Windows on Mathematical Meanings Learning Cultures and Computers
This book is the culmination of some ten years' theoretical and empirical investigation. Throughout this period, we have come into contact with many who have stimulated our thinking, some of whom belong to the community of Mathematics Educators. Our membe
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Mathematics Education Library VOLUME 17
Managing Editor A.J. Bishop, Monash University, Melbourne, Australia
Editorial Board H. Bauersfeld, Bielefeld, Germany J. Kilpatrick, Athens, U.S.A. C. Laborde, Grenoble, France G. Leder, Melbourne, Australia S. Tumau, Krakow, Poland
The titles published in this series are listed at the end o/this volume.
WINDOWS ON MATHEMATICAL MEANINGS LEARNING CULTURES AND COMPUTERS
by RICHARD NOSS & CELIA HOYLES University of London, u.K.
KLUWER ACADEMIC PUBLISHERS DORDRECHT I BOSTON I LONDON
Library of Congress Cataloging-in-Publication Data Noss. R1ch.rd. W1ndows on mathemat1cal mean1ngs : learn1ng cultures and computers I by R1ehard Noss & Cel1a Hoyles. p. ca. -- (Matheaat1cs educat10n 11brary ; v. 17) Inc I udes 1ndex. 1. Matheaat1es--Study and teach1ng. II. T1tle. III. Ser1es. CA11.N66
I. Hoyles. Cel1a. 1946-
1996
610' .71--dc20
96-17822
ISBN-13: 978-0-7923-4074-4
e-ISBN-13: 978-94-009-1696-8
001: 10.1007/978-94-009-1696-8
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 332, 3300 AH Dordrecht, The Netherlands.
Printed on acid-free paper
All Rights Reserved © 1996 Kluwer Academic Publishers Softcover reprint of the hardcover 1st edition 1996 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.
CONTENTS
Foreword Chapter 1. Visions of the mathematical 1. Reshaping mathematics, revisioning learning 2. Computers ... 3 .... and cultures 4. Windows on methodologies
Vlll
1 2
5 7 9
12 Chapter 2. Laying the Foundations 1. Introduction 12 2. Meanings in mathematics education: a brief survey 14 2.1. Meanings from mathematical objects 14 15 2.2. Meanings from problem solving 2.3. Meanings constructed by the individual learner 17 2.4. From enactive to reflective mathematical knowledge: 19 spirals of abstraction? 3. Vignette: The N-task 22 30 4. The influence of setting on mathematical behaviour 4.1. Problematising children's performance 31 4.2. Into the cul-de-sac: situated mathematical expression 33 5. Street mathematics 36 5.1. Meaning mathematically in the street and in school 36 38 5.2. The role of representations 41 6. A way out of the cul-de-sac? 6.1. Language and tools 42 6.2. Abstract versus concrete? 43 6.3. Returning to the vignette 47 7. Rethinking abstraction 48 Chapter 3. Tools and technologies 1. Computers and educational cultures 2. A preliminary case for programming 2.1. Computers and conviviality 3. The development of a programming culture 3.1. The developme
