Mathematical Enculturation A Cultural Perspective on Mathematics Edu
Mathematics is in the unenviable position of being simultaneously one of the most important school subjects for today's children to study and one of the least well understood. Its reputation is awe-inspiring. Everybody knows how important it is and everyb
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Mathematics Education Library VOLUME 6
Managing Editor
A.J. Bishop, Cambridge, U.K.
Editorial Board
H. Bauersfeld, Bielefeld, Germany J. Kilpatrick, Athens, U.S.A. G. Leder, Melbourne, Australia S. Turnau, Krakow, Poland G. Vergnaud, Paris, France
The titles published in this series are listed at the end 0/ this volume.
ALAN J. BISHOP Department of Education, University of Cambridge
MATHEMA TICAL ENCUL TURA TION A Cultural Perspective on Mathematics Education
KLUWER ACADEMIC PUBLISHERS DORDRECHT I BOSTON I LONDON
Library of Congress Cataloging-in-Publication Data Bishop, Alan J. Mathematical encuIturation. (Mathematics education library) Bibliography: p. Includes index. 1. Mathematics-Study and teaching. II. Series. QA11.B545 1988 507
ISBN-13: 978-0-7923-1270-3 DOl: 10.1007/978-94-009-2657-8
I.
Title. 87-32329
e-ISBN-13: 978-94-009-2657-8
Published by Kluwer Academic Publishers, P.O. Box 17,3300 AA Dordrecht, The Netherlands. Kluwer Academic Publishers incorporates the publishing programmes of D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A.
In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
03-0397-300 Is Third prinlig 1997
Printed on acid-free paper
All Rights Reserved
© 1991 Kluwer Academic Publishers
No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
TABLE OF CONTENTS
xi
PREFACE ACKNOWLEDGEMENTS
xiii
CHAPTER 11 Towards a Way of Knowing
The conflict My task Preliminary thoughts on Mathematics education and culture 1.4. Technique-oriented curriculum 1.5. Impersonal learning 1.6. Text teaching 1.7. False assumptions 1.8. Mathematical education, a social process 1.9. What is mathematical about a mathematical education? 1.10. Overview
1
1.1.
1
1.2. 1.3.
3
CHAPTER 21 Environmental Activities and Mathematical Culture
3 7 9
10 12 13 16 18
20
Perspectives from cross-cultural studies The search for mathematical similarities Counting Locating Measuring Designing 2.7. Playing 2.8. Explaining 2.9. From 'universals' to 'particulars' 2.10. Summary
20 22 23 28 34 38 42 48 55 59
CHAPTER 31 The Values of Mathematical Culture
60
2.1. 2.2. 2.3. 2.4. 2.5. 2.6.
3.1. 3.2. 3.3. 3.4. 3.5. 3.6. 3.7.
Values, ideals and theories of knowledge Ideology - rationalism Ideology - objectism Sentiment - control Sentiment - progress Sociology - openness Sociology - mystery v
60 62 65
69 72 75 77
vi
TABLE OF CONTENTS
CHAPTER 4/ Mathematical
Culture and the Child
4.1. 4.2. 4.3. 4.4.
Mathematical culture - symbolic technology and values The culture of a people The child in relation to the cultural group Mathematical enculturation
CHAPTER 5/ Mathematical
5.1. 5.2
