New Directions for Situated Cognition in Mathematics Education Mathematics Education Library VOLUME 45 Managing Editor A.J. Bishop, Monash University, Melbourne, Australia Editorial Board J.P. Becker, Illinois, U.S.A. C. Keitel, Berlin, Germany F. Leung, Hong Kong, China G. Leder, Melbourne, Australia D. Pimm, Edmonton, Canada A. Sfard, Haifa, Israel O. Skovsmose, Aalborg, Denmark The titles published in this series are listed at the end of this volume. Anne Watson Peter Winbourne (Editors) New Directions for Situated Cognition in Mathematics Education Ann Watson University of Oxford Oxford UK
[email protected] Peter Winbourne London South Bank Unviersity London UK
[email protected] Series Editor: Alan Bishop Monash University Melboure 3800 Australia
[email protected] Library of Congress Control Number: 2007939044 ISBN -13: 978-0-387-71577-3 e-ISBN-13: 978-0-387-71579-7 Printed on acid-free paper. ¤ 2008 Springer Science+Business Media, LLC. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 springer.com Contents Contributing Authors Introduction ANNE WATSON AND PETER WINBOURNE School Mathematics As A Developmental Activity STANISLAV ŠTECH Participating In What? Using Situated Cognition Theory To Illuminate Differences In Classroom Practices MARIA MANUELA DAVID AND ANNE WATSON vii 1 13 31 Social Identities As Learners And Teachers Of Mathematics MIKE ASKEW 59 Looking For Learning In Practice: How Can This Inform Teaching PETER WINBOURNE 79 Are Mathematical Abstractions Situated? MEHMET FATIH OZMANTAR AND JOHN MONAGHAN 103 ‘We Do It A Different Way At My School’ MARTIN HUGHES AND PAMELA GREENHOUGH 129 Situated Intuition And Activity Theory Fill The Gap JULIAN WILLIAMS, LIORA LINCHEVSKI AND BILHA KUTSCHER 153 vi Contents The Role Of Artefacts In Mathematical Thinking: A Situated Learning Perspective MADALENA PINTO DOS SANTOS AND JOÃO FILIPE MATOS 179 Exploring Connections Between Tacit Knowing And Situated Learning Perspectives In The Context Of Mathematics Education 205 CRISTINA FRADE, JORGE TARCÍSIO DA ROCHA FALCÃO Cognition And Institutional Setti