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  • Book
  • Open Access
  • © 2018

Building the Foundation: Whole Numbers in the Primary Grades

The 23rd ICMI Study

  • First ICMI study to provide a broad critical survey of research on early childhood mathematics and Whole Number Arithmetic

  • Produced through a comprehensive international study involving leading academics and designers in the field

  • Considers trends and future directions for early mathematics teaching and learning

Part of the book series: New ICMI Study Series (NISS)

Buying options

Softcover Book USD 59.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)

Table of contents (20 chapters)

  1. Front Matter

    Pages i-xxxi
  2. Introductory Section

    1. Front Matter

      Pages 1-1
    2. Social and Cultural Contexts in the Teaching and Learning of Whole Number Arithmetic

      • Maria G. Bartolini Bussi, Xu Hua Sun
      Pages 19-34Open Access
    3. Language and Cultural Issues in the Teaching and Learning of WNA

      • Xu Hua Sun, Maria G. Bartolini Bussi
      Pages 35-70Open Access
    4. On Number Language: A Commentary on Chapter 3

      • David Pimm
      Pages 71-87Open Access
  3. Working Group Chapters and Commentaries

    1. Front Matter

      Pages 89-89
    2. The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes

      • Xu Hua Sun, Christine Chambris, Judy Sayers, Man Keung Siu, Jason Cooper, Jean-Luc Dorier et al.
      Pages 91-124Open Access
    3. Whole Number Thinking, Learning and Development: Neuro-cognitive, Cognitive and Developmental Approaches

      • Joanne Mulligan, Lieven Verschaffel, Anna Baccaglini-Frank, Alf Coles, Peter Gould, Shengqing He et al.
      Pages 137-167Open Access
    4. Aspects that Affect Whole Number Learning: Cultural Artefacts and Mathematical Tasks

      • Maria G. Bartolini Bussi, Maitree Inprasitha, Ferdinando Arzarello, Hyman Bass, Ulrich Kortenkamp, Silke Ladel et al.
      Pages 181-226Open Access
    5. How to Teach and Assess Whole Number Arithmetic: Some International Perspectives

      • Jarmila Novotná, Berinderjeet Kaur, Ann Gervasoni, Mike Askew, Michiel Veldhuis, Catherine Pearn et al.
      Pages 251-286Open Access
    6. Connecting Whole Number Arithmetic Foundations to Other Parts of Mathematics: Structure and Structuring Activity

      • Hamsa Venkat, Sybilla Beckmann, Kerstin Larsson, Yan Ping Xin, Alessandro Ramploud, Limin Chen
      Pages 299-324Open Access
  4. Panels

    1. Front Matter

      Pages 341-341
    2. Tradition in Whole Number Arithmetic

      • Ferdinando Arzarello, Nadia Azrou, Maria G. Bartolini Bussi, Sarah Inés González de Lora Sued, Xu Hua Sun, Man Keung Siu
      Pages 343-373Open Access
    3. Special Needs in Research and Instruction in Whole Number Arithmetic

      • Lieven Verschaffel, Anna Baccaglini-Frank, Joanne Mulligan, Marja van den Heuvel-Panhuizen, Yan Ping Xin, Brian Butterworth
      Pages 375-397Open Access

About this book

This twenty-third ICMI Study addresses for the first time mathematics teaching and learning in the primary school (and pre-school) setting, while also taking international perspectives, socio-cultural diversity and institutional constraints into account. 

One of the main challenges of designing the first ICMI primary school study of this kind is the complex nature of mathematics at the early level. Accordingly, a focus area that is central to the discussion was chosen, together with a number of related questions. The broad area of Whole Number Arithmetic (WNA), including operations and relations and arithmetic word problems, forms the core content of all primary mathematics curricula. The study of this core content area is often regarded as foundational for later mathematics learning. However, the principles and main goals of instruction on the foundational concepts and skills in WNA are far from universally agreed upon, and practice varies substantially from country to country. As such, this study presents a meta-level analysis and synthesis of what is currently known about WNA, providing a useful base from which to gauge gaps and shortcomings, as well as an opportunity to learn from the practices of different countries and contexts. 


  • mathematics teaching and learning in the primary school
  • Whole Number Arithmetic
  • 23rd ICMI Study
  • WNA
  • international perspectives on primary math education
  • social-cultural diversity of early mathematics teaching
  • institutional constraints of early mathematics
  • arithmetic word problems
  • Whole number thinking, learning and development


“The book Building the Foundation: Whole Numbers in the Primary Grades is the documentation of the 23rd ICMI study. For those not familiar with this series, ICMI (International Commission on Mathematical Instruction) studies are international conferences supported by the Executive Committee of the International Commission of Mathematics Instruction. The participants in these conferences together produce a study volume which aims to offer a coherent, state-of-the-art representation of the domain of the study.” (Jorryt van Bommel and Hanna Palmér, Educational Studies in Mathematics, Vol. 100, 2019)

Editors and Affiliations

  • Department of Education and Humanities, University of Modena and Reggio Emilia, Modena, Italy

    Maria G. Bartolini Bussi

  • Faculty of Education, University of Macau, Macao, China

    Xu Hua Sun

Bibliographic Information

Buying options

Softcover Book USD 59.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)