grass growth on the southfacing slope (i.e., very intense rays disrupt the grasses' ability to conduct photosynthesis). How could you test these hypotheses? 1. Describe your experiment(s). 2. What are the predicted results of your experiment(s) assuming that the hypotheses are correct? 3. What result would show that hypothesis 1 is probably wrong? 4. What result would show that hypothesis 2 is probably wrong? Osmosis Quiz When a thin slice of red onion cells are bathed in salt water the red portion of each cell appears to shrink. What causes the red portion to appear to shrink? Hypothesis 1:Salt ions enter the space between the cell wall and the cell membrane and push on the cell membrane. Hypothesis 2:Water molecules attractive forces of the salt ions.

are charged thus leave the cell due to

Question: How could you use model cells made of dialysis tubing, a weighing devise, and solutions such as salt water, distilled water, and glucose to test these hypotheses? 1. Describe your experiment. 2. What are the predicted results assuming that the hypotheses are correct? 3. What result would show that hypothesis 1 is probably wrong? 4. What result would show that hypothesis 2 is probably wrong? [Note: These hypotheses were not intended to "scientifically valid" in the sense that when tested they would be supported. Rather, the intent of the quiz is to discover if students can devise tests of the hypotheses regardless of their empirical status.]

Quiz (94%), while success on the Mealworm Quiz dropped to 82%. Performance dropped even further to 57% on the "A" Mountain Quiz and to a dismal 18% on the Osmosis Quiz. What might be the cause or causes of this unexpected drop in performance? The working hypothesis tested by the present research is that the extent to which students successfully generate and test causal (as opposed to descriptive) hypotheses (see Chapter 3) depends on the presence or absence of two general levels of causal hypothesis-testing skill. The first hypothesized level involves hypothesis testing in contexts in which the tentative causal agents can be directly observed/sensed/ measured (e.g., the long or short strings and heavy or light weights on pendulums, the number of smelly leaves and light or dark areas at the ends of boxes), while the second involves causal hypothesis-testing in contexts in which the tentative causal agents are unobservable (i.e., imaginary/abstract/theoretical) such as

INTELLECTUAL DEVELOPMENT DURING THE COLLEGE YEARS

139

ions and charged molecules. Thus, successful performance depends in part on the abstractness of the hypotheses in question. To clarify this distinction between observable and unobservable causal agents, consider the nature of water. Students can directly observe water. At room temperature water appears as a clear liquid. Thus, it is not hard to imagine that the presence or absence of this clear liquid might influence mealworm behavior. In other words, students should have little difficulty in understanding (i.e., assimilating/representing) the hypothesis that mealworms may have moved to the right end of a box because of the clear liquid (called water) at that end. On the other hand, in the Osmosis Quiz, water is no longer treated as merely as a clear liquid. Instead it is conceived of as consisting of charged molecules. Of course students cannot see individual water molecules to know whether or not each really consists of two hydrogen atoms and one oxygen atom, much less whether or not each is charged. Thus, the hypothesis that unseen and ions leave cells because of their attraction to unseen charged molecules should be more difficult to assimilate/represent. Increased difficulty in representing and reasoning about unobservable entities may also stem from the increased complexity of the arguments needed to test their hypothesized role(s). For example, suppose the hypothesis is generated that red onion cells shrink when bathed in salt water because molecules exit the cells. Further, suppose this molecules-exiting hypothesis is pitted against an alternative that claims that the cells just appear smaller because and ions push on their cell membranes (see Table 1). The following argument and experiment using dialysis bags, which are assumed to have properties similar to those of cell membranes, can be used to test these alternatives: If...cells shrink because unobservable and ions push on their cell membranes, (ion-push hypothesis) and...a dialysis bag filled with distilled water is weighed, bathed in salt water for several minutes, and then reweighed, (proposed test) then...the bag should appear smaller while in the salt water, but should not lose weight. (prediction) The bag should not lose weight because the molecules, which presumably weigh some measurable amount, should not leave the bag. (theoretical rationale) But...suppose upon conducting the experiment, we find that the bag does lose weight. (observed result) Therefore...we would conclude that the ion-push hypothesis is probably wrong. (conclusion) Although this argument follows the same pattern used to test causal hypotheses about why pendulums swing fast or slow, it also includes a theoretical rationale. The theoretical rationale is needed to link the hypothesis and proposed test to the prediction. In other words, the theoretical rationale is needed to explain why the

140

CHAPTER 7

prediction follows. No such theoretical rationale is needed in the pendulum context because in that context the hypothesized cause and the experiment's independent variable are one and the same (i.e., the amount of weight hanging on the string), thus the prediction more obviously follows. Thus, inherent in this argument is the notion that causal hypothesis testing can be undertaken on two qualitatively different levels with success at testing hypotheses involving observable causal agents as a prerequisite for becoming proficient at testing causal hypotheses involving unobservable theoretical entities. In other words, students first become generally skilled at testing hypotheses about observable causal agents (skill that appears comparable to that of Piaget's fourth-stage called formal operational e.g., Inhelder & Piaget, 1958). And only then, given the necessary developmental conditions, do they become generally skilled at testing causal hypotheses about unobservable causal agents. Thus, a fifth, post-formal, stage of intellectual development is proposed. Importantly, the present developmental view sees declarative knowledge as a necessary but insufficient condition for successful fifth-stage hypothesis testing. Predictably, some hypothesis-testing situations appear to involve causal claims that fall between the extremes. For example, the second hypothesis advanced to explain the lack of grass on the south-facing slope on the "A" Mountain Quiz involves very intense sunlight - a readily observable factor - but also involves grasses' ability to conduct photosynthesis - a clearly unobservable process, which in theory involves unobservable entities such as molecules, photons, electrons and the like. Given the proposed distinction between the observable and the unobservable, one might wonder what influence technological advances such as the invention of increasingly powerful electron microscopes have had on the status of concepts such as atoms and molecules. For example, does the fact that photographs now exist presumably showing individual atoms reduce the status of the atom concept from theoretical to descriptive? I think not - primarily because the photographs merely reveal images that look like little round balls. Thus, one still does not actually see atoms. In other words, deciding whether or not the photographs actually show atoms is still a matter of interpretation - not observation. In summary, like William Perry's search for patterns of intellectual development during the college years (Perry, 1970), as well as those of other developmentallybased researchers who have sought developmental advances beyond Piaget's formal stage (e.g., Arlin, 1975; Commons, Richards & Armon, 1984; Epstein, 1986; Kramer, 1983; Hudspeth & Pribrum, 1990; Thatcher, 1991; Thatcher, Walker & Guidice, 1987; Riegel, 1973), the present hypothesis attempts to understand the cognition of college students not only in terms of declarative knowledge differences, but also in terms of general reasoning skills needed to process information, test alternative hypotheses, and construct theoretical concepts in qualitatively more powerful ways.

INTELLECTUAL DEVELOPMENT DURING THE COLLEGE YEARS

141

2. METHOD

2.1 Sample

The sample consisted of 667 undergraduate students (non-science majors) enrolled in a course entitled The Living World taught at a major southwest university during a recent fall semester. The students ranged in age from 15.8 years to 47.1 years (mean age = 19.64 years, SD = 3.02). 2.2 Design

The first step in testing the study's working hypothesis was the selection of a valid measure of scientific reasoning that included items testing students' skill in testing alternative hypotheses involving observable causal agents. Lawson's Classroom Test of Scientific Reasoning was selected for this purpose (Lawson, 1978). Because the original test does not include items explicitly assessing students' hypothesis testing skill in contexts in which the hypotheses involve unobservable entities, two new items that did so were invented and added (i.e., a Burning Candle item and a Red Blood Cells item). Thus, each new item should require developmentally more advanced reasoning skill than assessed by the original test. The modified test was then administered to students enrolled in The Living World at the start of the fall semester. Scores on the modified test were used to classify student responses into four developmental levels presumably reflecting their skill in testing both types of causal hypotheses (i.e., Level 3 = students not able to test hypotheses involving observable causal agents, Low Level 4 = students inconsistently able to test hypotheses involving observable causal agents, High Level 4 = students consistently able to test hypotheses involving observable causal agents, Level 5 = students able to test hypotheses involving unobservable causal agents). Levels 1 and 2 would correspond to the sensory-motor and preoperational stages respectively. However, Stage 1 and 2 thinking was not assessed as all students were assumed to have acquired at least Stage 3 reasoning skill. The course was then taught and records kept of student performance on course exams. The modified test was also administered at the end of the semester to assess test-retest reliability, to measure student progress in reasoning during the semester, and to determine whether assessed reasoning skill at the start or at the end of the semester is the better predictor of course performance. Next a transfer problem that, in theory, required Stage 5 hypothesis-testing skill was constructed and also administered at the end of the semester. The problem was considered to be a transfer problem because it was written within a context neither discussed nor explored in the course. More specifically, the problem involved testing a hypothesis about why balloons move forward or backward when a moving vehicle

142

CHAPTER

7

stops suddenly. Five multiple-choice questions assessing the declarative knowledge presumably needed to solve the transfer problem were also constructed and administered. Consequently, if Stage 5 reasoning skill alone is sufficient to solve the transfer problem, then reasoning skill alone should predict success. On the other hand, if declarative knowledge is sufficient, then it alone should predict success. Finally, if both Stage 5 reasoning skill and declarative knowledge are necessary, then both should predict success. Because the course introduced a number of biological and biochemical theories involving both observable and unobservable causal agents, a more general prediction was also advanced: If the modified reasoning test is a valid measure of general levels of hypothesis-testing skill, then course exam scores of the Level 3 students should be significantly lower than those of the Level 4 students; and exam scores of the Level 4 students should be significantly lower than those of the Level 5 students. This prediction is based on the assumption that causal hypothesis-testing skill plays a role in theoretical concept construction. In essence, the argument is made that even though exam items do not directly assess causal hypothesis-testing skill, such skill nevertheless plays a role in construction and retention of such concepts because students presumably do not come to the learning situation as "blank slates." Rather, they often come with alternative conceptions (i.e., hypotheses) that must be modified or replaced by scientific conceptions. Thus, concept construction often engages hypothetico-predictive reasoning skill. On the other hand, if classification into Level 5 by performance on the modified test does not reflect a general advance in reasoning, but instead represents the acquisition of domain-specific declarative knowledge needed to respond successfully to the two new test items (i.e., the Burning Candle and Red Blood Cells items), then Level 4 and Level 5 students should perform equally well. The following argument summarizes how the alternative hypotheses were tested: If...two general, developmentally-based, levels of causal hypothesis-testing skill exist i.e., Level 4 skill involving observable causal agents and Level 5 skill involving unobservable causal agents, (fifth-stage hypothesis) and...a sample of college students are classified as Level 4 or Level 5 reasoners based on a test of reasoning skill and are then administered a transfer problem presumably requiring Stage 5 hypothesis-testing skill, then...students classified as Level 4 reasoners should not solve the problem while students classified as Level 5 reasoners should solve the problem. Further, if...the fifth-stage hypothesis is correct, (fifth-stage hypothesis) and...students classified as Level 4 or Level 5 reasoners are subjected to a biology course in which several theoretical concepts are introduced and the students are then tested to determine the extent to which they understand those concepts, then...Level 4 students should demonstrate significantly less understanding than Level 5 students.

INTELLECTUAL DEVELOPMENT DURING THE COLLEGE YEARS

143

On the other hand, if...two levels of causal hypothesis testing skill do not exist and instead student performance differences on the reasoning skill test reflect differences in problemspecific declarative knowledge, (declarative-knowledge hypothesis) and...the declarative knowledge presumably required for solution of the transfer problem is assessed, then...Level 4 and 5 students should perform equally well on the transfer problem; transfer problem performance differences should correlate with declarative knowledge differences; and Level 4 and 5 students should demonstrate similar understanding of the theoretical concepts introduced in the biology course. 2.3 The Course

The Living World consists of three weekly 50-minute lectures (delivered by the course professor) and one weekly two-hour lab (each taught by a graduate student teaching assistants) each week for 15 weeks. In the order presented, course topics included the theories of evolution and natural selection, animal behavior theory, various physiological theories, theories of classical and molecular genetics, and theories of photosynthesis and cellular respiration. In most cases, topics were first explored and new terms first introduced in labs. Lectures then discussed the topics in more detail and applied them to additional biological and non-biological contexts. Thus, the course employed the learning cycle method of instruction (Eakin & Karplus, 1976; Karplus, 1977; Lawson, Abraham & Renner, 1989; Renner & Marek, 1990). 2.4 Predictor Variables

Reasoning Skill Level. Hypothetico-predictive reasoning skill (i.e., developmental level) was assessed by a 13-item written test based on reasoning patterns associated with causal hypothesis testing (i.e., the identification and control of variables, correlational reasoning, probabilistic reasoning, proportional reasoning, and combinatorial reasoning). As mentioned, the test was a modified version of Lawson's Classroom Test of Scientific Reasoning. With respect to causal hypothesis testing, the original test includes items in which the hypothetical causal agents are for the most part observable. For example, two items involve testing hypotheses in the context of the pendulum task mentioned above, two other items involve fruit fly responses to red and blue light and one item involves a light bulb's response to pushed buttons. Validity of the original test as a measure of general reasoning skill has been established by several studies (e.g., Lawson, 1978; 1979; 1980a; 1980b; 1982; 1983; 1987; 1990; 1992; 1995; Lawson & Weser, 1990; Lawson, Baker, DiDonato, Verdi & Johnson, 1993). An important aspect of the establishment of test validity, as was

144

CHAPTER

7

the case with many of Piaget's original tasks, was the need to demonstrate that performance differences on the items were caused by differences in reasoning skill and not by the presence or absence of domain-specific knowledge. In other words, items should require only specific knowledge that students can reasonably be presumed to have. In short, the studies have supported this presumption. The pendulum task is an excellent example of this point because all students presumably know what strings and weights are and what is meant by the phrase “swinging back and forth.” The modified test used in the present study contains 11 of the original items plus two new items that are hypothesized to require Stage 5 reasoning skill because each requires students to use hypothetico-predictive reasoning to reject causal hypotheses involving unobservable entities (i.e., dissolving molecules and pushing or attracting and ions). Of course, testing the validity of this claim, as opposed to the claim that the tasks merely measure the presence or absence of domainspecific declarative knowledge, is a central component of the present study. One of the items involves water rise in an inverted cylinder after the cylinder had been placed over a burning candle sitting in water. The other item involves changes in the appearance of red blood cells when bathed in salt water. The two new items appear as follows: The Burning Candle. The figure below at the left shows a drinking glass and a burning birthday candle stuck in a small piece of clay standing in a pan of water. When the glass is turned upside down, put over the candle and placed in the water, the candle quickly goes out and the water rushes up into the glass (as shown at the right).

This observation raises an interesting question: Why does the water rush up into the glass? Here is a possible explanation. The flame converts oxygen from the air to carbon dioxide. Because oxygen does not dissolve very rapidly in water, but carbon dioxide does, the newly formed carbon dioxide dissolves rapidly in the water lowering the air pressure inside the glass. Thus, the relatively higher air pressure outside the glass pushes the water up into the glass. a. Suppose you have the materials mentioned above plus some matches and some dry ice (dry ice is frozen carbon dioxide). Using these materials, describe a way to test this possible

INTELLECTUAL DEVELOPMENT DURING THE COLLEGE YEARS

145

explanation. b. What result of your test would show that this explanation is probably wrong? The Red Blood Cells. A student put a drop of blood on a microscope slide and then looked at the blood under a microscope. As you can see in the diagram below, the magnified red blood cells look like little round balls. After adding a few drops of salt water to the blood, the student noticed that the cells appeared smaller as shown below.

This observation raises an interesting question: Why do the red blood cells appear smaller? Here are two possible explanations: I: Salt ions push on the cell membranes and make them appear smaller. II: Water molecules are attracted to the salt ions so water molecules move out and leave the cells smaller.

Suppose you have a beaker, some salt water, a very accurate weighing devise, and some water-filled plastic bags. Suppose the plastic behaves just like red-bloodcell membranes. a. Describe an experiment using these materials to test the two explanations. b. What result of your experiment would show that explanation I is probably wrong? c. What result of your experiment would show that explanation II is probably wrong? Scoring. All test items required students to respond to a question or make a prediction in writing and to either explain how they obtained their answer, or in the case of quantitative problems, to show their calculations. Items were judged correct (a score of 1) if the correct answer and an adequate explanation or set of calculations were present. To obtain a correct score on the Burning Candle item, students had to propose an adequate experiment and describe what experimental result would show that the explanation was probably wrong. Two points were possible on the Red

146

CHAPTER

7

Blood Cells item - one for each explanation satisfactorily tested and shown to be probably wrong. Based on the nature of the test items and the number of each type of item, scores of 0-3 were classified as Level 3 (i.e., students not able to test hypotheses involving observable causal agents). Scores of 4-6 were classified as Low Level 4 (i.e., students inconsistently able to test hypotheses involving observable causal agents). Scores of 7-10 were classified as High Level 4 (i.e., students consistently able to test hypotheses involving observable causal agents). And scores of 11-13 were classified as Level 5 (i.e., students able to test causal hypotheses involving unobservable entities). A test-retest reliability coefficient of 0.65 was obtained by comparing student performance on the test administered at the start of the semester with test performance at the semester's end. Declarative Knowledge. The declarative knowledge believed to be involved in the Balloons Transfer Problem (see below) was measured by the following multiplechoice items, which were administered at the semester's end. No systematic attempt was made to introduce this knowledge during the semester.

1. Which of the following objects carries the most "umph" (momentum)? a. a pickup truck parked in your driveway b. a pickup truck traveling at 60 miles per hour (correct answer) c. a baseball traveling at 70 miles per hour d. a baseball sitting on a table 2. Air is composed of a. empty space. b. tiny stationary molecules. c. tiny moving and colliding molecules. (correct answer) 3. Air a. has weight. (correct answer) b. has no weight. 4. An air-filled balloon will fall to the floor because a. the floor is its "natural" place. b. static electricity will pull it down. c. it is heavier than the surrounding air. (correct answer) d. it is lighter than the surrounding air. 5. A helium-filled balloon will float in air because a. its "natural" place is up. b. static electricity will hold it up. c. it is heavier than the surrounding air. d. it is lighter than the surrounding air. (correct answer)

Scoring. Each question was scored as correct (1) or incorrect (0) for a 0 to 5 total score.

INTELLECTUAL DEVELOPMENT DURING THE COLLEGE YEARS

147

2.5 Dependent Variables The Balloons Transfer Problem. During the final laboratory period, students watched a video. The video showed a side view of a rubber balloon hanging by a string from the ceiling of a moving vehicle. Also shown was a floating mylar balloon attached by a string to the vehicle's back seat. When the vehicle came to an abrupt stop, the hanging balloon swung forward and the floating balloon swung backward. After viewing this on the videotape, students read the following and responded in writing: As you could see in the video, when the vehicle stopped, the hanging balloon went forward and the floating balloon went backward. This observation raises an interesting question: Why did the hanging balloon go forward while the floating balloon went backward? Here is a possible explanation. The hanging balloon is relatively heavy; so its momentum carried it forward when the vehicle stopped. The floating balloon, being lighter than air and having less momentum, went backward because as the vehicle stopped, the heavier air molecules inside the vehicle rushed forward and piled up at the front. Thus, the piled-up air molecules at the front pushed harder on the front side of the balloon than the relatively fewer air molecules on the balloon's backside. Thus, the balloon was pushed backward. Suppose you have two balloons just like those shown in the video, a large airtight chamber on wheels, and a vacuum pump (a pump that can extract air from airtight chambers). a. Describe an experiment using these materials to test the possible explanation. b. What result of your experiment would show that the explanation is probably wrong? Scoring. Responses were judged to be correct (a score of 1) or incorrect (a score of 0). All responses were evaluated based on the criterion that a correct response must contain the following experiment and argument: First secure the two balloons in the chamber as they were secured in the vehicle. Next use the pump to extract air from the chamber. Then set the chamber in motion and quickly stop it. If the balloons behave as they did in the vehicle (i.e., the hanging balloon moves forward and the floating balloon - which would now just rest on the seat - moves backward), then the explanation is probably wrong. This experiment and argument do not explicitly follow the hypothetico-predictive form. Nevertheless, the form was presumably used, i.e.: If...the lighter-than-air balloon went backwards when the vehicle in the videotape stopped because air molecules piled up at the front and pushed it backwards, (molecules-push-hypothesis) and...the described experiment is conducted, then...the lighter-than-air balloon should not move backwards. The lighter-than-air balloon should not move backwards because no air molecules remain in the chamber so they could not push it backwards. (theoretical rationale)

148

CHAPTER

7

But...suppose the proposed experiment is conducted and the lighter-than-air balloon still moves backward. Therefore...we would conclude that the explanation is probably wrong. Inter-rater agreement with a random subset of 100 student responses was 91%. Lecture Examinations. Three lecture exams written by the course professors were administered during the semester. Each exam contained from 26 to 40 multiplechoice items. Exams were machine scored with scoring adjusted so that each exam was worth 100 points for a total of 300 possible points. Table 2 contains example exam items. Note that these items assess understanding of theoretical conceptual systems as evolution, natural selection, combustion, energy transfer and loss within food chains, population regulation, gene transfer and reproductive strategies.

1. Which of the following is not a component of Darwin's theory of natural selection? a. Offspring tend to resemble their parents. b. Environments place limits on survival and reproduction. c. Individuals with heritable traits that enhance reproductive success leave more decedents than individuals lacking those traits. d. Within populations, lots of variation in traits can be observed among individuals. e. None of the above. (correct answer) 2. The protective coloration of many insect species is a good example of a. a vestigial trait. b. an acquired characteristic. c. one-step evolution. d. an adaptation. (correct answer) e. speciation. 3. Within a habitat, which of the following organisms would be least abundant? a. herbivorous insects b. plants c. Fungi d. eagles (correct answer) e. termites 4. Scientists have concluded that increases in the concentration of in the atmosphere over the past 100 years have been caused by a. decreased rates of plant photosynthesis due to lower light intensities. b. increased releases of volcanic gases. c. mobilization of long-term storage pools of carbon (fossil fuels, forests). (correct answer) d. increased bacterial growth in contaminated soils. e. atmospheric chemical reactions that release from organic molecules. 5. Which of the following is a good example of a density-independent population-regulating factor? a. contagious disease b. warfare and fighting c. malnutrition d. temperature drop to lethal levels (correct answer)

INTELLECTUAL DEVELOPMENT DURING THE COLLEGE YEARS

149

6. In pea plants, the purple allele is dominant to the white allele. A homozygous pea plant with purple flowers is crossed with a plant with white flowers. What percent of the offspring will have white flowers? a. 0% (correct answer) b. 25% c. 50% d. 75% e. 100% 7. Species vary widely in their reproductive potential. Some have many offspring while others have few. Which of the following species would you expect to survive better under highly competitive conditions? a. Small egg species because they can produce more offspring so at least some would survive. b. Small egg species because they spend less energy producing eggs so the parents have more time to insure their own survival. c. Large egg species because their young would start life larger and better able to compete. (correct answer) d. Large egg species because parents would waste less time laying eggs and thus have more time to secure more mates.

3. RESULTS

3.1

Reasoning Skill Level and Declarative Knowledge Performance

Figures 3a and 3b show student performance on the test of hypothesis-testing skill administered at the start of the semester and again at the end of the semester. Based on pretest performance, students were classified as follows: Level 3 = 66 students (11%); Low Level 4 = 198 students (34%); High Level 4 = 268 students (46%); and Level 5 = 52 students (9%). Posttest scores improved considerably (Dependent T = 29.6, df = 513, p < 0.001). Based on the same scoring criteria numbers and percentages of students at each level on the posttest were as follows: Level 3 = 12 students (2%); Low Level 4 = 71 students (11%); High Level 4 = 288 students (43%); and Level 5 = 296 students (44%). Declarative knowledge scores were moderately high: 354 students (53%) responded correctly to all five questions; 221 students (33%) responded correctly to four questions; 68 students (10%) responded correctly to three questions; 13 students (2%) responded correctly to two questions, 8 students (1%) responded correctly to one question; and three students (<1%) responded correctly to none of the questions. The following percentages of students responded correctly to the respective questions: question 1 = 72%, question 2 = 95%, question 3 = 75%, question 4 = 95%, and question 5 = 97%. Overall mean score on the three lecture exams 212 points, S.D. = 66.3. This represents a 71% success rate. Success rate on the Balloons Transfer Problem was 57%.

150

CHAPTER

7

INTELLECTUAL DEVELOPMENT DURING THE COLLEGE YEARS

3.2

151

Inter-correlations Among Study Variables

Table 3 shows Pearson product-moment correlation coefficients among the study variables. All coefficients were significant (p < .01) with the highest coefficient between the pre and posttest hypothesis-testing skill measures (0.65). The next highest coefficient was between the posttest hypothesis-testing skill measure and lecture exams (0.52). The lowest coefficient was between declarative knowledge and performance on the Balloons Transfer Problem (0.13).

3.3 Predicting Performance on The Balloons Transfer Problem

A two-way analysis of variance with reasoning skill level (posttest) and declarative knowledge score (0 to 5) used as predictors of performance on the Balloons Transfer Problem (scores of 0 or 1) revealed a significant main effect = 5.47, p < 0.001), a significant effect for reasoning skill level p< 0.001), and a significant effect for declarative knowledge p < 0.05). A stepwise multiple regression analysis was conducted to determine which predictor variable (declarative knowledge or reasoning skill level) was the better predictor of performance on the Balloons Transfer Problem. The analysis revealed that reasoning skill level, but not declarative knowledge, accounted for a significant amount of variance. However, the range in scores on the declarative knowledge measure was restricted as 643 of the 667 students (96%) responded correctly to three or more of the items. Perhaps with a greater range, declarative knowledge would also have been a significant predictor. Table 4 shows relationships among reasoning skill level, declarative knowledge and Balloons Transfer Problem performance in more detail. As you can see at the bottom of the table, success on the Balloons Transfer Problem improved consistently with reasoning skill level (i.e., combined column percentages are 17% success at Level 3, 33% success and Low Level 4, 57% success at High Level 4, and 65% success at Level 5). These percentages are shown graphically in Figure 4. The

152

CHAPTER

7

combined row percentages shown in the far right-hand column and in Figure 5 suggest that declarative knowledge is not as good a predictor of success on the Balloons Transfer Problem. Although the respective combined row percentages of 33%, 50%, 15%, 43%, 59% and 47% do not show a consistent increase with amount of declarative knowledge, only 24 students fell into the lowest three categories, thus these percentages may not be representative.

3.4 Predicting Lecture Exam Scores

Figures 6 and 7 show the relationship between reasoning skill level (as assessed by both pretest and posttest measures) and course performance (as determined total scores on the three lecture exams). As you can see, the predicted relationship between reasoning skill level and exam performance was found p< 0.001 for the hypothesis-testing skill pretest and p< 0.001 for the hypothesis-testing skill posttest). Tukey's post hoc tests conducted on both the pre and posttest showed that the mean scores of all group pairs differed significantly (p < 0.05). Although the primary purpose of this study was not to test hypotheses about how to promote the development of causal hypothesis-testing skill, possible causes of the observed pre to posttest gains (Figures 3a and 3b) deserve mention. First, small pre to posttest improvements have been traced to a test-retest effect (e.g., Lawson, Nordland & DeVito, 1974). But our former students' relatively poor performance on

INTELLECTUAL DEVELOPMENT DURING THE COLLEGE YEARS

153

154

CHAPTER 7

INTELLECTUAL DEVELOPMENT DURING THE COLLEGE YEARS

155

4. DISCUSSION Quizzes such as the “A: Mountain and Osmosis quiz (Table 1), strongly suggests that the substantial improvements in causal hypothesis-testing found here are difficult to come by and not likely to have been caused by a test-retest effect. Perhaps the most reasonable explanation for the substantial gains is that the students did in fact became better at testing alternative causal hypotheses and that this improvement came about because the course professors and graduate teaching assistants made a very conscious and concerted effort to make causal hypothesis testing the central theme of nearly every lecture and virtually all labs. Also, because previous research on the "teachability" of reasoning skill suggests that skill develops best when students are given repeated opportunities to test hypotheses in familiar and observable contexts prior to attempting to do so with unobservable entities, the labs and lectures were sequenced as such. For example, Westbrook & Rogers (1994) found that a 6-week ninth-grade unit on simple machines (e.g., levers, pulleys, and inclined planes) with readily observable variables was successful in promoting Level 4 reasoning skill when students were explicitly challenged to generate and test alternative hypotheses. Also, Shayer & Adey (1993) found that the Thinking Science Program (Adey, Shayer & Yates, 1989) was successful in boosting the achievement of students on the British National examinations not only in science and mathematics but in English as well. The Thinking Science Program is designed to develop scientific reasoning patterns by testing causal hypotheses first in observable contexts such as pitch pipes, shopping bags, and bouncing balls and then in unobservable contexts such as dissolving and burning chemicals. In short, it appears that similar efforts in the present course paid off for many students. Results of the initial test of the study’s central working hypothesis, which involved assessing student performance on the Balloons Transfer Problem, were somewhat equivocal. Recall that the argument was made that if Stage 5 reasoning skill alone was sufficient to solve the transfer problem, then reasoning skill alone should predict success. On the other hand, if declarative knowledge was sufficient, then it alone should predict success. Finally, if both Stage 5 reasoning skill and declarative knowledge were necessary, then both should predict success. Based on results of the stepwise multiple regression analysis, it appears that hypothesis-testing skill, but not declarative knowledge, significantly accounts for performance differences on the Balloons Transfer Problem (Table 4 and Figures 4 and 5). Level 5 students were in fact more successful than their less-skilled peers. But notice in Table 4 that only 65% of the Level 5 students responded successfully. One might wonder why the other 35% of the Level 5 students did not. It appears that their failure did not arise because they lacked some specific bit of declarative knowledge because, as noted, declarative knowledge did not predict problem success very well, particularly with the influence of hypothesis-testing skill held constant. If Level 5 skill alone is sufficient and truly general, then success should have been higher. But one should not expect 100% success. This is because, in theory,

156

CHAPTER 7

even for someone who knows in a general sense how to test Level 5 hypotheses (i.e., imagine some test condition that allows the generation of a specific prediction that may in fact not happen), each hypothesis-testing context is different, thus deciding how to test any specific Stage 5 hypothesis requires an element of creativity. In other words, even if someone understands in a general sense what needs to be done to test a causal hypothesis, they may not be able to come up with a good way to do so in any one context, particularly when given limited time, as was the case here. The case of physiologist Otto Loewi, who struggled for 17 years before he literally dreamed up a way to test his chemical transmission hypothesis, is a classic example of this point (see Koestler, 1964, p. 205). This interpretation seems consistent with that of Perkins & Salomon (1989, p. 19) when they claim that general cognitive skills exist but function in contextual ways. Also note that 17% of the Level 3 students, 34% of the Low Level 4 students, and 57% of the High Level 4 students responded successfully to the Balloons Transfer Problem. If Stage 5 hypothesis-testing skill is indeed necessary, then none of these students should have been successful. Perhaps the unexpected success of these students can at least partially be explained by the presence of overly suggestive "hints" contained in the wording of the problem (i.e., test the explanation using an airtight chamber on wheels and a pump that can extract air from airtight chambers). As predicted, Level 5 students performed significantly better than Level 4 students on the semester exams (Table 3 and Figures 6 and 7). Therefore, support has been found for the hypothesis that the skill used in testing causal hypotheses involving unobservable entities exists and is of general use in course performance (i.e., in understanding theoretical concepts and in responding correctly to exam items about such concepts). In other words, had success on the new test items (the Burning Candle item and the Red Blood Cells item) required only declarative knowledge specific to those items, then students classified at Level 5 would not have been more successful than students classified at Level 4 on exams testing concept understanding in other knowledge domains. 5. CONCLUSIONS AND INSTRUCTIONAL IMPLICATIONS In conclusion, the present results provide support for the hypothesis that general, causal hypothesis-testing skill beyond that assessed by typical sorts of Piagetianbased measures of formal stage reasoning exists and is used to test causal hypotheses about unobservable entities. Stage 5 (post formal) skill appears to have been used by students to succeed on the Balloons Transfer Problem and on course exams covering a wide range of theoretical topics. Yet the distinction between Stage 4 and 5 hypothetico-predictive reasoning does not appear entirely clear cut as an element of creativity and perhaps one or more yet to be identified factors (e.g., confidence, internal locus of control, "emotional" intelligence as defined by Goleman, 1995) may

INTELLECTUAL DEVELOPMENT DURING THE COLLEGE YEARS

157

play a role in determining the extent to which such hypothesis-testing skill may or may not be employed in novel contexts. Evidence suggests that the presence of declarative knowledge alone is not sufficient to produce successful hypothesis-testing performance at this theoretical level. This is not to say that declarative knowledge is unimportant to Stage 5 performance. Nevertheless, a number of students who apparently lacked one or more key declarative-knowledge concepts (i.e., momentum, relative density of gases, molecular nature of gases) gave evidence of having successfully tested a hypothesis about the cause of movement of two balloons on the Balloons Transfer Problem. Although future research is needed to explore the role of Stage 5 hypothesistesting skill in additional contexts (e.g., Chapter 10 explores the role of Stage 5 reasoning in rejecting nature-of-science misconceptions) and is needed to identify additional factors that play roles in determining if and when students employ such skill, it seems reasonable to suggest that making Stage 5 hypothesis-testing skill a central focus of college-level science instruction can be very effective, particularly when labs and lectures are sequenced to move from the observable and familiar to the unobservable and unfamiliar. In spite of the fact that our present sequencing of labs and lectures seems to be relatively effective, many students continued to exhibit difficulties in Stage 5 hypothesis testing. These difficulties included a continued confusion between descriptive and causal questions, between hypotheses and predictions, and between evidence (i.e., observed results) and conclusions. Clearly additional research is needed to determine how best to design curricula to eliminate these persistent problems.

This page intentionally left blank

CHAPTER 8

WHAT KINDS OF SCIENTIFIC CONCEPTS EXIST?

