Activity and Sign Grounding Mathematics Education
The advancement of a scientific discipline depends not only on the "big heroes" of a discipline, but also on a community’s ability to reflect on what has been done in the past and what should be done in the future. This volume combines perspectives on bot
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Michael H.G. Hoffmann Johannes Lenhard Falk Seeger (Editors)
Activity and Sign Grounding Mathematics Education
Springer
Michael H.G. Hoffmann, Georgia Institute of Technology, U.S.A. Johannes Lenhard, University of Bielefeld, Germany Falk Seeger, University of Bielefeld, Germany Library of Congress Cataloging-in-Publication Data Activity and sign: grounding mathematics education / Michael Hoffmann, Johannes Lenhard, Falk Seeger (editors). p. cm. Includes bibliographical references and index. ISBN 10: 0-387-24269-4 ISBN 13: 9870387242699 (acid-free paper)— ISBN 10: 0-387-24270-8 ISBN 13: 9870387242705 (E-book) 1. Mathematics—Study and teaching. 2. Mathematics—Philosophy. I. Hoffmann, Michael (Michael H.G.) II. Lenhard, Johannes. II Seeger, Falk. QA11.2.A28 2005 510’.71—dc22 2004066226 © 2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if the are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 9 8 7 6 5 4 3 2 1 springeronline.com
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TABLE OF CONTENTS
ACKNOWLEDGEMENT MICHAEL HOFFMANN, JOHANNES LENHARD and FALK SEEGER / Grounding Mathematics Education - Michael Otte's contribution MICHAEL OTTE / Mathematics, Sign and Activity
VII 1 9
A. SIGN PROCESSES PAUL ERNEST / Agency and Creativity in the Semiotics of Learning Mathematics SUSANNA MARIETTI / The Semiotic Approach to Mathematical Evidence and GeneraUzation MICHAEL HOFFMANN / Signs as Means for Discoveries. Peirce and His Concepts of "Diagrammatic Reasoning," "Theorematic Deduction," "Hypostatic Abstraction", and "Theoric Transformation" WILLIBALD DORJT^ER / Diagrammatic Thinking. Affordances and Constraints FALK SEEGER / Notes on a Semiotically Inspired Theory of Teaching and Learning
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45 57 67
B. SIGN PROCESSES IN THE MATHEMATICS CLASSROOM MARIA G. BARTOLINI BUSSI, MARIA ALESSANDRA MARIOTTI AND FRANCA FERRI / Semiotic Mediation in the Primary School: Diirer's Glass HEINZ STEINBRING / Do Mathematical Symbols Serve to Describe or Construct "Reahty"? - Epistemological Problems in Teaching Mathematics in the Field of Elementary Algebra NORMA PRESMEG / Metaphor and Metonymy in Processes of Semiosis in Mathematics Education ANNA SIERPINSKA / On Practical and Theoretical Thinking and Other False Dichotomies in Mathematics Education LUIS RADFORD / The Semiotics of the Schema. Kant, Piaget, and the Calculator
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91 105 117 137
C. MATHEMATICS EDUCATION