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:

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TO

MATT, BOB, BETSY and KRISTINA

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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

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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

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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

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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

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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.

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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

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CHAPTER

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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

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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.

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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

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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.

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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,

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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

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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.

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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.

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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.

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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

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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

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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

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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

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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

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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.

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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.

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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.

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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

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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."

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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

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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

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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.

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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

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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

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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)

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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)

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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.

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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).

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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

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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.

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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

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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

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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

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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

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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.

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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.

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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.

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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.

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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

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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

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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

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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.

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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

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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

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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

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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

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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

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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.

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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.

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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

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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.

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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.

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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:

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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)

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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.

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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

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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.

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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

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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

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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)

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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

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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

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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

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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

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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.

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..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.

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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

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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

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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

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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

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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

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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

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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

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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.

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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,

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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

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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

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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

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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

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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.

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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

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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).

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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 %).

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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

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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

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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).

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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.

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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.

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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.

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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.

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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

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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).

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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.,

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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

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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

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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.

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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

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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.

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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)

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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

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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.

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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

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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.

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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).

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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.

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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.

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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

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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.

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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)

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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

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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

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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

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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

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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

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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

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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

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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.

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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

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(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

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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.

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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