1. INTRODUCTION Following Northrop (1947), Lawson, Abraham & Renner (1989) described three general sources of meaning and proposed three general categories of concepts (i.e., mental constructs that have been linked to specific terms or phrases). At the most direct level, meaning can be derived from immediately sensed input giving rise to color concepts such as green/red/blue, external state concepts such as hot/cold, sharp/dull, and internal state concepts such as hunger, thirst, and tiredness. At this level complete meanings are immediately apprehended from the internal or external environment. Thus, a first category called concepts by apprehension can be identified. Secondly, consider the sources of meaning for terms such as table, chair, running, resting, taller and heavier. Meanings for these terms are derived from objects, events, and from comparisons of objects and events. Such meanings are not immediately apprehended. In Northrop's (1947) words: "...perceptual objects are not immediately apprehended factors; they are postulates of common sense so thoroughly and frequently and unconsciously verified through their deductive consequences that only the critical realize them to be postulated rather than immediately apprehended" (p. 93). In other words, objects such as tables and chairs and events such as running and resting and relations such as taller and heavier are mental constructions. Yet, we lose sight of this fact because we have gathered so much evidence to support their postulated existence. Hence, a second class called descriptive concepts can be identified. To understand descriptive concepts, one must mentally construct order from environmental encounters. In short, descriptive concepts allow us to order and describe our experiences (see Chapter 3). The third type of concept described by Lawson et al. (1989) is also derived by postulation and test. However, this type differs from descriptive concepts in that defining attributes are only indirectly testable. The primary use of these concepts is to function as explanations for events that need causes, but for which no causal agent can be perceived. Angels and ghosts fall into this category. Common examples from science are photons, electrons, atoms, molecules, and genes. These are called theoretical concepts. The reason for the existence of theoretical concepts can be found in a basic assumption that humans make about their world - events do not occur without causes. Thus, if we perceive an event, but cannot perceive objects or processes that caused the event, we do not conclude that the event is spontaneous and

159

160

WHAT KINDS OF SCIENTIFIC CONCEPTS EXIST?

without cause. Instead, using analogical reasoning (see Chapters 5 and 6), we may invent unseen objects and interactions to explain the event in perceptible causal terms. Because theoretical concepts are imagined and function to explain the otherwise unexplainable, they can be given whatever properties are necessary in terms of the theory of which they are a part. Thus, they derive meaning from the analogies upon which they are based and from the postulates of specific theories in which they reside (Lawson, 1958; Lewis, 1980, 1988; Northrop, 1947; Suppes, 1968). According to developmental theory, descriptive and theoretical concept construction are linked to intellectual development because the processes depend in part on procedural or 'operational' knowledge structures (i.e., reasoning patterns) as well as on prior declarative knowledge structures (cf., Anderson, 1980; Fosnot, 1996; Inhelder & Piaget, 1958; Karplus, 1977; Kuhn, 1989; Lawson, 1995; Piaget & Inhelder, 1969; von Glaserfeld, 1995). Development of procedural structures occurs gradually with age because it depends not only on maturation (e.g., Epstein, 1986; Hudspeth & Pribram, 1990; Thatcher, Walker, & Guidice, 1987) but also on experience (both social and physical) and on the individual's self-regulatory mechanisms. Thus, during intellectual development, concepts by apprehension come first. Then descriptive concepts are constructed during childhood followed by the construction of theoretical concepts during adolescence and adulthood. Of course this sequence does not mean that children do not often believe in ghosts, Santa Claus or the tooth fairy. Children may and often do form such beliefs. However, those beliefs typically are formed on the basis of what they have been told by adults rather than being constructed based on a consideration of the alternatives and the evidence. Similarly, when an adult attempts to construct concepts in a new field of study, the descriptive conceptual foundation must at least be partially in place before theoretical concepts are constructed. For example, Gregor Mendel (as well as other biologists at the time) knew that offspring tend to look like their parents and wondered why. In Mendel's case, he described observable 'phenotypes' of parent and offspring pea plants prior to constructing his theory of the nature and behavior of unobservable 'genotypes.' Here the descriptive concept of phenotype comes first and the theoretical concept of genotype comes second. In other words, one does not invent an explanation involving unseen theoretical entities (e.g., genes) until one has some puzzling observations to explain (e.g., Why do offspring tend look like their parents?). This theory of concept construction and intellectual development leads to the prediction that students at any one age who vary in the extent to which they have developed procedural knowledge structures (hypothetico-predictive reasoning patterns) should vary in the extent to which they can profit from science instruction aimed at teaching descriptive and theoretical concepts. This prediction has been confirmed by several previous studies (e.g., Cavallo, 1996; Germann, 1994; Johnson & Lawson, 1998; Kwon & Lawson, 2000; Lawson & Renner, 1975; Lawson &

CHAPTER 8

161

Thompson, 1988; Lawson & Weser, 1990; Renner & Marek, 1990; Shayer & Adey, 1993). Note that the present theory implies that in any field of investigation, the descriptive foundation should precede the introduction and testing of alternative theoretical explanations. However, it does not imply that all questions of causality should be avoided until students have developed higher-order reasoning patterns (cf., Metz, 1995). Rather, the view is that it is the process of generating and testing alternative theoretical possibilities that leads to the development of higher-order reasoning. Unfortunately, the introduction of theoretical concepts is usually not done in this way. Instead, most textbooks introduce them as "facts" and seldom bother to introduce the alternatives, the arguments, and the evidence used by scientists to arrive at such "facts." Thus, students are not provided opportunities to develop higher-level reasoning skill. Also, they are not provided opportunities to acquire understanding of how science works. 2. A FOURTH CLASS OF CONCEPTS: HYPOTHETICAL CONCEPTS The initial purpose of the research described in this chapter is to test the hypothesis that in addition to concepts by apprehension, descriptive concepts, and theoretical concepts, a fourth class of concepts exists. Like theoretical concepts, this class of concepts lacks observable exemplars. However, unlike theoretical concepts, such concepts could, in theory, derive meaning from observation if it were possible for one to extend the time frame over which the necessary observations are made. Such concepts are assumed to be more abstract than descriptive concepts, but less abstract than theoretical concepts, consequently should be of intermediate difficulty in terms of concept construction. The word hypothetical has been chosen to refer to this proposed fourth class of concepts. More specifically, the following terms, which were recently introduced to students in an introductory college biology course, are proposed to represent concepts that should be classified as descriptive because readily observable exemplars exist: environmental factors, food chains, populations, nocturnal, carnivore, stimulus and community. Further, the following terms, which were also introduced in the course, are proposed to represent hypothetical concepts because, even though instruction did not allow students to observe the processes/entities to which the terms refer, if observations were made for an extended time period, the processes/entities could in theory be observed: species (where species are defined as organisms that share enough characteristics to mate and produce viable offspring), limiting factors, fossils (where understanding of the process of fossilization is implied as fossils must be distinguished from non-fossilized organic remains), artificial selection, evolution, convergent evolution, and natural selection. And lastly, the following introduced terms are proposed to represent theoretical concepts because no matter how long one observes, observable exemplars cannot be seen:

162

WHAT KINDS OF SCIENTIFIC CONCEPTS EXIST?

osmosis, combustion, air pressure (in terms of colliding molecules), genes (within the context of classical Mendelian theory), molecules (in terms kinetic-molecular theory), photosynthesis, biogeochemical cycles. This classification scheme does not take into account Harre's (1986) distinction between realm 2 and realm 3 theories in which more powerful microscopes and telescopes can cause a realm-3 theory to become a realm-2 theory. In Harre's view, a realm-3 theory/concept becomes a realm-2 theory/concept when instruments become powerful enough to allow us to "observe" what previously was not observable. However, in my view once a concept is classified as theoretical (Hare's realm 3), it is not appropriate to later reclassify it at realm 2 because regardless of instrument resolution, the central cognitive issue remains one of interpretation not observation. For example, in spite of the fact that powerful electron microscopes can now focus on tiny ball-shaped objects, whether or not one interprets those ball-shaped objects as atoms, or perhaps just very small ball-shaped molecules, depends on one's theoretical perspective, rather than one's observational ability. Further, meaning of the term atom does not come from observations no matter how "close" those observations become. Instead, meaning continues to come from analogy and from the postulates of atomic-molecular theory. In summary, the proposed concept classification scheme argues that constructing descriptive concepts should be the easiest because meanings come from experience. Hypothetical concepts should be of intermediate difficulty because one has to imagine past or future events to derive meanings. And theoretical concepts should be the most difficult to construct because their meanings cannot be derived from observation regardless of how much time one has to do the observing. This hypothesis leads to the prediction that when student knowledge of specific descriptive, hypothetical and theoretical concepts is assessed, students should demonstrate significantly more knowledge of descriptive concepts than hypothetical concepts. Similarly, they should demonstrate significantly more knowledge of hypothetical concepts than theoretical concepts. These predictions are shown graphically in Figure 1, as is the prediction based on the alternative hypothesis that the introduced terms fall into only two categories (i.e., descriptive and theoretical). A further prediction can be stated. Because concept construction is hypothesized to depend in part on reasoning skill, students at differing developmental levels who receive instruction on all three kinds of concepts are predicted to vary in their ability to demonstrate knowledge of those specific concepts. In other words, students with less-advanced reasoning skill should demonstrate less knowledge than moreadvanced students. Presumably intellectual development proceeds from a) Level 3 - a descriptive level similar to Piaget's concrete operations stage, to b) Level 4 - a more advanced level similar to Piaget’s formal stage in which causal hypotheses can be tested, but only when the hypothesized causal agents are observable, to c) Level 5 - a still more advanced level in which hypotheses involving unseen theoretical entities can be tested. Consequently, students at the descriptive level (Level 3) are predicted to exhibit knowledge of descriptive concepts, but they should not exhibit knowledge

CHAPTER 8

163

of hypothetical or theoretical concepts. Further, students at Level 4 should exhibit knowledge of descriptive and hypothetical concepts, but not of theoretical concepts. And lastly, students at Level 5 should exhibit knowledge of all three types of concepts. These predictions are shown graphically in Figure 2. However, students at less-advanced developmental levels may demonstrate some knowledge of more advanced concepts because, as will be described below, the concept assessment measure consists of questions written at Bloom's knowledge level, a level that does not necessarily require "understanding" as defined by Bloom (1956). The reasoning behind the present research design can be summarized as follows: If...three types of increasingly abstract, developmentally sequenced scientific concepts exist, i.e., descriptive, hypothetical and theoretical, (developmentalsequence hypothesis) and...college students classified into three corresponding developmental levels (Levels 3, 4 and 5) receive biology instruction incorporating the three types of concepts and are then tested for knowledge of those concepts, then...(1) collectively the students should demonstrate significantly more knowledge of descriptive concepts than of hypothetical concepts than of theoretical concepts; (2) Level 3 students should demonstrate knowledge only of descriptive concepts; (3) Level 4 students should demonstrate knowledge only of descriptive and hypothetical concepts; and (4) Level 5 students should demonstrate knowledge of all three type of concepts.

164

WHAT KINDS OF SCIENTIFIC CONCEPTS EXIST?

3. METHOD

3.1 Subjects Subjects were 663 undergraduate students (non-science majors) enrolled in a course entitled The Living World (as described in Chapter 5). Students in this particular study ranged in age from 17.1 years to 54.2 years (mean age = 20.3 years, SD = 3.7).

CHAPTER 8

165

3.2 Design

A test designed to assess students' reasoning skill level (i.e., developmental level) was administered during the first week of the semester within regularly scheduled lab periods. The same test was re-administered during the last week of the semester again within regularly scheduled lab periods as part of a graded final exam. The exam also included 105 true/false questions designed to assess knowledge of the 21 concepts listed in the introduction. As a check on the usefulness of this researcher-developed classification scheme, a panel consisting of 10 pre-service biology teachers (biology majors, seniors and graduates) read the definitions of concept types that appear in the Appendix. The panel also read the biological concept definitions that also appear in the Appendix. They were then asked to individually classify each biological concept based on the presented definition into either the descriptive, intermediate or theoretical category. Then the entire panel met to discuss the classification of each concept and attempted to reach consensus. The extent of panel consensus, as well as the relationship of their classifications to those of the researchers, was then determined. 3.3 Instruments

Reasoning Skill Level. Reasoning skill level (developmental level) was assessed by a group-administered test based on reasoning patterns associated with hypothesis testing as described in Chapter 7. The same 13 items were included. However, instead of a free response format, multiple-choice responses were provided. Thus, the test consisted of a total of 26 multiple-choice items. For example, the response choices for the two Burning Candle items read as follows:

1. Using some or all of these materials, how could you best test this possible explanation? a. Saturate the water with carbon dioxide and redo the experiment noting amount of water rise. b. The water rises because oxygen is consumed; so redo the experiment in exactly the same way to show water rise due to oxygen loss. c. Conduct a controlled experiment varying only the number of candles to see if that makes a difference. d. Suction is responsible for water rise; so put a balloon over the top of an open- ended cylinder and place the cylinder over the burning candle. e. Redo the experiment but make sure it is controlled by holding all independent variables constant; then carefully measure amount of water rise.

2. What result of your test (mentioned above) would show that the explanation is probably wrong?

166

WHAT KINDS OF SCIENTIFIC CONCEPTS EXIST?

a. b. c. d. e.

The water rises higher than it did before. The water rises to the same as it did before. The water rises less than it did before. The balloon expands out. The balloon is sucked in.

And the response choices for the two Red Blood Cells items read as follows: 1. What result of the experiment would best show that explanation I is probably wrong? a. the bag loses weight b. the bag weighs the same c. the bag appears smaller

2. What result of the experiment would best show that explanation II is probably wrong? a. the bag loses weight b. the bag weighs the same c. the bag appears smaller Scoring. Each of the 26 questions (i.e., 13 two-part situations) required students to select the best answer from the choices provided. Correct responses were awarded one point. Based on the nature of the questions and the number of each question type, scores of 0-8 were classified as Level 3 (i.e., students not able to test hypotheses involving observable causal agents). Scores of 9-14 were classified as Low Level 4 (i.e, students inconsistently able to test hypotheses involving observable causal agents). Scores of 15-20 were classified as High Level 4 (i.e., students consistently able to test hypotheses involving observable causal agents). And scores of 21-26 were classified as Level 5 (i.e., students able to test hypotheses involving unobservable entities). A Cronbach's α reliability of 0.81 was obtained for the test when administered at the semester's end. Knowledge of Concepts. Five statements were constructed to assess knowledge associated with each of the 21 concepts. The intent was to write statements that only assessed knowledge associated with each concept and not reasoning patterns required by more advanced levels of assessment, e.g., higher Bloom levels such as analysis, application, evaluation and synthesis (Bloom, 1956). Even though Bloom considers comprehension to be the lowest level of understanding, questions were not written at this level to avoid, as much as possible, confounding what students knew about each term with general reasoning skill that may be called into action when attempting to answer questions at the comprehension and higher levels. During the exam, students read each statement and decided whether it was true or false and marked their answer sheets as such. The statements used to assess knowledge associated with the terms carnivore, population, limiting factors, natural

CHAPTER 8

167

selection, genes and osmosis appear in Table 1. Test reliability as estimated by Cronbach's was 0.70. This rather low estimate is perhaps due in part to the true/false nature of the items in which guessing can significantly contribute to success or failure on any one item.

Descriptive Concept Questions Carnivores are animals that eat other animals. (T) are animals that eat both plants and animals. (F) are classified as ecological producers. (F) must have fur. (F) live only on land. (F) A biological population represents organisms of a single type living and reproducing in particular location. (T) refers to both living and non-living components of biological communities. (F) can decrease in numbers over time. (T) can increase in numbers over time. (T) usually contains individuals with variable characteristics. (T) Hypothetical Concept Questions Limiting factors can increase in importance as population size increases. (T) can wipe out entire populations regardless of population size. (T) keep the reproductive potential of populations in check. (T) can be both living and non-living environmental influences. (T) can refer to non-biological aspects of the environment that limit population size. (T) According to natural selection theory, species change across time only when the following conditions are met: individuals with favorable characteristics produce more offspring than those with unfavorable characteristics. (T) environmental factors exist that limit population growth. (T) climatic conditions change across time. (F) characteristics acquired during individual lifetimes are passed to offspring. (F) favorable characteristics can be inherited. (T) Theoretical Concept Questions According to gene theory, gene pairs separate independently during zygote production. (F) during egg and sperm production genes recombine randomly. (F) genes are located in chromosomes. (T) an individual has at least one pair of genes for each observable characteristic. (T) one gene of a pair can dominate the expression of the other gene. (T) Osmosis will not occur when membranes block diffusion. (T)

168

WHAT KINDS OF SCIENTIFIC CONCEPTS EXIST?

occurs only through living cell membranes. (F) occurs when a dialysis bag filled with distilled water is placed in a glucose solution. (T) is not effected by temperature. (F) involves random ionic and/or molecular collisions. (T)

4. RESULTS

4.1

Agreements/Disagreements Using the Concept Classification Scheme

The Appendix reports the extent to which the researcher-developed concept classification scheme and the 10-member panel agreed on the classification of each biological concept. In short, the researchers and the panel were in complete agreement on all 7 of the concepts classified by the researchers as descriptive as well as on all 7 of the theoretical concepts. Complete agreement was also found on two of the intermediate/hypothetical concepts (i.e., evolution and convergent evolution). However, differences of opinion existed on the remaining five concepts classified by the researchers as intermediate/hypothetical. Only a slight difference existed for the concept of natural selection (i.e., 9/10 of the panel members classified the concept as intermediate). Moderate differences existed for the fossils concept (7/10 panel members classified the concept as intermediate) and for the limiting factors concept (6/10 panel members classified the concept as intermediate). Only 2/10 of the panel members classified the artificial selection concept as intermediate; 3/10 classified it as descriptive; 1/10 classified it as theoretical; and 4/10 remained undecided between the descriptive and intermediate categories. Interestingly, all 10 of the panel members disagreed with the researchers and classified the species concept as descriptive. 4.2 Student Reasoning Skill Levels

Scores on the test of reasoning skill administered at the start of the semester ranged from 3 to 24, Mean = 14.25, SD = 4.6. Scores on the test when readministered at semester's end ranged from 2 to 25, Mean = 18.24, SD = 4.54. A dependent T-test indicated that the distributions (shown in Figure 5) differed significantly (t = 14.99, p < 0.001). Table 2 shows mean scores for each of the 21 sets of concept questions grouped into the three concept categories as defined by the researchers. As shown, mean scores among the descriptive concepts ranged from 4.85 (environmental factors) to 3.78 (food chain), among the hypothetical concepts from 4.58 (fossils) to 3.40 (natural selection), and among the theoretical concepts from 4.16 (biogeochemical cycles) to 2.79 (combustion).

CHAPTER 8

169

170

WHAT KINDS OF SCIENTIFIC CONCEPTS EXIST?

Figure 6 shows overall student performance on the three concept categories using Guilford's equation (Guilford, 1936) for determination of item difficulty when chance success is a factor (i.e., with true/false questions chance alone may lead to a correct response 50% of the time). Results revealed that overall student performance on the descriptive, hypothetical and theoretical concept categories after eliminating chance success was 81.1%, 61.4% and 46.5% respectively. A multivariate analysis of variance with repeated measures found these overall performance differences to be statistically significant p < 0.001). All pair wise comparisons were also statistically significant (p < 0.001).

CHAPTER 8

171

4.3 Relationship Between Reasoning Skill Level and Concept Questions Figure 7 shows the relationship between reasoning skill level (as measured at the semester's end) and performance on the three categories of concept questions with chance success eliminated. The figure reveals a clear relationship between reasoning skill level and concept performance. Multivariate analysis of variance with repeated measures found these overall performance differences to be statistically significant p < 0.001). All pair wise comparisons were also statistically significant (p < 0.001). Figure 7 also reveals that performance for students at each of the four reasoning skill levels was higher on the descriptive concept questions than on the hypothetical concept questions, which in turn was higher than performance on the theoretical concept questions. Again, multivariate analysis of variance with repeated measures found these performance differences to be statistically significant: p< 0.001 for the Level 3 students; p < 0.001 for the Low Level 4 students; p < 0.001 for the High Level 4 students; and 423.36, p< 0.001 for the Level 5 students. All pair wise comparisons were statistically significant (p < 0.001) with the exception the non-significant difference

172

WHAT KINDS OF SCIENTIFIC CONCEPTS EXIST?

between the hypothetical and theoretical concept questions for the Level 3 students (p = 0.168).

5. DISCUSSION The finding that the 10-member panel and the researchers were in complete agreement on the classification of 16 of the 21 concepts suggests that the concept classification scheme can be used consistently, particularly to classify descriptive and theoretical concepts. All five of the classification disagreements occurred over concepts classified by the researchers at the intermediate/hypothetical level and concerned whether a concept should be classified as descriptive or intermediate. In retrospect, this is not surprising as this distinction often boils down to the likelihood of someone having the opportunity and patience to make the necessary observations. Consequently, when the necessary observational time frame extended well beyond the normal human lifetime, agreement was easy to reach (e.g., evolution, natural selection). On the other hand, when the observations could possibly be made during a single lifetime (e.g., artificial selection, limiting factors), disagreements were more numerous. The fact that all panel members classified the species concept as

CHAPTER 8

173

descriptive while the researchers classified it as intermediate suggests that the researchers may have misclassified this concept. The concept classification scheme led to the prediction that students would demonstrate significantly more knowledge of descriptive concepts than hypothetical concepts. Similarly, they would demonstrate significantly more knowledge of hypothetical concepts than theoretical concepts (see Figure 1). The observed results shown in Figure 6 are essentially as predicted. Therefore, the results support the hypothesis that these three kinds of scientific concepts exist. Importantly, in terms of the proposed distinction between hypothetical and theoretical concepts, the pair wise comparison between students’ performance on these two concept categories was also statistically significant (p <0.001). This result lends further support to validity of this proposed concept classification scheme. Because concept construction presumably depends in part on hypotheticopredictive reasoning skill, students at differing reasoning skill levels were predicted to vary in performance on the three categories of concept questions. More specifically, Level 3 students were predicted to exhibit knowledge of descriptive concepts, but not of hypothetical or theoretical concepts. Further, Level 4 students were predicted to exhibit knowledge of descriptive and hypothetical concepts, but not of theoretical concepts. And lastly, Level 5 students were predicted to exhibit knowledge of all three types of concepts. These predictions were shown in Figure 2. A comparison of the observed results (Figure 7) with the predicted results lends support to the hypothesis in the sense that more skilled reasoners did in fact perform significantly better than less skilled reasoners. But the actual relationship was not as clear-cut as predicted. For example, consider performance of the Level 3 students. These students were expected to perform as well as the Level 4 and 5 students on the descriptive concepts, but they did not. They were successful on only 41% of the descriptive concepts compared to the 57%, 62% and 71% success rates of their more developmentally advanced peers. Further, they were unexpectedly successful on 27% of the hypothetical questions and 20% of the theoretical questions, both of which were presumably beyond their intellectual grasp. Similar remarks can be made about the students at the other developmental levels. In other words, they were not as successful on some of the concepts questions as they should have been. While on others, they were more successful than they should have been. How can these departures from the predictions be explained? A look back at the concept questions suggests that the problem may stem, at least in part, from difficulties in creating questions that assess knowledge of only one type of concept at a time. For example, consider the set of statements designed to assess students' knowledge of the descriptive concept of carnivore (Table 1). Notice that the third statement mentions ecological producers. Thus, in addition to knowledge of carnivores, identifying this statement as true or false presumably also requires knowledge of ecological producers. An organism is a producer if it is capable of conducting photosynthesis. Recall that photosynthesis is a concept that has been

174

WHAT KINDS OF SCIENTIFIC CONCEPTS EXIST?

classified as theoretical. Thus, the attempt to assess knowledge of the descriptive carnivore concept may have been confounded by inclusion of a distracter that may require knowledge of the presumably more abstract photosynthesis concept. During construction of the concepts test, a concerted effort was made to avoid this problem. But in hindsight, it appears that the problem was not entirely avoided. Consequently, some of the concept questions were probably more difficult than they should have been, which may have led to lower performance than predicted. A related problem may stem from the psychological fact that concepts do not stand alone (e.g., Ausubel, 1963; Ausubel, Novak & Hanesian 1978; Wandersee, Mintzes & Novak, 1994). Rather concepts exist within complex conceptual systems such that knowledge, and understanding, of any one descriptive concept is "deepened" by the construction of other descriptive concepts as well as by hypothetical and theoretical concepts. For example, Level 3 students presumably can construct meaning of food chains given the appropriate experiences. Level 4 students can then construct meaning of the hypothetical concept of limiting factors and in so doing, their knowledge, and understanding, of food chains is "deepened" (e.g., biotic limiting factors express themselves via feeding relationships within food chains). Similarly, when Level 5 students construct knowledge of theoretical concepts such as atoms, molecules and photosynthesis, the concepts of food chains and limiting factors are revisited, but this time with even more precision, thus are "deepened" even further (e.g., food chains begin with plants because they are the only organisms capable of utilizing the energy of photons to synthesize organic "food" molecules from inorganic molecules found in their environments; food chains are limited in length because approximately 90% of the energy that enters each trophic level is "lost" as heat before it can enter the next trophic level). If the above discussion represents an accurate view of concept construction, then perhaps we have explained why the more skilled reasoners outperformed their less skilled peers on all three types of concept questions. But why did the Level 3 students demonstrate some success on the hypothetical and theoretical concept questions? And why did the Level 4 students demonstrate some success on the theoretical concept questions? Perhaps the most reasonable explanation is that in spite of lack of any "deep" understanding of such concepts, these students nevertheless retained some "bits" of knowledge that led to some success. For example, consider the set of statements designed to assess knowledge of the theoretical concept of gene (Table 1). As it turned out, student performance was relatively high on the third, fourth, and fifth statements (72%, 78% and 90% success respectively). This suggests that regardless of their developmental level, many students retained these "facts" about genes. Similarly, 82% of the students responded correctly to the statement that photosynthesis (presumably a theoretical concept) involves light-capturing pigment molecules. And 76% responded correctly to the statement that photosynthesis uses solar energy to combine with to produce carbohydrate and molecules.

CHAPTER 8

175

The implication is that understanding is by no means an all or none affair. Rather understanding may begin with the accumulation of specific "bits" of knowledge about abstract entities (e.g., ghosts are white, they are nocturnal) and processes, only to proceed further with the development of more advanced reasoning skill, which is then used to construct better understanding and/or reject prior misconceptions.) Unfortunately, the present results suggest that the development of Stage 5 reasoning skill, and the associated understanding of theoretical conceptual systems may be limited to a very small percentage of students, that is unless their future course work provokes continued intellectual development. 6. CONCLUSIONS AND EDUCATIONAL IMPLICATIONS

The present results provide support for the hypothesis that scientific concepts can be meaningfully classified into four, not three, general categories. In addition to previously identified apprehension, descriptive and theoretical concepts, a new class of hypothetical concepts has been identified. Hypothetical concepts are defined as those that, in theory, could derive meaning from observation if it were possible for one to extend the time frame over which the necessary observations are made. However, because in practice, such observations are either not possible or very unlikely, meaning must be derived from one's ability to imagine past or future events and situations. Thus, hypothetical concepts are of intermediate difficulty in terms of knowledge acquisition and understanding. The present results also provide support for the hypothesis that intellectual development during the college years is not complete when students develop the reasoning skill typically associated with Piagetian or neo-Piagetian conceptions of formal operational thinking. Rather, as previously suggested by others, 'post-formal' intellectual development occurs, at least for some students (e.g., Arlin, 1975; Castro & Fernandez, 1987; Commons & Miller, 1997; Commons, Richards & Armon, 1984; Commons, Trudeau, Stein, Richards & Krause, 1998; Perry, 1970; Perry, Donovan, Kelsey, Peterson, Statkiewicz & Allen, 1986; Welfel & Davison, 1986; Yan & Arlin, 1998). Evidence has been obtained consistent with the view that some students, perhaps less than one third (see Figure 5) develop reasoning skill associated with hypothesis testing when the hypothesized entities are unobservable. As has been found in previous studies, such hypothetico-predictive reasoning skill appears to facilitate the acquisition of knowledge about, and the understanding of, scientific concepts. Interestingly, the conclusion that a new class of hypothetical concepts exists seems to have been foreshadowed by philosopher C. S. Peirce over one hundred years ago. Although Peirce was virtually unknown during his lifetime (1839-1914), the publication of his collected papers in the 1930s led to great interest in his work during the 1940s and 1950s. As cited in Goudge (1950), Peirce believed in the existence of three types of hypotheses. The first type referred to facts unobserved

176

WHAT KINDS OF SCIENTIFIC CONCEPTS EXIST?

when the hypothesis was generated, but which could nevertheless have been observed. For example, you see a broken window and a nearby baseball and generate the hypothesis that the "flying" baseball broke the window. Peirce's second type was hypotheses that referred to facts not only unobserved but physically incapable of being observed. Peirce gave the following example: "Fossils are found; say, remains like those of fishes, but far in the interior of the country. To explain the phenomenon, we suppose the sea once washed over this land" (cited in Gould, 1950, p. 196). Concepts associated with this type of hypothesis are what we are calling hypothetical concepts. Lastly, Peirce's third type was hypotheses that referred to entities both factually and theoretically incapable of being observed. Goudge cites molecules, electrons and the luminiferous ether as examples. Clearly these are examples of what we are calling theoretical concepts. Because many, if not most, of the concepts that fill the syllabi of science courses are of the hypothetical and theoretical nature, the implication seems clear. High school and college science instructors should not only concern themselves with introducing new terms/concepts. They should also concern themselves with developing students' reasoning skill, with their continued intellectual development. To do this, a careful analysis of the kinds of concepts introduced, as well as the order and means of their introduction should become matters of concern. In introductory biology courses this means overturning the widespread and long standing tradition of starting courses with the theoretical concepts associated with chemistry (e.g., atomic and molecular structures) before progressing to the more descriptive and hypothetical concepts associated with whole organisms (e.g., Hepper, Hammon, Kass-Simon & Kruger, 1990). Clearly a reconfigured introductory biology course that starts with descriptive concepts and progresses to hypothetical concepts, and then to theoretical concepts, seems in order. Such changes may not only help students better understand concepts and promote their intellectual development, they might also help solve the widespread problem of college student attrition from the sciences (e.g., Rigdon & Tobias, 1991; Seymour & Hewitt, 1997; Sorensen, 1999).

CHAPTER 8

7. APPENDIX

7.1

Types of Concepts

People have ideas about how the world works. These ideas are sometimes called concepts. We use words or phrases to refer to our ideas/concepts, which can be classified into at least three types. 7.2 Theoretical Concepts Have you ever used your direct senses (microscopes do not count) to actually observe a single helium atom? Of course the answer is no. No person has ever observed a single atom of any kind simply because atoms are much too small to see with the naked eye. So how do we know that atoms exist? The answer is that we really do not know in any absolute sense. Instead the idea that atoms exist was proposed long ago and has subsequently been verified with so much indirect evidence that people no longer doubt their existence. Nevertheless, in spite of some recent photographs taken with very powerful electron microscopes showing what appear to be little round balls (atoms?), no person will ever be able to use the naked eye to directly observe an individual atom. Thus the concept of atoms (i.e., the idea that all matter consists of tiny unseen ball-shaped objects) is classified as a theoretical concept. The meaning of theoretical concepts comes not from direct sensory input but from the theories from which ideas originate. Other theoretical concepts about objects too small to see include things such as photons, electrons, quarks and any type of process that presumably involves knowing what takes place in terms of interacting atoms and molecules (e.g., diffusion, oxidation, glycolysis, anaerobic respiration). Because the entities and processes upon which theoretical concepts are based cannot be directly observed, acquiring understanding of theoretical concepts is relatively difficult. 7.3 Descriptive Concepts Have you ever used your direct senses to actually observe a single chair? Of course the answer is yes. You may be sitting in one now. No two chairs are identical in all respects. And some may be quite different from others (e.g., a baby's high chair and a recliner). Nevertheless, all chairs share enough observable characteristics to allow us to recognize them as chairs. And because chairs can be directly observed, if someone does not yet know what a chair is, we can show them one. Thus the chair concept derives meaning from direct observation of objects and is classified as a descriptive concept. We also form descriptive concepts of directly observed events 177

178

WHAT KINDS OF SCENTIFIC CONCEPTS EXIST?

(e.g., A girl is seen walking down a street. A dog is heard barking in the night.), and of directly observed situations (e.g., A boy is sitting on top of a box. Dirt is swept under a rug.). Other examples of descriptive concepts include eating, sleeping, hitting, crying, cars, boats, tables, furniture, next to, below, around, shorter, heavier, and so on. Notice that the concept of furniture is classified as descriptive in spite of the fact that we do not see the class furniture, rather we see individual objects (tables, chairs, sofas) that we group together in a larger class of objects that we call furniture. Nevertheless, the class concept of furniture is still considered descriptive because we can observe examples of its class members. Because the entities and processes upon which descriptive concepts are based can be directly observed, acquiring understanding of descriptive concepts is relatively easy. 7.4 Intermediate Concepts An intermediate class of concepts exists. Do you know where dinosaurs came from? Do you know what killed them some 65 million years ago? Do you know what produced the Grand Canyon in Northern Arizona? And do you know how ecological succession occurs on abandoned farmland in Georgia or why predator-prey populations often show cyclic oscillations? Of course nobody was alive when the dinosaurs arose, when they died, and when the Grand Canyon was carved. So direct observation of these events by humans is not possible. And although it may be possible for any one person to observe ecological succession and predator-prey population oscillations, these events generally take place on time scales that extend well beyond the normal person's experience. Thus our inability to make these sorts of observations is limited in a fundamentally different way than in the case of theoretical concepts. Our limitation here is not our senses but our relatively short life span or our inability to take the time to make the necessary observations. In other words, although we will never be able to use our senses to directly observe an atom because it its size, presumably we could have observed where the dinosaurs came from, what produced the Grand Canyon, and how succession occurs had we been around long enough and at the right time. Thus ideas/concepts about events that occur beyond the normal, or even possible, time frame of observation form an intermediate class of concepts. Additional examples include the geologist's concepts of plate tectonics, subduction, and orogeny and the paleontologist's concepts of speciation, adaptive radiation and extinction. Because the entities and processes upon which intermediate concepts are based are not directly observed, but could in theory be directly observed if the observational time period were extended beyond the normal, acquiring understanding of intermediate concepts is of intermediate difficulty.

CHAPTER 8

179

7.5 An Exercise in Classifying Concepts

Here are some terms or phrases including their definitions. Please classify them into one of the three concept classes defined above. Pay particular attention to the definitions as the classification of any one term/phrase may differ depending upon how it is being defined.

1. environmental factors: the observable factors surrounding an organism that may effect its growth and development, e.g., amount of soil, number and types of other organisms. (Researcher classification = descriptive. Panel classification 10/10 = descriptive). 2. molecule: a particle that results from the joining of two or more atoms. (Researcher classification = theoretical. Panel classification 10/10 = theoretical).

3. food chain: a sequence of feeding relationships starting with plants, moving through successive levels of animals; for example grass being eaten by a mouse that is in turn eaten by a snake, that is in turn eaten by a hawk. (Researcher classification = descriptive. Panel classification 10/10 = descriptive). 4. artificial selection: the selective breeding of organisms over several generations for the purpose of producing offspring with certain desired characteristics. (Researcher classification = intermediate. Panel classification 3/10 = descriptive; 2/10 = intermediate; 1/10 = theoretical; 4/10 undecided between descriptive and intermediate). 5. air pressure: the force exerted on a surface due to the collision of unseen gas molecules with that surface; the amount of force depends on the frequency of collisions, the mass of the colliding molecules and their speed. (Researcher classification = theoretical. Panel classification 10/10 = theoretical). 6. combustion: the rapid breaking apart and oxidation (i.e., addition of molecules) of relatively complex molecules to produce heat energy and usually light energy. (Researcher classification = theoretical. Panel classification 10/10 = theoretical).

7. convergent evolution: the independent evolution of similar characteristics within two or more populations of unrelated organisms as a result of living under similar selective pressures. (Researcher classification = intermediate. Panel classification 10/10 = intermediate). 8. nocturnal: a type of animal that is active at night. (Researcher classification = descriptive. Panel classification 10/10 = descriptive).

180

WHAT KINDS OF SCIENTIFIC CONCEPTS EXIST?

9. species: groups of organisms that may live in different locations but that share enough characteristics such that if they were brought into contact with each other they could mate and produce fertile offspring (i.e., fertile offspring are those that can in turn mate and produce their own offspring). (Researcher classification = intermediate. Panel classification 10/10 = descriptive).

10. osmosis: the diffusion of water

molecules through a selectively permeable membrane; from a region of relative high concentration of water molecules to a region of relatively lower concentration. (Researcher classification = theoretical. Panel classification 10/10 = theoretical).

11. limiting factors: environmental factors that act over an extended period of time to keep a population from living in a particular area or restrict its population size. (Researcher classification = intermediate. Panel classification 2/10 = descriptive; 6/10 = intermediate; 2/10 = undecided between descriptive and intermediate).

12. population: a group of organisms that appear to be of the same kind living together in a particular location. (Researcher classification = descriptive. Panel classification 10/10 = descriptive).

13. biogeochemical cycles: pathways in which atoms and molecules such carbon (C), oxygen nitrogen phosphorus (usually in the form of a phosphate ion and water cycle through living and non-living components of ecosystems. (Researcher classification = theoretical. Panel classification 10/10 = theoretical).

14. community: all of the organisms living and interacting in a particular area. (Researcher classification = descriptive. Panel classification 10/10 = descriptive).

15. evolution: the lengthy process by which some past species have gone extinct while others have changed to give rise to present-day species. (Researcher classification = intermediate. Panel classification 10/10 = intermediate).

16. natural selection: the evolutionary process in which organisms better suited to live in a particular environment are able to survive and pass on their helpful characteristics to subsequent generations. Natural selection is one of the most important processes causing evolutionary change. (Researcher classification = intermediate. Panel classification 9/10 = intermediate; 1/10 undecided between intermediate and theoretical).

