Humans-with-Media and the Reorganization of Mathematical Thinking In
This book offers a new conceptual framework for reflecting on the role of information and communication technology in mathematics education. Borba and Villarreal provide examples from research conducted at the level of basic and university-level education
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Mathematics Education Library VOLUME 39 Managing Editor A.J. Bishop, Monash University, Melbourne, Australia
Editorial Board J.P. Becker, Illinois, U.S.A. C. Keitel, Berlin, Germany G. Leder, Melbourne, Australia A. Sfard, Haifa, Israel 0. Skovsmose, Aalborg, Denmark S. Turnau, Rzeszdw, Poland
The titles published in this series are listed at the end of this volume.
Marcelo C. Borba M6nica E. Villarreal (Authors)
Humans-with-Mediaand the Reorganization of Mathematical Thinking Information and Communication Technologies, Modeling, Visualization and Experimentation
Preface by Ubiratan D’Ambrosio Afterword by Ole Skovsmose
- Springer
Marcelo C. Borba, State University of San Paulo at Rio Claro, Brazil Mónica E. Villarreal, University of Córdoba, Córdoba, Argentina
Library of Congress Cataloging-in-Publication Data Borba, Marcelo C. (Marcelo Carvalho) Humans-with-media and the reorganization of mathematical thinking: information and communication technologies, modeling, visualization, and experimentation / Marcelo C. Borba, Mónica E. Villarreal; preface by Ubiratan D’Ambrosio; afterword by Ole Skovsmose. p.cm.—(Mathematics education library; v. 39) Includes bibliographical references and index. ISBN 0-387-24263-5 (acid-free paper) -ISBN 0-387-24264-3 (E-book) 1. Mathematics –Study and teaching –Methodology. 2. Communication in science. I. Villarreal, Mónica E. II. Title. III. Series. QA11.2.B67 2005 510’.71—dc22 2004065301 2005 Springer Science+Business Media, Inc. 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, Inc., 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 know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if the 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. Printed in the United States of America. 9 8 7 6 5 4 3 2 1 springeronline.com
SPIN
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Dedication
This book is dedicated to Anne Kepple
Contents
Dedication
v
Contributing Authors
xi
Preface by Ubiratan D’Ambrosio
Xlll
Foreword
xvii
Acknowledgments
xxi
Why another book about technology and mathematics education? 1. Introduction
1 1
Information technology, reorganization of thinking and humans-with-media 1. The second industrial revolution and education 2. Reorganization of thinking 3. Intershaping relationship: stressing balance 4. Humans and technology: a history of separation 5. Media, humans and knowledge: possibilities of merging
9 9 11 15 17 21
Modeling as a pedagogical approach: resonance with new media 1. Introduction 2. Problem solving, problem posing and modeling 3. Roots of modeling in Brazil 4. P
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