Mathematics Education and Subjectivity Cultures and Cultural Renewal
This book rethinks mathematical teaching and learning with view to changing them to meet or resist emerging demands. Through considering how teachers, students and researchers make sense of their worlds, the book explores how some linguistic and socio-cul
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Mathematics Education Library VOLUME 51 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 K. Ruthven, Cambridge, United Kingdom A. Sfard, Haifa, Israel Y. Shimizu, Tsukuba, Japan O. Skovsmose, Aalborg, Denmark
For further volumes: http://www.springer.com/series/6276
Tony Brown
Mathematics Education and Subjectivity Cultures and Cultural Renewal
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Prof. Tony Brown Manchester Metropolitan University Education and Social Research Institute Didsbury Manchester, M20 2RR, UK [email protected]
Chapter Four results from work with Una Hanley. ISBN 978-94-007-1738-1 e-ISBN 978-94-007-1739-8 DOI 10.1007/978-94-007-1739-8 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2011931871 © 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)
Acknowledgements
I would firstly like to thank the people who have generously contributed to this book. The book commences with some joint writing with Krista Bradford resulting from a project in Africa, where I worked with British volunteers in schools and teacher colleges. Some material is used by kind permission of flm publishing. Chapter 2 draws on a paper published in Educational Studies in Mathematics. It also includes drawings by Sally Jackson and some writing by James Clegg, along with some very stimulating contributions from their colleagues in the class of 08/09. The work on planets was shared with Dave Heywood and Yvette Solomon. Thanks particularly to our students: Clare Crookall, Claire Shakeshaft and Jenny Taylor. Chapter 3 draws on an earlier paper in Educational Philosophy and Theory. It further includes an image inspired by the work of the mathematician Caroline Series, from the site maintained by Peter Liepa (brainjam.ca/fractals.html). Meanwhile, Chapter 4 results from work with Una Hanley. Chapters 5, 6 and 7 draw on material originally published in Educational Studies in Mathematics. This work provoked an exchange with Luis Radford and Norma Presmeg following my response to the special issue of that journal to which they contributed. Their response also appeared in the same journal. Subsequent conversations have resulted in major shifts in my thinking that I have sought to represent in this book. Bill Kirkby provided the work on Doubling Modulo. In the background, however, there were a number of people who have
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