17. external stimulus: an occurrence such as a flash of light or a poke external to an organism that provokes it to respond in some way. (Researcher classification = descriptive. Panel classification 10/10 = descriptive).

CHAPTER 8

181

18. gene: a basic hereditary unit consisting of a sequence of DNA nucleotide molecules within a chromosome. (Researcher classification = theoretical. Panel classification 10/10 = theoretical).

19. photosynthesis: the process by which chlorophyll molecules in green plants capture light energy and use it to combine and molecules together to produce glucose (i.e., molecules. (Researcher classification = theoretical. Panel classification 10/10 = theoretical).

20. carnivore: an animal that eats primarily meat. (Researcher classification = descriptive. Panel classification 10/10 = descriptive).

21. fossils: the remains of once living organisms preserved in rock through a lengthy process of fossilization (i.e., the replacement of living matter by rock-like matter). (Researcher classification = intermediate. Panel classification 1/10 = descriptive; 7/10 = intermediate; 2/10 = undecided between descriptive and intermediate).

This page intentionally left blank

CHAPTER 9 PSYCHOLOGICAL AND NEUROLOGICAL MODELS OF SCIENTIFIC DISCOVERY

1. INTRODUCTION Chapters 1 and 2 argued that learning is a constructive process that can be understood at the psychological level in terms of self-regulation. Further, selfregulation can be understood in terms of the underling neural networks in which an internally driven spontaneous process called adaptive resonance results in an eventual match of input with expectations and the construction of more adaptive mental structures. Can scientific discovery be understood using similar models? To answer this question we will need to find a discovery in which the scientist has left us with a detailed account of what took place, including what s/he was thinking during the discovery process. As one might expect, such detailed accounts are hard to come by. Consequently, while perusing some old books during a recent summer vacation, I was thrilled to find just such an account. Galileo Galilei wrote the account in 1610 describing how he discovered Jupiter's moons. The purpose of this chapter is to discuss what Galileo did during his discovery and then attempt to piece together the steps in his reasoning. Galileo's reasoning will then be modeled in terms of selfregulation and the neurological models introduced in previous chapters. We will then explore the "logic" and implications of the models in terms of scientific method and science instruction. 2. GALILEO'S DISCOVERY In 1610 in his Sidereal Messenger, Galileo Galilei reported some observations of heavenly bodies made by a new more powerful telescope of his invention. In that report Galileo claims to have discovered four never before seen "planets" circling Jupiter. As he put it: "I should disclose and publish to the world the occasion of discovering and observing four planets, never seen from the beginning of the world up to our times." (Galilei, 1610, as translated and reprinted in Shapley, Rapport & Wright, 1954, p. 59) Unlike many modern scientific papers, Galileo's report is striking in the way in which it chronologically reveals many of the steps in his discovery process. Thus, it provides an extraordinary opportunity to gain insight into the reasoning involved in an important scientific discovery. Galileo's key observations were made during the nights of January 7th, 8th, 10th and 11th in 1610. What follows is a step-by-step 183

CHAPTER 9

184

recapitulation of that report followed by an attempt to fill in gaps with how Galileo may have been reasoning as he interpreted his observations. Prior to January 7th Galileo's report begins with mention of his invention of a new more powerful telescope: At length, by sparing neither labor or expense, I succeeded in constructing for myself an instrument so superior that objects seen through it appear magnified nearly a thousand times..." (p. 58) Thus, Galileo had at his disposal an instrument that allowed observations of nature never before seen. Not surprisingly, he used his telescope to explore the heavens. Again in his words: But without paying attention to its use for terrestrial objects, I betook myself to observations of the heavenly bodies; and first of all, I viewed the Moon as near as if it was scarcely two semidiameters of the Earth distant. After the Moon, I frequently observed other heavenly bodies, both fixed stars and planets, with incredible delight... (p. 59)

At the time, stars were referred to as "fixed" because they were thought to be embedded in a "celestial sphere," which had been postulated to exist within ancient Greek Aristotelian theory (e.g., Holton & Roller, 1958, p. 107). January 7th During Galileo's initial explorations, he made a new observation on January 7th that he deemed worthy of mention: In his words: On the 7th day of January in the present year, 1610, in the first hour of the following night, when I was viewing the constellations of the heavens through a telescope, the planet Jupiter presented itself to my view, and as I had prepared for myself a very excellent instrument, I noticed a circumstance which I had never been able to notice before, owing to want of power in my other telescope, namely that three little stars, small but very bright, were near the planet; and although I believed them to belong to the number of the fixed stars, yet they made me somewhat wonder, because they seemed to be arranged exactly in a straight line, parallel to the ecliptic, and to be brighter than the rest of the stars equal to them in magnitude. The position of them with reference to one another and to Jupiter was as follows: (p. 59)

o

(east)

(west)

January 8th The next night Galileo made a second observation: ...when on January 8th...I found a very different state of things, for there were three little stars all west of Jupiter, and nearer together than on the previous night, and they were separated from one another by equal intervals, as the accompanying figure shows.

(east)

o

(west)

MODELS OF SCIENTIFIC DISCOVERY

At this point, although I had not turned my thoughts at all upon the approximation of the stars to one another, yet my surprise began to be excited, how Jupiter could one day be found to the east of all the aforementioned stars when the day before it had been west of two of them; forthwith I became afraid lest the planet might have moved differently from the calculation of astronomers, and so had passed those stars by its own proper motion. (pp. 59-60)

January 9th I, therefore waited for the next night with the most intense longing, but I was disappointed of my hope, for the sky was covered with clouds in every direction. (p. 60)

January 10th But on January 10th the stars appeared in the following position with regard to Jupiter, the third, as I thought, being hidden by the planet. (east)

(west)

O

When I had seen these phenomena, as I knew that corresponding changes of position could not by any means belong to Jupiter, and as, moreover, I perceived that the stars which I saw had always been the same, for there were no others either in front of behind, within the great distance, along the Zodiac - at length, changing from doubt into surprise, I discovered that the interchange of position which I saw belonged not to Jupiter, but to the stars to which my attention had been drawn and I thought therefore that they ought to be observed henceforward with more attention and precision. (p. 60)

January 11th Accordingly, on January 11th I saw an arrangement of the following kind: (east)

O

(west)

namely, only two stars to the east of Jupiter, the nearer of which was distant from Jupiter three times as far as from the star to the east; and the star furthest to the east was nearly twice as large as the other one; whereas on the previous night they had appeared nearly of equal magnitude. I, therefore, concluded, and decided unhesitatingly, that there are three stars in the heavens moving about Jupiter, as Venus and Mercury round the sun; (p. 60)

January 12th and Later ...which at length was established as clear as daylight by numerous other subsequent observations. These observations also established that there are not only three, but four, erratic sidereal bodies performing their revolutions round Jupiter... These are my observations upon the four Medicean planets, recently discovered for the first time by me. (pp. 60-61)

3. GALILEO'S REASONING

Background Knowledge as a Source of Hypotheses

185

186

CHAPTER 9

We now turn to an analysis of Galileo's report in an attempt to fill in gaps with how Galileo may have been reasoning. Let's start by considering what Galileo initially "brought to the table." In other words, what was Galileo's background (i.e., declarative) knowledge? Presumably this declarative knowledge will serve as a source of hypotheses when the need arises. Based on common knowledge at the time, it is safe to assume that Galileo's knowledge about heavily objects included at least the following three categories: 1. some objects - the fixed stars - are immovable because they are embedded in an external celestial sphere; 2. some objects within the celestial sphere - the planets - orbit the sun (e.g., Earth, Venus, Jupiter); 3. some objects - moons - orbit the planets that orbit the sun (e.g., our moon).1 Presumably these categories of heavenly objects function as "mental models" by which observations can be "assimilated" (cf., Grossberg, 1982; Johnson-Laird, 1983; Piaget, 1985). In other words, when new objects are seen, they can be assimilated into one of these categories. Also, if the category into which the new objects should be assimilated is unclear, the categories function as hypotheses, i.e., as categories into which the new objects might be placed (cf., Gregory, 1970) i.e., Observation: Three new objects are seen. Question: What are they? Alternative Hypotheses: They might be fixed stars. They might be planets. They might be moons. The process of using these categories as alternative hypotheses has been referred to as analogical reasoning or analogical transfer (see Chapter 5) in that the new observation is seen as similar to, or analogous to, prior observations. It should be pointed out that the processes of assimilation and hypothesis formation take place largely at the subconscious level. Also in many cases, the analogical transfer requires more insight than shown in Galileo's case because the "distance" between the analogous category and the target phenomenon is greater, e.g., Darwin's use of artificial selection as an analogue for natural selection, Kekule's use of snakes eating their tails as an analogue for the benzene ring. Galileo's Reasoning on January 7th Recall that concerning his January 7th observations, Galileo's stated: "I noticed a circumstance which I had never been able to notice before, owing to want of power in my other telescope, namely that three little stars, small but very bright, were near the planet." This statement is important because it suggests that his new 1 I am not attempting to explain how Galileo obtained this declarative knowledge. I am simply assuming that he had it prior to January 7th. There is however, no reason to believe that induction was involved in acquiring this declarative knowledge. As you will see later, the argument is advanced that induction, as a psychological process, does not exist. Rather, in my view, induction is the psychologist’s equivalent of the chemists’ phlogiston, the biologists’ vital force, and the physicists’ suction. Phlogiston, the vital force, and a pulling force called suction do not exist and most likely neither does induction. Indeed, the main thesis of this book is that thinking and learning is hypothetico-predictive in form. Consequently, if we were able to discover how Galileo obtained this declarative knowledge, I believe we would find that he obtained it in a hypothetico-predictive manner.

MODELS OF SCIENTIFIC DISCOVERY

187

observations have been immediately assimilated by his fixed-star category (listed as 1 above). But Galileo's continued thinking led to some initial doubt that he was really observing fixed stars as this following remark reveals: ...and although I believed them to belong to the number of the fixed stars, yet they made me somewhat wonder, because they seemed to be arranged exactly in a straight line, parallel to the ecliptic, and to be brighter than the rest of the stars, equal to them in magnitude. (p. 59)

Why would this observation lead Galileo to somewhat wonder? What could Galileo have been thinking that raised doubt? Of course we can never really know what was on Galileo's mind. But perhaps he was reasoning along these lines: If...the three objects are fixed stars, (fixed-star hypothesis) and...their sizes, brightness and positions are compared to each other and to other nearby stars, (planned test) then...variations in size, brightness and position should be random, as is the case for other fixed stars. (prediction) But..."they seem to be arranged exactly in a straight line, parallel to the ecliptic, and to be brighter than the rest of the stars." (observed result) Therefore...the fixed star hypothesis is not supported. Or as Galileo put it, "yet they made me somewhat wonder." (conclusion) So Galileo's reasoning might have gone something like this: first a new observation is made, next an initial hypothesis (they are fixed stars) is generated, then hypothetico-predictive reasoning about the initial hypothesis occurs, i.e., If...they really are fixed stars, and...I do such and such, then...such and such should be seen. But...such and such is not seen. Therefore...I have some doubt about my initial hypothesis. Galileo's Reasoning on January 8th The next night Galileo made a second observation. Again in his words: ...when on January 8th, I found a very different state of things, for there were three little stars all west of Jupiter, and nearer together than on the previous night, and they were separated from one another by equal intervals, as the accompanying figure shows.

(east)

O

(west) (pp. 59-60)

The new observation puzzled Galileo and raised another question. Once again in Galileo's words: At this point, although I had not turned my thoughts at all upon the approximation of the stars to one another, yet my surprise began to be excited, how Jupiter could one day be found to the east of all the aforementioned stars when the day before it had been west of two of them... (p. 60)

188

CHAPTER 9

But why should this observation puzzle Galileo? Basically the puzzling observation was that the stars were now closer together than before and all were west of Jupiter, but still along a straight line. I believe that this observation was puzzling because it was not the expected/predicted one based on the fixed-star hypothesis, i.e.: prediction - their positions relative to each other should be the same and they should not pass Jupiter; observation - the stars are closer together than on the previous night and they are now all west of Jupiter. Galileo continues, ...forthwith I became afraid lest the planet might have moved differently from the calculation of astronomers, and so had passed those stars by its own proper motion. (p. 60)

This statement suggests that Galileo has not yet rejected the fixed-star hypothesis. Instead he has generated an ad hoc hypothesis to possibly keep the hypothesis alive. In other words, Galileo thought that perhaps the astronomers made a mistake. He thought that perhaps their records were wrong about how Jupiter is supposed to move relative to the stars in the area. Let's call this the astronomers-made-a-mistake hypothesis. How could Galileo test the astronomers-made-a-mistake hypothesis? Consider the following: If...the astronomers made a mistake, (astronomers-made-a-mistake hypothesis) and...I observe the next night, (planned test) then...Jupiter should continue to move east relative to the stars, and the objects should look like this: (east) O (west) Of course we cannot know if this is how Galileo was really reasoning, but if he were reasoning along these lines, he would have had a very clear expectation (prediction) to compare with the observations he hoped to make the following night. Galileo's Reasoning on January 9th and 10th Galileo continues: I, therefore waited for the next night with the most intense longing, but I was disappointed of my hope, for the sky was covered with clouds in every direction. But on January 10th the stars appeared in the following position with regard to Jupiter, the third, as I thought, being hidden by the planet." (east)

O

(west) (p. 60)

What conclusion can be drawn from this observation in terms of the astronomersmade-a-mistake hypothesis? Consider the following argument: If...the astronomers made a mistake, (astronomers-made-a-mistake hypothesis) and...I observe the next night, (planned test) then...Jupiter should continue to move east relative to the "stars", and the objects should look like this:

189

MODELS OF SCIENTIFIC DISCOVERY

(east)

O

(west)

(prediction)

But...the objects did not look like this, instead they looked like this:

(east)

O

(west)

(observed result)

Therefore...the astronomers-made-a-mistake hypothesis is not supported. (conclusion) Let's return to the report to see what conclusion Galileo drew. Galileo states: When I had seen these phenomena, as I knew that corresponding changes of position could not by any means belong to Jupiter, and as, moreover, I perceived that the stars which I saw had always been the same, for there were no others either in front or behind, within the great distance, along the Zodiac - at length, changing from doubt into surprise, I discovered that the interchange of position which I saw belonged not to Jupiter, but to the stars to which my attention had been drawn... (p. 60)

So Galileo concluded that the astronomers had not made a mistake (i.e., the astronomers-made-a-mistake hypothesis should be rejected). In other words, the changes of position were not the result of Jupiter's motion. Instead they were due to motions of the "stars." Galileo's Reasoning on January 11th and Later Having rejected the astronomers-made-a-mistake hypothesis, Galileo is left with the task of formulating another explanation for his puzzling observations. It is not clear exactly when he formulated a viable explanation, but the following observation and remarks make it clear that he did not take long: Accordingly, on January 11th I saw an arrangement of the following kind: (east)

O

(west)

namely, only two stars to the east of Jupiter, the nearer of which was distant from Jupiter three times as far as from the star to the east; and the star furthest to the east was nearly twice as large as the other one; whereas on the previous night they had appeared nearly of equal magnitude. I, therefore, concluded, and decided unhesitatingly, that there are three stars in the heavens moving about Jupiter, as Venus and Mercury round the sun. (p. 60)

Galileo's remarks make it is clear that he has "conceptualized" a situation in which these objects are orbiting Jupiter in a way analogous to the way Venus and Mercury orbit the sun and in the way our moon orbits Earth. Thus, he has rejected the fixed star hypothesis and accepted an alternative in which the objects are orbiting Jupiter. How could Galileo have arrived at such a conclusion? Consider the following:

190

CHAPTER 9

If...the objects are orbiting Jupiter, (moon hypothesis - presumably drawn from his prior knowledge - his moon category) and...I observe the objects over several nights, (planned test) then...some nights they should appear to the east of Jupiter and some nights they should appear to the west. Further, they should always appear along a straight line on either side of Jupiter. (prediction) And...this is precisely how they appeared. (observed result) Therefore...the moon hypothesis is supported. (conclusion) Galileo's previous statement continues as follows: ...which at length was established as clear as daylight by numerous other subsequent observations. These observations also established that there are not only three, but four, erratic sidereal bodies performing their revolutions round Jupiter... These are my observations upon the four Medicean planets, recently discovered for the first time by me. (pp. 60-61)

4. MODELING THE REASONING INVOLVED IN SCIENTIFIC DISCOVERY

4.1 Galileo's Reasoning as Hypothetico-Predictive Science

The present hypothesis about the nature of Galileo's reasoning, and more generally about the reasoning involved in scientific discovery, is that it has as its core an If/then/Therefore pattern. As we have seen, the pattern involves, in order: 1) making a puzzling observation, 2) formulating a causal question, 3) formulating one or more hypotheses, 4) using a hypothesis and an imagined test to generate expected results/predictions, 5) making actual observations and comparing them with the expected observations, and 6) drawing conclusions as to the extent to which the initial hypotheses have or have not been supported. This hypothetico-predictive reasoning pattern can be modeled by the series of boxes shown in Figure 1. 4.2

Galileo's Reasoning Within Piaget's Self-Regulation Theory

As presented in Chapter 1, Piaget describes cognition in terms of self-regulation with its duel processes of assimilation and accommodation. Galileo's hypotheticopredictive reasoning fits nicely within Piaget's theory. In Piagetian terms, Galileo initially assimilated his observations using his fixed-star schema (i.e., "I noticed...that three little stars...were near the planet."). This assimilation then soon led to a small amount of disequilibrium when his fixed- star hypothesis was initially tested (i.e., "yet they made me somewhat wonder."). This initial disequilibrium resulted because certain characteristics of the new "stars" differed from typical stars

MODELS OF SCIENTIFIC DISCOVERY

191

(i.e., they were in a straight line and equidistant from one another). Disequilibrium

(i.e., they were in a straight line and equidistant from one another). Disequilibrium then grew when subsequent observations also did not match expectations drawn from the fixed star schema (i.e., How could Jupiter be found to the east of all the aformentioned stars when the day before it had been west of two of them?"). But Galileo's disequilibrium did not last long. After rejecting the ad hoc astronomer'smade-a-mistake hypothesis, Galileo rejected the fixed-star hypothesis. This rejection then led to an accommodation as Galileo generated a new hypothesis - the moon hypothesis - that the evidence supported. Generation and test of the moon hypothesis enabled Galileo to assimilate all of his observations without disequilibrium. Thus, equilibrium was restored.

192

CHAPTER 9

4.3 Galileo's Reasoning Within Neural Network Theory We can go farther than Piaget's general concepts of self-regulation, assimilation and accommodation to think about Galileo's reasoning. Chapter 2 introduced Grossberg's neural network theory of information processing complete with an account of activity within successive slabs of neurons within the brain. It should be pointed out Grossberg's theory does not contradict Piaget's theory. Rather it adds to it. The neural network theory (part of which is represented in Figure 2) can be used to understand what might have been going on in Galileo's mind in terms of neurological events.

MODELS OF SCIENTIFIC DISCOVERY

193

Figure 2 depicts two successive slabs of neurons in the brain, and According to the theory, sensory input (e.g., light coming from the three objects near Jupiter on the night of January 7th) excites an electrical pattern of activity at slab and sends a signal to inhibit nonspecific orienting arousal (OA). The electrical pattern at then excites another electrical pattern at the next slab of neurons at which feeds signals back to In the case of Galileo's initial observations, the pattern at corresponds to his star category and initially matches the pattern at So all is well both neurologically and conceptually. But as reported, Galileo's continued thinking led to a partial mismatch (e.g., his star category implied that stars should not be lined up along a straight lines and should not be equidistant from each other). This partial mismatch led Galileo to "somewhat wonder." Neurologically speaking, a mismatch (i.e., a new observation that does not match an expectation), causes quenching of activity at and shuts off inhibition of OA. OA is then free to search for another pattern (i.e., another hypothesis) to match the input. In other words, with Galileo's continued observations and thinking, the mismatch between the patterns at and presumably became so great that activity at was quenched. Thus, inhibition of orienting arousal was shutdown. Orienting arousal was then free to excite leading to a search for another pattern of activity to hopefully match the input pattern at On the conceptual level, Galileo's mind was now free to search for alternative hypotheses (e.g., the planet hypothesis, the moon hypothesis) to replace the rejected fixed star hypothesis. Once an activity pattern at was found that actually matched the input pattern at orienting arousal was shut down and Galileo's search was complete. He had "discovered" four new moons orbiting Jupiter.

4.4

Galileo's Reasoning Within the Levine/Prueitt and Kosslyn/Koenig Models

The Levine & Prueitt model introduced in Chapter 3 also seems to account for the processes involved in hypothesis testing. Figure 3 suggests how it can be used in the present context. As you may recall, the model includes feature nodes referred to as In Galileo's case, these nodes code input features (i.e., number of spots of light, the sizes of those spots, their positions). The input can be placed into categories (e.g., fixed stars, planets, moons) and coded by nodes in Once again, these categories serve as alternative hypotheses. The model also includes Habits and Biases nodes. The Habits node detects how often prior classifications have correctly and incorrectly been made. The Biases node is affected by activity in the habit nodes and by reinforcement. Further details of network function can be found in Levine & Prueitt (1989). The important point in terms of the present argument is that information processing, whether it involves basic descriptive concept formation, simple hypothesis testing, or the "discovery" of Jupiter's moons, is basically a hypothetico-predictive process driven by working memory in which new input is gathered and matched against prior categories stored in associative memory.

194

CHAPTER 9

Kosslyn and Koenig's model of brain function also introduced in Chapter 2 argues that the ability to visually recognize objects requires participation of the six major brain areas as shown in Figure 4. Kosslyn and Koenig's description of system functioning is about recognizing relatively complex objects present in the visual field during a very brief time period - not distant spots of light seen through a telescope. Nevertheless, the hypothetico-predictive nature of this system's functioning was made clear in Chapter 2. And all one need do to apply the same principles to

MODELS OF SCIENTIFIC DISCOVERY

195

Galileo's case, is to extend the time frame over which observations are made observations that will either match or not match predictions, thus allowing hypotheses to be tested.

4.5

Using Working Memory to Activate and Inhibit Input

Working memory is seated in the lateral prefrontal cortex. However, current research suggests that working memory cannot be pinned down to a single prefrontal region. Rather its location depends in part on the type of information being processed. With its many projections to other brain areas, working memory plays a crucial role in keeping representations active while it coordinates mental activity (Friedman & Goldman-Rakic, 1994; Fuster, 1989). Following Baddeley (1995), working memory, at least in adults, is seen as consisting of at least three components - a visuo-spatial scratchpad, a central executive, and a phonological loop. In Baddeley's model, the visuo-spatial scratch pad activates representations of objects and their properties, while the phonological loop does the same for linguistic representations. Research by Smith & Joniches (1994) and Paulesu et al. (1993) suggest a respective right and left hemisphere specialization for the scratch pad and loop. Working memory can be thought of as a temporary network to sustain

196

CHAPTER 9

information while it is processed. However, as we have seen, during reasoning, one must pay attention to task-relevant information and inhibit task-irrelevant information. Consequently, working memory involves more than simply allocating attention and temporarily keeping track of it. Rather, working memory actively selects information relevant to one's goals and actively inhibits irrelevant information. In terms of Galileo's reasoning and the Kosslyn/Koenig model, Figure 5 shows the contents of working memory in terms of one cycle of hypothetico-predictive reasoning. As you can see, in order to use hypothetico-predictive reasoning to generate and test his moon hypothesis, Galileo has to not only allocate attention to it and its predicted consequences, he also has to inhibit his previously generated fixedstar and astronomers-made-a-mistake hypotheses.

5. IS THERE A SCIENTIFIC METHOD? The central conclusion that can be drawn from the forgoing analysis of Galileo's reasoning is that his discovery of Jupiter's moons involved several cycles of hypothetico-predictive reasoning. And based on the introduced neural models, it

MODELS OF SCIENTIFIC DISCOVERY

197

would seem that Galileo's reasoning was hypothetico-predictive in form because the human brain is hard-wired to process input in a hypothetico-predictive fashion. As shown in Table 1, the hypothetico-predictive reasoning pattern seen in Galileo's discovery of Jupiter's moons can also be found in the discoveries of other scientists. As you may recall, we also saw this hypothetico-predictive pattern in the unlit barbecue scenario discussed in Chapter 1 and in several subsequent examples in other chapters. To summarize, hypothetico-predictive reasoning seems to involve the following seven elements, which are presumably coordinated in working memory in the prefrontal lobes: 1. Making an initial puzzling observation (e.g., Three new spots of light are observed near Jupiter.). 2. Raising a causal question (e.g., What are the spots of light? What is causing the spots of light?). 3. Using analogical reasoning to generate one or more possible hypotheses (e.g., The spots of light are fixed stars. Previous astronomers made a mistake. They are moons orbiting Jupiter.). Analogical transfer, or analogical reasoning involves borrowing ideas that have been found to "work" in one or more past related contexts and using them as possible solutions/hypotheses/guesses in the present context. 4. Supposing for the sake of argument and test, that the hypothesis under consideration is correct. This supposition is necessary so that a test can be imagined with relevant condition(s) that along with the hypothesis allow the generation of one or more predictions. 5. Carrying out the imagined test. The test must be performed/conducted so that its predicted result can be compared with the observed result of the actual test. 6. Comparing predicted and observed results. This comparison allows one to draw a conclusion. A good match means that the hypothesis is supported, but not proven, while a poor match means that something is wrong with the hypothesis, the test, or with both. Finding a good match between predicted and observed results means that the hypothesis in question is supported, but not proven because one or more unstated and perhaps un-imagined alternative hypotheses may give rise to the same prediction under the test condition (e.g., Hempel, 1966; Salmon, 1995). Similarly, a poor match cannot disprove or falsify a hypothesis in any ultimate sense. This is because the failure of predicted results to match observed results can arise from one of two sources, a faulty hypothesis or a faulty test. Consequently, before a plausible hypothesis is rejected, one has to be reasonably sure that its test is not faulty. And because one can never be certain the test is perfect, one cannot reject a hypothesis with certainty. We will return to this point below when discussing the relationship between hypothetico-predictive reasoning and some standard rules of propositional logic. 7. Recycling the procedure. The procedure must be recycled until a hypothesis is generated, tested, and supported on one or more occasions.

198

CHAPTER 9

How does blood travel in the body? Marcello Malpighi -1661 If...blood circulates by passing from arteries to veins through tiny vessels (William Harvey's circulation theory) and...the area between the arteries and veins is examined very closely (planned test) then...tiny connecting vessels, the postulated capillaries, should be observed (expected result). And...in 1661, 14 years after Harvey's death Malpighi focused his microscope at that area and "discovered" the postulated capillaries (observed result). Therefore...this crucial aspect of Harvey's circulation theory was supported (conclusion). Does matter consist of indivisible atoms? John Dalton -1810 If...matter consists of indivisible particles that have specific weights and combine with one another in specific ways (atomic-molecular theory) and...combinations of atoms are separated into their parts (planned test), then...the ratios of weights of those parts should be in simple whole-number ratios (prediction). And...as Dalton's experiments and calculations with gases revealed, the ratios of weights of those parts are in simple whole-number ratios (observed result). Therefore...atomic-molecular theory was supported (conclusion). What caused present-day species diversity? Charles Lyell - 1854 If...organisms changed over time (evolution theory), and...the kinds of organisms living in the past is examined in the fossil record (planned test), then...the younger, higher rock layers should contain more fossils of present-day species than do the older, lower rock layers (prediction). And...when Lyell compared fossil sea shells collected from four different rock layers, he found that the percentages of present-day species increased from the oldest to youngest layers from 3%, to 17%, to 42% and finally to 96% (observed result). Therefore... support for evolution theory was found (conclusion). How are characteristics passed from parent to offspring? Gregor Mendel - 1866 If...genes for seed color and shape assort independently when pollen and eggs are produced, and recombine randomly during fertilization (independent assortment and random recombination claims of Mendel's theory), and...second generation plants that presumably carry the YyRr genotype are crossed with other YyRr plants, or with themselves (planned test), then...four types of seeds should be produced in the third generation plants i.e., yellow-round, yellow-wrinkled, green-round, green-wrinkled, in a 9:3:3:1 ratio respectively (prediction). And...when Mendel conducted the test crosses, he counted a total of 556 seeds. Of these, 315 were yellow-round, 101 were yellowwrinkled, 108 were green-round and 32 were green-wrinkled (observed results). These numbers are very close to the expected 9:3:3:1 ratio. Therefore...support for these postulates was obtained (conclusion). What is inside atoms? Ernest Rutherford's discovery of the atomic nucleus -1907

MODELS OF SCIENTIFIC DISCOVERY

199

If...atoms consist mostly of fluid "globules" with a few tiny, solid electrons floating about (Thomson's theory) and...an alpha-particle emitter is aimed at a thin piece of metal foil with a photographic plate placed behind it (planned test), then...most of the alpha particles should pass straight through the fluid part of the foil's atoms and should strike and expose the photographic plate in a spot not much greater in diameter than the initial beam (prediction). And...Rutherford found that the beam passed straight through the foil, but was somewhat broadened, or "scattered." However, some of the particles came straight back. Therefore...support for Thomson's theory was found as was evidence that most of an atom's mass was concentrated in a minute atomic "nucleus."

This list by no means implies that doing science is simply a matter of applying a set of rules in some knee-jerk, lock-step fashion. On the contrary, one may know what is supposed to be done but fail none-the-less. As mentioned in Chapter 5, the use of analogical reasoning involves a creative act dependent in part on background declarative knowledge. Of course describing hypothesis generation in terms of creativity and analogical reasoning does not explain why some scientists (and science students) generate fruitful hypotheses while others do not. Clearly much research remains to be done to better understand this process. Similarly, much research remains to be done to understand how fruitful predictions are derived. In addition to the research on analogy cited above, other promising lines of cognitive research on scientific discovery can be found in Dunbar (1993), Klahr, Fay & Dunbar (1993) and Wagman (2000). Further, the conclusion that scientific discovery is hypothetico-predictive in nature does not imply that scientists are aware of the hypothetico-predictive nature of their reasoning. Indeed, as in Galileo's case, it seems likely that Galileo was very much unaware of his reasoning. He was simply trying to explain what he was seeing. But since Galileo's day, scientists and philosophers have collectively become more aware of the reasoning patterns that guide scientific discovery. Indeed, many relatively recent accounts of science place hypothesis generation and test squarely on center stage (e.g., Baker & Allen, 1977; Carey, 1998; Chamberlain, 1965; Giere, 1997; Hempel, 1966; Lewis, 1988; Medawar, 1969; Moore, 1993; Platt, 1964; Popper, 1965). However, these authors typically refer to scientific discovery as hypothetico-deductive, not as hypothetico-predictive. I have chosen the phrase hypothetico-predictive because the word deduction often connotes a rather rote application of deductive logic, i.e., If A > B, and B > C, then it deductively follows that A > C. In my view, seldom do scientific predictions follow so "automatically" or "logically" from premises. Instead, like hypothesis generation, generating reasonable predictions also involves elements of insight and creativity (e.g., Lawson, 1999; Lawson, 2000). Therefore, the phrase hypothetico-predictive may be more descriptive of what actually occurs during the reasoning process. A dramatic example of the need for creative thought in prediction generation can be seen in the research of Otto Loewi. For several years, Loewi had suspected that neural impulses were chemically transmitted from neurons to muscles. However, he was

200

CHAPTER 9

unable to think of a way to test this chemical-transmission hypothesis. Finally, one night in 1920, he literally dreamed up an experiment, complete with a prediction, that would do the trick. When he awoke the next morning, he immediately went to his lab and conducted the test. And to his delight, the observed results turned out just as predicted, providing support for his chemical-transmission hypothesis and eventually winning him a Nobel Prize (cf., Koestler 1964). And lastly, it should be pointed out that characterizing scientific discovery as hypothetico-predictive also does not imply that all observations that may bear on the validity of hypotheses must be made after the hypotheses have been generated. Indeed, occasionally observations are made and reported that only later, after a hypothesis has been generated, are seen as supportive or not supportive of that hypothesis. For example, a classic case is Erwin Chargaff's rules about the relative amounts of nucleotide bases in DNA known in the 1940s (i.e., adenine equals thymine, guanine equals cytosine). The reason (i.e., explanation) for Chargaff's rules, was not understood until the spring of 1953 when a young James Watson searching for the structure of DNA pushed cardboard models (analogies) of the bases together in various combinations until he noticed that an adenine-thymine pair held together by two hydrogen bonds was identical in shape to a guanine-cytosine pair also held together by two hydrogen bonds. This was a key puzzle piece that enabled Watson to construct a new and presumably better double-helical model of DNA (i.e., a puzzle piece that gave him a new and better hypothesis). Then by reasoning in a hypothetico-predictive fashion, Watson was finally able to explain Chargaff's rules because they were predicted by his new model/hypothesis. In other words, If...DNA is structured as a double helix with adenine always paired with thymine and with guanine always paired with cytosine, (Watson's double-helix hypothesis generated in the spring of 1953) and...the relative amounts of the bases in DNA are determined, as Chargaff had done in the 1940s, then...the amount of adenine should equal the amount of thymine and the amount of guanine should equal the amount of cytosine. (prediction derived by Watson in 1953) Or as Watson put it, "Chargaff's rules then suddenly stood out as a consequence of a double-helical structure for DNA." (Watson, 1968, p. 125) So Chargaff's rules are predicted by the double-helix hypothesis. Watson was also quick to point out that other "consequences" followed. Here is what he said about one of them: Even more exciting, this type of double helix suggested a replication scheme much more satisfactory than my briefly considered like-with-like pairing. Always pairing adenine with thymine and guanine with cytosine meant chains were complementary to each other. Given the base sequence of one chain, that of its partner was automatically determined. Conceptually it was thus very easy to visualize how a single chain could be the template for the synthesis of a chain with the complementary sequence. (p. 125)

MODELS OF SCIENTIFIC DISCOVERY

201

So the double-helix hypothesis "suggested a replication scheme" in which the two strands unzip and become templates for the synthesis of new complementary strands. And as you may know, this consequence led to the classic 1958 Meselson and Stahl experiment that can be summarized in the following standard hypothetico-predictive fashion: If...DNA replicates by adding a new strand to an old strand, (double-helix hypothesis) and...a test tube containing and DNA extracted from "hybrid" bacteria are spun in a centrifuge, (planned test) then...three distinct DNA bands should show up with the middle band exactly halfway between the other two. (prediction) The middle band should be exactly half way between the other two because it, according to the hypothesis, consists of DNA with one strand and one strand, thus should weigh exactly half as much as the DNA in the bottom band and twice as much as the DNA in the top band. (theoretical rationale) And...the results turned out as predicted. (observed result) Therefore...the double-helix hypothesis was supported. (conclusion) Table 2 lists the basic elements of science as a hypothetico-predictive enterprise. For those surprisingly few scientists who have become aware of these elements, they have become a powerful method. Indeed, for them, the elements have become the scientific method (e.g., Chamberlain, 1965; Feynman, 1965; Platt, 1964).

