This twenty-third ICMI Study, addresses for the first time in the history of ICMI studies, mathematics teaching and learning at the primary and pre-school levels. While the mathematics at this level is foundational, it is also complex in terms of the extent of interconnections, and in terms of the tensions between inductively derived and mathematical definitions that can both afford and constrain forward trajectories from these foundations. The international perspectives offered in this study bring these discussions to the fore, taking socio-cultural diversity and institutional constraints into account. The complexity of early mathematics led to a selection of a focus area for the discussion, with a number of questions connected to it: Whole Number Arithmetic (WNA), including operations and relations and arithmetic word problems. This focus forms the core content of all primary mathematics curricula and the study of this core content area is often regarded as foundational for later mathematics learning. However, the principles and main goals of instruction in the foundational concepts and skills in WNA are far from universally agreed upon, and practice varies substantially from country to country. This ICMI Study provides a meta-level analysis and synthesis of what is known about WNA in ways that provide an important and useful vantage point from which to gauge gaps and silences and an opportunity to learn from the practice of different countries and contexts.
Arvustused
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)
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
mathematicians 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.
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