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Richard Barwell · Philip Clarkson Anjum Halai · Mercy Kazima Judit Moschkovich · Núria Planas Mamokgethi Setati-Phakeng Paola Valero Martha Villavicencio Ubillús Editors

Mathematics Education and Language Diversity The 21st ICMI Study

New ICMI Study Series VOLUME Published under the auspices of the International Commission on Mathematical Instruction under the general editorship of Ferdinando Arzarello, President Cheryl E. Praeger, Vice-President.

Abraham Arcavi, Secretary-General

For further volumes: http://www.springer.com/series/6351 Information on the ICMI Study programme and on the resulting publications can be obtained at the ICMI website http://www.mathunion.org/ICMI/ or by contacting the ICMI SecretaryGeneral, whose email address is available on that website.

Richard Barwell • Philip Clarkson Anjum Halai • Mercy Kazima Judit Moschkovich • Núria Planas Mamokgethi Setati Phakeng • Paola Valero Martha Villavicencio Ubillús Editors

Mathematics Education and Language Diversity The 21st ICMI Study

Editors Richard Barwell Faculty of Education University of Ottawa Ottawa, ON, Canada

Philip Clarkson Australian Catholic University Fitzroy, VIC, Australia

Anjum Halai Institute for Educational Development East Africa Aga Khan University Dar es Salaam, Tanzania Judit Moschkovich University of California, Santa Cruz Santa Cruz, CA, USA

Mercy Kazima University of Malawi Zomba, Malawi Núria Planas Universitat Autònoma de Barcelona Barcelona, Catalonia-Spain University of South Africa Pretoria, South Africa Paola Valero Aalborg University Aalborg, Denmark

Mamokgethi Setati Phakeng University of South Africa Pretoria, South Africa Martha Villavicencio Ubillús Ministerio de Educación Lima, Peru

ISSN 1387-6872 New ICMI Study Series ISBN 978-3-319-14510-5 DOI 10.1007/978-3-319-14511-2

ISSN 2215-1745

(electronic)

ISBN 978-3-319-14511-2

(eBook)

Library of Congress Control Number: 2015944108 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 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 c