202

CHAPTER 9

6. DOES BACONIAN INDUCTION QUALIFY AS AN ALTERNATIVE SCIENTIFIC METHOD? But do other methods of doing science exist? Clearly many past scholars have thought so and some still do. A well-known candidate proposed during Galileo's day is Francis Bacon's method of induction first published in two volumes in 1605 and in 1620 (Bacon, 1900, revised ed.). Bacon's brand of induction is generally described as a process in which one reasons from particulars to general conclusions. Suppose, for example, you taste a green apple and find it sour. You taste another green apple and find it sour as well, and so on. From these particular observations, induction presumably is at work when you draw the general conclusion that all green apples are sour. Clearly research based on this "enumerative" style of induction does not fit the pattern identified in Tables 1 and 2. Others have argued that this sort of inductive reasoning - as opposed to a more general sort of induction defined simply as any thought process that increases the semantic information in its initial observations or premises (cf., Johnson-Laird, 1993, p. 60; Holland, Holyoak, Nisbet & Thagard, 1986, especially Chapter 11; and Bisanz, Bisanz & Korpan, 1994) - is of limited value in science because the world is so complex that if one lacks a hypothesis or theory and prediction to guide one's observations, those observations are not likely to amount to anything of scientific value, e.g.: A moment's reflection reveals that data collection in the absence of a hypothesis has little or no scientific value. Suppose, for example, that one day you decide to become a scientist and having read a standard account of the scientific method you decide to collect some data. Where should you begin? Should you start by cataloging all the items in your room, measuring them, weighing them...? Clearly there's enough data in your room to keep you busy for the rest of your life. (Schick & Vaugh, 1995, p. 191) Observation is always selective. It needs a chosen object, a definite task, an interest, a point of view, a problem. (Popper, 1965, p. 46) How odd it is that anyone should not see that all observation must be for or against some view if it to be of any service. (Charles Darwin, as quoted in Schick & Vaughn, 1995, p. 191) In sum, the maxim that data should be gathered without guidance by antecedent hypotheses about the connections among the facts under study is self-defeating, and is certainly not followed in scientific inquiry. On the contrary, tentative hypotheses are needed to give direction to scientific investigation. (Hempel, 1966, p. 13) Inductive theory provides no formal incentive for making one observation rather than another. Any adequate account of scientific method must include a theory of incentive or special motive. We cannot browse over the field of nature like cows at pasture. (Medawar, 1969, p. 29)

MODELS OF SCIENTIFIC DISCOVERY

203

The fact remains that the Baconian concept of science, as an inductive science, has nothing to do with and even contradicts today's form of science. (Malherbe, 1996, p. 75) There are, then, no generally applicable 'rules of induction', by which hypotheses or theories can be mechanically derived or inferred from empirical data. The transition from data to theory requires creative imagination. Scientific hypotheses and theories are not derived from observed facts, but invented in order to account for them. (Hempel, 1965, p. 15) Induction, i.e., inference based on many observations, is a myth. It is neither a psychological, nor a fact of ordinary life, nor one of scientific procedure. (Popper, 1965, p. 53) There is no such thing as inductive logic. (Musgrave, 1999, p. 395)

Based on the view expressed in these quotes, it should not be surprising to find that even Bacon himself did not use enumerative induction in his attempts to do science. According to Jevons (1969), in Bacon's attempt to discover the nature of heat, Bacon came to the startling correct conclusion that heat is a motion of the smaller particle of bodies. But he did so not using induction, but using hypotheticopredictive reasoning. To which Jevons added: It seems an amazing sort of conjurer's trick to play on oneself. And yet one should not, perhaps, blame him too much for having half-deceived himself into a belief in 'true induction'. Plenty of others have, after all, been equally mesmerized by his eloquence, or at least deluded by the same appearances, and they include scientists of great distinction. (p. 71)

Clearly, we can lay Baconian induction as a scientific method to rest. In fact, if we accept Popper and Musgrave's position, then such a cognitive process does not even exist. In other words, human intuition may strongly suggest that such an inductive process is at work, but upon closer inspection, we find that the mind simply does not work that way. Rather, it would appear that the mind does not wait around for multiple exemplars before generating an idea about what is being observed. Indeed, had humans ever existed who actually used such a slow approach to information processing, it seems likely that natural selection would have seen to it that they, and their plodding inductivist genes, were eliminated, perhaps by some predator whose avoidance required a faster mode of information processing.

6.1 Is Combinatorial Analysis a Viable Alternative?

Perhaps you are familiar with a research approach sometimes referred to as combinatorial analysis. Chemists often use this approach when they attempt to discover a chemical for some specific job - say cure a disease. The approach basically amounts to modifying a complex chemical over and over again, or

204

CHAPTER

9

systematically forming various combinations of chemicals, until one modification or combination happens to work. Use of this approach can be seen in the classic research of Paul Erlich conducted during the early 1900s in search of a cure for syphilis (De Kruif, 1926). In 1907, knowing that arsenic was poisonous, Erlich began painstakingly modifying an arsenic-containing compound called Atoxyl in hopes of finding a modification that would kill the disease agent but not the patient. Each modified form was injected into mice infected with a trypanosome (Trypanosoma equinum). Finally in 1909, on the 606th try, Erlich found a modified compound that killed the trypanosome and spared the mouse. When compound number 606 was injected into people suffering from syphilis - a venereal disease caused by the spirochete Treponema pallidum - the spirochete was killed and the people were spared. Therefore, Erlich had discovered a cure for syphilis. Does Erlich's approach constitute an alternative scientific method? If we consider each of the 606 chemical compounds as a random attempt at a disease cure, then it would seem so. Certainly, Erlich's approach seems to rely more on trial and error and on luck than on guiding hypotheses, theories and predictions. But a closer look at Erlich's discovery of compound 606 reveals that it was in fact hypothesis driven. During the 1880s, Erlich became fascinated with the use of dyes to stain tissues. At first, he used his dyes on preserved tissues. But in the late 1880s, he began injecting them into living animals. When he injected methylene blue into a rabbit's ear, he discovered that the dye traveled through the rabbit's body until it reached and stained only the nerve endings. This observation led Erlich to advance a hypothesis with a bold prediction. In Erlich's mind, living tissue was really nothing more than complex chemicals, just like his dyes. Also Erlich believed that chemical reactions were very specific. For example, chemical A might react with chemical B, but not with chemicals C, D, and E. So when he saw that the methylene blue stained nerve endings and nothing else, he predicted that chemicals could be injected into infected animals and that the chemicals would attack and kill only the infecting microbes. Thus, the reasoning that guided Erlich's painstaking and lengthy research can be seen as hypothetico-predictive, i.e.: If...living tissues consist of chemical compounds and chemical reactions are selective, (selective-chemical-reactions hypothesis) and...an arsenic-containing chemical compound, which is known to react with and destroy living tissue, is systematically modified and then injected into animals infected with microbes, (planned test) then...eventually a modified compound should be found that will interact with and destroy the microbes and spare the infected animal (prediction). And...compound 606 was found to do just that. (observed result) Therefore...the selective chemical reactions hypothesis is supported. (conclusion) Seen in this light, the chemists' approach of modifying and/or combining chemical compounds to produce a desired effect may differ in degree from the more

MODELS OF SCIENTIFIC DISCOVERY

205

insightful use of hypothetico-predictive reasoning employed by Galileo, but it does not differ in kind.

6.2

Are There Multiple Scientific Methods?

Having rejected combinatorial analysis as a true alternative to hypotheticopredictive science, and having rejected Baconian induction as a method at all, are we then left with hypothetico-predictive science as the only method of doing science? Could hypothetico-predictive reasoning be at work in all scientific discoveries? Certainly this singular view of scientific method is not without its detractors. For example, Eflin, Glennan & Reisch (1999) recently echoed the often- voiced view that multiple scientific methods exist (cf., Botton & Brown, 1998; Kimball, 1967; Lederman, 1983; Lederman, Wade & Bell, 1998; McComas, 1996; McComas, Almazroa & Clough, 1998). Regrettably these authors do not identify what those other methods might be. Nola (1999) does mention several alternative scientific methods and discusses the business of trying to decide among them. Nola seems to be arguing that it may not be possible to decide among alternative theories of scientific method because doing so would require one to adopt a particular scientific method to test the alternatives. And in Nola's view, we cannot decide what testing method to use until we know which method is the right one! This apparent paradox appears analogous to trying to decide if an external world really exists. Elsewhere, (Lawson, 2000), I have argued that we can never know for certain if the external world does or does not exist. But this of no practical consequence because even the simplest of behaviors requires that we hypothesize that it does exist and then behave accordingly. If that subsequent behavior is successful, then we not only retain that behavior, but we also have evidence that our initial hypothesis about the existence of an external world is correct - in spite of our lack of proof. The same may hold for testing alternative theories of scientific method. By analogy, we may never know for certain which theory of scientific method is correct. But that does not matter. Instead we proceed by hypothesizing that each in turn is correct and then see where each gets us. For example, to test the present hypotheticopredictive theory of scientific method, we first hypothesize that this is how science is done and then attempt to generate several predicted consequences (e.g., whenever an important scientific discovery is made, an analysis of the scientist's reasoning will reveal that he/she generated and tested alternative explanations during the discovery process). We then compare our predictions with evidence. A good correspondence between predictions and evidence would support the hypothesis. Presumably, this approach "works" in that it has helped us understand how Galileo and a few other scientists have made their discoveries. Alternatively, if one adopts a Baconian theory of scientific method, one would be obliged to use his methodology to test his theory. Consequently, one would observe

206

CHAPTER 9

several examples of science at work and then let enumerative induction take over in hopes that the "true" scientific method would emerge from the examples. How might this work? Suppose we start with a case study of Galileo's discovery of Jupiter's moons. Do we examine Galileo's report for evidence of enumerative induction? This may seem like the reasonable thing to do. But according to Bacon's rules, we cannot do this because this would amount to generating the hypothesis that induction is at work and then using this induction hypothesis to generate a prediction about what should be seen in the report. In other words, we would be using the hypotheticopredictive method! Interestingly, Jevons (1969) argues that Bacon himself used the hypothetico-predictive method in his own research. In short, we would find that Bacon's inductivist theory of scientific method does not "work." Therefore, evidence would be obtained to allow the rejection of this alternative. Other theories of scientific method would run into similar problems.

7. THE "LOGIC" OF HYPOTHETICO-PREDICTIVE REASONING AND SCIENTIFIC DISCOVERY As mentioned, the hypothetico-predictive reasoning involved in scientific discovery cannot lead to proof or disproof in any ultimate sense. Thus, one might wonder how it relates to standard rules of conditional logic such as modus tollens and modus ponens. Let's see how these rules apply to the case of the unlit barbecue introduced in Chapter 1. You may recall that I had just arrived home and my wife asked me to check the meat on our backyard barbecue. Upon doing so I discovered that its flames had gone out. This discovery prompted a search for the cause and the generation and test of two hypotheses, a wind hypothesis and an empty gas tank hypothesis. The standard conditional logic of modus tollens reads as follows: p implies q; not-q; therefore, not-p. So in the context of testing the wind hypothesis, we get the following: If...the wind blew out the flames, (p) and...I stick a lighted match in the lighting hole, then...the barbecue should relight. (q) But...the barbecue did not relight. (not-q) Therefore...the wind did not blow out its flames. (not-p) However, as previously pointed out, the failure of an observed result to match a predicted result may not stem from a faulty hypothesis. Rather the failure may stem from a faulty test. Consequently, a more "reasonable" application of modus tollens might read as follows: If...the wind blew out the flames, (p) and...I stick a lighted match in the lighting hole, then...the barbecue should relight (q) - assuming nothing goes wrong with the test.

MODELS OF SCIENTIFIC DISCOVERY

207

But...the barbecue did not relight. (not-q) Therefore...most likely the wind did not blow out its flames (not-p) - unless of course something did go wrong with the test. Next consider the conditional logic of modus ponens, i.e., p implies q; p; therefore q. Interestingly, this logic does not appear to apply to the barbecue situation as the following illustrates: If...the wind blew out the flames, (p) and...I stick a lighted match in the lighting hole, then...the barbecue should relight. (q) And...the wind did blow out the flames. (p) Therefore...the barbecue should relight. (q) Clearly, this argument makes no sense. The point of hypothetico-predictive reasoning is to test an idea. On the other hand, the point of modus ponens seems to be to generate a "logical" prediction. So once again, a standard logical rule seems to fail to capture the essence of hypothetico-predictive reasoning. Interestingly, the logical fallacy known as affirming the consequent seems to do a better job than modus ponens (cf., Hempel, 1966, pp. 6-7). Affirming the consequent reads as follows: p implies q; q; therefore p. In the context of the unlit barbecue we get the following: If...the tank is out of gas, (p) and...the tank is lifted, then...it should feel light. (q) And...it does feel light. (q) Therefore...the tank is out of gas. (p) But as previously noted, drawing this conclusion represents a logical fallacy. The conclusion is also "unreasonable" because the tank could feel light for other reasons (i.e., alternative hypotheses exist that have not been tested and eliminated). For example, perhaps the tank feels light but still contains a small amount of gas. Perhaps this is why I checked the gas gauge and found it pointed at empty before I was satisfied that the cause of the unlit barbecue was indeed an empty gas tank. Consequently, the more reasonable conclusion that one draws from these kinds of data is that the initial hypothesis has been supported, but one cannot be certain that it is correct. The following summarizes the necessary modifications. For modus tollens: If...p, and...the planned test, then...probably q. (assuming that nothing goes wrong with the test)

208

CHAPTER 9

But...not-q. Therefore...probably not-p. (meaning that the hypothesis p is not supported, but not disproved) And for affirming the consequent: If...p, and...the planned test, then...probably q. (assuming that nothing goes wrong with the test) And...q. Therefore...possibly p. (meaning that the hypothesis is supported, but not proven as other hypotheses could lead to the same prediction) Consequently, the rules of modus tollens and modus ponens do not fully capture the essence of hypothetico-predictive reasoning. But this does not mean that humans are unreasonable. Said another way, it would appear that our brains do not necessarily reason with these rules of conditional logic. But this is not a bad thing because these rules are not necessarily reasonable!

8. CONCLUSION AND INSTRUCTIONAL IMPLICATIONS

Regardless of the number of scientific methods that may ultimately be identified, the present analysis suggests that many, if not all, scientific discoveries are hypothetico-predictive in nature. Given that several studies have found that many secondary school and college students exhibit difficulties in reasoning in a hypothetico-predictive manner in causal contexts (i.e., Levels 4 and 5), and that these difficulties lead not only to difficulties in problem solving and understanding hypothetical and theoretical science concepts, but also to difficulties in understanding the nature of science and mathematics, more emphasis on teaching students to reason in a hypothetico-predictive manner is urged (e.g., Cavallo, 1996; Germann, 1994; Germann & Aram, 1996; Hurst & Milkent, 1996; Johnson & Lawson, 1998; Keys, 1994; Kuhn, 1989; Lawson, 1992a; 1992b; Lawson, 1999; Lawson & Thompson, 1988; Lawson & Worsnop, 1992; Noh & Scharmann, 1997; Shayer & Adey, 1993; Westbrook & Rogers, 1994; Wong, 1993; Zohar, Weinberger & Tamir, 1994). Certainly a start could be made with an astronomy lesson in which students make the same observations made by Galileo on the night of January 7, 1610. Students could then attempt to explain those observations through the generation of alternative hypotheses and predictions. Student brainstorming could then be followed by subsequent observations in which the alternative hypotheses are tested by the comparison of predicted and observed results. Indeed, a general pattern of instruction could emerge in which a variety of student explorations lead to puzzling observations. These puzzling observations would then lead to the posing of causal questions and to the generation of alternative causal hypotheses. Then students

MODELS OF SCIENTIFIC DISCOVERY

209

would be challenged to test those alternatives through the explicit comparison of predicted and observed results. Although the present advocacy of such a hypothetico-predictive mode of instruction is not necessarily new (see for example the learning cycle method of instruction initially developed by the Science Curriculum Improvement Study, e.g., Karplus & Thier, 1967; Lawson, 1967; Lawson, Abraham & Renner, 1989), few science curricular materials currently exist in which these elements are explicitly included. Therefore, what curriculum developers need to do is to design more lessons in which these elements are made explicit. In conclusion, the present chapter paints human reasoning and scientific discovery in terms of cycles of hypothetico-predictive reasoning - reasoning in which working memory accesses and sustains hypotheses from associative memory to be tested and then actively seeks predictions and evidence that follow. In most instances, for most people, these reasoning cycles occur without conscious awareness on their part. And most certainly, unlike the streamlined If/then/Therefore arguments presented in this chapter, the cycles most often occur with many fits and starts. Nevertheless, successful hypothetico-predictive reasoning, while not necessarily logical, is reasonable, and follows the If/then/Therefore pattern presumably because the brain is "hard-wired" to process information in this way. Successful reasoning also involves the inhibition of previously rejected hypotheses and/or irrelevant information. But due to a variety of conditions, including lack of maturation of the frontal lobes, frontal lobe damage, and lack of relevant physical and social experience, human reasoning is not always successful. At higher levels, failure may result from a lack of any fruitful hypotheses to test, or more often, a premature acceptance of a pet hypothesis, often with little or no evidence in its favor. This leads to a failure to consider alternatives and potentially relevant evidence, or in terms of problem solving, a failure to consider and test alternative solution strategies - a condition of perseveration often referred to as fixation or functional fixedness in the problem-solving literature (e.g., Dominowski & Dallob, 1995). A recent classic example of a collective reasoning failure has been reported by Angell (1996) in which juries have awarded plaintiffs huge sums of money based on the claim (i.e., the hypothesis) that breast implants cause connective tissue disease. Amazingly, these awards were made prior to the collection of any real scientific evidence to test the hypothesis. Indeed, when that evidence was finally collected, it turned out not to match predictions from the hypothesis. For example, in one study, the hypothesis led to the prediction of a higher incidence of disease in women with implants than in a comparable group of women without implants. But the evidence revealed exactly the same disease incidence in both groups (Gabriel et al., 1994). Examples such as this indicate that many adults do not understand the power and importance of hypothetico-predictive reasoning (e.g., they fail to see the need to put their pet hypotheses to the test, they fail to generate and/or consider alternative hypotheses, they fail to understand the need to generate predictions, they confuse

210

CHAPTER 9

hypotheses with predictions, they do not understand how to gather and properly analyze evidence, they confuse results with conclusions). The example also indicates the importance of emotion in the deployment - or lack of deployment - of such reasoning. This is an issue not dealt with in the present chapter, but one of considerable importance nonetheless (e.g., Damasio, 1994; LeDoux, 1996). Clearly, an unmet educational challenge is the design and implementation of instructional programs that enable all students to develop and successfully employ hypotheticopredictive reasoning at the highest levels.

CHAPTER 10 REJECTING NATURE OF SCIENCE MISCONCEPTIONS BY PRESERVICE TEACHERS

1. INTRODUCTION Past and recent calls for science curricular reform emphasize the need to teach science as a process of creative and critical inquiry. Teaching inquiry science is seen by many as the best way to help students develop scientific reasoning skill, construct science concepts, and construct an understanding of the nature of science (e.g., American Association for the Advancement of Science [AAAS], 1928; 1989; 1990; Educational Policies Commission, 1961; 1966; National Science Foundation, 1996; National Research Council, 1995; National Society for the Study of Education, 1960). Accordingly, educating preservice teachers in how to teach inquiry science is a central goal of a senior-level teaching methods course that I have been teaching for several years. In spite of having completed, or having almost completed, an undergraduate major in biology, most preservice teachers (i.e., students) who enroll in this course initially hold several misconceptions about the nature of science (i.e., NOS misconceptions). The NOS misconceptions are similar to those described by McComas (1996) (e.g., hypotheses become theories which become laws; experiments are the principle route to scientific knowledge; hypotheses can be proved and disproved). Fortunately, my attempts to help students overcome such NOS misconceptions have met with some success. Others have reported similar successes (for reviews see McComas, Clough, & Almazroa, 1998; Abd-El-Khalick, 1999). However, as is usually the case, in spite of substantial NOS gains made by some students, others gain little. Importantly, previous research has yet to identify student variables consistently related to NOS gains (e.g., Billeh & Hasan, 1975; Carey & Stauss, 1969; Carey & Stauss, 1970; Lavach, 1969; Olstad, 1969; Sharmann, 1988a; Sharmann, 1988b). Thus, when given NOS instruction, it is still not known why some students make substantial NOS gains while others do not. Consequently, the study described in this chapter will advance and test the hypothesis that the ability to make substantial NOS gains as a consequence of instruction requires that students reject NOS misconceptions, which in turn depends on their skill in testing causal hypotheses involving unobservable theoretical entities - previously designated as Stage 5 hypothetico-predictive reasoning skill (see Chapters 7 and 8). 211

212

CHAPTER 10

2. THEORETICAL BACKGROUND In theory, causal hypothesis testing can be undertaken on two qualitatively different levels. The development of skill in testing first-order causal hypotheses (i.e., those involving observable causal agents) is seen as a prerequisite for developing skill at testing second-order hypotheses (i.e., those involving unobservable theoretical entities and processes such as photons, gravitons, genes, phlogiston, N-rays, photosynthesis, DNA replication). During adolescence, some students first develop skill at testing first-order causal hypotheses using reasoning patterns comparable to those of Piaget's formal operational thinker (e.g., Inhelder & Piaget, 1958). For example, following a comprehensive review of the psychological literature, Moshman (1998, p. 972) concluded: "In fact, there is surprisingly strong support for Piaget's 1924 proposal that formal or hypothetico-deductive reasoning deliberate deduction from propositions consciously recognized as hypothetical plays an important role in the thinking of adolescents and adults but is rarely seen much before the age of 11 or 12." Given the necessary developmental conditions (i.e., physical and social experience, neurological maturation, self-regulation), some students then develop post-formal or Stage 5 reasoning skill. Importantly, because modern science is essentially an enterprise in which scientists generate and test the validity of unseen theoretical entities and processes (see Chapter 9), anyone lacking Stage 5 reasoning skill should be hindered in their ability to assimilate this abstract aspect of science and to reject prior NOS misconceptions. More specifically, the present theory argues that advanced NOS understanding comes about via a reflective process in which someone with Stage 5 reasoning skill reasons through a number of examples of theoretical (i.e., Stage 5) science, and then reflects on those examples to assimilate common NOS elements and reject prior misconceptions. Consequently, if students lack the Stage 5 reasoning skill needed to reason through the examples and alternative NOS misconceptions/conceptions (e.g., a theory is a well-supported hypothesis vs. a theory is an explanation for a broad class of related phenomena regardless of the amount of support), they will be unable to reject prior misconceptions and will fail to make substantial NOS gains. Of course, some-less abstract NOS elements can be understood without Stage 5 skill (e.g., scientists observe nature, collect data, write reports). But the present hypothesis is that to understand science as a process of generating and testing alternative knowledge claims about unobservable theoretical entities and processes, one must have previously developed Stage 5 reasoning skill that allows the same. The argument concerning how the studies' working hypothesis will be tested can be summarized as follows: If...prior development of Stage 5 reasoning skill is necessary to reject NOS misconceptions and gain NOS understanding, (Stage 5 hypothesis) and...a sample of preservice teachers found to vary in developmental level (i.e., Levels 3, 4 and 5) are a) administered a NOS pretest, b) subjected to inquiry

REJECTING NATURE OF SCIENCE MISCONCEPTIONS

213

instruction in which NOS elements and examples are explicitly discussed, and c) administered a NOS posttest, (planned test) then...students with Stage 5 reasoning skill should assimilate that instruction, should reject prior NOS misconceptions, and should demonstrate significantly greater NOS gains than students lacking such reasoning skill. (prediction) On the other hand, if...Stage 5 reasoning skill does not exist (i.e., does not represent a developmental advance over Stage 4), then...assessed level of reasoning skill should not correlate with NOS gains. (prediction) 3. METHOD

3.1 Subjects Subjects were 23 students (9 males and 14 females, mean age = 26.5 years, SD = 6.4 years) enrolled in a senior-level college course for pre-service secondary school biology teachers called Methods of Teaching Biology taught at a major southwest university (USA). All 23 students had completed, or were soon to complete, an undergraduate major in biology. The biology major requires completion of 40 credits in biology and 22 credits in supporting courses in chemistry, physics, geology, mathematics and the history of science. 3.2 Design The first step in testing the studies' working hypothesis was administration of a test of students' skill in testing Stage 4 and 5 hypotheses. The test was administered on the first day of the semester. A Likert-type survey of NOS understanding was also administered at that time (see below). The course, which included several inquiry lessons designed to explicate the theoretical nature of science, was then taught. The NOS survey was then re-administered at the semester's end as part of the course final exam. At no time during the semester did the instructor reveal to students what he believed to be the correct responses on the NOS survey. Nor were students told that survey would be re-administered at the end of the semester. Consequently, students could not simply memorize the instructor's responses. Hence, student responses on the posttest survey presumably reflected their NOS beliefs as opposed to those of the instructor. Nevertheless, as described below, the instructor did explicitly discuss NOS elements on several occasions within the context of specific inquiry lessons and historical examples, and repeatedly made it clear that a course goal was the construction of NOS understanding.

CHAPTER 10

214

3.3 Instruments Reasoning Skill Level. Reasoning skill level (i.e., developmental level) was assessed by use of the written test described and used in the study discussed in Chapter 7. As you may recall, the test is based on reasoning patterns associated with hypothesis testing (i.e., the identification and control of variables, correlational reasoning, probabilistic reasoning, proportional reasoning, and combinatorial reasoning) and includes items with both observable and unobservable causal agents. Test scores allow students to be classified into one of four developmental levels: Level 3 = students not able to test hypotheses involving observable causal agents; Low Level 4 = students inconsistently able to test hypotheses involving observable causal agents; High Level 4 = students consistently able to test hypotheses involving observable causal agents; Level 5 = students able to test causal hypotheses involving unobservable entities. A split-half reliability coefficient of 0.66 was computed for the present sample. This figure seems reasonable given the relatively few test items and the relatively small sample size (n = 23). The study discussed in Chapter 8 found a Cronbach's reliability of 0.81 when a 24 item multiple-choice version of the test was administered to a sample of 663 undergraduate biology students. NOS Misconceptions. NOS misconceptions were assessed by use of the 13-item Likert-type survey that appears in Table 1. The 13 items focus on the meaning of terms such as hypothesis, prediction, theory, law, proof, truth, fact, and conclusion. Responses were used to generate a single NOS score by awarding 0 to 4 points for each item depending upon how closely the response corresponded to the response as indicated in the table. Thus, total NOS scores could range from 0 to 52. A percent score was also computed for each student. To do so, responses that agreed or strongly agreed (or disagreed or strongly disagreed) with the correct response were used. For example, Item 3 states: A hypothesis is an educated guess of what will be observed under certain conditions. Thus, a student who selected the "disagree" response was awarded 1 point and a student who selected the "strongly disagree" response was awarded 2 points. Students who were awarded 2 points on all 13 items received a maximum of 26 points (i.e., 100%).

1=strongly disagree 2=disagree 3=don't know 4=agree 5=strongly agree

1. The central goal of science is to explain natural phenomena. Although obtaining accurate descriptions of natural phenomena plays an important role in science, explanation is proposed as the central goal. In other words, at its core science is an attempt to

REJECTING NATURE OF SCIENCE MISCONCEPTIONS

215

understand/explain the causes of natural phenomena. Knowing what happens is not enough. Scientists want to know why things happen. Preferred response = 5.]

2.

Scientific explanations are derived from controlled observations of nature. [Upon initial reading, this statement sounds accurate. However upon reflection, the statement is misleading because scientific explanations (i.e., hypotheses/theories) initially come from (i.e., are derived from) use of the creative process of analogical reasoning. Once explanations are derived via analogical reasoning, controlled experiments may be used to test those explanations. Preferred response =1.]

3.

A hypothesis is an educated guess of what will be observed under certain conditions. [In the context of the methods course, a hypothesis was defined as a tentative explanation for some puzzling phenomenon, i.e., a proposed cause. One can certainly observe the puzzling phenomenon, but typically one does not observe its cause. For example, water rises when a cylinder is inverted over a burning candle sitting in a pan of water. This phenomenon is puzzling and can be observed. However, one cannot observe the cause of the water rise, which presumably is due to molecules of hot air escaping from the cylinder and the external air's relatively greater density and pressure pushing on the external water's surface. Preferred response =1.]

4. A conclusion is a statement of what was observed in statement number 3 above. [A conclusion was defined in the course as a statement regarding the relative support or lack of support for a tested hypothesis or theory. For example, suppose one advances the hypothesis that water rises in the inverted cylinder mentioned above because is created by combustion and this newly created dissolves more rapidly in water than the original To test this hypothesis one could compare the amount of water rise in two containers. One container would contain saturated water while the other would contain normal water. The hypothesis leads to the prediction that the water should rise higher in the container with normal water because the excess would dissolve in this water but would be "blocked" by the saturated water in the other container. When the experiment is conducted, we find that the water rises to the same level in both containers. This result does not support the initial hypothesis. Therefore, the conclusion would be that the dissolving hypothesis was not supported. In other words, one observes puzzling phenomena and one observes experimental results, but one does not observe hypotheses and conclusions. Preferred response = 1.]

5. Hypotheses/theories cannot be proved to be true beyond any doubt [Because any two hypotheses or theoretical claims may lead to the same predicted result, eventual observation of that predicted result cannot reveal which hypothesis or theoretical claim is correct. For this reason, supportive evidence cannot prove a hypothesis or theory correct. Preferred response = 5.]

6. Hypotheses/theories can be disproved beyond any doubt. [Contradictory evidence can arise due to an incorrect hypothesis/theory or to a faulty test (e.g., one in which all other variables were not held constant). Further, because it is not possible to be certain that all other variables were in fact held constant, contradictory evidence cannot disprove a hypothesis or theory. Preferred response = 1.]

7. To be scientific, a hypothesis must be testable. [As discussed in Item 8 below, hypothesis testing requires the generation of a prediction and a comparison of predicted and observed results. A good match supports the hypothesis. However, a mismatch between predicted and observed results contradicts the hypothesis and may lead to its rejection. Explanations that rely on supernatural powers, such as those of a God, may lie beyond the

216

CHAPTER 10

scope of science. Such explanations become un-testable when the supernatural entity becomes so powerful that it can do anything hence predict everything. An explanation that predicts everything becomes un-testable because there is no observation that could contradict a prediction. Preferred response = 5.]

8. To be tested, a hypothesis must lead to a prediction. [Hypothesis testing requires the generation of a prediction and a comparison of the predicted result with the observed result. The prediction may be of the classic sort generated in controlled experimentation. For example: If...water rises in the inverted cylinder because oxygen has been consumed (hypothesis), and...water rise with one, two, and three candles is measured while holding all other variables constant (controlled planned experiment), then...the height of water rise should be the same regardless of the number of burning candles (prediction). The prediction may involve circumstantial evidence. For example: If...O. J. Simpson killed Nichol Brown Simpson (hypothesis), and...a sample of the blood found in O.J.'s Ford Bronco is compared with a sample of Nichol's blood (planned test), then...the two blood samples should match (prediction). Or the prediction may involve correlational evidence. For example: If...breast implants cause connective tissue disease (hypothesis), and...the incidence of connective tissue disease in a sample of women with implants is compared to the disease incidence in a matched sample of women without implant (planned test), then...the disease incidence should be higher in the implant group than in the non-implant group (prediction). Descriptive (i.e., generalizing hypotheses) also require predictions for their test. For example, suppose one generates the descriptive hypothesis that all swans are white. Testing this hypothesis requires the following reasoning and resulting prediction: If...all swans are white, and...I observe several additional swans (planned test), then...they should all be white (prediction). Thus, regardless of the type of hypothesis being tested and type of evidence collected, hypothesis testing requires the generation of one or more predictions. Preferred response = 5.] 9. A hypothesis that gains support becomes a theory. [Like hypotheses, theories are explanations of nature. Hypotheses attempt to explain a specific observation, or a group of closely related observations. Theories attempt to explain broad classes of related observations, hence tend to be more general, more complex, and more abstract than hypotheses. Consequently, a hypothesis, regardless of the amount of support that may be obtained, does not become a theory. Preferred response = 1.] 10. A theory that gains support becomes a law. [Tested and accepted generalizations (i.e., laws) describe nature in terms of identifiable patterns (e.g., F = ma, more candles make more water rise, the sun rises in the east and sets in the west). Explanations (both hypotheses and theories) attempt to provide causes for such patterns. Regardless of the amount of support that an explanation may obtain, that explanation does not become description. Hence, theories do not become laws. Preferred response = 1.] 11. Truth is attainable via proof through repeated supporting observations. [As mentioned in items 5 and 6 above, proof and disproof are not possible. Hence the attainment of Truth in any ultimate sense is also not possible regardless of the number of times a supporting observation may be made. Preferred response = 1.] 12. The central goal of science is to discover facts about nature. [As mentioned in item 1, the central goal of science is to explain natural phenomena, not discover facts. Given that proof and disproof are not possible, the discovery of "facts" (i.e., certainties) is not even possible. Preferred response = 1.]

REJECTING NATURE OF SCIENCE MISCONCEPTIONS

217

13. Scientific statements that are just a theory are of little value. [Scientific theories (i.e., explanations for broad classes of related phenomena) are of considerable value. Non-tested theories guide research. Tested and accepted theories provide conceptual coherence and may lead to useful applications. Preferred response = 1.]

3.4 NOS Instruction: The Methods Course

The methods course is part of the university's teacher preparation program. Generally, preservice teachers take the course the semester prior to student teaching. The course emphasizes inquiry methods, thus is neither a lecture nor a lab course in the traditional sense. Rather, the lab is used to provoke initial explorations, which are followed by the introduction and explication of related terms, which are then followed by application/extension activities. In other words, the course utilizes the learning cycle teaching method (e.g., Biological Science Curriculum Studies, 1992; Karplus, 1974; Karplus & Thier, 1967; Kral, 1997; Lawson, Abraham, & Renner, 1989; Marek & Cavallo, 1997; Science Curriculum Improvement Study, 1970). The first half of the course is designed with the explicit goal of teaching the NOS elements listed in Table 2. The elements are based in large part on the theory of scientific method introduced in Chapter 9. During the second half, students attempt to apply this understanding to the design and delivery of inquiry lessons. The course begins with a series of inquiries in which students generate and test hypotheses/theories involving unobservable entities and/or processes. In this sense, the course attempts to teach the nature of science by doing science. However, while doing science, historical examples and key elements of the scientific process are explicitly discussed so that attention is repeatedly focused on those elements (i.e., on specific scientific questions, on hypotheses/theories, on their tests, and on conclusions). In this sense, the course employs what Bell, Lederman & Abd-ElKhalick (1998) and Abd-El-Khalick (1999) call an explicit approach to NOS instruction.

1.

2.

Science is a human activity that attempts to explain nature by raising and answering causal questions. Science consists of its methods plus the explanations and descriptions that have been obtained. Basic to doing science is the generation and test of alternative explanations. A creative process, sometimes called analogical reasoning, is used to generate explanations. The initial generation of several alternatives reduces bias because they make it less likely to become overly committed to any specific explanation. Tentative explanations are tested by use of an If/then/Therefore reasoning pattern. A test begins by supposing that the explanation under consideration is true and by

218

CHAPTER 10

imagining some test condition(s) that allows the derivation of one or more predictions. Data (observed results) are then gathered and compared with the predictions. A good match provides support for the explanation, while a poor match contradicts the explanation and may lead to its rejection. 3. Proposed generalizations (i.e., descriptive hypotheses) and proposed explanations are both tested by use of the If/then/Therefore reasoning pattern. However accepted generalizations (sometimes called laws) describe nature in terms of identifiable patterns (e.g., more candles make more water rise, the sun rises in the east and sets in the west), while explanations (both hypotheses and theories) attempt to provide causes for such patterns. 4. People do science to find causes. People want to know the causes of things to satisfy their curiosity - basic research - or so that their new knowledge can be put to practical use - applied research. 5. Like hypotheses, theories are explanations of nature. But while hypotheses attempt to explain a specific observation, or a group of closely related observations, theories attempt to explain broad classes of related observations, hence tend to be more general, more complex, and more abstract. 6. Theory testing, like hypothesis testing, involves use of If/then/Therefore reasoning. But because of the additional complexity, theories can seldom be tested in their entirety. Rather, they most often are tested component by component. Further, because of the additional abstractness, theory testing often requires the inclusion of a theoretical rationale, which links abstract non-observable (i.e., theoretical) causal agents with observable experimental manipulations (independent variables). 7. Theory testing may be further complicated when an advocate of a contradicted theory decides to modify, rather than reject, the theory. The modification may involve a change in a basic component, or the addition of new components. Modifications are intended to keep the theory consistent with the evidence. Nevertheless, theories that meet with repeated contradiction are generally replaced, particularly when a reasonable non-contradicted alternative exists. 8. Although it is common practice to speak as though entities such as oxygen and carbon dioxide have been "discovered" in a manner similar to the way someone discovers a lost treasure, this practice is misleading. Instead, entities such as oxygen and carbon dioxide, like the vital force and phlogiston, can be better understood as conceptual inventions, albeit conceptual inventions that have been so thoroughly tested that their existence is no longer in question. 9. Because any two hypotheses or theoretical claims may lead to the same predicted result, eventual observation of that predicted result can not tell you which hypothesis or theoretical claim is correct. For this reason, supportive evidence cannot prove a hypothesis or theory correct. 10. Contradictory evidence can arise due either to an incorrect hypothesis/theory or to a faulty test (e.g., one in which not all other variables were held constant). Further, because it is not possible to be certain that all other variables were in fact held constant, contradictory evidence cannot disprove a hypothesis or theory. 11. Science and religion are fundamentally different "ways of knowing." Science asks one to generate alternative explanations and then consult nature as a way of testing the alternatives. Scientific conclusions, which must remain somewhat tentative, come at the end of the process. On the other hand, religion asks that one accept a particular explanation at the outset based on faith. Religious knowledge is considered absolute and nature need not be consulted as a way of testing.

