Teaching and Learning About Whole Numbers in Primary School
This book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished – the analytical meaning, defined by the number system, and the representational meaning, identified by the use
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Terezinha Nunes Beatriz Vargas Dorneles Pi-Jen Lin Elisabeth Rathgeb-Schnierer
Teaching and Learning About Whole Numbers in Primary School
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
Terezinha Nunes Beatriz Vargas Dorneles Pi-Jen Lin Elisabeth Rathgeb-Schnierer •
•
Teaching and Learning About Whole Numbers in Primary School
Pi-Jen Lin Graduate Institute of Mathematics and Science Education National Hsinchu University of Education Hsinchu City Taiwan
Terezinha Nunes Department of Education University of Oxford Oxford UK Beatriz Vargas Dorneles Universidade Federal do Rio Grande do Sul Porto Alegre Brazil
ISSN 2366-5947 ICME-13 Topical Surveys ISBN 978-3-319-45112-1 DOI 10.1007/978-3-319-45113-8
Elisabeth Rathgeb-Schnierer University of Education Weingarten Weingarten Germany
ISSN 2366-5955
(electronic)
ISBN 978-3-319-45113-8
(eBook)
Library of Congress Control Number: 2016948110 © 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 Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits 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, provide a link to the Creative Commons license and indicate if changes were made. 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. 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 imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Because we are incapable of grasping quantity directly by sight, we have invented numbers. (Guedj 1998, p. 15)
Acknowledgments
The authors are grateful to the institutions and people who have contributed to the work reported here. Lee Hsiu-Fei from the National Taitung University, Taiwan
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