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Radical constructivism

Transcript of Radical Constructivism

Radical Constructivism

Studies in Mathematics Education Series

Series Editor Paul Ernest School of Education University of Exeter Exeter 1 2 3 4 The Philosophy of Mathematics Education Paul Ernest Understanding in Mathematics Anna Sierpinska Mathematics Education and Philosophy: An International Perspective Edited by Paul Ernest Constructing Mathematical Knowledge: Epistemology and Mathematics Education Edited by Paul Ernest Investigating Mathematics Teaching: A Constructivist Enquiry Barbara Jaworski Radical Constructivism: A Way of Knowing and Learning Ernst von Glasersfeld

5 6

Studies in Mathematics Education Series: 6

Radical Constructivism:A Way of Knowing and Learning

Ernst von Glasersfeld


RoutledgeFalmer, 11 New Fetter Lane. London EC4P 4EE RoutledgeFalmer, 29 West 35th Street. New York NY 10001

E.von Glasersfeld 1995 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without permission in writing from the Publisher. First published in 1995 This edition published in the Taylor & Francis e-Library, 2003. Routledge Falmer is an imprint of the Taylor & Francis Group A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data are available on request ISBN 0-203-45422-7 Master e-book ISBN

ISBN 0-203-76246-0 (Adobe eReader Format) ISBN 0 7507 0387 3 cased ISBN 0 7507 0572 9 limp


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


Preface by Series Editor Preface Acknowledgments List of Figures Chapter 1 Growing up Constructivist: Languages and Thoughtful People Which Language Tells It as It Is? The Wrong Time in Vienna Growing Roots in Dublin Interdisciplinary Education A Close Look at Meanings The American Connection Introduction to Psychology Collaboration with a Chimpanzee Discovering Piaget From Mental Operations to the Construction of Reality A Decisive Friendship Teaching Experiments The Spreading of Constructivist Ideas Retirement and a New Beginning Support from Physics and Philosophy of Science Chapter 2 Unpopular Philosophical Ideas: A History in Quotations Objectivity Put in Question The Pre-Socratics Theological Insights Modern Science Widens the Rift A Failure and an Achievement of Descartes Lockes Forgotten Reflection The Exaggeration of the Blank Slate A Reinterpretation of Berkeley

xi xiii xv xvi

1 2 3 4 6 7 8 9 11 12 13 15 17 18 19 20

24 25 26 27 28 30 31 32 33vii


Humes Deconstruction of Perceptual Relations Bentham and VicoPioneers of Conceptual Analysis Kants Transcendental Enterprise A Re-assessment of Causality New Fuel for Instrumentalism Hypotheses and Fictions The Foundation of Language Analysis Conclusion Chapter 3 Piagets Constructivist Theory of Knowing The Biological Premise Active Construction Beginnings The Construction of Experiential Reality Individual Identity Assimilation From Reflexes to Scheme Theory Accommodation The Concept of Equilibration Learning Different Types of Abstraction Stages of Development The Observer and the Observed Experience and Reality Conclusion Chapter 4 The Construction of Concepts Analysis of Operations The Concept of Change The Concept of Motion Generating Individual Identity Space and Time Conclusion Chapter 5 Reflection and Abstraction Reflection Abstraction Generalization The Notion of Re-presentation Re-presenting Past Experiences Recognition The Need of an Agentviii

34 36 38 41 42 45 46 48 53 54 56 57 58 60 62 64 65 67 68 69 71 72 73 74 76 79 80 82 84 86 87 89 90 91 92 93 94 95 96


