Contents

Part I Introductory Section

1 Building a Strong Foundation Concerning Whole Number Arithmetic in Primary Grades: Editorial Introduction …… 3

Maria G. Bartolini Bussi and Xu Hua Sun

2 Social and Cultural Contexts in the Teaching and Learning of Whole Number Arithmetic …… 19

Maria G. Bartolini Bussi and Xu Hua Sun

3 Language and Cultural Issues in the Teaching and Learning of WNA ……35

Xu Hua Sun and Maria G. Bartolini Bussi

4 On Number Language: A Commentary on Chapter 3…… 71

David Pimm

Part II Working Group Chapters and Commentaries

5 The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes……91

Xu Hua Sun, Christine Chambris, Judy Sayers, Man Keung Siu, Jason Cooper, Jean-Luc Dorier, Sarah Inés González de Lora Sued, Eva Thanheiser, Nadia Azrou, Lynn McGarvey, Catherine Houdement, and Lisser Rye Ejersbo

6 Reflecting on the What and Why of Whole Number Arithmetic: A Commentary on Chapter 5…… 125

Roger Howe 

7 Whole Number Thinking, Learning and Development: Neuro-cognitive, Cognitive and Developmental Approaches…… 137

Joanne Mulligan, Lieven Verschaffel, Anna Baccaglini-Frank, Alf Coles, Peter Gould, Shengqing He, Yunpeng Ma, Jasmina Milinković, Andreas Obersteiner, Nicole Roberts, Nathalie Sinclair, Yanling Wang, Shu Xie, and Der-Ching Yang

8 Whole Number Thinking, Learning and Development: A Commentary on Chapter 7…… 169

Pearla Nesher

9 Aspects that Affect Whole Number Learning: Cultural Artefacts and Mathematical Tasks…… 181

Maria G. Bartolini Bussi, Maitree Inprasitha, Ferdinando Arzarello, Hyman Bass, Ulrich Kortenkamp, Silke Ladel, Caroline Lajoie, Yujing Ni, Thomas Rottmann, Veronica Sarungi, Sophie Soury-Lavergne, and Jenny Young-Loveridge

10 Artefacts and Tasks in the Mathematical Preparation of Teachers of Elementary Arithmetic from a Mathematician’s Perspective: A Commentary on Chapter 9 …… 227

Bernard R. Hodgson

11 How to Teach and Assess Whole Number Arithmetic: Some International Perspectives……. 251

Jarmila Novotná, Berinderjeet Kaur, Ann Gervasoni, Mike Askew, Michiel Veldhuis, Catherine Pearn, and Xu Hua Sun

12 How to Teach and Assess Whole Number Arithmetic: A Commentary on Chapter 11…… 287

Claire Margolinas

13 Connecting Whole Number Arithmetic Foundations to Other Parts of Mathematics: Structure and Structuring Activity ……299

Hamsa Venkat, Sybilla Beckmann, Kerstin Larsson, Yan Ping Xin, Alessandro Ramploud, and Limin Chen

14 Structuring Structural Awareness: A Commentary on Chapter 13…… 325

John Mason Part III Panels

15 Tradition in Whole Number Arithmetic …… 343

Ferdinando Arzarello, Nadia Azrou, Maria G. Bartolini Bussi, Sarah Inés González de Lora Sued, Xu Hua Sun, and Man Keung Siu Contents

16 Special Needs in Research and Instruction in Whole Number Arithmetic…… 375

Lieven Verschaffel, Anna Baccaglini-Frank, Joanne Mulligan, Marja van den Heuvel-Panhuizen, Yan Ping Xin, and Brian Butterworth

17 Professional Development Models for Whole Number Arithmetic in Primary Mathematics Teacher Education: A Cross-Cultural Overview……399

Jarmila Novotná, Maria G. Bartolini Bussi, Sybilla Beckmann, Maitree Inprasitha, Berinderjeet Kaur, Xu Hua Sun, Hamsa Venkat, and Mike Askew Part IV Plenary Presentations

18 The Theory of School Arithmetic: Whole Numbers ……439

Liping Ma and Cathy Kessel

19 Quantities, Numbers, Number Names and the Real Number Line……465 Hyman Bass

20 Low Numeracy: From Brain to Education……477

Brian Butterworth

Appendices……489

Author Index……515

Subject Index……527