Mathematics Education as a Research Domain: A Search for Identity An

No one disputes how important it is, in today's world, to prepare students to un­ derstand mathematics as well as to use and communicate mathematics in their future lives. That task is very difficult, however. Refocusing curricula on funda­ mental concept

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New ICMI Studies Series Volume 4 Published under the auspices of The International Commission on Mathematical Instruction under the general editorship of Miguel de Guzman, President

Mogens Niss, Secretary

The titles published In this series are listed at the end of Book 2.

Mathematics Education as a Research Domain: A Search for Identity An ICMI Study Book 1 Edited by:

Anna Sierpinska Concordia University, Montreal, Quebec, Canada

and

Jeremy Kilpatrick University of Georgia, Athens, Georgia, USA

Springer-Science+Business Media, B.V.

Library of Congress Cataloging-in-Publication Data Mathematics education as a research domain : a search for identity : an ICMI study / edited by Jeremy Kilpatrick and Anna Sierpinska. p. cm. — (New ICMI studies series ; v. 4) Includes index. 1. Mathematics—Study and teaching—Research. Jeremy. II. Sierpinska, Anna. III. Series. QA11.M3757 1997

I. Kilpatrick,

510'.71—dc21

ISBN 978-94-010-6186-5

97-20240

ISBN 978-94-011-5194-8 (eBook)

DOI 10.1007/978-94-011-5194-8

Printed on acid-free paper

A l l Rights Reserved © 1998 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1998 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

BOOK 1

Foreword

ix

Part I: The ICMI Study Conference Discussion Document List of Participants What is the Specific Object of Study in Mathematics Education? Report of Working Group 1 What are the Aims of Research in Mathematics Education? Report of Working Group 2 What are the Specific Research Questions or Probtematiques of Research in Mathematics Education? Report of Working Group 3 What are the Results of Research in Mathematics Education? Report of Working Group 4 What Criteria Should Be Used to Evaluate the Results of Research in Mathematics Education? Report of Working Group 5

3 9 9 14 20 23 28

ALAN J. BISHOP

Research, Effectiveness, and the Practitioners' World

33

Part II: Mathematics Education as a Research Discipline JOSETIE ADDA

A Glance Over the Evolution of Research in Mathematics Education

49

NORMA C. PRES MEG

Balancing Complex Human Worlds: Mathematics Education as an Emergent Discipline in its Own Right

57

PAUL ERNEST

A Postmodern Perspective on Research in Mathematics Education

71

ERICH CH. WITIMANN

Mathematics Education as a 'Design Science'

87

ROBERTA MURA

What is Mathematics Education? A Survey of Mathematics Educators in Canada

105

vi

TABLE OF CONTENTS

GUNNAR GJONE

Programs for the Education of Researchers in Mathematics Education

117

Part III: Goals, Orientations and Results of Research in Mathematics Education GILAH C. LEDER

The Aims of Research

131

JAMES HIEBERT

Aiming Research Toward Understanding: Lessons We Can Learn From Children

141

NERIDA F. ELLERTON & M. A. ('KEN') CLEMENTS Transforming the Int