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Radical Constructivism: a Way of Knowing and Learning. Studies in Mathematics Education Series: 6 DOCUMENT RESUME ED 381 352 SE 056 049 AUTHOR von Glasersfeld, Ernst TITLE Radical Constructivism: A Way of Knowing and Learning. Studies in Mathematics Education Series: 6. REPORT NO ISBN-0-7507-0387-3 PUB DATE 95 NOTE 231p. AVAILABLE FROMFalmer Press, Taylor & Francis Inc., 1900 Frost Road, Suite 101, Bristol, PA 19007. PUB TYPE Books (010) Viewpoints (Opinion/Position Papers, Essays, etc.) (120) EDRS PRICE MF01/PC10 Plus Postage. DESCRIPTORS *Concept Formation; *Constructivism (Learning); Elementary Secondary Education; Foreign Countries; *History; Language Role; *Mathematics Education IDENTIFIERS *Piaget (Jean); Radical Constructivism ABSTRACT This book gives a definitive theoretical account of radical constiructivism., a theory of knowing that provides a pragmatic approach to questions about reality, truth, language and human understanding. The chapter are:(1) "Growing up Constructivist: Languages and Thoughtful People," (2) "Unpopular Philosophical Ideas: A History in Quotations," (3) "Piaget's Constructivist Theory of Knowing," (4) "The Construction of Concepts," (5) "Reflection and Abstraction," (6) "Constructing Agents: The Self and Others," (7) "On Language, Meaning, and Communication," (8) "The Cybernetic Connection," (9) "Units, Plurality and Number," and (10) "To Encourage Students' Conceptual Constructing." Each chapter contains notes. (Contains 218 references.) (MKR) *********************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. *********************************************************************** a,Aical ,,onstructivis A ayof Knowing and Learning ErnstvonGlasersfel U DEPARTMENT OF EDUCATION Office of Educational Research and improvement ED CATIONAL RESOURCES INFORMATION CENTER (ERIC) T s document has been reProduCed es eceivect from see person or organisation Originating it O Minor changes have been mad* to improve "PERMISSION TO REPRODUCE THIS reproduction Quality MATERIAL HAS BEEN GRANTED BY Points of view Of opmions stated m this docu merit do not noceasorily represent official OERI position or polity PM; GAVrkl_ TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC)" &Zs The Falmer Press 2 BEST COPY AVAILABLE Radical Constr activism 3 Studies in Mathematics Education Series Series Editor Paul Ernest School of Education University of Exeter Exeter I The Philosophy of Mathematics Education Paul Ernest 2 Understanding in Mathematics Anna Sierpinska 3 Mathematics Education and Philosophy: An International Perspective Edited by Paul Ernest 4 Constructing Mathematical Knowledge: Epistemology and Mathematics Education Edited by Paul Ernest 5 Investigating Mathematics Teaching: A Constructivist Enquiry Barbara jaworski 6 Radical Constructivism: A Way of Knowing and Learning Ernst von Glasersfeld 4 Studies in Mathematics Education Series: 6 Radical Constructivism: A Way of Knowing and Learning Ernst von Glasersfeld The calmer Press (A member of the Taylor & Francis Group) London * Washington, D.C. 5 ..111 UK The Palmer Press, 4 John Street, London WC1N 2ET USA The Palmer Press, Taylor & Francis Inc., 1900 Frost Road, Suite 101, Bristol, PA 19007 (1) E. von Glasersfeld 1995 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmittedinany form or by any means, electronic, mechanical, photocopying, recording or otherwise, without permission in writ- ing from the Publisher. First published in 1995 A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publicaticn Dataare available on request ISBN 0 7507 0387 3 cased Jacket design by Caroline Archer Typeset in 10/12 pt Bembo by Graphicraft Typesetters Ltd., Hong Kong. Printed in Great Britain by Burgess Science Press, Basingstokeon paper which has a specified pH value on final paper manufacture ofnot less than 7.5 and is therefore 'acid free'. Epigraph The only given is the way of taking. Roland Barthes . Objectivity is the delusion that observations could be made without an observer. Heinz von Foerster 7 Contents Preface by Series Editor Preface Acknowledgments List of Figures Chapter 1 Growing up Constructivist: Languages and Thoughtful People 1 Which Language Tells It 'as It Is'? 2 The Wrong Time in Vienna 3 Growing Roots in Dublin 4 Interdisciplinary Education 6 A Close Look at Meanings 7 The American Connection 8 Introduction to Psychology 9 Collaboration with a Chimpanzee 11 Discovering Piaget 12 From Mental Operations to the Construction of Reality 13 A Decisive Friendship 15 Teaching Experiments 17 The Spreading of Constructivist Ideas 18 Retirement and a New Beginning 19 Support from Physics and Philosophy of Science 20 Chapter 2 Unpopular Philosophical Ideas: A History in Quotations 24 Objectivity Put in Question 25 The Pre-Socratics 26 Theological Insights 27 Modern Science Widens the Rift 28 A Failure and an Achievement of Descartes 30 Locke's Forgotten Reflection 31 The Exaggeration of the 'Blank Slate' A Reinterpretation of Berkeley 33 iii 7.