A Journey in Mathematics Education Research Insights from the Work o
This book presents ideas developed by Paul Cobb and his colleagues that have significantly influenced the field of mathematics education over the past three decades. In this volume, they are brought together for readers to present a clear view of how the
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Mathematics Education Library VOLUME 48 Managing Editor A.J. Bishop, Monash University, Melbourne, Australia
Editorial Board M.G. Bartolini Bussi, Modena, Italy J.P. Becker, Illinois, U.S.A. M. Borba, Rio Claro, Brazil B. Kaur, Singapore C. Keitel, Berlin, Germany G. Leder, Melbourne, Australia F. Leung, Hong Kong, China D. Pimm, Edmonton, Canada K. Ruthven, Cambridge, United Kingdom A. Sfard, Haifa, Israel Y. Shimizu, Tennodai, Japan O. Skovsmose, Aalborg, Denmark
For further volumes: http://www.springer.com/series/6276
Erna Yackel · Koeno Gravemeijer · Anna Sfard Editors
A Journey in Mathematics Education Research Insights from the Work of Paul Cobb
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Editors Erna Yackel Purdue University Calumet 730 Roy St Dyer, Indiana, 46311 USA [email protected]
Koeno Gravemeijer Eindhoven University of Technology Eindhoven School of Education Campus TU/e, Traverse 3.27 5600 MB Eindhoven The Netherlands [email protected]
Anna Sfard University of Haifa Dror Street 4 68135 Tel Aviv Apt. 11 Israel [email protected]
ISBN 978-90-481-9728-6 e-ISBN 978-90-481-9729-3 DOI 10.1007/978-90-481-9729-3 Springer Dordrecht Heidelberg London New York © Springer Science+Business Media B.V. 2011 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Paul dedicates this book to his mother, to the memory of his father, and to Jenny, his partner in life for over 35 years.
Foreword
Paul Cobb’s contributions to research in mathematics education in the past quarter century have been outstanding and exemplary. The progression of his understanding represented in this very valuable and enjoyable volume corresponds in important ways to a progression of concepts and methods that developed in the field of mathematics education research and, more generally, in the learning sciences. Cobb’s trajectory is a prototype of the field’s progress. He has played, and continues to play, a major role in shaping the problems, methods, and explanations that the field has developed, and, in turn, the problems, methods, and explanations he has developed have been shaped by those that others in the field have developed. In this foreword, I hope to make two points, both of which relate Cobb’s extraordinary contributions to the advancement of the learning sciences, especially in mathematics education research, during the time that he (and I) have been active members of these communities. First, I describe my understanding of some ways in which the field has progressed. Cobb’s progression is prototypical and seminal in the field’s conceptual trajectory during this period, as I understand it, alth
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