REJECTING NATURE OF SCIENCE MISCONCEPTIONS

219

A Sample Lesson. To obtain a better sense of how NOS instruction proceeded, consider the initial inquiry lesson based on materials contained in Gases and Airs (Elementary Science Study, 1974; also see Peckham, 1993; and Lawson, 1999). The lesson began with students working in teams of two. Each team set a burning candle upright in a pan of water using a small piece of clay. A cylinder was then inverted over the burning candle and placed in the water. Shortly after, the candle flame went out and water rose in the cylinder. These puzzling observations raised two major causal questions: Why did the flame go out? And why did the water rise? Students answered the first question by assuming that the flame reduced the amount of oxygen in the cylinder until too little remained to sustain combustion, thus the flame died. This assumption was not challenged, so the class moved on to the second question to which several explanations were collectively generated. Once explanations had been generated and listed on the board, the instructor asked students to label the list. In other words, what in the students' opinion should this list of possible explanations be called? After a brief discussion, students agreed that they were hypotheses - to which the instructor then offered a definition of the term hypothesis as follows: A hypothesis is a possible explanation, a possible cause, of a specific puzzling observation. Students were then asked to reflect on where their hypotheses had come from. When students replied that they had been generated from past experiences that were seen as somehow similar/analogous to the present situation, the phrase analogical reasoning was introduced and defined as the creative process of hypothesis generation in which causal entities and/or processes that have been found to act in past similar situations are borrowed and used as possible casual agents in the present situation. Students were also explicitly told that this view of hypothesis generation is contrary to the view that hypothesis generation involves closer observation of the phenomena that provoked the causal question(s), i.e., the water rising in the cylinder. In other words, observations may provoke causal questions but they are not the source of hypotheses, instead hypotheses come from prior knowledge (see Table 2 Element 2). Students were then told that their next task was to test the alternative hypotheses (i.e., explanations) using If/and/then reasoning to derive one or more specific expected results (i.e., predictions). For example, the following hypothetico-predictive argument generates different expected results from two alternative explanations: If...water is sucked up because oxygen is consumed, (consumed-oxygen hypothesis) and...water rise with one, two, and three candles is measured, (planned test) then...the height of water rise should be the same regardless of the number of burning candles. (prediction) This result is predicted because there is only so much oxygen in the cylinder. So more candles will burn up the oxygen faster; but they will not burn up more oxygen. (theoretical rationale) On the other hand,

220

CHAPTER 10

If...the water rises because some air in the cylinder was heated, expanded, some escaped, and the remainder then cooled and contracted, (air-expansion-and-escape hypothesis) then...more candles should cause more water to rise because more candles will heat more air, thus more will escape, which in turn will be replaced by more water when the remaining air cools and contracts. (prediction) Once derived in this fashion, the expected results were called predictions. Several examples were provided to explicate the difference between a hypothesis (i.e., a tentative explanation) and a prediction (i.e., a derived consequence of a hypothesis and its planned test). As mentioned, in addition to several lessons in which the hypothetico-predictive reasoning pattern was used to test hypotheses, the course introduced examples from the history of science and from contemporary science to illustrate the other NOS elements listed in Table 2. For example, Element 9 states that supportive evidence cannot prove that a hypothesis or theory is true. As discussed in Chapter 9, the belief that science can prove knowledge claims true is incorrect because science tests knowledge claims (i.e., hypotheses/theories) by setting up If/and/then arguments and then by comparing predictions with observed results. If the predicted and observed results match, then support, but not proof, has been found. Proof is not possible because two or more knowledge claims may lead to the same prediction. And because knowledge claims are the product of human imagination, they are potentially unlimited in number. Therefore, finding support for one claim does not prove that claim or rule out other possible claims. This point was made to students using a number of examples including the following: Suppose you notice that the sun crosses the sky from east to west and ask, why? In response to this causal question, you generate the hypothesis that it does so because the sun orbits a stationary earth. How could this stationary-earth hypothesis be tested? Consider the following argument: If...the sun crosses the sky from east to west because it orbits a stationary earth, (stationary-earth hypothesis) and...we remain in one spot and plot the sun's movements over the next five days, (planned test) then...each day it should rise in the east, cross the sky and set in the west. (prediction) And...sure enough, when the observations are made during the next five days, the sun does just that. (observed result) Therefore...the prediction and observed results match, so the stationary- earth hypothesis has been supported. But it has not been proven true because an alternative hypothesis might lead to the same prediction. For example,

REJECTING NATURE OF SCIENCE MISCONCEPTIONS

221

if...the sun remains stationary while the earth rotates on an axis from west to east, (rotating-earth hypothesis) and...we conduct the same test, (planned test) then...each day the sun should rise in the east, cross the sky and set in the west. (prediction) Note how these examples presumably require students to assimilate and use hypothetico-predictive arguments. Note also that the hypotheses being tested are about entities and processes that cannot be directly observed (i.e., burned up molecules and a rotating earth). Would a student who initially does not understand the difference between a hypothesis and a prediction, or one who believes that hypotheses are derived directly from observations (rather than from analogies), or one who believes that scientific knowledge claims can be proven true, be convinced otherwise by participating in such inquiries and by being provided such examples? According to the present hypothesis, the answer is yes, but only if that student has previously developed Stage 5 reasoning skill. Otherwise, the arguments will "fall on deaf ears." In other words, the present hypothesis is that many of the other NOS elements listed in Table 2 are at a similarly abstract level, thus also require Stage 5 reasoning skill for understanding. 4. RESULTS AND DISCUSSION

4.1 Reasoning Skill Level

Scores on the measure of reasoning skill ranged from 4 to 11 (mean score = 8.05, SD = 2.2). Based on individual scores, four students were classified at Level 3, three students were classified at Low Level 4,11 students were classified at High Level 4, and five students were classified at Level 5. 4.2 Pre and Posttest NOS Scores

NOS scores on the pretest ranged from 18 to 35 (mean = 23.9, SD = 4.2). Posttest scores ranged from 24 to 50 (mean = 39.4, SD = 6.3). A dependent T-test revealed that the posttest scores were significantly higher than pretest scores (T = 42.4, df = 22, p< 0.001). Table 3 shows the percentage of students responding in each answer category on both the pre and posttest. The table reveals that some NOS misconceptions remained for some students. For example, the percentage of students who agreed with Item 3: A hypothesis is an educated guess of what will be observed under certain conditions, dropped considerably from the pre to posttest (95% to 22%). In spite of this positive shift, 22% of the students still confused hypotheses with predictions. In other words, it would seem that these students failed to

CHAPTER 10

222

understand that a prediction, not a hypothesis, is an educated guess of what will be observed under certain conditions. Similarly, 30% of the students still agreed with Item 6: Hypotheses/theories can be disproved beyond any doubt. And in spite of the fact that the course included several examples in which hypotheses and theories were distinguished by differences in generality, complexity and abstractness, rather than by degree of support, 35% of the students still agreed with Item 9: A hypothesis that gains support becomes a theory. To summarize, it seems that although significant gains in NOS understanding were made, misconceptions remained for a number of students. 4.3 Relationship Between Reasoning Skill Level and Posttest NOS Performance Figure 1 shows percent success on the NOS pretest and posttest for students at each reasoning skill level. As shown, students at all four levels performed poorly on the pretest. No relationship between reasoning skill level and pretest NOS performance is apparent. However, the posttest results revealed substantial NOS gains as well as the predicted positive relationship between reasoning skill level and NOS performance (i.e., Level 3 = 30.8%; Low Level 4 = 51.3%; High Level 4 = 68.8%; Level 5 = 83.1%). These group differences were statistically significant p < 0.01). Therefore, this result provides support for the hypothesis that Stage 5 reasoning skill facilitates the rejection of NOS misconceptions and the construction of NOS understanding. The result also supports the view that developmental advances in reasoning skill beyond Piaget's formal stage occur, at least among some students. 5.

CONCLUSIONS AND INSTRUCTIONAL IMPLICATIONS

Preservice biology teachers who enrolled in the present methods course did so with several NOS misconceptions. This came as no surprise given that 1) previous studies have found similar misconceptions (e.g., Lederman, 1992; Lederman, Wade,

REJECTING NATURE OF SCIENCE MISCONCEPTIONS

223

224

CHAPTER 10

& Bell, 1998; McComas, Clough & Almazora, 1998), 2) biology instructors typically spend little time explicating the nature of science (personal observation), and 3) many biology texts contain several NOS misconceptions (e.g., Gibbs & Lawson, 1992). However, the present methods course, with its emphasis on inquiry and its explicit approach to teaching the nature of science, produced substantial pre to posttest NOS gains. Importantly, the size of these gains was related to students' level of hypothetico-predictive reasoning skill. This finding provides support for the hypothesis that Stage 5 reasoning skill, defined as skill needed to test alternative hypotheses involving unobservable theoretical entities, exists and helps students gain NOS understanding, presumably by enabling them to reason through arguments and evidence for and against alternative NOS conceptions, and eventually reject those that are inconsistent with that evidence. If future studies corroborate the existence of a fifth stage of intellectual development as well as this view of the acquisition/construction of NOS understanding, then it will follow that, in addition to attempting to improve NOS understanding, teacher preparation programs (particularly the science and mathematics courses in those programs) should spend increased effort in developing Stage 5 reasoning skill. If preservice teachers graduate without Stage 5 reasoning skill, it seems likely that they will be find it difficult to teach modern science as a process of creative and critical inquiry.

CHAPTER 11

IMPLICATIONS FOR THE NATURE OF KNOWLEDGE AND INSTRUCTION

1. INTRODUCTION Previous chapters have painted learning in terms of cycles of hypotheticopredictive reasoning. Apparently learning all the way from the sensory-motor behaviors of infants to the novel discoveries of scientists occurs in a hypotheticopredictive fashion because this is how the brain has evolved to process information. Piaget used the phrase self-regulation (equilibration) to refer to the process on the psychological level. Thanks to Steven Grossberg and his theory of adaptive resonance, we now have a neurological account of self-regulation. And thanks to Grossberg's learning equation, we can understand why a teaching approach that allows students to explore nature, to discover what they do not know, and to eventually make connections with what they do know (often using analogies), makes learning more motivating, easier, better understood, longer lasting and more transferable. Neurologically speaking, when new input contradicts predictions (i.e., when an adaptive resonance is not found), arousal is turned on and an internally driven search for a match begins. In short, disequilibrium is motivating. Further, when the new input finally meets internal neural activity from prior learning (i.e., when both pre and postsynaptic neurons are active), new synaptic connections are made, connections that are in turn connected with prior connections. Thus, just as a folder filed in the correct cabinet with several cross references can be more easily found and used than one piled randomly on a shelf, so too can such new connected learning. Outstars, introduced in Chapter 5, also have extremely important consequences for instruction. As you recall, outstars are responsible for chunking (i.e., for concept formation). As we have seen, neurons exist in distinct layers in the brain with outstars of a "higher" layer sending axons down into a "lower" layer. In turn, the neurons of the "lower" layer send axons down into a still "lower" layer, and so on. Thus, we have a hierarchical neurological structure isomorphic with, and likely responsible for, our conceptual hierarchies. In other words, we construct and store our conceptual knowledge in hierarchical systems presumably because the very neurons that store those concepts are arranged hierarchically (cf., Gazzaniga, Ivry & Mangun, 1998, pp. 167-169). Outstars might also be responsible for If/and/then thinking. The general rationale for this hypothesis goes like this: Due to past hypothetico-predictive learning, you 225

226

CHAPTER 11

already have a layer of outstars that have chunked your concept of an elephant. Suppose you now see a big, gray, floppy ear. The activity pattern provoked by this input fires neurons on successively higher more inclusive layers until the pattern fires your ensemble of outstars that collectively represent an elephant. Thus, thanks to observation of the big, gray, floppy ear, your "elephant" outstars are activated. Thus, you suspect that you are looking at part of an elephant, i.e., your mind subconsciously generates the descriptive elephant hypothesis. Next, due to prior connections of the elephant outstars with other elephant features (in lower slabs), activation of the higher-slab elephant outstars in turn actives lower-slab features such as a hose-like trunk feature, a string-like tail feature, a stump-like leg feature, and so on. In this way, activation of the elephant outstars carries with it specific expectations as well as the following If/and/then argument: If...I really am looking at an elephant ear, (descriptive hypothesis) and...I shift my attention forward, (behavioral test) then...I should see a hose-like trunk. (prediction) Once this prediction has been activated in a lower slab, working memory in the prefrontal cortex can now direct an attention shift forward and allow new input to be processed. If that new input matches the prediction, then you have support for the elephant hypothesis: And... I do see a hose-like truck. (observed result) Therefore...I probably am looking at an elephant. (conclusion) Thanks to the Levine and Pruiett model introduced in Chapter 3, we also have a neurological explanation for why conceptual change can be so difficult. Not only does conceptual change often involve constructing new mental representations (i.e., forming new outstars), it also requires overcoming previously acquired neural biases. On the psychological level, conceptual change involves not only what has been called "representing ability," but it also involves "inhibiting ability." Thus, for conceptual change, we need to "represent" new conceptions and "inhibit" old misconceptions. Lastly, as Piaget claimed, we have found that intellectual development is partially dependent on neurological maturation and is stage-like in the sense that sensorymotor learning precedes linguistic learning, which precedes categorical learning, which precedes causal learning. But unlike Piaget, we have found considerable evidence for what has been called "stage retardation" (i.e., adolescents and adults functioning at lower levels than their age would suggest) and for the existence of a fifth stage, a stage that appears necessary for understanding and doing modern science, and importantly for teaching science in the investigative way advocated by current reform documents.

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

227

Because procedural knowledge structures play a crucial role in learning and because the experiences of many students have failed to provoke the development of fourth and fifth-stage reasoning skills, teachers need to select, sequence and teach the subject matter in ways that provoke the development of more advanced reasoning skills. Before providing examples of instruction that can provoke the development of reasoning skill, thus insure that stage retardation does not occur, let's consider the implications of the present hypothetico-predictive account of brain functioning and learning for some of the alternative brands of constructivism currently found in the literature. 2.

IMPLICATIONS FOR ALTERNATIVE BRANDS OF CONSTRUCTIVISM

Much recent debate has centered on the relative merits of alternative constructivist positions of knowledge acquisition and epistemology. For example, Staver (1998) in staking out an extreme version of constructivism for education wrote: "For constructivists, observations, objects, events, data, laws, and theory do not exist independent of observers. The lawful and certain nature of natural phenomena are [sic] properties of us, those who describe, not of nature, what is described. ...constructivists begin this work without first assuming an independent reality" (p. 503). And Driver, Asoko, Leach, Mortimer & Scott (1994) emphasized the social aspect of constructivism when they stated: "...scientific knowledge is symbolic in nature and socially negotiated. The objects of science are not the phenomena of nature but constructs that are advanced by the scientific community to interpret nature" (p. 5). Lastly, Fosnot (1996) described a theory of constructivism that "...describes knowledge as temporary, developmental, nonobjective, internally constructed, and socially and culturally mediated" (p. ix). Realism stands in contrast to these constructivist views. Hwang (1996) defines a realist as one who believes that: "...the world exists and is organized independent of us, our language, and our methods of inquiry" (p. 345). Realist critics of constructivism, such as Matthews (1994), have argued: "For all its faults, the scientific tradition has prompted rationality, critical thinking and objectivity. It instills a concern for evidence, and for having ideas judged not by personal or social interest, but by how the world is" (p. 2.). In a similar vein, Osborne (1996) concluded: "This [social constructivism] has led to the portrayal of science as a process of constructing and manipulating representations which bear no necessary relation to any ontological reality. In so doing constructivists have forgotten that it is the world that imposes constraints on human thought, and not human thought that imposes constraints on the world" (pp. 76-77). More recently, Matthews (1998) summarized several key differences between realist and constructivist beliefs as follows: Realists believe that science aims to tell us about reality, not about our experiences; that is knowledge claims are evaluated by reference to the world, not by reference to their

228

CHAPTER 11

personal, social, or national utility; that scientific methodology is normative, and consequently distinctions can be made between good and bad science; that science is objective in the sense of being different from personal, inner experience; that science tries to identify and minimize the impact of non-cognitive interests (political, religious, gender, class) in its development; that decision making in science has a central cognitive element and is not reducible to mere sociological considerations, and so on. (p. 166)

The hypothetico-predictive theory of brain function and learning presented in this book implies a theoretical resolution to the debate between these sorts of constructivist and realist positions. The present position is that focusing on knowledge acquisition in terms of the underlying learning pattern will help resolve the debate. In other words, understanding how humans acquire knowledge informs us about the nature of the knowledge acquired.

2.1 Does the External World Really Exist? First, it should be emphasized that learning is a hypothesis generation and testing enterprise where the term hypothesis is defined in its broadest sense, i.e., any statement under test, no matter whether it purports to describe some particular fact or event or to express a general law or some other more complex causal proposition. Importantly, in order to test any and all such hypotheses, each hypothesis must initially be taken to be true.1 This may seem backwards. But according to previous examples, this is the way learning occurs. Importantly, hypotheses include entities such as ghosts, photons, vital forces and phlogiston. This means that we have to suppose that these entities exist so that test conditions can be imagined and predictions can be drawn. In the end we may decide that the entities do not exist. But to arrive at this conclusion, we first had to assume that they do exist! To further clarify this point, briefly consider the Needham-Spallanzani controversy over the existence of the vital force. As you may recall, during the 1700s, John Needham, among others, believed that living things possessed a special vital force. Further, when this force entered dead material it would spontaneously give it life. But Lazzaro Spallanzani thought otherwise. Nevertheless, to test Needham's vital force idea, Spallanzani had to assume that the vital force existed so that he could reason in a hypothetico-predictive way something like this: If...the vital force exists and acts on nonliving matter to bring it to life, (vital-force hypothesis) 1 As discussed below (see Concluding Remarks), I am not talking here about the statistical practice of initiating research by stating a "null hypothesis." The statistician's null hypothesis is not a hypothesis at all. Rather it is a prediction, more correctly, it is a null prediction (e.g., no significant difference will be found in student performance after two different instructional treatments). In my view, calling a null prediction a null hypothesis is not only confusing it does not serve its purported purpose of making the researcher less biased. In my view, the route to less biased research is to start with alternative hypotheses (cf., Chamberlain, 1965) - not with a confusing linguistic convention.

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

229

and...some bottles are heated for a few minutes and others for an hour, and some are corked and others sealed with a flame, (Spallanzani's planned test) then...after several days, microbes should be found in all the bottles. (prediction) All bottles should contain microbes because the vital force should act regardless of length of bottle heating or method of sealing. (theoretical rationale) But...days later after conducting his experiment, all of the corked bottles were full of microbes. The sealed bottles boiled only a short time were also teaming with microbes. However, no microbes were in the bottles boiled for an hour and then sealed. (observed results) Therefore...Spallanzani concluded that Needham's vital force does not exist. (conclusion)2 The key point is that entities such as the vital force, epicycles, heavy water, and N rays must be assumed to exist in order to test their existence and to possibly conclude that they do not exist after all. Awareness of this aspect of the knowledge acquisition process is extremely important because it allows us to set aside the debate about the existence or non-existence of the external world. In short, the debate is not settled by concluding that the external world exists independent of an observer (the realist position). Rather the debate is set aside by the realization that to learn at higher levels, the learner must assume the external world's independent existence, regardless of whether it actually exists or not. Thus, contrary to the constructivist position advanced by Staver (1998, p. 503) in which "...constructivists begin this work without first assuming an independent reality," to learn at higher levels one must begin by assuming that the external world exists (and that it is knowable). In fact, this proposition and its alternative (i.e., the external world does not exist unless it is in direct view) has already been generated and tested by every single child during their sensory-motor stage of development. Thus as a scientist, if you fail to make the initial assumption that the external world exists you get nowhere. Worse yet, if you refuse to assume the independent existence of the external world, in spite of your sensory-motor knowledge that is telling you otherwise, you could suffer some unfortunate consequences. Suppose, for example, you find yourself in the middle of a freeway staring down an oncoming car and fail to make the assumption. If you do, you will likely end up dead. Clearly it pays to assume that the oncoming car exists, even though we cannot be certain that it does. But where does a scientist arrive if s/he assumes that the external world exists and is knowable? The answer turns out to be somewhere short of absolute Truth (for the reasons stated previously), but certainly closer to developing workable mental representations of that assumed-to-exist external world than extreme social constructivists would have us believe. This is because, in addition to our ability to argue the merits and demerits of our various representations with others, we have our assumed-to-exist external world against which we can test our representations, i.e., 2 Of course we would conclude that the vital-force hypothesis was not supported.

230

CHAPTER 11

our hypotheses and theories. Thus, the issue amounts to whether or not science makes progress.3 The answer is that it does, but that progress is by no means without fits and starts and some backtracking. Convincing evidence for scientific progress surrounds us everywhere from computers that run on electrons, to cars and airplanes that run on exploding fossil fuels, to doctors that save lives each day with prescriptions of antibiotics, not to mention satellites that orbit the earth, and space ships that have gone to the moon and back. To deny that these technological advances rest on sound scientific theory is nonsense. An additional point should be made. It makes sense to refer to the initial mental representations as constructions because they are not directly "given" in the context of current learning experiences. Instead, mental representations are either culled from past experiences stored in long-term memory or are "constructed" from basic sensory input. For example, neurological research previously reviewed (e.g., Kosslyn & Koenig, 1995; Mishkin and Appenzeller, 1987) makes it clear, at least with respect to vision, complex mental representations do not arise from direct sensory input. Rather, as shown in Figure 1, visual sensory input is processed along two separate pathways that result in progressively more complex mental "constructions." As shown, initial processing of visual input, which arrives from the retina by way of the lateral geniculate body, takes place in the striate cortex. Individual neurons in the striate cortex respond to simple elements in the visual field such as spots of color and edges. Visual processing continues along the lower pathway, which extends down toward the inferior temporal cortex. Along the way, a number of diverging and converging channels "construct" broader properties of objects, such as overall shape and color. At the lower end of the pathway neurons are sensitive to a variety of properties and a broad expanse of the visual field, which suggests that fully processed information about objects converge there. Also as shown in Figure 1, spatial relationships among two or more objects are processed along an upper cortical pathway.

2.2 A Further Thought on the Primacy of Physical Feedback Several years ago following administration of the task shown in Figure 2, two 13year-old boys were overheard arguing. The argument went something like this. First boy: I think the water will rise higher when the lead ball sinks because it's heavier than the aluminum one. Second boy: No, you are wrong! They will push the water up the same amount because both balls are the same size. Weight doesn't matter. First boy: Yes, weight matters. My brother is a lot heavier than I am and when he gets in the bathtub the water goes up a lot higher than when I get in!

3

Here the term progress is understood as science's ability to construct knowledge (i.e., mental representations) that generates predictions that better match observations.

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

231

How can this dispute be settled? How do these boys, or anyone for that matter, learn which variable, weight or volume, is key? It would seem that no amount of social negotiation suffices. Rather what needs to be done is to perform two simple experiments more or less as follows: If...the amount of water rise depends on an object's weight, (weight hypothesis) and...two objects of different weight, but equal volume, are submerged in water, (planned test) then...the heavier object should produce more water rise. (prediction) But...the heavier object does not produce more water rise. (result) Therefore...the weight hypothesis is not supported. (conclusion) On the other hand, if...the amount of water rise depends on an object's volume, (volume hypothesis) and...two objects of different volume, but equal weight, are submerged in water, (planned test) then...the larger object should produce more water rise. (prediction) And...the larger object does produce more water rise. (result) Therefore...the volume hypothesis is supported. (conclusion)

232

CHAPTER 11

Thus, physical feedback (i.e., the water rises the same in the first experiment and higher in the second) is the primary vehicle for resolving disputes about alternative knowledge claims. The primacy of physical feedback in knowledge acquisition is at odds with social constructivism in which, according to Latour & Woolgar (1979; 1986), success depends on a theory's proponents ability to 'extract compliance' from others (cf., Slezak, 1994a; 1994b). This is not to say that social interaction may not be helpful. But it cannot be the central means of knowledge acquisition. In fact, as Gardner (1994) points out, the acquisition of new knowledge is typically associated with distinctly asocial behavior. Based on detailed case studies of seven highly creative people, Gardner concludes, "...at the time of greatest breakthrough, our creators were in one sense very much alone. Often they had physically withdrawn from other individuals" (p. 154). In reviewing several decades of research on the nature and measurement of creativity, Eysenck (1994) makes much the same point when he lists several characteristics associated with creative people such as quarrelsomeness, lack of sociability and even outright hostility. As mentioned, this is not to argue that social interaction cannot be helpful. It can be helpful in many ways (e.g., in sharing and clarifying problems, in suggesting alternative hypotheses, in suggesting possible test conditions, in criticizing conducted tests, in collecting and analyzing results). But in the end, feedback from the physical world is the ultimate arbitrator of which knowledge claims are accepted or rejected.

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

233

3. THE EXISTENCE OF STAGES IN INTELLECTUAL DEVELOPMENT

As mentioned, the present view of learning and development implies the existence of developmental stages - although not necessarily discontinuous stages and not necessarily as theoretically characterized by Piaget. Initially, sensed colors, lines, and angles and the child's ability to create "undifferentiated wholes" provide the mental representations that are either rejected or retained by virtue of their ability to produce predictions that are either met or unmet in a world of sensory-motor feedback (e.g., lifting the cover either does or does not reveal the ball, sucking on the bottle either does or does not produce milk). Once such testing has created a stable world of interacting objects, these objects, their characteristics, and their behaviors can then be used to test the validity of mental representations at higher stages. In other words, intellectual development is a process in which the products of one stage must be largely in place before progress can be made on subsequent stages because prior constructions are used to test subsequent higher-order representations. For example, John Dalton compared predicted and observed outcomes regarding the measurable weights of gases to test the hypothesis that unobservable atoms exist. Gregor Mendel compared predicted and observed outcomes regarding the ratios of observable pea plant characteristics to test the hypothesis that unobservable genes (he called them "factors") exist. And as we have seen, Lazzaro Spallanzani compared predicted and observed outcomes regarding the observable growth of microbes to test the hypothesis that an unobservable vital force exists. None of these tests could have been conducted had the scientists not previously constructed a sensory-motor world of interacting and observable objects during their early childhoods. More will be said about this below. A rudimentary form of hypothetico-predictive reasoning is present at birth. We can be fairly certain of this because the reasoning pattern can be found in nonhumans. For example, Hauser (2000) conducted a revealing experiment with rhesus monkeys. First, a monkey was shown an eggplant - a favorite food item. In full view, the eggplant was then placed behind a screen. A second eggplant was then placed behind the screen. Then when the screen was lifted, the length of time the monkey looked at the two revealed eggplants was measured, which turned out to be about one second. Next the conditions were changed. In the initial changed condition, one eggplant was placed behind the screen followed by a second eggplant. Then without the monkey knowing it, the second eggplant was removed. Now when the screen was lifted, the monkey looked at the unexpected one remaining eggplant for about three to four seconds. The same increase in looking time occurred when a third eggplant was secretly added and then revealed. Thus, the monkey had a clear expectation of seeing two eggplants and when either one or three eggplants showed up unexpectedly, the monkey was puzzled as evidenced by the increase in looking time. In the first unexpected condition, the monkey's hypothetico-predictive "reasoning" can be summarized like this:

234

CHAPTER 11

If...one eggplant is placed behind the screen, and...another is added, then...there should be two eggplants behind the screen (expected result prediction). But...there is only one eggplant (unexpected result). Therefore...I am puzzled and need to look at the puzzling situation longer. Given that this pattern of hypothetico-predictive in humans is present at birth, developmental changes involve changes in the contexts to which the reasoning pattern can be applied. Let's see how this might work in somewhat more detail in terms of stages that correspond in a general way to Piaget's well-known stages (e.g., Inhelder & Piaget, 1958; Piaget & Inhelder, 1969). 3.1 Stage 1: The Sensory-Motor Stage (birth to about 18 months)

Of course, children during the first 18 months of life do not generate verbal hypothetico-predictive arguments. Nevertheless, their overt behavior, like monkeys, suggests that their pre-verbal reasoning follows the hypothetico-predictive pattern. For example, Chapter 2 discussed the processing of both visual and auditory input in terms of the hypothetico-predictive pattern. Also consider Piaget's famous object permanence task in which an experimenter, in full view of the infant, hides a ball under one of two covers. Diamond (1990) has shown that infants as young as five months will reach under the cover for the hidden ball indicating that they retain a mental representation of the ball even though it is out of sight. Further, such behavior suggests that the infant is reasoning in the following way: If...the ball is still where he/she put it, even though I can no longer see it, (empirical representation) and...I reach under the cover where it was hidden, (behavioral test) then...I should find the ball. (prediction) And...I do find the ball. (result) Therefore...I have support for the hypothesis that the ball was still where she put it. (conclusion) In agreement with Meltzoff (1990), the infant's representation is called empirical because it is of an event that has been empirically experienced. That is, the infant actually saw the ball hidden under the cover. In Chapter 2, we also saw this pattern of information processing in Laurent's attempt to suck milk from his bottle: If...what I see is my bottle, (empirical representation) and...I lift and suck, (behavioral test) then...I should suck milk. (prediction)

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

235

But...I do not suck milk. Instead I am sucking glass! (result) Therefore...something is wrong, either with my initial idea (i.e., my hypothesis that I am seeing my bottle) or with my behavior. I cannot tell which. So I am frustrated. (conclusion) In short, the primary goal at this stage is to construct a stable world of interacting objects by generating and testing initially undifferentiated representations about that world in a hypothetico-predictive fashion and by comparing sensory-motor feedback with predictions. 3.2 Stage 2: The Preoperational or "Nominal" Stage (about 18 months to 7 years) The major achievement of Stage 2 is the acquisition of language and its use in naming the objects, events and situations constructed during Stage 1. For example, consider the following dialogue (from Gesell 1940, p. 55) between two children aged four and five: FourFiveFourFiveFourFive-

I know that Pontius Pilate is a tree. No. Pontius Pilate is not a tree at all. Yes. It was a tree, because it says, 'He suffered under a Pontius Pilate', so it must have been a tree. No. I am sure Pontius Pilate was a person and not a tree. I know he was a tree, because he suffered under a tree, a big tree. No. He was a person, but he was a very big person.

The question here is, what object(s) are the words "Pontius Pilate" supposed to label? The children have generated two conflicting nominal (naming) hypotheses. The first nominal hypothesis claims that the words "Pontius Pilate" are used to label a tree. The second claims that the words are used to label a person. Four's hypothetico-predictive argument in favor of the first hypothesis might go something like this: If...Pontius Pilate is a name for a tree, (tree hypothesis) and...we check the context in which the words "Pontius Pilate" are used, (test) then...we should find that people suffer under Pontius Pilate. (prediction) [Presumably the child has generated this prediction because his associative memory links the word "under" with the word "tree."] And...it says, 'He suffered under a Pontius Pilate'. (result) Therefore...Pontius Pilate must have been a tree. (conclusion) Notice that Five does not counter Four's argument with one of his own. He merely asserts that Pontius Pilate was not a tree. Instead he was a person. Nevertheless, Five does point out that Pontius Pilate was a very big person apparently one big enough to suffer under!