Meaning as Re-presentation The Power of Symbols Piagets Theory of Abstraction Form and Content Four Kinds of Abstraction The Question of Awareness Operational Awareness Conclusion Philosophical Postscript Chapter 6 Constructing Agents: The Self and Others The Illusion of Encoded Information The Reality of Experience Analysis of Empirical Construction The Question of Objectivity Corroboration by Others The Elusive Self The Notion of Environment The Perceived Self Sensory Clues Reflected Images The Social Self Conclusion Chapter 7 On Language, Meaning, and Communication The Semantic Basis Language Games The Construction of Meaning Language and Reality Theory of Communication How We May Come to Use Language To Understand Understanding Why Communication? Why Language? Chapter 8 The Cybernetic Connection Declaration of the American Society for Cybernetics Feedback, Induction, and Epistemology A Learning Mechanism Cognitive Development The Inductive Basis of Instrumental Learning Negative Feedback as Information The Nature of Hypothetical Models

98 99 100 101 103 105 108 109 110 113 115 116 118 119 120 121 123 124 125 126 126 128 129 130 133 134 136 138 139 141 143 146 146 150 152 153 153 155 157ix


Chapter 9

Units, Plurality and Number An Elusive Definition Things and Units Conception Rather than Perception The Attentional Model An Iteration of Pulses The Genesis of Plurality The Abstract Concept of Number The Pointing Power of Symbols Mathematical Certainty

160 160 163 164 167 168 170 171 173 174 176 176 178 179 179 181 183 184 185 186 188 190 191 192

Chapter 10

To Encourage Students Conceptual Constructing What Is Our Goal? Teaching Rather than Training Environmental Stimuli Reinforcement The Deceptive Character of Language The Orienting Function Perceptual Materials A Geometric Point The Need to Infer Students Thinking Help Rather than Instruction Fostering Reflection The Secret of Social Interaction A Final Point

References Index of Names Subject Index

193 205 209


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, semiotics, hermeneutics, post-structuralism and post-modernism. The series Studies in Mathematics Education consists 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 practitioners most powerful tool in understanding and 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 Education will encourage the development and dissemination of theoretical perspectives in mathematics education as well as their critical scrutiny. It aims to have a major impact on the development of mathematics education as a field of study into the twentyfirst century. In the past decade or two, the most important theoretical perspective to emerge in mathematics education has been that of constructivism. This burst onto the international scene at the exciting and controversial Eleventh International Conference on the Psychology of Mathematics Education in Montral, in the Summer of 1983. No one who was there will forget Ernst von Glasersfelds calm and authoritative plenary panel presentation on radical constructivism, and his replies to critics. That controversy confirmed his earlier observation that To introduce epistemological considerations into a discussion of education has always been dynamite (Glasersfeld, 1983, p.41). Ironically, the attacks on radical constructivism at that conference, which were perhaps intended to fatally expose its weaknesses, served as a platform from which it was launched to widespread international acceptance and approbation. In this volume Ernst von Glasersfeld offers what I believe to be the definitive theoretical account of radical constructivism. It is an elegantly written and thoroughly argued account of this epistemological position, providing a profound analysis of its central concepts. Although he indicates hisxi

Preface by Series Editor

debt to Jean Piaget (and indeed to collaborators such as Leslie P. Steffe), Glasersfeld shows that the roots of radical constructivism are much older. A great strength of the book consists in the two genealogies of knowledge which are offered as an orientating basis. These veritable genetic epistemologies trace the development of the central ideas of radical constructivism along two tracks. The first is the history of philosophy from the pre-Socratic masters of Ancient Greece to the present. The second is his own intellectual biography. In it Glasersfeld illustrates how a number of lines of thought from cybernetics, linguistics, developmental psychology, cognitive science and philosophy became synthesized into radical constructivism. Given these diverse roots, I expect this first full articulation of the theory to have an influence that extends beyond mathematics education. Radical constructivism is a progressive research programme with many strengths. To mention but two, it is first of all a sceptical position in epistemology, which incorporates a fallibilist view of mathematics. This is consistent with much of the latest work in the philosophy of mathematics, as earlier volumes in the series show. Secondly, radical constructivism continues to grow and develop. The definitive account that this book provides will in no way inhibit its continu