Discourse Perspective of Geometric Thoughts
Sasha Wang revisits the van Hiele model of geometric thinking with Sfard’s discursive framework to investigate geometric thinking from a discourse perspective. The author focuses on describing and analyzing pre-service teachers’ geometric discourse across
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In der Reihe werden Arbeiten zu aktuellen didaktischen Ansätzen zum Lehren und Lernen von Mathematik publiziert, die diese Felder empirisch untersuchen, qualitativ oder quantitativ orientiert. Die Publikationen sollen daher auch Antworten zu drängenden Fragen der Mathematikdidaktik und zu offenen Problemfeldern wie der Wirksamkeit der Lehrerausbildung oder der Implementierung von Innovationen im Mathematikunterricht anbieten. Damit leistet die Reihe einen Beitrag zur empirischen Fundierung der Mathematikdidaktik und zu sich daraus ergebenden Forschungsperspektiven.
Herausgegeben von Prof. Dr. Gabriele Kaiser Universität Hamburg
Sasha Wang
Discourse Perspective of Geometric Thoughts With a foreword by Anna Sfard, University of Haifa
Sasha Wang Boise State University Idaho, USA
Perspektiven der Mathematikdidaktik ISBN 978-3-658-12804-3 ISBN 978-3-658-12805-0 (eBook) DOI 10.1007/978-3-658-12805-0 Library of Congress Control Number: 2016933534 Springer Spektrum © Springer Fachmedien Wiesbaden 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer Spektrum imprint is published by Springer Nature The registered company is Springer Fachmedien Wiesbaden GmbH
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Foreword What does geometry, the science of space and shape, have to do with talking, the art of juggling words? On the face of it, not much. Indeed, geometry, at least as it is learned in schools, seems to be occurring mainly in images, and images, they say, speak for themselves. At a closer look, however, geometry begins where the visual means alone can no longer tell a story. This is what happens when relations between shapes, rather than the shapes as such, become the protagonists of the narrative. Through words, geometric figures stop being a collection of lonely individuals and start showing hitherto unsuspected family ties. Indeed, it is because of the common elements detectable within definitions of figures rather than of the figures themselves that we cluster different
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