Knowing_and_Teaching_Elementary_Mathemat (1)

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Knowing and TeachingElementary MathematicsTeachers’ Understanding of FundamentalMathematics in China and the United StatesAnniversary EditionLiping MaNEW YORK AND LONDON
First edition published 1999by Lawrence Erlbaum Associates, Inc.This anniversary edition published 2010by Routledge270 Madison Avenue, New York, NY 10016Simultaneously published in the UKby Routledge2 Park Square, Milton Park, Abingdon, Oxon OX14 4RNRoutledge is an imprint of the Taylor & Francis Group, an informa businessThis edition published in the Taylor & Francis e-Library, 2010.To purchase your own copy of this or any ofTaylor & Francis or Routledge’s collection of thousands of eBooksplease go to www.eBookstore.tandf.co.uk.© 1999 Lawrence Erlbaum Associates, Inc.© 2010 Taylor & FrancisAll rights reserved. No part of this book may be reprinted or reproduced orutilized in any form or by any electronic, mechanical, or other means, nowknown or hereafter invented, including photocopying and recording, or inany information storage or retrieval system, without permission in writingfrom the publishers.Trademark Notice: Product or corporate names may be trademarks orregistered trademarks, and are used only for identification andexplanation without intent to infringe.Library of Congress Cataloging-in-Publication DataMa, Liping.Knowing and teaching elementary mathematics: teachers’ understanding offundamental mathematics in China and the United States/Liping Ma.p. cm—(Studies in mathematical thinking and learning)Includes bibliographical references and index.1. Mathematics—Study and teaching (Elementary)—United States.2. Mathematics—Study and teaching (Elementary)—China. 3. Comparativeeducation. I. TitleQA135.5.M22 2010372.70973–dc22 2009049390ISBN 0-203-85634-1 Master e-book ISBNISBN 10: (hbk) 0-415-87383-5ISBN 10: (pbk) 0-415-87384-3ISBN 10: (ebk) 0-203-85634-1ISBN 13: (hbk) 978-0-415-87383-3ISBN 13: (pbk) 978-0-415-87384-0ISBN 13: (ebk) 978-0-203-85634-5
Page 2 and 3: Knowing and TeachingElementary Math
Page 6 and 7: To Jianfeng, Sushu, and John,and to
Page 8 and 9: viii Contents5. Teachers’ Subject
Page 10 and 11: xAuthor’s Preface to the Annivers
Page 12 and 13: xiiAuthor’s Preface to the Annive
Page 14 and 15: xivSeries Editor’s Introduction t
Page 16 and 17: ForewordLee S.ShulmanThe Carnegie F
Page 18 and 19: xviii Forewordbe tests that assess
Page 20 and 21: AcknowledgmentsAbout 30 years ago,
Page 22 and 23: xxii AcknowledgmentsI would like to
Page 24 and 25: xxiv Introductionthe measurement mo
Page 26 and 27: xxvi Introductionschool or college
Page 28 and 29: xxviii IntroductionChapters 1 throu
Page 30 and 31: Chapter 1Subtraction With Regroupin
Page 32 and 33: Subtraction with Regrouping: Approa
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Multidigit Number Multiplication: D
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Chapter 3Generating Representations
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For some reason it is in the back o
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Generating Representations: Divisio
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We also encourage students to solve
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of math.” She said she used to ha
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been changed. Now what is known is
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While the U.S. teachers tended to u
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Exploring New Knowledge: The Relati
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Teachers’ Subject Matter Knowledg
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105These four properties are interr
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Chapter 6Profound Understanding Of
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Profound Understanding of Fundament
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Chapter 7ConclusionAs I said at the
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Conclusion 125as necessarily preced
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Conclusion 127Time is an issue here
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Conclusion 129evidence, students wo
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AppendixFIG. A.1. The U.S. teachers
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ReferencesArmstrong, B., & Bezuk, N
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References 135Kaput, J., & Nemirovs
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References 137Stein, M., Baxter, J.
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Fang and Paine’s “Bridging pola
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Liping Ma’s “Knowing and Teachi
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Author Index161Ferrucci, B., 150, 1
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Author Index163Simon, M., xxviii, x
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Subject Index165commutative law, 39
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Subject Index167knowledge,see also
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Subject Index169teacher preparation
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