Building the Foundation: Whole Numbers in the Primary Grades: The 23rd ICMI Study

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. .

Part I. Introductory section -- Chapter 1. Building a strong foundation concerning whole numbers arithmetic in primary grades: editorial introduction -- Chapter 2. Social and cultural contexts in the teaching and learning of whole numbers arithmetic -- Chapter 3. Language and cultural issues in the teaching and learning of whole number arithmetic -- Chapter 4. Reflecting on number language: a commentary on Chapter 3 -- Part II. Working group chapters and commentaries -- Chapter 5. What and why of whole number arithmetic: foundational ideas from history, language, and societal changes -- Chapter 6. Reflecting on the what and why of whole numbers arithmetic: a commentary on Chapter 5 -- Chapter 7. Whole number thinking, learning and development: neuro-cognitive, cognitive and developmental approaches -- Chapter 8. Whole number thinking, learning and development: a commentary on Chapter 7 -- Chapter 9. Aspects that affect whole number learning: cultural artefacts and mathematical tasks -- Chapter 10. Artefacts and tasks in the mathematical preparation of teachers of elementary arithmetic from a mathematician’s perspective: a commentary on Chapter 9 -- Chapter 11. How to teach and assess whole number arithmetic: some international perspectives -- Chapter 12. How to teach and assess whole number arithmetic: a commentary on Chapter 11 -- Chapter 13. Connecting whole number arithmetic foundations to other parts of mathematics: structure and structuring activity -- Chapter 14. Structuring structural awareness: a commentary on Chapter 13. Part III -- Panels -- Chapter 15. Panel on tradition in whole number arithmetic -- Chapter 16 -- Panel on special needs in research and instruction in whole number arithmetic -- Chapter 17. Panel on professional development models for whole number aritmetic in primary mathematics teacher education: a cross-cultural overview -- Part IV -- Plenary presentations -- Chapter 18. The theory of school arithmetic: whole numbers -- Chapter 19. Quantities, numbers, number names and the real number -- Chapter 20. Low numeracy: from brain to education -- Part V. Appendices.