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Mathematics EducationICMI ColumnMariolina Bartolini Bussi (Università di Modena e Reggio Emilia, Italy) and Jean-Luc Dorier (Université de Genève,Switzerland)The 23rd ICMI Study: Primary MathematicsStudy on Whole NumbersCo-Chairs: Mariolina Bartolini Bussi & Sun XuhuaA new study will be conducted by the International Commissionon Mathematical Instruction. This study, the 23rdled by the ICMI, addresses for the first time mathematicsteaching and learning in primary school (and pre-school),taking into account inclusive international perspectives,socio-cultural diversity and institutional constraints. Thebroad area of Whole Number Arithmetic (WNA), includingoperations and relations and arithmetic word problems,forms the core content of all primary mathematicscurricula. The study of this core content area is oftenregarded as foundational for later mathematics learning.However, the principles and main goals of instruction inthe foundational concepts and skills in WNA are far fromuniversally agreed upon, and practice varies substantiallyfrom country to country. An ICMI study that provides ameta-level analysis and synthesis of what is known aboutWNA would provide a useful base from which to gaugegaps and silences and an opportunity to learn from thepractice of different countries and contexts.Whole numbers are part of everyday language in mostcultures but there are different views on the most appropriateage at which to introduce whole numbers in theschool context. Whole numbers, in some countries, areintroduced in pre-school, where the majority of childrenattend before the age of 6. In some countries, primaryschooling comprises Grades 1–6; in others it comprisesGrades 1–5. Thus the entrance age of students for primaryschool may vary from country to country. For thesereasons, this study addresses teaching and learning WNAfrom the early grades, i.e. the periods in which WNA issystematically approached in formal schooling – in somecontexts this includes pre-school.Primary schooling is compulsory in most countries(in all Western countries), although there is considerablevariation in the facilities, resources and opportunities forstudents. This is the uneven context where mathematicsteaching and learning takes place. Mathematics is a centralfeature of early education and the content, quality anddelivery of the curriculum is of critical importance in viewof the kinds of citizens each country seeks to produce.In the international literature, there are many contributionsabout primary school mathematics. In manycases, especially in the West, early processes of mathematicalthinking, often observed in early childhood (i.e.3–8 year-old children), are also investigated by cognitiveand developmental psychologists. They sometimes studythe emergence of these processes in clinical settings,where children are stimulated by suitable models so asto observe the emergence of aspects such as one-to-onecorrespondences, counting, measuring and other proc-esses. In several countries, Piaget’s theory has been veryinfluential despite criticism. Neuroscientists have alsobeen studying for some years the emergence of “numbersense”. However, recent perspectives highlight that whatis still needed is serious and deep interdisciplinary workwith experts in mathematics education.The ICMI has acknowledged that it is timely to launch,for the first time in its history, an international study thatspecifically focuses on early mathematics education thatis both basic and fundamental. When foundational processesare concerned, a strong epistemological basis isneeded. This is where the involvement of the ICMI addsvalue with respect to analyses carried out in other fields.Such epistemological analysis was part of the classicalworks of professional mathematicians (e.g. Klein, Smithand Freudenthal) who played a major role in the historyof the ICMI and considered mathematics teaching as awhole.The ICMI study will be organised around five themesthat provide complementary perspectives on approachesto early WNA in mathematics teaching and learning. Contributionsto the separate themes will be distinguishedby the theme’s specific foci and questions, although itis expected that interconnections between themes willemerge and warrant attention.The five themes are: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 ofmathematics.Themes 1 and 2 address foundational aspects from thecultural-historic-epistemological perspective and fromthe (neuro)cognitive perspective. What is especiallyneeded are reports about the impact of foundational aspectson practices (both at the micro-level of students andclassrooms and at the macro-level of curricular choices).Themes 3 and 4 address learning and teaching, respectively,although it is quite difficult, sometimes, to separatethe two aspects; for example, in some languages and cultures(e.g. Chinese, Japanese and Russian) the two wordscollapse into only one.Theme 5 addresses the usefulness (or the need) toconsider WNA in connection with (or as the basis for)the transition to other kinds of numbers (e.g. rationalnumbers) or with other areas of mathematics traditionallyseparated from arithmetic (e.g. algebra, geometryand modelling).ICMI Study 23 is designed to enable teachers, teachereducators, researchers and policymakers around the50 EMS Newsletter June 2014