The Philosophy of Mathematics Education

[Pages:344]The Philosophy of Mathematics Education

The Philosophy of Mathematics Education

Paul Ernest

? Paul Ernest 1991

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First published 1991

This edition published in the Taylor & Francis e-Library, 2004.

RoutledgeFalmer is an imprint of the Taylor & Francis Group

British Library Cataloguing in Publication Data Ernest, Paul

The philosophy of mathematics education. 1. Education. Curriculum subjects: Mathematics. Teaching. I. Title 510.7 ISBN 0-203-49701-5 Master e-book ISBN

ISBN 0-203-55790-5 (Adobe eReader Format) ISBN 1-85000-666-0 (Print Edition) ISBN 1-85000-667-9 pbk Library of Congress Cataloging-in-Publication Data is available on request

Contents

List of Tables and Figures

viii

Acknowledgments

ix

Introduction

xi

Rationale

xi

The Philosophy of Mathematics Education

xii

This Book

xiv

Part 1 The Philosophy of Mathematics

1

1 A Critique of Absolutist Philosophies of Mathematics

3

Introduction

3

The Philosophy of Mathematics

3

The Nature of Mathematical Knowledge

4

The Absolutist View of Mathematical Knowledge

7

The Fallacy of Absolutism

13

The Fallibilist Critique of Absolutism

15

The Fallibilist View

18

Conclusion

20

2 The Philosophy of Mathematics Reconceptualized

23

The Scope of the Philosophy of Mathematics

23

A Further Examination of Philosophical Schools

27

Quasi-empiricism

34

3 Social Constructivism as a Philosophy of Mathematics

42

Social Constructivism

42

Objective and Subjective Knowledge

45

Social Constructivism: Objective Knowledge

49

A Critical Examination of the Proposals

60

4 Social Constructivism and Subjective Knowledge

68

Prologue

68

The Genesis of Subjective Knowledge

69

v

Contents

Relating Objective and Subjective Knowledge of Mathematics

81

Criticism of Social Constructivism

85

5 The Parallels of Social Constructivism

89

Introduction

89

Philosophical Parallels

89

Sociological Perspectives of Mathematics

93

Psychological Parallels

101

Conclusion:A Global Theory of Mathematics

106

Part 2 The Philosophy of Mathematics Education

109

6 Aims and Ideologies of Mathematics Education

111

Epistemological and Ethical Positions

111

Aims in Education: An Overview

121

7 Groups with Utilitarian Ideologies

137

Overview of the Ideologies and Groups

137

The Industrial Trainers

140

The Technological Pragmatists

151

8 Groups with Purist Ideologies

168

The Old Humanists

168

The Progressive Educators

181

9 The Social Change Ideology of the Public Educators

197

The Public Educators

197

A Critical Review of the Model of Ideologies

214

10 Critical Review of Cockcroft and the National Curriculum

217

Introduction

217

The Aims of Official Reports on Mathematics Education

219

The National Curriculum in Mathematics

224

Conclusion

230

11 Hierarchy in Mathematics, Learning, Ability and Society

232

Hierarchy in Mathematics

232

Hierarchy in Learning Mathematics

238

The Hierarchy of Mathematical Ability

243

Social Hierarchy

248

Inter-relating Mathematical, Ability, and Social Hierarchies

254

12 Mathematics,Values and Equal Opportunities

259

Mathematics and Values

259

Anti-racist and Multicultural Mathematics Education

266

Gender and Mathematics Education

274

Conclusion

279

vi

Contents

13 Investigation, Problem Solving and Pedagogy

281

Mathematics Results from Human Problem Posing and Solving

281

Problems and Investigations in Education

283

The Power of Problem Posing Pedagogy

291

Conclusion

295

References

297

Index

317

vii

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