New ICMI Study Series Maria G. Bartolini Bussi Xu Hua Sun Editors Building the Foundation: Whole Numbers in the Primary Grades The 23rd ICMI Study New ICMI Study Series Published under the auspices of the International Commission on Mathematical Instruction (ICMI) Series Editors: Jill Adler, ICMI President Ferdinando Arzarello, ICMI Past President Abraham Arcavi, ICMI Secretary General 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 Secretary General, whose email address is available on that website. More information about this series at http://www.springer.com/series/6351 Maria G. Bartolini Bussi • Xu Hua Sun Editors Building the Foundation: Whole Numbers in the Primary Grades The 23rd ICMI Study Editors Maria G. Bartolini Bussi Xu Hua Sun Department of Education and Humanities Faculty of Education University of Modena and Reggio Emilia University of Macau Modena, Italy Macao, China ISSN 1387-6872 ISSN 2215-1745 (electronic) New ICMI Study Series ISBN 978-3-319-63554-5 ISBN 978-3-319-63555-2 (eBook) https://doi.org/10.1007/978-3-319-63555-2 Library of Congress Control Number: 2017960195 © The Editor(s) (if applicable) and The Author(s) 2018. This book is an open access publication. Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, 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. 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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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Foreword The International Commission on Mathematical Instruction (ICMI) was established at the Fourth International Congress of Mathematicians held in Rome in 1908. It was initiated to support active interests in school education which were widespread among mathematicians at the time. ICMI is crucial for the International Mathematical Union (IMU), because education and research cannot be separated from each other. ICMI and the IMU function together for mathematics like the two wheels of a cart, since ICMI develops education systems which enable mathematics to prevail in society, while the IMU contributes to society through the development of pure and applied mathematical sciences. I have been serving the IMU as President since January 2015. Since I served the IMU previously (1995–2002), I have noticed that ICMI and the IMU are working together to establish collaborations given that mathematics education is a major preoccupation of most scientific organisations nowadays. My first physical involvement with ICMI as IMU President started with my par- ticipation in the ICMI Study 23 Conference in Macao in May/June 2015. The ICMI Study 23 was planned and run jointly by its local and foreign co-chairs, with support from the University of Macau. The International Program Committee (IPC) meeting of ICMI Study 23 in Berlin was also supported by the IMU Secretariat. I saw that the support and cooperation of ICMI and the IMU have been essential throughout these activities. I was very pleased to learn that ICMI Study 23 addressed, for the first time, mathematics teaching and learning in primary school (and pre-school as well) for all, and I believe that it will have a larger impact for later mathematics knowing. I hope the volume supports the whole of mathematics education. Kyoto University Shigefumi Mori Kyoto, Japan v Preface I am particularly proud of the publication of this 23rd volume in the series of ICMI Studies, not only since this means that a long scientific and organisational work has been happily accomplished, but also for the outstanding quality of its content and for the absolute relevance of the theme. ICMI Study 23 fully realises the objectives of ICMI ‘to offer a forum for promoting reflection, collaboration and the exchange and dissemination of ideas on the teaching and learning of mathematics from pri- mary to university level’. Concentrating on whole numbers in primary grades repre- sents a relevant signal of interest for a crucial moment in educational programmes everywhere in the world. Never as in this case it is truer that the study addresses a theme of particular significance to contemporary mathematics education. The content of the volume is in perfect consonance with the overall ICMI pro- grammes, according to which ‘ICMI works to stimulate the creation, improvement and dissemination of recent research findings and of the available resources for instruction (e.g curricular materials, pedagogical methods, the appropriate use of technology, etc.). The objective is of providing links among educational research- ers, curriculum designers, educational policy makers, teachers of mathematics, mathematicians, mathematics educators and others interested in mathematical edu- cation around the world’. The people of this study have worked on a project that is challenging both scien- tifically and culturally: the topics in the chapters and in the panel reports of the book, the commentaries on them written by eminent scholars, and the two appendi- ces face a large horizon of themes that go well beyond mathematics and show how focusing on the learning and teaching of whole numbers is an immensely demand- ing task that requires a wide range of competencies in addition to mathematics, from linguistics to ethnomathematics, to neuroscience and more. The processes according to which kids learn and elaborate whole numbers and their properties are incredibly rich and intermingled with the culture where they live and with which they can speak and think, as well as with the artefacts, which the tradition of their countries or the most recent technology allows them to use. vii viii Preface The book builds, in this sense, a real-world map of whole number arithmetic: even if it is far from being complete, it does cover many regions of the world, from East to West, from North to South, including many non-affluent countries. The con- tributions from the different cultures illustrate the fascinating enterprise of the mathematics teachers at the primary level, who from the one side speak the univer- sal language of mathematics, but from the other side can link it to the specific lan- guage and cultural environment of their own countries, in order to make it accessible to their students. This amazing synthesis emerges clearly from the research and practice described in the volume, which has the not-common capacity of intertwin- ing the rigour of mathematics, linguistics, cognitive sciences, etc. with the extraor- dinary different ways according to which numbers are alive in the different regions. It is particularly significant that the study and the volume also had the contribu- tions of invited people from another relevant IMU-ICMI programme, the ‘Capacity and Networking Project (CANP)’, aimed to enhance mathematics education at all levels in developing countries so that their people are capable of meeting the chal- lenges these countries face. Their inputs have been important, since they empha- sised the problems and the specificities of teaching whole numbers in those countries and contributed to the richness and variety of voices in the volume. The 536 pages of the book demonstrate the incredibly intense work of this study, which lasted almost five years, from the appointment of the International Program Committee and its two co-chairs at the end of 2012, to the preparation and organisa- tion of its Conference, which was held in Macao in June 2015, to the last intense work for the preparation and editing of this book, which, as it is usual for the ICMI Study volumes, does not consist of the proceedings of the meeting, but is a further elaboration of the discussions and results reached during the meeting itself. I followed all these phases, and I must say that without the incredible work of the IPC and particularly of the two co-chairs, Profs. Maria G. Bartolini Bussi and Xu Hua Sun, we could not have now so nice a book, which is really a reference and a source of inspiration for theory, research and practice to all the community of researchers, practitioners and policymakers in mathematics education, especially, but not only, those interested in mathematical education at the primary level. On behalf of the ICMI EC and of the ICMI larger family, I wish to thank all of them here for their remarkable work.