Becoming a Mathematician An international perspective

Mathematicians are everywhere and nowhere: although they play key roles in industry and research, business and science, the people who use the ideas and tools of the mathematics are often invisible and difficult to identify. This leads to a lack of clarit

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Mathematics Education Library VOLUME 56 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

Leigh N. Wood • Peter Petocz • Anna Reid

Becoming a Mathematician An international perspective

Leigh N. Wood Faculty of Business and Economics Macquarie University North Ryde, NSW, Australia

Peter Petocz Department of Statistics Macquarie University North Ryde, NSW, Australia

Anna Reid Sydney Conservatorium of Music University of Sydney Macquarie Street Sydney, NSW, Australia

ISBN 978-94-007-2983-4 e-ISBN 978-94-007-2984-1 DOI 10.1007/978-94-007-2984-1 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2012932852 © Springer Science+Business Media B.V. 2012 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)

Contents

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Introduction: How Does a Person Become a Mathematician? ........... What This Book Is About ......................................................................... Why Is Mathematics Important? ............................................................... How People Come to Work with Mathematics ......................................... Learning Mathematics .............................................................................. Researching the Experience of Learning and Working with Mathematics ...................................................................................... Dramatis Personae .................................................................................... References .................................................................................................

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How Do Mathematics Students Think of Mathematics? – A First Look ............................................................ Introduction ............................................................................................... Previous Investigation of Views of Mathematics ...................................... Our Study of Students’ Conceptions of Mathematics............................... Conceptions of Mathematics..................................................................... (1) Mathematics Is About Components ............................................... (2) Mathematics Is Abou