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Advances in Mathematics Education

Editors: Prof. Dr. Gabriele Kaiser, University of Hamburg Prof. Dr. Bharath Sriraman, The University of Montana

Bharath Sriraman Lyn English

Theories of Mathematics Education
Seeking New Frontiers

Prof. Bharath Sriraman Dept of Mathematical Sciences The University of Montana Missoula, MT 59812-0864 USA

Prof. LynEnglish Centre for Learning Innovation Queensland University of Technology Victoria Park Road Kelvin Grove, QLD 4059 Australia

ISBN 978-3-642-00741-5 e-ISBN 978-3-642-00742-2 DOI 10.1007/978-3-642-00742-2 Springer Heidelberg Dordrecht London New York
Library of Congress Control Number: 2009938521 © Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. Allrights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in itscurrent version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free forgeneral use. Cover design: deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (

Series Preface

Advances in Mathematics Education is a new and innovative book series published by Springer that builds on the success and the rich history of ZDM—The International Journal on Mathematics Education (formerly known as Zentralblatt für Didaktik derMathematik). One characteristic of ZDM since its inception in 1969 has been the publication of themed issues that aim to bring the state-of-the-art on central sub-domains within mathematics education. The published issues include a rich variety of topics and contributions that continue to be of relevance today. The newly established monograph series aims to integrate, synthesize and extend papersfrom previously published themed issues of importance today, by orienting these issues towards the future state of the art. The main idea is to move the field forward with a book series that looks to the future by building on the past by carefully choosing viable ideas that can fruitfully mutate and inspire the next generations. Taking inspiration from Henri Poincaré (1854–1912), who said “To createconsists precisely in not making useless combinations and in making those which are useful and which are only a small minority. Invention is discernment, choice”, this is our attempt to create something new for the field by making useful combinations of existing ideas with those that are considered to be at the frontiers of the field of mathematics education research today, to carefully select fromthe past and cross-fertilize ideas across generations with the hope of producing something relevant, forward oriented, synthetic and innovative. The series is supported by an editorial board of internationally well-known scholars, who bring in their long experience in the field as well as their expertise to this series. The members of the editorial board are: Ubiratan D’Ambrosio (Brazil), MiriamAmit (Israel), Jinfa Cai (USA), Helen Forgasz (Australia), and Jeremy Kilpatrick (USA). We hope that the first book in this series on Theories of Mathematics Education provides a prototype of the book series. Theories of Mathematics Education carries forward and consolidates the work and voices of four generations of mathematics education researchers. The book’s inspiration lies in the work of...
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