= Contents Hume's Deconstruction of Perceptual Relations 34 Bentham and Vico Pioneers of Conceptual Analysis 36 Kant's 'Transcendental Enterprise' 38 A Re-assessment of Causality 41 New Fuel for Instrumentalism 42 Hypotheses and Fictions 45 The Foundation of Language Analysis 46 Conclusion 48 Chapter 3 Piaget's Constructivist Theory of Knowing 53 The Biological Premise 54 Active Construction 56 Beginnings 57 The Construction of Experiential Reality 58 Individual Identity 60 Assimilation 62 From Reflexes to Scheme Theory 64 Accommodation 65 The Concept of Equilibration 67 Learning 68 Different Types of Abstraction 69 Stages of Development 71 The Observer and the Observed 72 Experience and Reality 73 Conclusion 74 Chapter 4 The Construction of Concepts 76 Analysis of Operations 79 The Concept of Change 80 The Concept of Motion 82 Generating Individual Identity 84 Space and Time 86 Conclusion 87 Chapter 5 Reflection and Abstraction 89 Reflection 90 Abstraction 91 Generalization 92 The Notion of Re-presentation 93 Re-presenting Past Experiences 94 Recognition 95 The Need of an Agent 96 Inn Contents Meaning as Re-presentation 98 ThePower of Symbols 99 Piaget's Theory of Abstraction 100 Form and Content 101 Four Kinds of Abstraction 103 The Question of Awareness 105 Operational Awareness 108 Conclusion 109 Philosophical Postscript 110 Chapter 6 Constructing Agents: Tl:e Self and Others 113 The Illusion of Encoded Information 115 The Reality of Experience 116 Analysis of Empirical Construction 118 The Question of Objectivity 119 Corroboration by Others 120 The Elusive Self 121 The Notion of Environment 123 The Perceived Self 124 Sensory Clues 125 Reflected Images 126 The Social Self 126 Conclusion 128 Chapter 7 On Language, Meaning, and Communication 129 The Semantic Basis 130 Language Games 133 The Construction of Meaning 134 Language and Reality 136 Theory of Communication 138 How We May Come to Use Language 139 To Understand Understanding 141 Why Communication? Why Language? 143 Chapter 8 The Cybernetic Connection 146 Declaration of the American Society for Cybernetics 146 Feedback, Induction, and Epistemology 150 A Learning Mechanism 152 Cognitive Development 153 The Inductive Basis of Instrumental Learning 153 Negative Feedback as 'Information' 155 The Nature of Hypothetical Models 157 ix X10 Contents Chapter 9 Units, Plurality and Number 160 An Elusive Definition 160 Things and Units 163 Conception Rather than Perception 164 The Attentional Model 167 An Iteration of Pulses 168 The Genesis of Plurality 170 The Abstract Concept of Number 171 The 'Pointing Power' of Symbols 173 Mathematical Certainty 174 Chapter 10 To Encourage Students' Conceptual Constructing 176 What Is Our Goal? 176 Teaching Rather than Training 178 I'nvironmental Stimuli 179 Reinforcement 179 The Deceptive Character of Language 181 The Orienting Function 183 Perceptual Materials 184 A Geometric Point 185 The Need to Infer Students' Thinking 186 Help Rather than Instruction 188 Fostering Reflection 190 The Secret of 'Social' Interaction 191 A Final Point 192 References 193 Index of Names 205 Subject Index 209 Preface by Series Editor Mathematics education is now established worldwide as a major area of study, with numerous dedicated journals and conferences serving national and international communities of scholars. Research in mathematics education is also becoming more theoretically orientated. Vigorous new perspectives are pervading it from disciplines and fields as diverse as psychology, philosophy, logic, sociology, anthropology, history, feminism, cognitive science, semiot- ics, hermeneutics, post-structuralism and post-modernism. The seriesStudies in Mathematics Educationconsists of research contributions to the field based on disciplined perspectives that link theory with practice. It is founded on the philosophy that theory is the practitioner's most powerful tool in understand- ing anu changing practice. Whether the practice is mathematics teaching, teacher education, or educational research, the series will offer new perspectives to assist in clarifying and posing problems and to stimulate debate. The series Studies in Mathematics Educationwill encourage the development and dissemi- nation of theoretical perspectives in mathematics education as well as their critical scrutiny. It aims to have a major impact on the development of math- ematics education as a field of study into the twenty-first century. In the past decade or two, the most
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