Early Algebraization A Global Dialogue from Multiple Perspectives
In recent years there has been increased interest in the development of students’ algebraic thinking in the elementary and middle school grades. This important and timely new volume contains the most comprehensive collection of research focused on early a
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Editors: Prof. Dr. Gabriele Kaiser, University of Hamburg Prof. Dr. Bharath Sriraman, The University of Montana
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Jinfa Cai
Eric Knuth
Editors
Early Algebraization A Global Dialogue from Multiple Perspectives
Prof. Jinfa Cai Dept. Mathematical Sciences University of Delaware Ewing Hall 501 Newark, DE 19716 USA [email protected]
Prof. Eric Knuth University of Wisconsin-Madison Teacher Education Building, 225 N. Mills Street Madison, WI 53706 USA [email protected]
ISSN 1869-4918 e-ISSN 1869-4926 ISBN 978-3-642-17734-7 e-ISBN 978-3-642-17735-4 DOI 10.1007/978-3-642-17735-4 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011922614 © Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights 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 its current 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 for general use. Cover design: deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Foreword
Early Algebraization: A Global Dialogue from Multiple Perspectives is the second monograph in the Advances in Mathematics Education (AiME) series launched by Springer in 2009. The book follows in the tradition of Theories of Mathematics Education (Sriraman and English, monograph 1), stemming from a previous ZDM issues on early algebraic thinking (vol. 37, no. 1, 2005 and vol. 40, no. 1, 2008). That is, although it uses the previous issues as a basis for the current monograph, the monograph itself goes beyond simply revisiting the past. It conveys the present state of the art on existing research on early algebraization since 2005. The eight previous articles (five from vol. 37 and 3 from vol. 40) have been reworked and updated in addition to 18 new chapters from researchers involved in early algebraization research projects in different parts of the world, which include 4 commentaries on the scope of the research. The book editors Jinfa Cai and Eric Knuth have compiled the book in three substantial parts between the bookends of a general introduction and an overall commentary addressing perspectives for research and teaching in this domain of inquiry. These three parts of the book examine curricular, cognitive and instructional components of early algebraizat
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