236

CHAPTER 11

3.3 Stage 3: The Concrete Operational or "Categorical" Stage (7 years to early adolescence) The acquisition of language to name objects, events and situations during Stage 2 now allows the child to apply hypothetico-predictive reasoning to a new level, the level of seriating and classifying, i.e., creating variables and higher-order classes/categories of unseen objects, events and situations. The observable and named objects of Stage 2, such as tables and chairs, become the un-observable categories, such as furniture, of Stage 3. As you recall from Chapter 3, a series of classification tasks, including the Mellinark Task, were administered to children ranging in age from 6 to 14 years. Carefully sequenced instruction was then used to teach the children how to use hypothetico-predictive reasoning to discover the relevant features, e.g., If...tiny spots make a creature a Mellinark, (descriptive hypothesis) and...I look at all of non-Mellinarks in row 2, (planned test) then...none of them should have tiny spots. (prediction) But...some do have tiny spots. (observed result) Therefore...tiny spots are not the key feature - or at least not the only key feature. (conclusion) As reported, none of the six-year-olds was able to generate and/or comprehend this sort of argument, whereas half of the seven-year-olds were, as were virtually all of the older children. As mentioned, the younger children's failure is most likely related to relatively late maturation of the frontal lobes. The present position is that Stage 3, which begins at age seven, involves use of the hypothetico-predictive pattern to seriate and to categorize the objects, events, and situations in the child's environment - all mediated by language. At this stage, descriptive hypotheses are tested by comparing predictions with prior Stage 2 constructions such as "spots," "tails," and "curvy sides." 3.4 Stage 4: The Formal Operational or "Hypothetical" Stage (middle to late adolescence) At roughly age 11-12 years, some adolescents become increasingly able to use language to apply hypothetico-predictive arguments to causal, rather than categorical/descriptive hypotheses. Consider once again the causal question, what causes differences in the rates at which pendulums swing? To answer this question, one must generate and test alternative causal hypotheses (cf., Inhelder and Piaget 1958):

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

237

If...changes in swing rates are caused by the amount of weight hanging on the end, (causal weight hypothesis) and...the weights are varied while holding other possible causes constant, (planned test) then...rate of pendulum swing should vary. (prediction) But...the rates do not vary. (observed result) Therefore...the weight hypothesis is not supported. (conclusion) Clearly the reasoning pattern is the same as in the prior three stages. Thus, again the difference between Stage 4 reasoning and prior Stage 3 reasoning is not the pattern. Instead, the difference is what the pattern can be applied to. Stage 3 reasoning is about testing descriptive hypotheses (descriptive/generalizing hypotheses). Stage 4 reasoning is about testing causal hypotheses. The Stage 4 causal test above involves an experiment in which the possible cause is manipulated. In other words, the proposed cause is the amount of weight and the experiment's independent variable is also the amount of weight. Importantly, this variable can be easily manipulated because weight differences can be sensed. 3.5 Stage 5: The Post-Formal or "Theoretical" Stage (late adolescence and early adulthood) Consider the Burning Candle Item introduced in Chapter 7. As you may recall, the central causal question in that context was: What caused the water to rise? Suppose a student generates the explanation that the water raised because the flame consumed the oxygen under the cylinder. Thus the resulting vacuum "sucked" the water up. This consumed-oxygen hypothesis can be tested using the following hypothetico-predictive argument: If...the water raised because the flame converts oxygen to carbon dioxide, which dissolves more easily the oxygen thus produces a partial vacuum, which in turn causes the water rise, (dissolving-carbon-dioxide hypothesis) and...the height of water rise in two containers is compared - one with saturated water and the other with normal water, (planned test) then...the water should rise higher in the container with normal water. (prediction) This result is predicted because the in the other container's water will block from dissolving, thus the partial vacuum will not be created and the water will not rise as high. (theoretical rationale/warrant) But...the water rises the same in both containers. (observed result) Therefore...the dissolving-carbon-dioxide hypothesis is not supported. (conclusion) Although once again identical to prior reasoning in form, this argument differs in at least two important ways. First, here the proposed cause is unseen (i.e.,

238

CHAPTER 11

theoretical). At Stage 4, the proposed cause was observable. And second, unlike Stage 4 reasoning where a proposed cause and the independent variable of an experiment designed to test it were one and the same, this is no longer the case. In the above experiment, the independent variable is the amount of carbon dioxide in the water, while the proposed cause is an unseen and theoretical partial vacuum presumably created by lack of carbon dioxide molecules. Because the proposed cause and the independent variable are not the same, a warrant (a theoretical rationale - a warrant) must be generated to link the two so that a reasonable test can be conducted. For these reasons, Stage 5 reasoning, called post-formal or theoretical, is more difficult than Stage 4 reasoning, and presumably not achieved until late adolescence, if at all (e.g., Chapters 7,8,10). 3.6 Why is Intellectual Development Stage-Like? Based on the previous section, we can understand why intellectual development is stage-like. In addition to probable maturational constraints (see Chapters 3 and 4), during each stage the individual constructs something new that can be constructed only following the previous stage because the products of that previous stage are used in testing the possible constructions (i.e., the hypotheses) of the subsequent stage. For example, suppose we generate the hypothesis that matter consists of tiny invisible and indivisible particles called atoms. Like John Dalton, we can use Stage 5 reasoning to test this atomic hypothesis as follows: If...matter consists of invisible/indivisible particles that have specific weights and combine with one another in specific ways, (atomic hypothesis) and...combinations of atoms (i.e., molecules) are decomposed into their parts, (planned test) then...the ratios of weights of those parts should be in simple whole number ratios. (prediction) And...the ratios of weights of those parts are in simple whole number ratios. (observed result) Therefore...the atomic hypothesis is supported. (conclusion) Notice that testing the atomic hypothesis requires that we compare predicted and observed weight ratios of decomposed molecules. As you may know, comparing ratios involves proportional reasoning, a Stage 4 construction. Thus, this Stage 5 construction (i.e., atoms) could not have taken place without the prior Stage 4 construction of proportions. Similarly, testing Stage 4 hypotheses requires use of prior Stage 3 constructions. Consider Inhelder and Piaget's bending rods task (Inhelder & Piaget 1958, Chapter 3). To test the Stage 4 causal hypothesis that variation in rod thickness causes

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

239

variation in amount of rod bend (i.e., thinner rods bend more than thicker rods), one would reason as follows: If...differences in rod bending is caused by rod thickness, (thickness hypothesis) and...equal weights are hung on two rods that vary only in thickness, (planned test) then...the thinner rod should bend more. (prediction) And...the thinner rod does bend more. (observed result) Therefore...the thickness hypothesis is supported. (conclusion) Thus, in this Stage 4 argument, to test the causal thickness hypothesis (one can directly observe/sense thickness differences), we must determine which of the two rods bends more and which bends less. In other words, we need to have already constructed a Stage 3 "distance" variable, which we can label as "distance of bending." So to test a Stage 4 hypothesis, we use a prior Stage 3 construction (i.e., conservation of distance/length). Likewise, testing Stage 3 descriptive hypotheses requires use of Stage 2 object-word constructs and testing Stage 2 linguistic hypotheses require use of Stage 1 object constructs. 4. HOW DOES INTELLECTUAL DEVELOPMENT OCCUR? How does procedural knowledge develop? Of course we have answered this question in a general way by agreeing with Piaget that intellectual development occurs through self-regulation, i.e., by engaging in cycles of hypothetico-predictive reasoning and by "internalizing" not only the products of that process but by internalizing (i.e., chunking, forming outstars) its procedures as well. This raises the question of just what provokes this internalization. According to Piaget (1976) a process he calls reflective abstraction is involved. Reflective abstraction progresses from the use of spontaneous actions to the use of explicit, verbally mediated, rules to guide behavior. Reflective abstraction occurs when the subject is prompted to reflect first on his/her actions and later on arguments with others. Thus, the cause of reflective abstraction is contradiction by the physical environment and verbally by other people, as was the case of the four-year-old who believed Pontius Pilate was a tree. The result of reflective abstraction is that the person gains declarative knowledge and also becomes more aware of and skilled in use of the procedures used in gaining that knowledge (i.e., the declarative knowledge gets chunked via outstars, and so do the procedures). This view of intellectual development helps clarify why "stage retardation" occurs, i.e., why some students fail to develop Stage 4 and perhaps Stage 5 reasoning skills. Suppose, for example, that many years ago two identical islands existed in the Pacific Ocean, each inhabited by 10,000 islanders, each isolated from the outside world, and each ruled by an all-powerful king. Whenever questions arose, the islanders asked their king for answers. Each king provided the answers and whatever

240

CHAPTER 11

each king said was considered true. But one day, a foreign ship arrived at one of the islands. Over time, a vigorous trading relationship was established between that island and several foreign countries. Importantly, not only did the ships bring many new goods, the sailors on them brought many new ideas. These ideas spread throughout the island's population. Some of these new ideas contradicted the "truths" previously handed down by the king. Soon the islanders began wondering which ideas were actually correct and more importantly, they began wondering how they could tell. Eventually, an upheaval took place in which the king was overthrown and replaced by a government run by the people. Several decades later, an anthropologist arrived on the island to study the island's culture. As part of her study, she administered a reasoning test to the island's teenagers and adults. Soon after, the anthropologist discovered the other island. She was the first "outsider" to discover this island, which was still controlled by an allpowerful, truth-dispensing king. She administered the reasoning test to the teenagers and adults on this island as well. Question: Which population of islanders do you think did better on the reasoning test? Which population had more Stage 4 and perhaps Stage 5 reasoners? Why? I hope you agree that the reasoning skills of the islanders on the first island should be better. Piaget would seem to be agreeing when he stated in 1928 that the development of advanced reasoning occurs as a consequence of "the shock of our thoughts coming into contact with others, which produces doubt and the desire to prove" (Piaget, 1962, p. 204). Piaget went on to state: The social need to share the thought of others and to communicate our own with success is at the root of our need for verification. ...argument is therefore, the backbone of verification. Logical reasoning is an argument which we have with ourselves, and which produces internally the features of a real argument. (p. 204)

In other words, the growing awareness of and ability to use internalized arguments to guide one's thinking and decision making occurs as a consequence of attempting to engage in arguments of the same sort with others in which alternative hypotheses are put forward and accepted or rejected as the basis of evidence and reason as opposed to authority or emotion. Clearly, if alternative ideas do not exist, then no external arguments ensue, and no internalization of patterns of argumentation results. This position seems consistent with that of Vygotsky (1962) who views speech as social in origin and only with time does it come to have self-directive properties that eventually result in internalized, self-directive, thought. Similarly, Luria (1961) proposed that the progressive differentiation of language to regulate behavior occurs in four steps. First, the child learns the meaning of words; second, language can serve to activate behavior but not limit it; third, language can control behavior through activation or inhibition via communication from an external source; and fourth, the internalization of language can serve a self-regulating function through instructions to oneself.

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

241

4.1 Developing the Procedure of Controlled Experimentation To obtain an understanding of how instruction can provoke the development of procedural knowledge, consider the procedure of controlled experimentation. Young children have little difficulty in determining when a previous test is "fair" or "not fair" when the variables concerned are familiar (Wollman, 1977). However, they lack a general plan of attack or general strategy to use in setting up "fair comparisons" ahead of time and in unfamiliar situations. In other words, after a test has been performed they may be able to state if it is fair or not. However, they are unable to use their intuition as a general guide to behavior. Where does their intuitive understanding come? Presumably it comes from situations in which children make comparisons and attempt to evaluate the validity of those comparisons. For example, suppose two children run a race. When the race is over and one child has lost, she blames the loss on the fact that she was wearing street shoes while her friend was wearing tennis shoes. So she claims that the race was not "fair." In other words, intuitions come from argumentation about the truth or falsity of statements (e.g., "I can run faster than you can." "No, you can't, I can run faster than you"). The point is this: from environmental encounters such as this, children develop intuitive understanding of procedures involving the control of variables, probabilities, proportion, etc. However, these intuitions have yet to be transformed into internally mediated learning and problem-solving procedures. Let's discuss how this can happen with respect to controlling variables. The discussion is based on an experiment (Lawson & Wollman, 1976) with 9- and 13-year-old children who were initially unable to control variables in a general sense. After four half-hour individual training sessions, these same children were clearly able to demonstrate skill in controlling variables systematically and, in most cases, unhesitatingly. Further, as evidence of general skill in using this procedure, their skill transferred to new tasks, both manipulative and pencil-paper. Session 1. The first session began by introducing the child to the intent and format of the training. S/he was told that a number of materials would be used to teach him/her how to perform "fair tests." The materials were familiar: three tennis balls (two relatively bouncy and one considerably less bouncy), two square pieces of cardboard, two square pieces of foam rubber and a table. The child was told that the first problem was to see which ball was the bounciest. To find out, s/he would instruct the experimenter what to do and the experimenter would carry out the instructions. Although each session varied somewhat, each child began by telling the experimenter to drop two balls to see which bounced higher (height of bounce then became the dependent variable). The experimenter would then drop two balls but drop them from different heights (an uncontrolled experiment). The child would then respond by saying: "That isn't fair. Drop them from the same height." On the next trial the height would be equalized, however, one ball was dropped so that it hit the table top, while the other hit the floor (again an uncontrolled experiment). This

242

CHAPTER 11

procedure was followed by continually intervening with new uncontrolled variables (spin one ball, push one ball, let one ball hit cardboard or foam rubber). Children were then given a verbal rule (i.e., a test is "fair" if all the factors, variables, that might make a difference were the same for both balls, except, of course, for the difference in the balls themselves). And each test in which these factors differed was called an "unfair test." Following introduction of this verbal rule, several additional examples were demonstrated and discussed. The overall intent of this first session was to allow each child to generate his/her own testing procedures, which were then contradicted. Presumably the contradictions forced the children to reflect on the inadequacies of their procedures. The verbal rule was then introduced in a context in which they could gain initial understanding. At the onset, virtually all children demonstrated an intuitive feel for fairness and responded by saying: drop them from the same height, make them both hit the floor, don't spin one, etc. Also following each test, they were able to accept or reject tests as fair or unfair. But importantly, none could state a general procedure for performing fair tests prior to the test itself (i.e., to perform a fair test, keep all the factors equal except the one being tested). Not even the most articulate children responded by telling the experimenter to have "everything the same" for both balls. Even when asked to summarize their instructions without mentioning specific factors, they were at a loss for words. This phenomenon seems very much like the experience of "knowing" something is true, but not being able to put it into words. Presumably, the extension of this intuitive understanding to the point where it can be expressed verbally and applied to monitor one's thinking constitutes the essence of "development" (i.e., construction of the relevant outstars). Session 2. The second session began by reminding the child of the intent of the training and by pointing out the new materials. New materials were six metal rods of varying size, shape, and material (Inhelder & Piaget, 1958). These were placed on the table and the child was asked to classify them in as many ways as possible. This was done to determine his/her skill in forming the classes of size, shape, and material and to insure that these differences in the rods were noted. The rods were then placed into a stationary block of wood and all the factors (variables) that might affect the amount of bending (the dependent variable) were discussed. The child was then asked to perform "fair tests" to find out if length, thickness, shape, and material, as well of the amount of weight hung on the rods, affects the amount of bending. Whenever the child performed a test, s/he was asked: Is it a fair test? Why is it fair? Can you be sure that this rod bends more than that one only because it is thinner? Is there any other reason (an uncontrolled variable) why it might be bending more? These questions and others were used to focus the child's attention on all the relevant variables, to recognize ambiguous experiments, and to understand the need for a procedure that keeps "all factors the same" except the one being tested. A number of examples and counter-examples were discussed at length. The procedure of controlled experimentation was of course identical to that of the first. However, the materials, the context, differed.

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

243

Session 3. The child was asked to experiment with an apparatus called a Whirly Bird (Science Curriculum Improvement Study, 1970). The Whirly Bird consists of a base that holds a post and an arm that attaches to the post. When pushed or propelled by a wound rubber band, the arm spins around like the rotor on a helicopter. Metal weights can be placed at various positions along the arm. The child was briefly shown how the Whirly Bird works and was asked to find out all factors that affect the times the arm spins before coming to rest (the dependent variable). Possible variables included the number of times the rubber band was wound, the number of rubber bands, the number of weights placed on the arm, the position of the weights, how tightly the arm and post were fastened together, the angle of the base, etc. Following exploration, the child was asked to perform "fair tests" to show that the independent variables mentioned actually did make a difference. Again, whenever a test was performed, children were asked questions that forced them to reflect on their actions (e.g.: Was it a fair test? Why was it fair? Does it show that the factor really makes a difference? Why else might the arm spin have spun more times? Were all other factors held constant?). The general intent of this session was similar to that of the second session as well as the fourth and final session. The strategies underlying the questions were identical in all sessions. The symbolic notation (the language used) remained invariant, while transformations in imagery were gained by first using familiar materials, and then by using unfamiliar materials. Children were given a variety of tasks and were allowed to choose their own procedures for performing them. When mistakes were made, the children were forced to reflect back on their procedures and were challenged to correct them. Session 4. Physical materials were replaced by written problems. Written problems represented an additional step away from the concrete and towards the abstract. Probing questions relative to children's understanding of the written problems were asked as was done in the previous sessions. In a sense learning by doing was replaced by learning by discussion (language alone). The following two written problems were presented and discussed at length. Written Problem 1. Fifty pieces of various parts of plants were placed in each of five sealed jars of equal size under different conditions of color of light and temperature. At the start of the experiment each jar contained 250 units of carbon dioxide. The amount of carbon dioxide in each jar at the end of the experiment is shown in Table 1. Which two jars would you select to make a fair comparison to find out if temperature makes a difference in the amount of carbon dioxide used?

244

CHAPTER 11

Written Problem 2. An experimenter wanted to test the response of mealworms to light and moisture. To do this he set up four boxes as shown in the Figure 1 below. He used lamps for light sources and watered pieces of paper in the boxes for moisture. In the center of each box he placed 20 mealworms. One day later he returned to count the number of mealworms that had crawled to the different ends of the boxes (see below).

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

245

Results. The four training sessions clearly resulted in students who had internalized the meaning of the rule: "To identify a specific cause, it alone must be varied while other possible causes must be held constant." Importantly, they were capable of using the rule to design and conduct controlled experiments in novel contexts. Therefore, the results support the hypothesis that for intuitions to manifest themselves in the form of useful linguistic rules, for intellectual development to occur, children need: (1) a variety of problems requiring a specific procedure for solution, (2) contradictions to their proposed procedures that force them to more closely attend to what they are doing or not doing, and (3) terms/phrases that remain invariant across transformations in materials - in this instance the key terms/phrases were "fair test" and "unfair test." This is essentially the position taken by Bruner & Kenney (1970) studying problem-solving procedures in mathematics. They taught eight-year-olds the mathematical procedure of factoring, the distributive and commutative properties of addition and multiplication, and quadratic function. They summarized the process in this way: It begins with instrumental activity, a kind of definition of things by doing. Such operations become represented and summarized in the form of particular images. Finally, and with the help of symbolic notation that remains invariant across transformations in imagery, the learner comes to grasp the formal or abstract properties of the things he is dealing with. (p. 494)

In other words, development begins with physical experience with objects. Physical experience provokes children with tasks and provides a mental record of what has been done and seen. Contradictions by others, or by the physical world, forces reflection on the procedures used to generate the results. By a closer inspection of the procedures, i.e., by noting the differences between procedures that produced good results and those that produced contradicted results, the child becomes aware of what s/he should and should not do. The introduction of verbal rules (symbolic notation) also aids in the identification of successful procedures. Finally, additional experiences that require the same procedure are provided along with the repetition of the symbolic notation. This allows the student to "reflectively abstract" the procedure from the particular situations. As mentioned, recent research indicates that such abstract procedural rules, once acquired, reside in neurons (most likely outstars as described in Chapter 2) in the prefrontal cortex (Wallis, Anderson & Miller, 2001). To summarize, development is initiated by context-specific environmental encounters that provoke self-regulation. But thanks to the process of reflective abstraction and chunking, the brain constructs and stores abstract (i.e., general) rules that can then be applied across a variety of novel domains to facilitate learning in those novel domains. For example, I can still recall my seventh grade science teacher

246

CHAPTER 11

telling us to conduct several specific experiments and repeatedly asking if we had conducted "controlled" experiments. At the time, I had no idea what she meant by a "controlled" experiment. But one day several days after the experiments were completed, I was reflecting on those experiments and on her questions when suddenly it "clicked" (an adaptive resonance occurred and outstars formed). At that moment, I understood what a controlled experiment was and have been able to apply that understanding (abstract rule) ever since. 5.

DEVELOPING STAGE 5 REASONING SKILL IN THE CLASSROOM

How can teachers apply what we have learned about intellectual development in the classroom? This section will consider a lesson designed to help students develop Stage 5 reasoning skill as well as acquire a better understanding of kinetic-molecular theory. The lesson turns out to be particularly interesting because it also exemplifies several aspects of the nature of science and requires conceptual change as students often arrive with two rather deep-seated misconceptions (i.e., flames "consume" oxygen and a pulling force called "suction" exists). The lesson begins with a burning candle held upright in a pan of water using a small piece of clay. Shortly after a cylinder is inverted over the burning candle and placed in the water, the candle flame goes out and water rises in the cylinder. These observations raise two major causal questions, Why did the flame go out? And why did the water rise? The generally accepted answer to the first question is that the flame converted the oxygen in the cylinder to carbon dioxide such that too little oxygen remained to sustain combustion, thus the flame died. The generally accepted answer to the second question is that the flame transfers kinetic energy (motion) to the cylinder's gas molecules. The greater kinetic energy causes the gas to expand, which results in some escaping out the bottom. When the flame goes out, the remaining molecules transfer some of their kinetic energy to the cylinder walls and then to the surrounding air and water. This causes a loss of average velocity, fewer collisions, and less gas pressure (a partial vacuum). This partial vacuum is then filled by water rising into the cylinder until the air pressure pushing on the outside water surface is equal to the air pressure pushing on the inside surface (Peckham, 1993). This lesson is a particularly good way to reinforce the idea that science is an alternative explanation generation and testing enterprise as the initial explanations students often generate to explain why the water rises are experimentally contradicted, hence mental disequilibrium results along with the need for accommodation. In other words, their ideas need to be replaced. As mentioned, a common student explanation is that oxygen is "used up," thus a partial vacuum is created, which "sucks" water into the cylinder. Typically, students fail to realize that when oxygen "burns" it combines with carbon producing gas of equal volume (hence no partial vacuum is created). Students also often fail to realize that a vacuum cannot "suck" anything. Rather the force causing the water to rise is a push from the

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

247

relatively greater number of air molecules hitting the water surface outside the cylinder. Student experiments and discussions provide an opportunity to modify these misconceptions by introducing a more satisfactory explanation of combustion and air pressure. An opportunity also exists to portray science as an intellectually stimulating and challenging way of using theories, in this case kinetic-molecular theory to explain nature (see Table 2).

1. The universe contains matter, which is composed of tiny particles (atoms am 2.

3. 4. 5. 6. 7.

combinations of atoms called molecules) and light, which consists of still smaller particles called photons. Atoms/molecules are in constant motion. They strike other atoms/molecules and transfer some or all of their motion (kinetic energy) to these particles. An energy source, such as a flame, consists of rapidly moving particles that can transfer some, or all, of their motion to nearby particles through collisions. Attractive forces between atoms or molecules can be broken, causing the atoms or molecules to move apart, which in turn can cause collisions and transfers of energy (motion). Molecular bonds can form between atoms when they strike one another. Temperature is a measure of the amount of motion (average kinetic energy) of the atoms/molecules in a solid, liquid, or gas (i.e., the more motion the greater the temperature). Air pressure is a force exerted on a surface due to collisions of air particles (i.e., more particles at higher velocities = greater air pressure).

5.1 Starting the Lesson

Start the lesson by pointing out the following materials: aluminum pie pans birthday candles matches modeling clay cylinders (open at one end) jars (of various shapes, sizes) beakers and/test tubes/flasks syringes & rubber tubing baking soda ice dry ice balloons

248

CHAPTER 11

pH paper Have each student select a partner. Tell each pair to pour some water into the pan. Stand a candle in the pan using a small piece of clay for support. Then light the candle and put a cylinder, jar, flask, or beaker over the candle so that it covers the candle and sits in the water. Then observe what happens and repeat the procedure several times varying several independent variables (e.g., the number of candles, amount of water, type of cylinder) to determine their possible effects. You should also tell students that they will not only be challenged to generate several alternative explanations for what they observe, but they will also be challenged to design experiments to test the alternatives. (Of particular interest is the fact that on a number of past occasions several students - and even some teachers - believe that they have completed the lesson when they have identified variables that affect the level of water rise. They don't even realize that their "theoretical" task has just begun!). 5.2 Generating Alternative Hypotheses Allow the initial exploration to proceed as long as students are making good progress. You may need to stop them after about 30-40 minutes to discuss observations, preliminary questions and possible explanations. During the discussion, observations should be listed on the board and you should ask students to state the key causal question(s). As mentioned, the most obvious causal questions are, why did the flame go out? And why did the water rise? Alternative explanations that students may generate to answer the second question include: 1. The oxygen is "burned up" creating a partial vacuum. So the water is "sucked" in to replace it. 2. gas forms by burning. When the cools, it changes to liquid filling the cylinder. 3. As the candle burns, it consumes but produces an equal volume of The dissolves in the water more easily than the original thus produces a partial vacuum. The water is then "sucked" in. 4. The candle produces smoke, which collects in the cylinder and attracts (pulls) the water up. 5. Burning converts to which is a smaller molecule. Thus takes up less space creating a partial vacuum, which "sucks" the water up. 6. The candle's heat causes the air around it to expand. After the candle goes out, air cools, air pressure is reduced, and the water is pushed in by greater air pressure outside. (If no one proposes this explanation you will have to propose it yourself. But make sure that you do not give students the impression that this is the "correct" explanation. Rather it is simply an idea that a student in another class generated, which should be tested along with the others).

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

249

7. Here is an explanation that I like to add to the students' list: A Wizard named Sparky lives on campus and sucks the water up. (Sparky is the name of our university sports mascot). 5.3 Testing the Alternatives

Now that student brainstorming has generated several possible explanations, remind students that this is a science class. Consequently, their next task is to test the alternatives. Also remind them that to test a possible explanation one must conduct experiments with clearly stated expected results (predictions). You may want to provide an example, or simply challenge students to put their heads together to see what they can come up with. This may be an excellent time for the bell to ring so that you they can think up experiments as a homework assignment. If you do decide to offer an example, use the If/and/then form like this: If...explanation 1 is correct, that is water is "sucked" in to replace the oxygen (consumed-oxygen explanation) and...the height that water rises with one, two , three, or more candles (all other things being equal) is measured, (test conditions) then...the height of water rise should be the same regardless of the number of burning candles (prediction). This result is predicted presumably because there is only so much oxygen in the cylinder to be burned. So more candles will burn up the available oxygen faster than fewer candles, but they will not burn up more oxygen. Hence, the water rise should be the same. Note that the assumption is made that before they go out, more candles do not consume more oxygen than fewer candles (theoretical rationale). Now have students conduct their experiments and report results. Results of the example experiment show that the number of burning candles affects the water level (the more candles the higher the water level). Therefore, the consumed-oxygen explanation has been contradicted. Also the water rises after the candles go out, not while they are burning - another observation that contradicts the explanation. Measuring the total volume of water before and after the water has risen inside can test explanation 2, the water-created-by-burning explanation. If this explanation is correct, then the total volume of water should increase considerably. Students can test explanation 3, which claims that the dissolves in the water, in a couple of ways. One way involves a comparison of the amount of water rise in containers with saturated water versus normal water. The explanation leads to the prediction that the water level should rise higher in the cylinder with normal water. One can use dry ice (or sodium bicarbonate and acid) to produce gas. Its solubility in water can be tested. The pH of water shaken with and the pH of the water below a candle that has just gone out can be compared. Also if the explanation

250

CHAPTER 11

is correct, a cylinder filled with gas from the dry ice (presumably when inverted and placed in water should cause water to rise, but water doesn't. Filling a cylinder with smoke and inverting it in water. Can test explanation 4, the smoke-attracts-water explanation. If this explanation is correct, then the water should rise. I will leave it to you to figure out a way to test explanation 5, the is-asmaller-molecule explanation. Explanation 6, the heat-causes-air-expansion explanation, leads to the prediction that bubbles should be seen escaping out the bottom of the cylinder (assuming that the cylinder is quickly placed over the candles while the air is still expanding). It also leads to the prediction that more candles should cause more water to rise presumably because more candles will heat more air, thus, more will escape, which in turn will be replaced by more water. (Although one candle burning over a longer time period releases as much energy as three candles burning a shorter time, one candle will not raise the cylinder's air temperature as much because energy is dissipated rather quickly). Initially students do not take explanation 7, the Sparky-sucks explanation seriously. So they don't bother to test it. But at my insistence, they soon come up with the idea to conduct the experiment off campus based on the following reasoning: If...the water rises because Sparky sucks it up, (Sparky explanation) and...the experiment is conducted off campus, (test condition) then...the water should not rise. (prediction) - presumably because Sparky's powers exist only on campus. But...they surmise that the water does rise off campus. (observed result) Therefore...the Sparky explanation can be rejected. (conclusion) I reply to this argument that, because they are ASU students, Sparky travels with them off campus. Consequently, he can still make the water rise. So their experiment does not really contradict the Sparky explanation after all. Students then propose to have the experiment done by telephoning a non-ASU student and asking him/her to conduct the experiment off campus. Then when the non-ASU student finds that the water still rises, students can conclude that the Sparky explanation can be rejected. But Sparky's powers can travel through phone lines, I tell them, so the water should still rise. At this point most students catch on to the game being played, which essentially amounts to giving Sparky ever-expanding powers. And once Sparky's powers become limitless, the Sparky explanation can no longer be tested. Thus, continued belief in Sparky becomes a matter of faith, not evidence. In other words, Sparky becomes a religious, god-like, entity, not a scientific (i.e., testable) entity. This discussion is important because it clarifies this essential difference between religion and science for many students for the first time.

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

5.4

251

Introducing and Applying Kinetic-Molecular Theory

After all the alternatives have been tested and the results discussed, you should carefully summarize and clarify the explanation that is most consistent with the evidence. You can also introduce the term air pressure and the major postulates of the kinetic-molecular theory as they pertain to the present phenomenon. You should also discuss the common misconception of "suction" in this context. Kineticmolecular theory implies that suction (as a force that can pull/suck up water) does not exist (i.e., the water is being pushed into the cylinder by moving particles of air rather than being sucked by some intuitively-generated but nonexistent pulling force). To allow students to apply kinetic-molecular theory and the concept of air pressure to a new situation, provide each team a piece of rubber tubing, a syringe, a beaker and a pan of water. Instruct them to invert the beaker in the pan of water and fill it with water in that position with the mouth of the beaker submerged. Some students will make futile efforts to force water through the tube into the beaker before discovering that they must extract the air through the tube. Now have them attempt to explain why the water rose without using the word suction. As a homework assignment, challenge students to find a way to insert a peeled, hard-boiled egg into a bottle with an opening that is smaller in diameter than the egg. They must not touch the egg with anything after it has been placed on the opening. After a small amount of water in the bottle has been heated, it is only necessary to place the smaller end of the egg over the opening of the bottle to form a seal. The egg will be forced into the bottle by the greater air pressure outside as the air inside cools. You may also ask students to drink a milk shake with a straw and then challenge them to explain how the milk shake gets into their mouths. 6. CONCLUDING REMARKS In addition to providing students with experience in using Stage 5 theoretical reasoning to generate and test alternative hypotheses, the candle-burning lesson exemplifies several important elements of the nature of science (NOS) as described in Chapters 9 and 10 (e.g., science attempts to accurately describe and explain nature; basic to science is the generation and testing of alternative explanations; the generation of several alternatives encourages an unbiased test as one is less likely to be committed to any specific explanation; tentative explanations are tested by use of hypothetico-predictive reasoning; science and religion are different "ways of knowing."). Although the lesson can introduce and perhaps reinforce such NOS elements, they represent generalizations, and as such can be learned only superficially from single-shot instruction such as the candle-burning lab, no matter how engaging it may be. Both developmental theory and experience argue that learning about the nature of

252

CHAPTER 11

science and developing theoretical reasoning skill are long-term propositions, which like learning to draw in a mirror, require repeated attempts in a variety of contexts. For example, the preservice biology teachers from Chapter 10 experienced the candle-burning lab as just described and then prepared lab reports in which they tried to construct written hypothetico-predictive arguments regarding each hypothesis tested. As expected, their written arguments were sound when the hypothesized causal agents were observable (e.g., heated clay releases water into the cylinder; heated water expands into the cylinder). But most arguments were faulty when the causal agents were unobservable (e.g., oxygen molecules were consumed). Three types of faulty arguments were common: those with missing or confused elements, those in which predictions did not follow from hypotheses and planned tests, and those that failed to consider alternative hypotheses (Lawson, 2002). However, on the positive side, developing higher-order reasoning skill in "older" groups of students such as this is considerably easier than in "younger" groups (e.g., Lawson, 1982) presumably because the older students have not only undergone further neurological maturation, they also have additional experiences that can enrich and broaden the instructional experiences. The problem of developing fifth-stage reasoning skill and nature-of-science understanding is compounded by the fact that students often encounter misleading statements about the nature of science, not only from television reports and newspaper articles claiming that science has proved, or disproved, such and such, but even from science textbook authors and teachers. Most likely you have seen textbook authors claim that with mounting supporting evidence hypotheses become theories, which in turn become laws, or give examples of the scientific method in which they fail to recognize the crucial difference between hypotheses and predictions (cf., Gibbs & Lawson, 1992). What college student has not heard about null hypotheses. As mentioned, the statistician's null hypothesis is not really a hypothesis. Instead it is a prediction - a null prediction at that (e.g., no significant difference should be found in the incidence of connective-tissue disease between women with and without breast implants). Little wonder that many students - and the general public - are often confused. Another problem is that many teachers "cover" so much content that they do not leave time for students to question and discuss issues related to the nature of science. Also the lab is often seen as an opportunity to verify lecture topics rather than do "real" (real to the students that is) inquiries. To help solve this problem in our nonmajors college course, we no longer try to closely articulate lecture and lab so that when students need to take two or three weeks to answer a particularly difficult question in lab, they can take the time to do so. Another threat to success is the current rush to incorporate high-tech machines such as computers and videodisc players into instructional settings. These devices may be beneficial, but only so long as they do not replace actual hands-on, minds-on inquiries that allow students to generate and test alternative hypotheses and theories. Indeed, we would do well to keep firmly in mind the American Association for the Advancement of Science's

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

253

central teaching principle which states that: "Teaching should be consistent with the nature of scientific inquiry" (AAAS, 1989, p. 147). Many science courses suffer from another problem. Having been designed largely by subject-matter experts, they are often structured to make sense from an already knowledgeable teacher's perspective, but not necessarily from an inquiring learner's perspective. Thus, biology courses often take a "micro-to-macro" approach, which begins at the highly abstract and theoretical atomic and molecular levels and only later addresses more-familiar, less-abstract topics at the organism, population and community levels. Some recent textbooks have tried to remedy this problem by taking a "macro-to-micro" approach. Thus they start big at the biome level and work their way down to ecosystems, communities, populations, organisms, etc. But this approach also fails to recognize that inquiry and concept construction progress from the familiar and "concrete" to the unfamiliar and abstract. Students are organisms, not biomes, so student inquiries should start at the organism level and then move toward either progressively smaller or progressively larger levels of organization. Indeed, here the history of science has much to offer in terms of helping us identify "natural" routes of inquiry, routes that past scientists have taken and routes that present students can also take - routes that should lead to scientific literacy - that is, to students who know what science is and how to do it. 6.1 Measuring Inquiry Instruction in the Classroom

The instructional approach described in the candle-burning lesson has been described as an inquiry approach, sometimes as a learning cycle approach, and has consistently been found to improve student achievement (e.g., Eakin & Karplus, 1976; Karplus, 1977; Lawson, Abraham & Renner, 1989; Renner & Marek, 1990). Recently a classroom observational instrument called The Reformed Teaching Observational Protocol (RTOP) has been developed to quantitatively assess the extent to which elements of inquiry/learning cycle instruction have been embedded in lessons (Piburn, Sawada, Turley, Falconer, Benford, Bloom, & Judson, 2000). The RTOP consists of 25 statements (see Table 3). Each statement is scored on a 0-4 "Never Occurred" to "Very Descriptive" scale. Thus, the RTOP allows observers to rate instruction on a 0 to 100 scale reflective of the extent to which reformed/inquiry instructional practices are used. Importantly, measured RTOP scores and student achievement (i.e., reasoning skills, concept understanding and NOS understanding) in a wide variety of science and mathematics courses have been found to very highly correlated (e.g., Lawson et al., 2002). In other words, in classes that score high on the RTOP, student achievement (i.e., the classroom average score) tends to be high, whereas in classes with low RTOP scores, the classroom averages tend to be low. Good teaching practices improve student achievement!

254

CHAPTER 11

LESSON DESIGN AND IMPLEMENTATION 1. 2. 3. 4.

5.

The instructional strategies and activities respected students' prior knowledge and the preconceptions inherent therein. The lesson was designed to engage students as members of a learning community. In this lesson, student exploration preceded formal presentation. The lesson encouraged students to seek and value alternative modes of investigation or problem solving. The focus and direction of the lesson was often determined by ideas originating with students.

CONTENT Propositional Knowledge 6. The lesson involved fundamental concepts of the subject. 7. The lesson promoted strongly coherent conceptual understanding. 8. The instructor had a solid grasp of the subject matter content inherent in the lesson. 9. Elements of abstraction (i.e., symbolic representations, theory building) were encouraged when it was important to do so. 10. Connections with other content disciplines and/or real world phenomena were explored and valued.

Procedural Knowledge 11. Students used a variety of means (models, drawings, graphs, concrete materials, manipulatives, etc.)

to represent phenomena. 12. Students made predictions, estimations and/or hypotheses and devised means for testing them. 13. Students were actively engaged in thought-provoking activity that often involved critical assessment

of procedures. 14. Students were reflective about their learning. 8. Intellectual rigor, constructive criticism, and the challenging of ideas were valued. CLASSROOM CULTURE Communicative Interactions 16. Students were involved in the communication of their ideas to others using a variety of means and media. 17. The instructor's questions triggered divergent modes of thinking. 18. There was a high proportion of student talk and a significant amount of it occurred between and among students. 19. Student questions and comments often determined the focus and direction of classroom discourse. 20. There was a climate of respect for what others had to say. Student/Instructor Relationships 21. Active participation of students was encouraged and valued.

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

255

22. Students were encouraged to generate conjectures, alternative solution strategies, and ways of interpreting evidence. 23. In general, the instructor was patient with students. 24. The instructor acted as a resource person, working to support and enhance student investigations. 25. The metaphor "instructor as listener" was very characteristic of this classroom.

6.2 Is Scientific Thinking Natural? According to Matthews (1994), "... Western science is not natural, is does not automatically unfold as children either confront the world, or participate in their culture" (p. 161). In a sense, the difficulty that many adolescents and adults experience in using hypothetico-predictive reasoning in theoretical contexts supports this view. Yet the main implication of this book is that at least at its roots, hypothetico-predictive reasoning is natural. Indeed, it is way in which we all learn, presumably because evolutionary forces (i.e., natural selection) have wired the mind to work in this way. But this is not to say that use of the pattern at earlier stages means that it will automatically be used at higher stages. One might wonder how characteristic this pattern of learning is of the typical science and mathematics classroom. Clearly, if are simply told specific "facts" (e.g., the phases of mitotic cell division are prophase, metaphase, anaphase and telophase; the product of the means equals the product of the extremes) and are then asked to recite these "facts" on tests, the learning pattern is of little or no use. However, if instructional tasks allow students to generate and test their own ideas, then the pattern is of considerable use. Further, whenever students encounter conceptual change instruction (e.g., Wandersee, Mintzes & Novak, 1994) in which concepts introduced during instruction contradict prior concepts, the pattern is also called into use. Recall the task shown in Figure 2 and the debate between the two boys over which variable - weight or volume - determines water displacement. Unfortunately, most instruction seldom requires hypothetico-predictive reasoning. Thus, modifying instruction to help students develop skill in using hypothetico-predictive reasoning at the highest level, the level of scientific thought, is an unmet educational challenge. Importantly, the present view of development and learning implies that progress toward this goal will not be made by adoption of instructional approaches that do not allow students to participate in the knowledge construction process or ignore or denigrate the key role played by the physical world in the test of their alternative hypotheses and theories (even though we cannot be absolutely certain that such a world exists). One final thought: This book has included fairly detailed accounts of specific research studies (i.e., Chapters 3, 4, 6, 7, 8 and 10). Not only were the conclusions drawn in those studies important in developing the book's central arguments, they

256

CHAPTER 11

also provided specific examples of how hypothetico-predictive research can be conducted and reported in science and mathematics education. In my view, too few such studies are designed and written in this hypothetico-predictive manner, and suffer as a consequence (see the appendix for a well known behavioral ecologist's view). In fact, in my view the entire field suffers as a consequence. Thus, if this book encourages other researchers to adopt a hypothetico-predictive approach to their research and writing, I will be pleased.

