Modelling and Applications in Mathematics Education The 14th ICMI St
The overall goal of Modelling and Applications in Mathematics Education is to provide a comprehensive overview of the state-of-the-art in the field of modelling and applications in mathematics education. Key issues are dealt with, among which are the foll
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New ICMI Study Series
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VOLUME 10 Published under the auspices of the International Commission on Mathematical Instruction under the general editorship of Michele Artigue, President
Bernard R. Hodgson, Secretary-General
The titles published in this series are listed at the end of this volume.
Werner Blum Peter L. Galbraith Hans-Wolfgang Henn Mogens Niss (Editors)
Modelling and Applications in Mathematics Education ith
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Werner Blum University of Kassel/ Germany
Hans-Wolfgang Henn University of Dortmund/ Germany
Peter L. Galbraith The University of Queensland/ Australia
Mogens Niss Roskilde University/ Denmark
Library of Congress Control Number: 2006932713 ISBN-13: 978-0-387-29820-7 ISBN-10: 0-387-29820-7 e-lSBN-13: 978-0-387-29822-1 e-lSBN-10: 0-387-29822-3
Printed on acid-free paper. © 2007 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. While the advice and information in this book are believed to be true and accurate at the date of going to press, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.
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TABLE OF CONTENTS
PREFACE
xi
1
INTRODUCTION
1
MoGENS Niss, WERNER Introduction
2
PLENARIES
33
CLAUDIALSINA
35
2.1
1 BLUM
& PETER
GALBRAITH
3
Less chalk, less words, less symbols ... more objects, more context, more actions 2.2
MORTEN BLOMH0J & TOMAS HOJGAARD JENSEN
45
What's all the fuss about competencies? 2.3
JERE CONFREY & ALAN MALONEY
57
A theory of mathematical modelling in technological settings 2.4
HELEN M . DOERR
69
What knowledge do teachers need for teaching mathematics through applications and modelling? 2.5
PETER GALBRAITH
79
Beyond the low hanging fruit 2.6
BRIAN GREER, LIEVEN VERSCHAFFEL & SWAPNA MUKHOPADHYAY
89
Modelling for life: Mathematics and children's experience 2.7
GABRIELE KAISER & KATJA MAASS
99
Modelling in lower secondary mathematics classroom - problems and opportunities 2.8
HENRY POLLAK
Mathematical modelling - A conversation with Henry Pollak
109
vi
TABLE OF CONTENTS
ISSUES IN APPLICATIONS AND MODELLING
121
3.1
EPISTEMOLOGY AND MODELLING
123
3.1.0
JERECONFREY
125
Epistemo
