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Norma Presmeg Luis Radford Wolff-Michael Roth Gert Kadunz

Semiotics in Mathematics Education

ICME-13 Topical Surveys Series editor Gabriele Kaiser, Faculty of Education, University of Hamburg, Hamburg, Germany

More information about this series at http://www.springer.com/series/14352

Norma Presmeg Luis Radford Wolff-Michael Roth Gert Kadunz •

•

Semiotics in Mathematics Education

Wolff-Michael Roth Lansdowne Professor of Applied Cognitive Science University of Victoria Victoria, BC Canada

Norma Presmeg Department of Mathematics Illinois State University Normal, IL USA Luis Radford École des Sciences de l’Education Université Laurentienne Sudbury, ON Canada

ISSN 2366-5947 ICME-13 Topical Surveys ISBN 978-3-319-31369-6 DOI 10.1007/978-3-319-31370-2

Gert Kadunz Department of Mathematics Alpen-Adria Universitaet Klagenfurt Klagenfurt Austria

ISSN 2366-5955

(electronic)

ISBN 978-3-319-31370-2

(eBook)

Library of Congress Control Number: 2016935590 © The Editor(s) (if applicable) and The Author(s) 2016. This book is published open access. Open Access This book is distributed under the terms of the Creative Commons AttributionNonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, a link is provided to the Creative Commons license, and any changes made are indicated. The images or other third party material in this book are included in the work’s Creative Commons license, unless indicated otherwise in the credit line; if such material is not included in the work’s Creative Commons license and the respective action is not permitted by statutory regulation, users will need to obtain permission from the license holder to duplicate, adapt, or reproduce the material. 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 Thi