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

257

7. APPENDIX

7.1 An Interview With A Practicing Biologist About Scientific Method and Science Teaching What follows is a transcription of an interview with John Alcock. Alcock is a well-known behavioral ecologist, author of over 100 research papers and a topselling behavioral ecology textbook. Alcock clearly lays out alternative hypotheses, expected/predicted results and their tests in a recent paper entitled "Provisional rejection of three alternative hypotheses on the maintenance of a size dichotomy in males of Dawson's burrowing bee, Amegilla dawsoni" (Alcock, 1996). Alcock was interviewed to learn about his views on scientific method and how it affects his approach to research and to science teaching (Alcock's responses appear in italics). How do you do science? In other words, do you have a general plan of attack, a general set of strategies, a general method that you use from one study to the next? Yes, in terms of selection of topics I am committed to studies of insect mating behavior. The basic technique is the standard one. I am using evolutionary theory to come up with questions. Once I have questions, I am developing hypotheses that are consistent with selection theory and testing them the old-fashioned way. What is the old-fashioned way? By using them to generate predictions for which it is possible to collect data so that we can examine the validity of the predictions. Once you have data, how do you examine their validity? Well, by matching the expected results against the actual ones. How do you draw conclusions from that? Or do you? Yes, in my case the conclusions are invariably in the form of the data support or invalidate the particular hypothesis. How general is this technique of generating and testing hypotheses? For example, is it limited to your field of research? I believe it is fundamental to all science. It is the essence of what is called the scientific method. The scientific method? Is there only one? I think, well, there is descriptive science, which is the foundation for asking causal questions. And the kind of science which has the greatest significance for everybody - the causal question answering science for which this hypothesis-testing technique is, I believe, fundamental. I have never seen any study, never had anyone explain to me how any study did not use this particular approach, even if they claimed that there are multiple scientific approaches. Does this method, this thinking process actually guide your research? Very selfconsciously, yes. Do you think the method applies to other professional fields, even to non-professional aspects of one's life? I certainly do. I think you could actually have, as E. O. Wilson has argued (Wilson, 1998), a superior economics, a far superior sociology, a far superior women's studies, were this technique applied

258

CHAPTER 11

vigorously throughout. Laying out the hypotheses, thinking through the predictions in advance, is hugely helpful. How did you come to use this method? At this stage, I cannot recreate the steps that led to my current firm views. But it did have something to do with thinking through teaching biology to undergraduates. How about when you were a graduate student at Harvard? Did you use the method then? I was definitely unaware of what I was doing, just following through. Well, the scientific method is common sense, logic I'd say, and not that obscure. But I wasn't self-conscious. It was intuitive and intuitive throughout much of my early career. I only became aware of it in the past 10 to 15 years, perhaps in conjunction with teaching undergraduates. I do not know. Do you think that other people's research would be improved by explicit use of the method? I think it would be improved in two ways. First, it would help the researcher be more systematic in thinking through what he or she should be looking for. There is a tendency to think of alternative hypotheses after the fact and then try to scramble about and hand wave your way out of the problem. Were it actually applied rigorously in advance, it would save your self a lot of heartache and wasted effort. Second, it would have a huge positive effect in the writing of the paper in which it would enable you to convince your colleagues that you had done what you set out to do. Papers that utilize something along the lines of the hypothesis, prediction, outcome, conclusion format, are papers that are readily understood. How good are typical college undergraduates at using this reasoning process, this method? I think that the typical undergraduate has a intuitive grasp of it. Because so much of life revolves around figuring out what caused this or that to happen. And people generally do a decent job at it, of course with all sorts of interesting exceptions. But obviously being self consciously aware of what they are doing and the nature of the logic, the average undergraduate doesn't have a clue. Is trying to improve their understanding and use of the method important? Sure, this is the fundamental goal of my undergraduate biology course. How do you go about trying to improve their reasoning and the ability to use the method? I would say the key weapons are exam questions, sample questions, and quiz questions so that students are forced to put a label on a hypothesis as opposed to a prediction, or forced to look at data and say no, that is not the conclusion, that is the actual result that was gathered to test the hypothesis with the conclusion being hypothesis rejected, hypothesis accepted. Do your lectures contain examples of this sort of reasoning? Yes. I write every lecture to revolve around hypothesis, prediction, test, conclusion - every single one. How successful have you been? I have a feeling that I reach about one third of the students at a level that ought to be there. The next one third, I reach with intermediate effectiveness. And the bottom one third, I definitely do not affect. What needs to be done in your course or elsewhere to be more successful? If high schools worked at conveying an enthusiasm for this issue, if that were to happen, then obviously we would be way ahead; and we could move to a farther point down the turn pike. Generously, there are maybe ten major conceptual systems in biology

IMPLICATIONS FOR KNOWLEDGE AND INSTRUCTION

259

that every student should know. And the foundation for those conceptual systems is always the scientific method. So that should be the premier goal and understanding the ten major conceptual systems is the secondary goal. All the other material is information that will be entering one ear and passing out the other. So if you were ultimately successful in an introductory undergraduate course, does this mean that the teacher in subsequent courses could forget about this method. No, I think it is entirely useful to keep going over it in each new context. At some future date when the scientific method is used in disciplines other than science, then the student could move from class to class with the beautiful result that what he/she learned in the science class is applicable in the humanities class and vice versa. Understanding how valid discoveries and conclusions are made ought to be of extreme interest to any educated person. Is there anything else you would like to add? Yes. It seems that the missing element in all of this is getting a social and emotional context in which a student can absorb this information. I do not know why it is compelling to me. But it is. I find it fascinating to look at a paper and figure out what the process was, how the results were constructed. But I know that this enthusiasm is not shared by most undergraduates. So there has to be another tack to get them involved.

This page intentionally left blank

REFERENCES Abd-El-Khalick, F. (1999). The influence of history of science courses on students' conceptions of the nature of science. Unpublished doctoral dissertation. Oregon State University, Corvallis, OR. Adey, P., Shayer, M. & Yates, C. (1989). Thinking Science: Classroom Activities in Secondary Science. Surrey, England: Thomas Nelson and Sons. Ahn, S. (1995). The Effects of Mental Capacity and Size of Chunk of Problem Solver and Mental Demand of Problem on Science Problem Solving. Unpublished Doctoral Dissertation. Cheongwon, Chungbuk: Korea National University of Education. Albus, J.S. (1981). Brains, Behavior, and Robotics. Peterborough, NH: BYTE Books. Alcock, J. (1996). Provisional rejection of three alternative hypotheses on the maintenance of a size dichotomy in males of Dawson's burrowing bee, Amegilla dawsoni (Apidae, Apinae, Anthphorine). Behavioral Biology and Sociobiology, 39, 181-188. Ambrose, A. & Lazerowitz, M. (1948). Fundamentals of Symbolic Logic. New York: Rinehart & Company,

Inc. American Association for the Advancement of Science. (1928). On the place of science education. School Science and Mathematics, 28, 640-664. American Association for the Advancement of Science. (1989). Science For All Americans. Washington, DC: Author. American Association for the Advancement of Science. (1990). The Liberal Art of Science. Washington, DC: Author. Amsler, M. (1987). Creativity and the Imagination. Newark: University of Delaware Press. Andersen, R.A. (1987). Inferior parietal lobule function in spatial perception and visuomotor integration. In F. Plum (Vol. Ed.), & V.B. Mountcastle (Sec. Ed.), Handbook of Physiology, Section 1: The Nervous System, Volume 5: Higher Functions of the Brain. Bethesda, MD: American Physiological Society. Anderson, J.R. (1980). Cognitive Psychology and Its Implications. San Francisco, USA: Freeman. Anderson, J.R. (1983). The Architecture of Cognition. Cambridge, MA: Harvard University Press. Angell, M. (1996). Evaluating the health risks of breast implants: The interplay of medical science, the law, and public opinion. The New England Journal of Medicine, 334(23), 1513-1518. Arlin, P.K. (1975). Cognitive development in a adulthood: A fifth stage? Developmental Psychology, 11, 602-606. Ausubel, D.P. (1963). The Psychology of Meaningful Verbal Learning. New York: Grune & Stratton. Ausubel, D.P., Novak, J.D. & Hanesian, H. (1978). Educational Psychology: A Cognitive View. (2nd Ed.). New York: Holt, Rinehart and Winston. Bacon, F. (1900). Advancement of Learning and Novum Organum (Revised ed.). New York: The Colonial Press. Baddeley, A. (1995). Working memory. In M.S. Gazzaniga (Ed.), The Cognitive Baker, J.J.W. & Allen, G.E. (1977). The Study of Biology (3rd Ed.). Menlo Park, CA: Addison-Wesley. Baker, S.C., Rogers, R.D., Owen, A.M., Frith, C.D., Dolan, R.J., Frackowaik, R.S.J. & Robbins, T.W. (1996). Neural systems engaged by planning: A PET study of the Tower of London task. Neuropsychologia, 34(6), 515-526.

261

262

REFERENCES

Baker, W.P. (1994). Analogic Instruction, Reasoning Level, and Achievement in College Genetics. Unpublished Doctoral Dissertation. Tempe, AZ: Arizona State University. Baker, W.P. & Lawson, A.E. (2001). Complex instructional analogies and theoretical concept acquisition in college genetics. Science Education, 85, 665-683. Bauer, R.H. & Fuster, J.M. (1976). Delayed-matching and delayed-response deficit from cooling dorsolateral prefrontal cortex in monkeys. Journal of Comprehensive Physiology and Psychology, 90(3), 293-302. Bell, R.L., Lederman, N.G. & Abd-El-Khalick, F. (1998). Implicit versus explicit nature of science instruction: An explicit response to Palmquist and Finley. Journal of Research in Science Teaching, 35(9), 1057-1061. Beveridge, W.I.B. (1950). The Art of Scientific Investigation. London: Heinemann. Biela, A. (1993). Psychology of Analogical Inference. Stuttgart, Germany: Hirzel Verlag. Billeh, V.Y. & Hasan, O.E. (1975). Factors influencing teachers' gain in understanding the nature of science. Journal of Research in Science Teaching, 12(3), 209-219. Biological Science Curriculum Studies. (1992). Science & Technology: Investigating Human Dimensions. Dubuque, Iowa: Kendall/Hunt. Bisanz, J., Bisanz, G.L. & Korpan, C.A. (1994). Inductive Reasoning. In, Sternberg, R.J. (Ed.). Thinking and Problem Solving. San Diego: Academic Press. Black, F.W. & Sturb, R.L. (1976). Constructional apraxia in patients with discrete missile wounds of the brain. Cortex, 12, 212-220. Blinkov, S. M. & Glezer, I.I. (1968). The Human Brain in Figures and Tables. New York: Plenum. Bloom, B.S. (Ed.). (1956). Taxonomy of Educational Objectives: Cognitive Domain. New York: Longmans, Green and Co. Boden, M.A. (1994). What is creativity? In Boden, M.A. (Ed.), Dimensions of Creativity. Cambridge, MA: The MIT press. Botton, C. & Brown, C. (1998). The reliability of some VOSTS items when used with preservice secondary science teachers in England. Journal of Research in Science Teaching, 35(1), 53-71. Bringuier, J. (1980). Conversations with Jean Piaget. Chicago: University of Chicago Press. Brown, D.E. & Clement, J. (1989). Overcoming misconceptions via analogical reasoning: Abstract transfer versus explanatory model construction. Instructional Science, 18, 237-261 Bruner, J.S. (1962). On Knowing: Essays for the Left Hand. Cambridge: Belknap Press., Harvard University Press. Bruner, J.S. (1963). The Process of Education. Cambridge, MA: The Harvard University Press. Bruner, J.S. & Kenney, H.J. (1970). Representation and mathematics learning. In W. Kessen & C. Kuhlman [Eds.], Cognitive Development in Children. Chicago: University of Chicago Press. Burmester, M.A. (1952). Behavior involved in critical aspects of scientific thinking. Science Education, 36(5), 259-263. Campbell, D.T. & Stanley. J.C. (1966). Experimental and quazi-experimental designs for research. Chicago: Rand McNally. Carey, R.L. & Stauss, N.G. (1969). An analysis of the relationship between prospective teachers' understanding of the nature of science and certain academic variables. Bulletin of the Georgia Academy of Science, 27(3) 148-158. Carey, R.L. & Stauss, N.G. (1970). An analysis of experienced science teachers' understanding of the nature of science. School Science and Mathematics, 70(5), 366-376.

REFERENCES

263

Carey, S.S. (1998). A Beginner's Guide to Scientific Method. (2nd ed.). Belmont, CA: Wadsworth. Castro, E.A. & Fernandez, F.M. (1987). Intellectual development beyond formal operations. International Journal of Science Education, 9(4), 441-447. Cavallo, A.M.L. (1996). Meaningful learning, reasoning ability, and students' understanding and problem solving of topics in genetics. Journal of Research in Science Teaching, 33, 625-656. Chamberlain, T.C. (1965). The method of multiple working hypotheses. Science, 148, 754-759. (Original work published 1897) Chelune, G.J. & Baer, R.A. (1986). Developmental norms for the Wisconsin Card Sorting Test. Journal of Clinical and Experimental Neuropsychology, 8, 219-228. Choi, B. & Hur, M. (1987). Relationships between the cognitive levels of students and understanding of concrete and formal science context. Journal of the Korean Association for Research in Science Education, 7(1), 19-32. Cicerone, K.D., Lazar, R.D. & Shapiro, W.R. (1983). Effects of frontal lobe lesions on hypothesis sampling during concept formation. Neuropsychologia, 21(5), 513-524. Clausen, J., Keck, D. & Hiesey, W. (1948). Carnegie Institute Washington Publication 581. Clement, J. (1989). Learning via model construction and criticism. In G. Glover, R. Ronning, & C. Reynolds (Eds.), Handbook of creativity: Assessment, theory and research (pp. 341-381). New York: Plenum. Cohen, M.R. & Nagel, E. (1934). An Introduction to Logic and Scientific Method. London: Routledge and Kegan Paul. Cole, M. & Cole, S.R. (1989). The Development of Children. New York: Scientific American Books, W.H. Freeman & Co. Commons, M.L. & Miller, P.M. (1997). A theory of conceptual intelligence: Thinking, learning, creativity, and giftedness. Contemporary Psychology, 42(11), 981-982. Commons, M.L., Richards, F.A. & Armon, C. (Eds.). (1984). Beyond Formal Operations: Late Adolescent Cognitive Development. New York: Praeger. Commons, M.L., Trudeau, E.J., Stein, S.A., Richards, F.A. & Krause, S.R. (1998). Hierarchical complexity of tasks shows the existence of developmental stages. Developmental Review, 18(3), 237-278. Damasio, A.R, (1994). Descartes' Error: Emotion, Reasoning, and the Human Brain. New York: G.P. Putnam. Daniel, P.M. & Whitteridge, D. (1961). The representation of the visual field on the cerebral cortex in monkeys. Journal of Physiology, 159, 203-221. Darwin, C. (1898). The Origin of Species by Means of Natural Selection. New York: Appleton (6th Ed.). De Kruif, P. (1926). Microbe Hunters. New York: Harcourt Brace. De Ribaupierre, A. & Pascual-Leone, J. (1979). Formal operation and M-power: A neo-Piagetian investigation, New Directions for Child Development, 5(1), 1-43. Dempster, F.N. (1992). The rise and fall of the inhibitory mechanism: Toward a unified theory of cognitive development and aging. Developmental Review, 12, 45-75. Desimone, R. & Ungerleider, L.G. (1989). Neural mechanisms of visual processing in monkeys. In H. Goodglass & A.R. Damasio (Eds.), Handbook of Neuropsychology. New York: Elsevier. Desimone, R., Albright, T.D., Gross, C.G. & Bruce, C.J. (1984). Simultaneous selective properties of inferior temporal neurons in the macaque. Journal of Neuroscience, 4, 2051-2062.

264

REFERENCES

Diamond, A. (1990). The Development and Neural Bases of Inhibitory Control in Reaching in Human Infants and Infant Monkeys. In A. Diamond (Ed.), The Development and Neural Basis of Higher Cognitive Functions. New York: Academy of Sciences. Dominowski, R.L. & Dallob, P. (1995). Insight and problem solving. In R.J. Sternberg & J.E. Davidson (Eds.), The Nature of Insight. Cambridge, MA: MIT Press. Dreistadt, R. (1968). An analysis of the use of analogies and metaphors in science. Journal of Psychology, 68, 97-ll6. Driver, R. Asoko, H., Leach, J., Mortimer, E. & Scott, P. (1994). Constructing Scientific Knowledge in the Classroom, Educational Researcher 23, 5-12. Duit, R. (1990). On the role of analogies, similes and metaphors in learning science. Paper presented at the Annual Meeting of the American Educational Research Association, Atlanta, April. Dumsha, T.C., Minard, J. & McWilliams, J. K. (1973). Comparison of two self-administered field dependency measures. Perceptual and Motor Skills, 36(1), 252-254. Dunbar, K. (1993). Concept discovery in a scientific domain. Cognitive Science, 17, 397-434. Dupin, J.J. (1989). Analogies and "modeling analogies" in teaching: Some analogies in basic electricity. Science Education, 73, 207-224. Eakin, J. R. & Karplus, R. (1976). Science Curriculum Improvement Study (SCIS) Final Report. Berkeley, CA: Regents of the University of California. Educational Policies Commission. (1961). The Central Purpose of American Education. Washington, DC: National Education Association. Educational Policies Commission. (1966). Education and the Spirit of Science. Washington, DC: National Education Association. Elementary Science Study. (1974). Gases and Airs: Teachers' Guide. New York: McGraw Hill. Elementary Science Study. (1974). Teachers' Guide far Attribute Games and Problems. New York: McGrawHill. Elfin, J.T. Glennan, S. & Reisch, G. (1999). The nature of science: A perspective from the philosophy of science. Journal of Research in Science Teaching, 36(1), 107-116. Epstein, H.T. (1974a). Phrenoblysis: Special brain and mind growth periods. I. Human brain and skull development. Developmental Psychology, 7(3), 207-216. Epstein, H.T. (1974b). Phrenoblysis: Special brain and mind growth periods. I. Human mental development. Developmental Psychology, 7(3), 217-224. Epstein, H.T. (1978). Growth spurts during brain development: Implications for educational policy and practice. In J.S. Chall & A.F. Mirsky (Eds.), Education and The Brain: The Seventy-seventh Yearbook of the National Society for the Study of Education (pp. 343-370). Chicago: The University of Chicago Press. Epstein, H.T. (1986). Stage in human brain development. Developmental Brain Research, 30, 114-119. Epstein, H.T., Toepfer, Jr. & C.F. (May, 1978). A neuroscience basis for middle grades education. Educational Leadership, 656-660. Eysenck, H.J. (1994). The Measurement of Creativity, in M.A. Boden (Ed), Dimensions of Creativity. Cambridge, MA: The MIT Press. Farah, M.J. (1990). Visual Agnosia: Disorders of Object Recognition and What They Tell Us About Normal Vision. Cambridge, MA: MIT Press. Fauconnier, G & Turner, M. (2002). The Way We Think: Conceptual Blending and the Mind’s Hidden

REFERENCES

265

Complexities. New York: Basic Books. Feynman, R. (1965). The Character of Physical Law. Cambridge, MA: MIT Press. Finke, R.A., Ward, T.B. & Smith, S.M. (1992). Creative Cognition: Theory, Research and Applications. Cambridge, MA: MIT Press. Flick, L. (1991). Where concepts meet percepts: Stimulating analogical thought in children. Science Education, 75, 215-230. Fosnot, C.T. (1996). Constructivism: A psychological theory of learning. In C.T. Fosnot (Ed.). Constructivism: Theory, Perspectives, and Practice. New York: Teacher's College Press. Fosnot, C.T. (Ed.). (1996). Constructivism: Theory, Perspectives, and Practice. New York: Teachers College Press. Friedel, A.W., Gabel, D.L. & Samuel, J. (1990). Using analogues for chemistry problem solving: Does it increase understanding? School Science & Mathematics, 90, 674-682. Friedman, H.R. & Goldman-Rakic, P.S. (1994). Coactivation of prefrontal cortex and inferior parietal cortex in working memory tasks revealed by 2DG functional mapping in the rhesus monkey. Journal of Neuroscience, 14, 2775-2788. Funster, J.M. (1989). The Prefrontal Cortex: Anatomy, Physiology, and Neuropsychology of the Frontal Lobe. (2nd ed.). New York: Raven Press. Fuster, J.M. (1973). Unit activity in prefrontal cortex during delayed-response performance: Neuronal correlates of transient memory. Journal of Neurophysiology, 36(1), 61-78. Fuster, J.M. (1989). The Prefrontal Cortex: Physiology and Neuropsychology of the Frontal Lobe (2nd ed.). New York: Raven Press. Futuyma, D.J. (1979). Evolutionary Biology. Sunderland, Mass.: Sinauer. Gabel, D.L & Samuel, K.V. (1986). High school students' ability to solve molarity problems and their analogue counterparts. Journal of Research in Science Teaching, 23, 165-176. Gabriel, S.E., O'Fallon, W.M., Kurland, L.T., Beard, C.M., Woods, J.E. & Melton, I.I. (1994). Risk of connective-tissue disease and other disorders after breast implantation. New England Journal of Medicine, 330, 1697-1702. Galilei, G., (1610). The Sidereal Messenger. In, Shapley, H., Rapport, S. & Wright, H. (Eds.), (1954). A Treasury of Science. New York: Harper & Brothers. Gardner, H. (1994). The Creator's Patterns. In M. A. Boden (Ed.), Dimensions of Creativity. Cambridge, MA: The MIT Press. Gazzaniga, M.S., Ivry, R.B. & Mangun, G.R. (1998). Cognitive Neuroscience: The Biology of the Mind. New York: Norton. Gentner, D. (1989). The mechanisms of analogical learning. In S. Vosniadou & A. Ortony (Eds.), Similarity and Analogical Reasoning. Cambridge: Cambridge University Press. Germann, P.J. (1994). Testing a model of science process skills acquisition: An interaction with parents' education, preferred language, gender, science attitude, cognitive development, academic ability, and biology knowledge. Journal of Research in Science Teaching, 31(7), 749-783. Gesell, A. (1940). The First Five Years of Life. New York: Harper. Gibbs, A. & Lawson, A.E. (1992). The nature of scientific thinking as reflected by the work of biologists and biology textbooks. The American Biology Teacher, 54 (3), 137-152. Giere, R.N. (1997). Understanding Scientific Reasoning. (4th ed.). New York: Harcourt Brace.

266

REFERENCES

Gilbert, S.W. (1989). An evaluation of the use of analogy, simile, and metaphor in science texts. Journal of Research in Science Teaching, 26, 315-327. Globerson, T. (1983). Mental capacity and cognitive functioning: Developmental and social class differences. Developmental Psychology, 19(2), 225-230. Globerson, T. (1985). Field dependence/independence and mental capacity: A developmental approach. Developmental Review, 5, 261-273. Goldman-Rakic, P.S. (1990). The prefrontal contribution to working memory and conscious experience. Experimental Brain Research, 79(3), 445-456. Goldman-Rakic, P.S. & Friedman, H.R. (1991). The circuitry of working memory revealed by anatomy and metabolic imaging. In H.S. Levin, H.M. Goleman, D. (1995). Emotional Intelligence. New York: Bantam Books. Goudge, T.A. (1950). The Thought of C.S. Peirce. Toronto: University of Toronto Press. Green, J.C. (1958), The Death of Adam. Ames: Iowa State University Press. Gregory, R.L. (1970). The Intelligent Eye. New York: McGraw-Hill. Grossberg, S. (1982). Studies of Mind and Brain. Dordrecht, Holland: D. Reidel. Grossman, S.P. (1967). A Textbook of Physiological Psychology. New York: Wiley. Guilford, J.P. (1936). The determination of item difficulty when chance success is a factor. Psychometrika, 1, 259-264. Halpern, D.F., Hansen, C. & Riefo, D. (1990). Analogies as an aid to understanding and memory. Journal of Educational Psychology, 82, 298-305. Hanson, N.R. (1958). Patterns of Discovery. London: Cambridge University Press. Harre, R. (1986). Varieties of Realism: A Rationale for the Natural Sciences. Oxford, UK: Basil Blackwell. Hauser, M.D. (2000). What do animals think about numbers? American Scientist, 88, 144-151. Haxby, J.V., Grady, C.L., Horowitz, B., Ungerleider, L. G., Miskin, M., Carson, R.E., Herscovitch, P., Schapiro, M.B. & Rapoport, S.I. (1991). Dissociation of object and spatial visual processing pathways in human extrastriate cortex. Proceedings of the National Academy of Sciences of the United States of America, 88, 1621-1625. Heaton, R.K., Chelune, G.J. Tally, J.L., Kay, G.G. & Curtiss, G. (1993). Wisconsin Card Sorting Test Manual: Revised and Expanded. Psychological Assessment Resources, Inc. Heaton, R.K. (1981). Wisconsin Card Sorting Test Manual. Odessa, Fl.: Psychological Assessment Resources. Hebb, D.O. (1949). The Organization of Behavior. New York: John Wiley and Sons. Hempel, C. (1966). Philosophy of Natural Science. Upper Saddle River, NJ: Prentice-Hall. Heppner, F., Hammon, C., Kass-Simon, G. & Kruger, W. (1990). A de facto standardized curriculum in US college biology and zoology. Bioscience, 40(2), 130-134. Hestenes, D. (1992). Modeling games in a Newtonian world. American Journal of Physics, 55, 440-454. Hoffman, R.R. (1980). Metaphor in science. In P.R. Honeck & R.R. Hoffman (Eds.), The Psycholinguistics of Figurative Language. Hillsdale, NJ: Erlbaum. Hofstadter, D.R. (1981). Metamagical themas: How might analogy, the core of human thinking, be understood by computers? Scientific American, 249, 18-29. Hofstadter, D.R. (1995). Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought. New York: Basic Books. Holland, J.H., Holyoak, K.J., Nisbett, R.E. & Thagard, P.R. (1986). Induction: Processes of

REFERENCES

267

Inference, Learning, and Discovery. Cambridge, MA: MIT Press. (see especially Chapter 11) Holton, G. & Roller, D.H.D. (1958). Foundations of Modern Physical Science. Reading, MA: AddisonWesley. Hudspeth, W.J. & Pribram, K.H. (1990). Stages of brain and cognitive maturation. Journal of Educational Psychology, 82(4), 881-884. Hurst, R.W. & Milkent, M.M. (1996). Facilitating successful problem solving in biology through application of skill theory. Journal of Research in Science Teaching, 33(5), 541-552. Hwang, A.S. (1996). Positivist and constructivist persuasions in instructional development. Instructional Science, 24, 343-356. Hwang, K., Park, I. & Kim, T. (1989). A study on scientific thinking of Korean high school students. Journal of the Korean Association for Research in Science Education, 9(1), 19-37. Inhelder, B. & Piaget, J. (1958). The Growth of Logical Thinking From Childhood to Adolescence. New York: Basic Books. Jardine, D.W. & Morgan, G.A.V. (1987). Analogy as a model for the development of representational abilities in children. Educational Theory, 37, 209-217. Jeon, Y. & Jang, H. (1995). The Group Embedded Figure Test. Seoul, Korea: Korean Testing Center. Jevons, F.R. (1969). The Teaching of Science. London: George Allen and Unwin Ltd. Johnson, M. (1987). The Body in the Mind. Chicago: University of Chicago Press. Johnson, M.A. & Lawson, A.E. (1998). What are the relative effects of reasoning ability and prior knowledge on biology achievement in expository and inquiry classes? Journal of Research in Science Teaching, 35(1), 89-103. Johnson-Laird, P.N. (1983). Mental Models. Cambridge, MA: Harvard University Press. Johnson-Laird, P.N. (1993). Human and Machine Thinking. Hillsdale, NJ: Erlbaum. Karplus, R. (1974). The learning cycle. In The SCIS Teacher's Handbook. Berkeley, CA: Regents of the University of California. Karplus, R. (1977). Science teaching and the development of reasoning. Journal of Research in Science Teaching, 14(2), 169-175. Karplus, R. & Lavatelli, C. (1969). The Developmental Theory of Piaget: Conservation. San Francisco: Davidson Film Producers. Karplus, R. & Thier, H.D. (1967). A New Look at Elementary School Science. Chicago: Rand McNally. Keys, C.W. (1994). The development of scientific reasoning skills in conjunction with collaborative assignments: An interpretive study of six ninth-grade students. Journal of Research in Science Teaching, 31(9), 1003-1022. Kim, J. & Kwon, J. (1994). An analysis of the momentum effect by students cognitive characteristics. Journal of the Korean Association for Research in Science Education, 14(1), 70-84. Kimball, M.E. (1967). Understanding the nature of science: A comparison of scientists and science teachers. Journal of Research in Science Teaching, 5(2), 110-120. Klahr, D. (2000). Exploring Science: The Cognition and Development of Discovery Processes. Cambridge, MA: The MIT Press. Klauer, K.J. (1989). Teaching for analogical transfer as a means of improving problem solving, thinking and learning. Instructional Science, 18, 179-192. Knight, R. & Grabowecky, M. (1995). Escape from linear time: Prefrontal cortex and conscious experience. In M.S. Gazzaniga (Ed.), The Cognitive Neuroscience, (pp. 1357-1371). Cambridge, MA: MIT Press.

268

REFERENCES

Koestler, A. (1964). The Act of Creation. London: Arkana Penguin Books. Korthagen, F. & Lagerwerf, B. (1995). Levels in learning. Journal of Research in Science Teaching, 32(10), 1011-1038. Kosslyn, S.M. & Koenig, O. (1995). Wet Mind: The New Cognitive Neuroscience. New York: The Free Press. Kral, E.A. (1997). Scientific reasoning in a high school English course. Skeptical Inquirer, 21(3), 34-39. Kramer, D.A. (1983). Post-formal operations? A need for further conceptualization. Human Development, 26, 91-105. Krikorian, R., Bartok, J. & Gay, N. (1994). Tower of London procedure: A standard method and developmental data. Journal of Clinical and Experimental Neuropsychology, 16(6), 840-850. Kuhn, D. (1989). Children and adults as intuitive scientists. Psychological Review, 96(4), 674-689. Kwon, Y.J. (1997). Linking prefrontal lobe functions with reasoning and conceptual change. Unpublished doctoral dissertation. Arizona State University. Kwon, Y.J. & Lawson, A.E. (2000). Linking brain growth with the development of scientific reasoning ability and conceptual change during adolescence. Journal of Research in Science Teaching, 37(1), 44-62. Latour, B. & Woolgar, S. (1979). Laboratory Life: The Construction of Scientific Facts. London: Sage. Latour. B. & Woolgar, S. (1986). Laboratory Life: The Construction of Scientific Facts (2nd Ed.). London: Sage. Lavach, J.F. (1969). Organization and evaluation of an inservice program in the history of science. Journal of Research in Science Teaching, 6, 166-170. Lawson, A.E. (1978). The development and validation of a classroom test of formal reasoning. Journal of Research in Science Teaching, 15(1), 11-24. Lawson, A.E. (1979). Relationships among performances on group-administered items of formal reasoning. Perceptual and Motor Skills, 48, 71-78. Lawson, A.E. (1980a). The relationship among levels of intellectual development, cognitive style and grades in a college biology course. Science Education, 64(1), 95-102. Lawson, A.E. (1980b). Reply to: Concurrent validity in tests of Piagetian developmental levels. Journal of

Research in Science Teaching, 17(4), 349-350. Lawson, A.E. (1982a). The reality of general cognitive operations. Science Education, 66(2), 229-241. Lawson, A.E. (1982b). The relative responsiveness of concrete operational seventh grade and college students to instruction in formal reasoning. Journal of Research in Science Teaching, 19(1), 63-78. Lawson, A.E. (1983). Predicting science achievement: The role of developmental level, disembedding ability, mental capacity, prior knowledge and beliefs. Journal of Research in Science Teaching, 20(2), 117129. Lawson, A.E. (1987a). The four-card problem resolved? Formal operational reasoning and reasoning to a contradiction. Journal of Research in Science Teaching, 24(10), 953-970. Lawson, A.E. (1987b). Classroom test of scientific reasoning: Revised pencil-paper edition. Tempe: Arizona State University. Lawson, A.E. (1990). The use of reasoning to a contradiction in grades three to college. Journal of Research in Science Teaching, 27(6), 541-552. Lawson, A.E. (1995). Science Teaching and the Development of Thinking. Belmont, CA.: Wadsworth.

REFERENCES

269

Lawson, A.E. (1999). What should students learn about the nature of science and how should we teach it? Journal of College Science Teaching, 28(6), 401-411. Lawson, A.E. (2000). How do humans acquire knowledge? And what does that imply about the nature of knowledge? Science & Education, 9, 577-598. Lawson, A.E., Alkhoury, S., Benford, R., Clark, B. & Falconer, K.A. (2000). What kinds of scientific concepts exist? Concept construction and intellectual development in college biology. Journal of Research in Science Teaching, 37, 996-1018. Lawson, A.E., Baker, W.P., DiDonato, L., Verdi, M.P. & Johnson, M.A. (1993). The role of physical analogies of molecular interactions and hypothetico-deductive reasoning in conceptual change. Journal of Research in Science Teaching, 30(9), 1073-1086. Lawson, A.E. & Bealer, J.M. (1984). The acquisition of basic quantitative reasoning skills during adolescence: Learning or development? Journal of Research in Science Teaching, 21(4), 417-423. Lawson, A.E., Bloom, I., Falconer, K., Hestenes, D., Judson, E., Piburn, M.D., Sawada, D., Turley, J. & Wyckoff, S. (2002). Evaluating College Science and Mathematics Instruction. Journal of College Science Teaching. 31(6), 388-393. Lawson, A.E., Carlson, E., Sullivan, F., Wilcox, R. S. & Wollman, W.T. (1976). Biology Teaching and Development of Reasoning. Berkeley, CA: Regents of the University of California. Lawson, A.E., Clark, B. Cramer-Meldrum, E., Falconer, K.A., Sequist, J.M. & Kwon, Y.J. (2000). The development of scientific reasoning in college biology: Do two levels of general hypothesis-testing skills exist? Journal of Research in Science Teaching, 37(1), 81-101. Lawson, A.E., Drake, N., Johnson, J., Kwon, Y.J. & Scarpone, C. (2000) How good are students at testing alternative explanations involving unseen entities? The American Biology Teacher, 62(4), 246-252. Lawson, A.E., Karplus, R. & Adi, H. (1978). The acquisition of prepositional logic and formal operational schemata during the secondary school years. Journal of Research in Science Teaching, 15(6), 465478. Lawson, A.E. & Lawson, C.A. (1979). A theory of teaching for conceptual understanding, rational thought and creativity. In A.E. Lawson (Ed.), The Psychology of Teaching for Thinking and Creativity. AETS Yearbook. Columbus, OH: ERIC/SMEAC. Lawson, A.E., McElrath, C.B., Burton, M.S., James, B.D., Doyle, R.P., Woodward, S.L., Kellerman, L. & Snyder, J.D. (1991). Hypothetico-deductive reasoning and concept acquisition: Testing a constructivist hypothesis. Journal of Research in Science Teaching, 28(10), 953-970. Lawson, A.E., Nordland, F.H. & DeVito, A. (1974). Piagetian formal operational tasks: A crossover study of learning effect and reliability. Science Education, 58(2), 267-276. Lawson, A.E. & Renner, J.W. (1975). Relationships of concrete and formal operational science subject matter and the developmental level of the learner. Journal of Research in Science Teaching, 12(4), 347-358. Lawson, A.E. & Thompson, L.D. (1988). Formal reasoning ability and misconceptions concerning genetics and natural selection. Journal of Research in Science Teaching, 25(9), 733-746. Lawson, A.E. & Weser, J. (1990). The rejection of nonscientific beliefs about life: The effects of instruction and reasoning skills. Journal of Research in Science Teaching, 27(6), 589-606. Lawson, A.E. & Wollman, W.T. (1976). Encouraging the transition from concrete to formal cognitive functioning - an experiment. Journal of Research in Science Teaching, 13(5), 413-430.

