Whole numbers

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  • ICMI Study 2014-2015


This document announces a new study to be conducted by the International Commission on Mathematical Instruction. This study, the twenty-third led by ICMI, addresses for the first time mathematics teaching and learning in the primary school (and pre-school), taking into account inclusive international perspectives, sociocultural diversity and institutional constraints. The broad area of Whole Number Arithmetic (WNA) including operations and relations and arithmetic word problems form 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 in the foundational concepts and skills in WNA are far from universally agreed upon, and practice varies substantially from country to country. Primary schooling is compulsory in most countries (in all Western countries), although there is considerable variation in the facilities, resources, and opportunities for students. This is the uneven context where mathematics teaching and learning takes place. Mathematics is a central feature of early education and the content, quality, and delivery of the curriculum is of critical importance in view of the kinds of citizens each country seeks to produce. ICMI has acknowledged that it is timely to launch, for the first time in its history, an international study that especially focuses on early mathematics education that is both basic and fundamental mathematically. When foundational processes are concerned, a strong epistemological basis is needed. This is where the involvement of ICMI adds value with respect to analyses carried out in other fields. Such epistemological analysis was part of classical works of professional mathematicians (e.g., Klein, Smith, and Freudenthal) who played a major role in the history of ICMI and considered mathematics teaching as a whole. The ICMI Study will be organized around five themes that provide complementary perspectives on approaches to earlyWNA in mathematics teaching and learning. Contributions to the separate themes will be distinguished by the theme’s specific foci and questions; although it is expected that interconnections between themes will emerge and warrant attention. The five themes are the following: 1. The why and what of WNA 2. Whole number thinking, learning, and development 3. Aspects that affect whole number learning 4. How to teach and assess WNA 5. Whole numbers and connections with other parts of mathematics.


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