270

REFERENCES

Lawson, A.E. & Worsnop, W.A. (1992). Learning about evolution and rejecting a belief in special creation: Effects of reflective reasoning skill, prior knowledge, prior beliefs and religious commitment. Journal of Research in Science Teaching, 29 (2), 143-166. Lawson, C.A. (1958). Language, Thought and the Human Mind. East Lansing: Michigan State University Press. Lawson, C.A. (1967). Brain Mechanisms and Human Learning. Boston: Houghton Mifflin. Lederman, N.G. (1983). Delineating classroom variables related to students' conceptions of the nature of science. Dissertation Abstracts International, 45, 483A. (University Microfilms No. 84-10, 728). Lederman, N.G. (1992). Students' and teachers' understanding of the nature of science: A review of research. Journal of Research in Science Teaching, 29(4), 331-359. Lederman, N.G., Wade, P.D. & Bell, R.L. (1998). Assessing the nature of science: What is the nature of our assessments? Science & Education, 7, 595-615. LeDoux, J. (1996). The Emotional Brain. New York: Touchstone. Levine, D.S. & Prueitt, P.S. (1989). Modeling some effects of frontal lobe damage: Novelty and perserveration. Neural Networks, 2, 103-116. Lewis, R.W. (1980). Evolution: A system of theories. Perspectives in Biology and Medicine, Summer, 551572. Lewis, R.W. (1988). Biology: A hypothetico-deductive science. The American Biology Teacher, 50(6), 362-367. Luria, A.R. (1961). The Role of Speech in the Regulation of Normal and Abnormal Behavior. Oxford: Pergamon. Luria, A.R. (1973). The Working Brain: An Introduction for Neuropsychology. New York: Basic Books. Luria, A.R. (1980). Higher Cortical Function in Man, (2nd Ed). New York: Consultants Bureau. Luria, A.R. & Tsvetkova, L.S. (1964). The programming of construction activity in local brain injuries. Neuropsychologia, 2(1), 95-107. Malherbe, M. (1996). Bacon's method of science. In Peltonen, M. (Ed.), The Cambridge Companion to Bacon. Cambridge, England: Cambridge University Press. Marek, E. & Cavallo, A. (1997). The Learning Cycle: Elementary School Science and Beyond. Portsmouth, NH: Heinemann. Matthews, M. (1994). Science Teaching: The Role of the History and Philosophy of Science. New York: Routledge. Matthews, M. (1998). In defense of modest goals when teaching about the nature of science, Journal of Research in Science Teaching, 35(2), 161-174. Matthews, M.R. (Ed.) (1998). Constructivism in Science Education: A Philosophical Examination. Dordrecht, The Netherlands: Kluwar Academic Publishers. Maunsell, J.H.R. & Newsome, W.T. (1987). Visual processing in monkey extrastriate cortex. Annual Review of Neuroscience, 10, 363-401. McCarthy, G., Puse, A., Constable, R.T., Krystal, J.H., Gore, J. & Goldman-Rakic, P.S. (1996). Activation of human prefrontal cortex during spatial and object working memory tasks measured by functional MRI. Cerebral Cortex, 6(4), 600-611. McComas, W.F. (1996). Ten myths of science: Reexamining what we think we know about the nature of science. School Science and Mathematics, 96(1), 10-16.

REFERENCES

271

McComas, W.F., Almazroa, H. & Clough, M.P. (1998). The nature of science in science education: An introduction. Science & Education, 7, 511-532. McKellar, P. (1957). Imagination and Thinking. New York: Basic Books. Medawar, P.B. (1969). Induction and Intuition in Scientific Thought. Philadelphia, PA: American Philosophical Society. Meltzoff, A.N. (1990). Towards a developmental cognitive science. In Neural and Developmental Basis of Higher Cognitive Functioning. A. Diamond (Ed.). New York: Academy of Sciences. Merrium-Webster. (1986). Webster's Third New International Dictionary. Springfield, MA: MerriumWebster Inc. Metz, K.E. (1995). Reassessment of developmental constraints on children's science instruction. Review of Educational Research, 65(2), 93-127. Miller, G. A. (1956). The Magical Number Seven, Plus or Minus Two. Psychological Review, 63, 81-97. Milner, B. (1963). Effects of different brain lesions on card sorting Archives of Neurology, 9(1), 90-100. Milner, B. (1964). Some effects of frontal lobectomy in man. In J. M. Warren & K. Akert (Eds.), The Frontal Granular Cortex and Behavior, (pp. 313-334). New York: McGraw-Hill. Minstrell, J. (1980). Conceptual development of physics students and identification of influencing factors. Unpublished research report, Mercer Island School District, Washington. Miskin, M. (1978). Memory in monkeys severely impaired by combined but not separate removal of amygdala and hippocampus. Nature, 273, 297-298. Mishkin, M. & Appenzeller, T. (1987). The anatomy of memory. Scientific American, 256(6), 80-89. Mishkin, M., Malamut, B. & Bachevalier, J. (1984). Memories and habits: Two neural systems. In G. Lynch, J. McGaugh, & N. Weinberger (Eds.), Neurobiology of Learning and Memory (pp. 65-77). New York: Guilford. Miyashita, Y. & Chang, H.S. (1988). Neuronal correlate of pictorial short-term memory in the primate cortex. Nature, 331,68-70. Moore, J. (1993). Science as a Way of Knowing: The Foundations of Modern Biology. Cambridge, MA: Harvard University Press. Moshman, D. (1998). Cognitive development beyond childhood. In D. Kuhn & R.S. Siegler (Eds.). Handbook of Child Psychology: Vol. 2. Cognition, Perception, and Language (5th Ed.). New York: Wiley. Musgrave, A. (1999). How to do without inductive logic. Science & Education, 8, 395-412. Musheno, B.V. & Lawson, A.E. (1999). Effects of learning cycle and traditional text on comprehension of science concepts by students at differing reasoning levels. Journal of Research in Science Teaching, 36(1), 23-37. National Research Council. (1995). National Science Education Standards. Washington, D.C.: National Academy Press. National Science Foundation. (1996). Shaping the Future. Washington, DC: Author. National Society for the Study of Education. (1960). Rethinking Science Education (59th Yearbook, Part I). Chicago: University of Chicago Press. Nauta, W.J.H. (1971). The problem of the frontal lobe: A reinterpretation. Journal of Psychiatric Research, 8, 167-187. Niaz, M. & Lawson, A. E. (1985). Balancing chemical equations: The role of developmental level and mental capacity. Journal of Research in Science Teaching, 22(1), 41-51.

272

REFERENCES

Noh, T. & Scharmann, L.C. (1997). Instructional influence of a molecular-level pictorial presentation of matter on students' conceptions and problem-solving ability. Journal of Research in Science Teaching, 34(2), 199-217. Nola, R. (1999). On the possibility of a scientific theory of scientific method. Science & Education, 8, 427-

439. Northrop, F.S. (1947). The Logic of the Sciences and the Humanities. New York: Macmillan. Olstad, R.G. (1969). The effect of science teaching methods on the understanding of science. Science Education, 53(1), 9-11. Osborne, J.E. (1996). Beyond Constructivism. Science Education, 80(1), 53-82. Pascual-Leone, J. (1969). Cognitive Development and Cognitive Style: A General Psychological Integration. Unpublished doctoral dissertation, University of Geneva. Pascual-Leone, J. (1970). A mathematical model for the transition rule in Piaget's developmental stages. Acta Psychologica, 32, 301-345. Pascual-Leone, J. & Ijaz, H. (1989). Mental capacity testing as a form of intellectual development. In R. J. Samuda, Kong, S. L., Cummins, J., Lewis, J. & Pascual-Leone, J., Assessment and Placement of Minority Students, (pp. 143-171). Toronto: C. J. Hogrefe. Pascual-Leone, J. & Smith, J. (1969). The encoding and decoding of symbols by children. Journal of Experimental Child Psychology, 8(2), 328-355. Paulesu, E., Frith, D.D. & Frackowiak, R.S.J. (1993). The neural correlates of the verbal component of working memory. Nature, 362, 342-345. Peckham, G.D. (1993). A new use for the candle and tumbler myth. Journal of Chemical Education, 70(12), 1008-1009. Perkins, D.N. & Salomon, G. (1989). Are cognitive skills context-bound? Educational Researcher, 18(1), 16-25. Perry, B., Donovan, M.P., Kelsey, L.J., Peterson, J. Statkiewicz, W. & Allen, R.D. (1986). Two schemes of intellectual development: A comparison of development as defined by William Perry and Jean Piaget. Journal of Research in Science Teaching, 23(1), 73-83. Perry, W.G. Jr. (1970). Forms of Intellectual and Ethical Development In The College Years: A Scheme. New York: Holt, Rinehait & Winston, Inc. Piaget, J. (1929a). Les races lacustres de la Limnaea stagnalis and recherches sur la rapports de l'adaptation hereditaire avec la milieu. Bulletin biologique de la France et de la Belgique, 62, 424. Piaget, J. (1929b). Adaptation de la Limnaea stagnalis aux milieux lacustres de la Suisse romande. Revue Suisse de Zoologie, 36, 263. Piaget, J. (1952). The Origins of Intelligence in Children. New York: International Universities Press. Piaget, J. (1954). The Construction of Reality in the Child. New York: Basic Books. Piaget, J. (1962). Judgment and Reasoning in the Child. London: Routledge & Kegan Paul. (first published in 1928) Piaget, J. (1964). Cognitive development in children: Development and learning. Journal of Research in Science Teaching, 2(3), 176-186. Piaget, J (1970). Genetic Epistemology. New York: Norton. Piaget, J. (1971a). Biology and Knowledge. Chicago: University of Chicago Press.

REFERENCES

273

Piaget, J. (1971b). Problems of equilibration. In C.F. Nodine, J.M. Gallagher & R.H. Humphreys, (Eds.) Piaget and Inhelder: On Equilibration. Proceedings of the First Annual Symposium of the Jean Piaget Society, May. Piaget, J. (1975). From noise to order: The psychological development of knowledge and phenocopy in biology. The Urban Review, 8(3), 209. Piaget, J. (1976). Piaget's theory. In B. Inhelder & H.H. Chipman (Eds.), Piaget and His School. New York: Springer-Verlag. Piaget, J. (1978). Behavior and Evolution. New York: Random House. Piaget, J. (1985). The Equilibration of Cognitive Structures: The Central Problem of Intellectual development. Chicago and London: The University of Chicago Press. Piaget, J. & Inhelder, B. (1962). Le Development des Quantites Physiques chez L'enfant. Neuchatel: Delachauz and Neistel. Piaget, J. & Inhelder, B. (1969). The Psychology of the Child. New York: Basic Books. Piattelli-Palmerini, M. (Ed.) (1980). Language and Learning: The Debate Between Jean Piaget and Noam Chomsky. Cambridge: Harvard University Press. Piburn, M., Sawada, D., Turley, J., Falconer, K., Benford, R., Bloom, I. & Judson, E. (2000). Reformed Teaching Observation Protocol (RTOP) Reference Manual. ACEPT Technical Report No. IN00-3. Tempe, AZ: Arizona Board of Regents, (available from the ACEPT website: acept.asu.edu) Platt, J.R. (1964). Strong inference. Science, 146, 347-353. Popper, K.R. (1965). Conjectures and Refutations: The Growth of Scientific Knowledge. New York: Basic Books. Popper, K.R. (1959). The Logic of Scientific Discovery, Basic Books, New York. Popper, K.R. (1965). Conjectures and Refutations: The Growth of Scientific Knowledge. New York: Basic Books. Posner, M.I. (1988). Structures and functions of selective attention. In T. Boll, & B.K. Bryant, (Eds.), Clinical Neuropsychology and Brain Function: Research, Measurement and Practice. Washington, D.C: American Psychological Association. Rendel, J.M. (1967). Canalization and Gene Control. London: Logos Press. Renner, J.W. & Marek, E.A. (1990). An educational theory base for science teaching. Journal of Research in Science Teaching, 27(3), 241-246. Riegel, K.F. (1973). Dialectic operation: The final period of cognitive development. Human Development, 16, 346-370. Rigdon, J. & Tobias, S. (1991). Tune in, turn off, dropout: Why so many college students abandon science after introductory courses. The Sciences, Jan/Feb, 16-20. Robinson, R. & Niaz, M. (1991). Performance based on instruction by lecture or by interaction and its relationship to cognitive variables. International Journal of Science Education, 13(2), 203-215. Salmon, M.H. (1995). Introduction to Logic and Critical Thinking (3rd Edition). Fort Worth, TX: Harcourt Brace. Schadé, J.P. & Van Groenigen, W.B. (1961). Structural organization of the human cerebral cortex. Acta Anatomica, 47(1-2), 74-111. Scharmann, L.C. (1988a). Locus of control: A discriminator of the ability to foster an understanding of the nature of science among preservice elementary teachers. Science Education, 72(4), 453-465.

274

REFERENCES

Scharmann, L.C. (1988b). The influence of sequenced instructional strategy and locus of control on preservice elementary teachers' understanding of the nature of science. Journal of Research in Science Teaching, 25(7), 589-604. Schick, T.S. Jr. & Vaughn, L. (1995). How to Think About Weird Things: Critical Thinking for a New Age. Mountain View, CA: Mayfield. Science Curriculum Improvement Study. (1970a). Environments: Teacher's Guide. Chicago: Rand McNally. Science Curriculum Improvement Study. (1970b). Subsystems and Variables: Teacher's Guide. Chicago: Rand McNally. Seymour, E. & Hewitt, N. (1997). Talking About Leaving: Why Undergraduates Leave the Sciences. Boulder, CO: Westview Press. Shallice, T. (1982). Specific impairment of planning. In D. E. Broadbent, F.R.S., & L. Weiskrantz, F.R.S. (Eds.), The Neuropsychology of Cognitive Function: Philosophical Transactions of the Royal Society of London, Series B, (298), 199-209. London: The Royal Society. Shayer, M. & Adey, P.S. (1993). Accelerating the development of formal thinking in middle and high school students IV: Three years after a two-year intervention. Journal of Research in Science Teaching, 30, 351-366. Shimamura, A.P., Gershberg, F.B., Jurica, P.J., Mangels, J.A. & Knight, R.T. (1992). Intact implicit memory in patients with focal frontal lobe lesions. Neuropsychologia, 30(10), 931-937. Simon, H.A. (1974). How big is a chunk? Science, 183,482-488. Simons, P.R.J. (1984). Instructing with analogies. Journal of Educational Psychology, 76, 513-527. Slezak, P. (1994a). Sociology of scientific knowledge and scientific education: Part I. Science & Education, 3, 265-294. Slezak, P. (1994b). Sociology of scientific knowledge and scientific education Part II: Laboratory life under the microscope. Science & Education, 3, 329-355. Smith, E.E. & Jonides, J. (1994). Working memory in humans: Neuropsychological evidence. In M.S. Gazzaniga (Ed.), The Cognitive Neurosciences (pp. 1009-1020). Cambridge, MA: MIT Press. Sorensen, K.H. (1999). Factors influencing retention in introductory biology curriculum. Paper presented at the Annual Meeting of the National Association for Research in Science Teaching. March 29, Boston, MA. Squire, L.R. & Zola-Morgan, S. (1991). The medial temporal lobe memory system. Science, 253, 1380-1386. Staver, J.R. (1998). Constructivism: Sound theory of explicating the practice of science and science teaching. Journal of Research in Science Teaching, 35(5), 501-520. Stavy, R. (1991). Using analogy to overcome misconceptions about conservation of matter. Journal of Research in Science Teaching, 28(4), 305-313. Stebbins, R.C. & Allen, B. (1975). Simulating evolution. American Biology Teacher, 37(4), 206. Sternberg, R.J. & Davidson, J.E. (Eds.) (1995). The Nature of Insight. Cambridge, MA: The MIT Press. Stuss, D.T. & Benson, D.F. (1986). The Frontal Lobes. New York: Raven Press. Suarez A. & Rhonheimer, M. (1974). Lineare function. Zurich: Limmat Stiftung. Suppes, P. (1968). The desirability of formalization in science. Journal of Philosophy, 65, 651-664. Teuber, H.L. (1972). Unity and diversity of frontal lobe functions. Acta Neuropsychologica Experimenta, 32, 615-656. Thatcher, R.W. (1991). Maturation of the human frontal lobes: Physiological basis of staging. Developmental Neuropsychology, 7(3), 397-419.

REFERENCES

275

Thatcher, R.W., Walker, R.A. & Giudice, S. (1987). Human cerebral hemispheres develop at different rates and ages. Science, 236, 1110-1113. Thompson, B., Pitts, M.M. & Gipe, J.P. (1983). Use of the Group Embedded Figure Test with children. Perceptual and Motor Skills, 57(1), 199-203. Tootell, R.B.H., Silverman, M.S., Switkes, E. & De Valois, R.L. (1982). Deoxyglucose analysis of retinotopic organization in primate striate cortex. Science, 218,902-904. Treisman, A.M. & Gelade, G. (1980). A feature of integration theory of attention. Cognitive Psychology, 12, 97-136. Treisman, A.M. & Gormican, S. (1988). Feature analysis in early vision: Evidence from search asymmetries. Psychological Review, 95, 15-48. Ulinski, P.S. (1980). Functional morphology of the vertebrate visual system: An essay on the evolution of complex systems. American Zoologist, 20,229-246. Ungerleider, L.G. & Mishkin, M. (1982). Two cortical visual systems. In D.J. Ingle, M.A. Goodale, & R.J.W. Mansfield (Eds.), Analysis of Visual Behavior. Cambridge, MA: MIT Press. Van Heile, P.M. (1986). Structure and Insight, A Theory of Mathematics Education. Orlando, EL: Academic Press. Von Foerster, H. (1984). On constructing a reality. In P. Watzlawick (Ed.), The Invented Reality: How Do We Know What We Believe We Know? New York: Norton. Von Glaserfeld, E. (1995). Radical Constructivism: A Way of Knowing and Learning. London: The Falmer Press. Vygotsky, L.S. (1962). Thought and language. Cambridge, MA: The MIT Press. Waddington, C.H. (1959). Canalization of development and genetic assimilation of acquired characters. Nature, 183(4676), 1654. Waddington, C.H. (1966). Principles of Development and Differentiation. New York: Macmillan. Waddington, C.H. (1975). The Evolution of an Evolutionist. Ithaca, NY: Cornell University Press. Wagman, M. (2000). Scientific Discovery Processes in Humans and Computers. Westport, Conn: Praeger. Wallace, D.B. & Gruber, H.E. (1989). Creative People At Work. New York: Oxford University Press. Wallas, G. (1926). The Art of Thought. New York. Harcourt Brace. (Reprinted in P.E. Vernon (Ed.), Creativity. Middlesex, England: Penguin Education). Wallis, J.D., Anderson, K.C. & Miller, E.K. (2001). Single neurons in prefrontal cortex encode abstract rules. Nature, 411, 953-956. Wandersee, J.H., Mintzes, J.J. & Novak, J.D. (1994). Research on alternative conceptions in science. In D. Gabel (Ed.), Handbook on Research in Science Teaching and Learning. New York: MacMillan. Ward, C., & Herron, J.D. (1980). Helping students understand formal chemical concepts. Journal of Research in Science Teaching, 17(5), 387-400. Watson, J.D. (1968). The Double Helix. Penguin Books: New York. Webb, M.J. (1985). Analogies and their limitations. School Science and Mathematics, 85,645-650. Weinberger, D.R., Berman, K.F. & Illowsky, B. (1988). Physiological dysfunction of dorsolateral prefrontal cortex in schizophrenia, III: a new cohort and evidence for a monoaminergic mechanism. Archive of General Psychiatry, 45(7), 609-615. Weinberger, D.R., Berman, K.F. & Zec, R.F. (1986). Physiological dysfunction of dorsolateral prefrontal cortex in schizophrenia, I: regional cerebral blood flow (rCBF) evidence. Archive of General Psychiatry, 43(2), 114-125.

276

REFERENCES

Welfel, E.R. & Davison, M.L. (1986). The development of reflective judgement during the college years: A four year longitudinal study. Journal of College Student Development, 27(3), 209-216. Westbrook, S.L. & Rogers, L.N. (1994). Examining the development of scientific reasoning in ninth-grade physical science students. Journal of Research in Science Teaching, 31(1), 65-76. Westbrook, S.L. & Marek, E.A. (1991). A cross-age study of student understanding of the concept of diffusion. Journal of Research in Science Teaching, 28, 649-660. Wilson, E.O. (1998). Consilience: The Unity of Knowledge. New York: Knopf. Witkin, H .A., Moore, C. A., Goodenough, F. R., & Cox, P. W. (1977). Field-dependent and fieldindependent cognitive styles and their educational implications. Review of Educational Research, 47(1), 1-64. Witkin, H. A., Oltman, P. K., Raskin, E., & Karp, S. A. (1971). A Manual for the Embedded Figures Tests. Palo Alto, CA: Consulting Psychological Press. Wollman, W. (1977). Controlling variables: Assessing levels of understanding. Science Education, 61(3), 371-383. Wollman, W.T., & Lawson, A.E. (1978). The influence of instruction on proportional reasoning in seventh graders. Journal of Research in Science Teaching, 15(3), 227. Wong, E.D. (1993). Self-generated analogies as a tool for constructing and evaluating explanations of scientific phenomena. Journal of Research in Science Teaching, 30(4), 367-380. Yakolev, P. I., & Lecours, A. R. (1967). The myelogenetic cycles of regional maturation of the brain. In A. Minkwski (Ed.), Regional Development of the Brain in Early Life, (pp. 3-70). Philadelphia: Davis. Yan, B. & Arlin, P.K. (1998). Nonabsolute/relativistic thinking: A common factor underlying models of postformal reasoning? Journal of Adult Development, 2(4), 223-240. Zohar, A., Weinberger, Y. & Tamir, P. (1994). The effect of biology critical thinking project on the development of critical thinking. Journal of Research in Science Teaching, 32(2), 183-196.

INDEX

A Abduction 76 Abstraction 111, 136, 240, 247, 257 Accommodation 5, 6, 20-25, 50, 191, 192, 248 Action potential 31 33, 34, 58, 81 Activity equation Adaptation 11, 13, 148 40, 104 Adaptive resonance 43, 44 Additive strategy, 208 Affirming the consequent 49 Algorithmic strategies 9, 103, 119, 159, 186, 197, 199, 215, 217, 221 Analogical reasoning 9, 103, 119, 186 Analogical transfer 12, 24, 26, 44, 50, 78, 82, 102, 108-111, 114-117, 123-131, 162, Analogy 197, 204 38, 39 Arousal system 1, 6, 12, 15, 19-23, 49, 50, 103, 186, 190, 191 Assimilation 20, 21 Assimilation schemata 26-28, 196, 209, 235 Associative memory 25 Attention window 75 Attentional gating 28 Auditory buffer 31, 33, 35, 116 Axon B

26 Basal forebrain 1-7, 12, 21, 22, 28, 36-39, 42-45, 49, 50, 55, 79, 104, 137, Behavior 143, 160, 206, 232-242, 257 73, 75 Bias node 17 Bonellia 55 Bottom-up 80, 97, 123 Brain growth spurt 29, 30 Brain stem C

Canalization Causal hypothesis Causal question 235, 236, 248, 258 Cell body Cell membrane Central executive

15-18 80 7, 9, 80, 88, 135, 137, 190, 197, 201, 219, 220 31, 106, 107 31, 125, 129, 138 195 277

278

INDEX

29-31 Cerebral cortex 31 Chemical transmitter 109, 110 Chunking 35 Classical conditioning 85, 87, 122, 127, 141,143 Classroom Test of Scientific Reasoning 135, 136, 158 Cognitive skills 204 Combinatorial analysis 85, 143, 214 Combinatorial reasoning 159-161 Concepts by apprehension 79, 81, 120-122, 133, 226, 248, 258 Conceptual change 206-208 Conditional logic 71-73 Conjunctive concepts 25 Connectionist models 22 Conservation of number 122 Conservation of weight 2, 11, 227, 232 Constructivism 15, 36, 45-50, 58, 97, 220, 239 Contradiction 86, 122, 144, 214, 242 Control of variables 43, 81, 122, 144, 214 Correlational reasoning 99 Creative thinking 61 Creature cards 100, 101,227 Critical thinking 209, 218, 244 Curriculum D

Darwinism 12-15 Declarative knowledge 10, 11, 83, 100, 140, 142-146, 153-157, 186, 199, 240 9, 200, 212 Deduction 80 Dendrite Descriptive concepts 59, 68, 70, 79, 80, 98, 159-164, 169, 173-178 57, 58, 122, 217, 226, 236 Descriptive hypothesis Developmental level 58, 122, 144, 164, 165, 174, 212, 213 79 Developmental stage 37, 80 Differentiated Dipole 38, 39 Discovery 1, 2, 26, 45, 183, 190-193, 197-200 202, 204, 205, 208, 216 Disembedding ability 85, 94 Disequilibrium 6, 20-25, 36, 50, 190, 191, 225, 248 E

Embryological development

15

INDEX

279

Emotional boost 51 Encoding 26 Enumerative induction 202, 206 Environment 1-3, 7, 11-13, 17, 20-22, 25, 75, 95 104, 157, 165, 180, 235, 238 Environmental pressure 18-22 Epigenetic landscape 16, 19, 20 Epistemology 227 Equilibration 12, 225 Evolution 11-13, 20, 29, 121, 143, 148, 161, 168, 170, 172, 179, 180, 198 Expectation 4, 6, 36, 40, 41, 104, 188, 192, 193, 234 F

Falsification Feedback Fifth stage Figural Intersection Test Forgetting Formal operational stage Fourth-stage Frontal lobe damage

Frontal lobes Frustration

70, 73

10, 33, 34, 39, 40-51, 83, 85, 111-117, 232-235 97, 134, 224, 225 85, 87 34, 117 123 140 74, 75, 80, 86, 209 72-76, 95, 97, 209, 236 36, 97 G

31, 33 15 12, 15, 19-23 13, 15, 19, 20, 160, 198 85, 88

Generating potential Genetic assimilation Genome Genotype Group Embedded Figures Test H

73 Habit node 26 Hippocampus Hunger drive 37-45 30, 37 Hypothalamus 161-163, 167, 168, 173-175 Hypothetical concepts 8, 86, 200, 212 Hypothetico-deductive Hypothetico-predictive 8, 28, 29, 57-59, 67-71, 75, 79-82, 88, 97, 120-123 132-136, 142-144, 148, 156, 172, 176, 187, 190-211, 220-228, 233-240, 252, 256, 257

280

INDEX

I

99-101 Illumination Incubation 99-101 2, 202-206 Induction Inductive science 203 Inheritance of initially acquired characteristics 15 80, 83-96, 226 Inhibiting ability Innatism 2 Inquiry science 211 Intellectual development 11, 12, 26, 59, 70, 79, 98, 160, 162, 172, 175, 176, 226, 233, 238, 239, 245, 246 11, 79, 159 Intelligence Internal drive 36, 44 Internalization 2, 23, 239, 240 Intuition construction 3, 4, 8, 25, 258 L

Lateral geniculate nucleus 30, 31, 37, 40 Learning 1-11, 22, 25, 26, 32-37, 42, 47, 50-55, 79-83, 95, 103-118, 142, 143, 183, 209, 218, 225-233, 243, 245, 252-258 Learning cycle 54 Learning equation 35, 51, 58, 118, 225 Level 3 122, 127, 131-133, 141, 142, 146 151, 153, 156, 162-164, 172-175, 214, 224, 225 Level 4 122, 127, 131-133, 141-146 151, 153, 155, 156, 162-164, 172-175, 214, 224, 225 Level 5 141-145, 151, 154, 155, 156, 163-166, 172-175, 214, 224, 225 Limbic thalamus 26 Limnaea 13, 14,20 Locus of control 159 Logic 2, 71-74, 98, 183, 198, 200, 203, 207, 208, 261 Logico-mathematical knowledge 25 Long-term memory (ltm) 33, 104 M

Macro-to-micro approach 253 Matching strategy 66, 67, 70, 77, 81 Mellinark Task 55, 60, 68, 69, 73, 80, 236 Memory 4, 25-33, 45, 49, 53, 81, 86, 103-105, 109, 118, 193-197, 210, 224, 228 Mental capacity 2, 82, 86-91, 95, 96, 109 Mental reorganization 23-25

INDEX

Mental structure Misconceptions 132, 157, 174, 211-214, 224-249 Micro-to-macro approach, Modus ponens Modus tollens Motor control system Mutation Myelinization

281

1, 4, 12, 20-22, 34 25, 79, 81, 96-97, 119-121, 128, 253 206-208 206-208 38 13, 20, 22 80, 81

N

Natural selection 12-15, 23, 102, 118, 121, 143, 148, 161, 167-173, 182, 186, 204, 258 208, 211-214, 219, 223, 224, 246, 252, 253 Nature of science Neo-Darwinism 12 Neostriatum 11 Neural model 36 Neural processing 49 Neural rebound 38 Neurons 26, 29-37, 40, 80, 105-117, 190, 191, 200, 225, 230, 243 Nominal stage 233 30, 37, 40-42, 46-48, 104, 105 Nonspecific arousal Nos misconceptions 211, 212 O

Occipital lobe On-center, off-surround Orienting arousal

25 110 39-42, 45, 50, 105, 192, 193 P

Parallel distributed processing Parietal lobe Patterns of argumentation Perseveration Phenocopy Phenotype Phonological loop Physical experience Planning ability Post-formal, stage Post-synaptic activity

25 25 240 75, 83, 84, 210 2 13-15, 19, 20, 160 195 247 84, 92 140 51, 57, 58, 105

282

INDEX

43-50 12 74 99-101, 218, 226 51, 55, 105, 117 81, 143,214 45, 49, 50, 82, 210, 242, 247 10, 100, 160, 227, 240-241 9 25, 43, 47-50, 143, 214, 238 79, 80 9, 28, 187, 188, 197, 201, 219

Pouring Water Task Pragmatism Preoperational stage Preparation Pre-synaptic activity Probabilistic reasoning Problem-solving Procedural knowledge Production systems Proportional reasoning Puberty Puzzling observation R

227 Realism 11, 59, 68, 71, 79-86, 90-98, 120, 132-135, 140-144, Reasoning skill 152-157, 161-177, 211-227, 240, 248, 254, 256 256 Reformed Teaching Observational Protocol 81, 226 Representing ability Resting potential 31 Reticular formation 30, 39 S

Science Curriculum Improvement Study 218 Scientific method 135, 183, 202-206, 218, 255, 257-259 11, 12, 16, 20-26, 49, Self-regulation 59, 183, 190, 191, 212, 225, 239, 247 Sensory cortex 30, 37-42, 45 3 Sensory impressions 6, 79, 80, 122, 141, 225, 226, 228, 233, 235 Sensory-motor Social constructivism 225 Social experience 59,98, 1 2 1 , 2 1 2 Special creation 121 Spinal cord 29 158, 213, 237, 240 Stage 4 134, 141-142, 155-157, 175, 211-227, 237-241, 248, 251 Stage 5 Stage retardation 226, 227, 240 Stimulus 32 Synapse 31, 33 Synaptic strength 33-35, 106, 107

INDEX

283

T

Temporal lobe Terminal knobs Thalamus Theoretical concepts 134, 143, 159-164, 168, 170, 173-179 Top-down search Tower of London Test Transmitter release rate Trial-and-error

11, 25 31 30 79, 82, 98, 99, 119-122,

28 84, 88 34, 51 5

U

3, 37, 233, 235

Undifferentiated V

Ventral subsystem Verification Visual buffer Visual memory Visuo-spatial scratchpad Vital force Vitalism

25 100-101, 241 25 26 195 2, 220, 228, 229, 233 121, 132 W

Wisconsin Card Sorting Task Working memory

73, 75, 80-84 26, 195

This page intentionally left blank

Science & Technology Education Library Series editor: William W. Cobern, Western Michigan University, Kalamazoo, U.S.A.

Publications 1. W.-M. Roth: Authentic School Science. Knowing and Learning in Open-Inquiry Science Laboratories. 1995 ISBN 0-7923-3088-9; Pb: 0-7923-3307-1 2. L.H. Parker, L.J. Rennie and B.J. Fraser (eds.): Gender, Science and Mathematics. Shortening the Shadow. 1996 ISBN 0-7923-3535-X; Pb: 0-7923-3582-1 3. W.-M. Roth: Designing Communities. 1997 ISBN 0-7923-4703-X;Pb: 0-7923-4704-8 4. W.W. Cobern (ed.): Socio-Cultural Perspectives on Science Education. An International Dialogue. 1998 ISBN 0-7923-4987-3; Pb: 0-7923-4988-1 5. W.F. McComas(ed.): The Nature of Science in Science Education. Rationales and Strategies. 1998 ISBN 0-7923-5080-4 6. J. Gess-Newsome and N.C. Lederman (eds.): Examining Pedagogical Content Knowledge. The Construct and its Implications for Science Education. 1999 ISBN 0-7923-5903-8 7. J. Wallace and W. Louden: Teacher’s Learning. Stories of Science Education.2000 ISBN 0-7923-6259-4; Pb: 0-7923-6260-8 8. D. Shorrocks-Taylor and E.W. Jenkins (eds.): Learning from Others. International Comparisons in Education. 2000 ISBN 0-7923-6343-4 9. W.W. Cobern: Everyday Thoughts about Nature. A Worldview Investigation of Important Concepts Students Use to Make Sense of Nature with Specific Attention to Science. 2000 ISBN 0-7923-6344-2; Pb: 0-7923-6345-0 10. S.K. Abell (ed.): Science Teacher Education. An International Perspective. 2000 ISBN 0-7923-6455-4 11. K.M. Fisher, J.H. Wandersee and D.E. Moody: Mapping Biology Knowledge. 2000 ISBN 0-7923-6575-5 12. B. Bell and B. Cowie: Formative Assessment and Science Education. 2001 ISBN 0-7923-6768-5; Pb: 0-7923-6769-3 13. D.R.Lavoie and W.-M. Roth (eds.): Models of Science Teacher Preparation. Theory into Practice. 2001 ISBN 0-7923-7129-1 14. S.M. Stocklmayer, M.M. Gore and C. Bryant (eds.): Science Communication in Theory and Practice, 2001 ISBN 1-4020-0130-4; Pb: 1-4020-0131-2 ISBN 1-4020-0514-8 15. V.J. Mayer (ed.): Global Science Literacy. 2002 16. D. Psillos and H. Niedderer (eds.): Teaching and Learning in the Science Laboratory. 2002 ISBN 1-4020-1018-4 17. J.K. Gilbert, O. De Jong, R. Justi,D.F. Treagust and J.H. Van Driel (eds.): Chemical Education: Towards Research-based Practice. 2003 ISBN 1-4020-1112-1 18. A.E. Lawson: The Neurological Basis of Learning, Development and Discovery. Implications for Science and Mathematics Instruction. 2003 ISBN 1-4020-1180-6

KLUWER ACADEMIC PUBLISHERS – DORDRECHT / BOSTON / LONDON