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Le point de vue Maria Bartolini Bussi et Xuhua Sun, co-présidente de ICMI 23

Primary mathematics study on whole numbers (the ICMI Study 23)

Maria G. (Mariolina) Bartolini Bussi and Xuhua Sun, co-chairs of the ICMI Study 23


This study was launched by ICMI at the end of 2012, with the appointment of two co-chairs (Mariolina Bartolini Bussi and Xuhua Sun) and of the International Program Committee (IPC), which on behalf of ICMI is responsible for conducting the Study. It is the first Study launched by ICMI with a specific focus on primary school. The members of the IPC are: Maria G. Bartolini Bussi, Sun Xuhua, Berinderjeet Kaur, Hamsa Venkatakrishnan, Jarmila Novotná, Joanne Mulligan, Lieven Verschaffel, Maitree Inprasitha, Sybilla Beckmann, Sarah González de Lora, Abraham Arcavi (ICMI Secretary General) ex officio. The ICMI advisors are Ferdinando Arzarello (ICMI President) and Roger E. Howe (ICMI liaison).

The study

In January 2014 the IPC meeting took place in Berlin, at the IMU Secretariat, which generously supported the costs. The meeting aimed at producing the Discussion Document; defining in a preliminary manner the criteria for collecting the participants in the Study Conference and defining the way of disseminating the Discussion Document and the call for papers.

  • Five themes (each corresponding to a Working Group in the Conference) were identified and assigned to pairs of members of the IPC:
  • The why and what of whole number arithmetic (Sun Xuhua, Sybilla Beckmann)
  • Whole number thinking, learning, and development (Joanne Mulligan, Lieven Verschaffel)
  • Aspects that affect whole number learning (Maria G. Bartolini Bussi, Maitree Inprasitha)
  • How to teach and assess whole number arithmetic (Berinderjeet Kaur, Jarmila Novotna)
  • Whole numbers and connections with other parts of mathematics (Sarah González de Lora, Hamsa Venkatakrishnan).

Three plenary speakers were invited: Liping Ma (The theoretical core of whole number arithmetic), Brian Butterworth (Low numeracy: from brain to education) and Hyman Bass (Quantities, numbers, number names, and the real number line).

Three plenary panels were identified:

  • Traditions in whole number arithmetic (chaired by Ferdinando Arzarello);
  • Special needs in research and instruction in whole number arithmetic (chaired by Lieven Verschaffel);
  • Whole numbers aritmetics and teacher education (chaired by Jarmila Novotná)

The francophone community answered with enthusiasm to the call for papers. The first submitted paper came from France. At the end 9 papers (out of the total number of 67) were selected. Most of them have French authors or co-authors, but others come from different regions or represent examples of international cooperation between teams from different countries. Although sometimes it was not easy to find the most suitable theme, because of overlappings, most papers concerned the theme 1 and theme 3 with a major focus is on foundational aspects (theme 1) and on the context features which may affect leaning (theme 3).


Theme 1: The why and what of whole number arithmetic

Christine Chambris (LDAR, Université de Cergy-Pontoise, France) presents the paper Mathematical basis for place value throughout one century of teaching in France, reporting about the transition from the“new math” period (70s) to the changes in the 80s, highlighting the weight of the mathematical basis of the place value representation.

Catherine Houdement and Frédérick Tempier (Université Paris Diderot, France) present the paper Teaching numeration units: why, how and limits), reporting about two teaching experiments about place value, where the complexity of the teaching-learning process (for both teachers and students) is analysed.

Jean-Luc Dorier (Université de Genève, Switzerland), in the paper Key issues for teaching numbers with Brousseau's theory of didactical situations, presents Brousseau’s theory of didactical situations and its close interaction with the history of mathematics and reports the key stages of a teaching sequence of the concept of numbers for students from age 4 to 6.

Nadia Azrou (University Yahia Farès, Médéa) in the paper Spoken and written numbers in a post-colonial country: the case of Algeria reports on the historical and linguistic background of the most widespread languages spoken in Algeria and summarizes some of the issues with spoken and written arithmetic. It is a the first step of a project aiming at developing an intervention in teacher education that will be designed to enhance students’ awareness of differences in representing numbers in different l anguages and promote students’ cultural identities.

Theme 3: Aspects that affect whole number learning

The issue of teacher education is considered also by Bernard R. Hodgson and Caroline Lajoie from Québec. In the paper The preparation of teachers in arithmetic: a mathematical and didactical approach, they stress the complementary role of mathematicians and mathematics educators in pre-service teacher education, describing, on the one hand, the foundations of whole number arithmetic and, on the other hand, the integration of the didactical component of the preparation of teachers.

The findings of an collaborative projects involving research teams in two countries (France and Italy) are reported by Sophie Soury-Lavergne (IFÉ ENS de Lyon, France) & Michela Maschietto (UNIMORE, Italy), in the paper Number system and computation with a duo of artefacts: the Pascaline and the e-Pascaline. They report about the use of a duo of artefacts, constituted by a mechanical arithmetic machine and its digital counterpart, to enable six-year old French students to learn about numbers. They analyse the separate conceptualisation processes involved in the use of physical and virtual artefacts.

The outline of an international report commissioned by the World Bank is presented by Alain Mercier & Serge Quilio in the paper The efficiency of primeray level mathematics teaching in French-speaking countries: a synthesis. The authors report about the way educational systems work, so as to understand how teachers and pupils interact within the framework of these systems of knowledge transmission.

Theme 4: How to teach and assess whole number arithmetic

The same authors of the last paper, together with Gérard Sensevy present the paper Arithmetic and comprehension at primary school, where a design-based research study (involving 180 experimental classes) in the first grade is reported. They present the rationale and the for this curriculum and analyse some examples of the students’ written work.

Anna Barry, Jarmila Novotná & Bernard Sarrazy, drawing on international cooperation between teams in France and Czech Republic, present the paper Experience and didactical knowledge. The case of didactical variability in solving problems. They show that the knowledge of variables that determine the difficulty of an additive problem differs considerably from one teacher to another. They show that neither the teaching experience nor teacher education can account for these differences: thus it must be the differences in pedagogical beliefs that enable to explain these differences in the didactical knowledge.

The Conference and the Study volume

The Study Conference will be held in Macau (June 3-7, 2015) with around 90 participants including: the IPC members, the ICMI advisors, plenary speakers, authors of accepted papers and a group of observers. Five observers, invited by the University of Macau and the ICMI, come from the CANP (Capacity & Networking Project, The Mathematical Sciences and Education in the Developing World) that is the major development focus of the international bodies of mathematicians and mathematics educators.

Macau is unique in its role in Chinese mathematics education. For example, in the seventeen century, the first Macau`s Jesuits Matteo Ricci translated Euclid`s Elements with Guangqi Xu and the first arithmetic book on European pen calculation. His contribution changed Chinese mathematics education and gave Chinese people their first access to real images of western mathematics. We believe that this heritage of mixed traditions under the influence of the Confucian educational heritage can provide a resource for new thinking in global mathematics education development.

The ICMI Study Conference will serve as the basis for the production of the Study Volume. The character of the volume is rather unique to ICMI studies and is different from proceedings, edited books and handbooks. Although the volume exploits the contributions appearing in the proceedings, the collective production will be started during the Conference, drawing on the discussions and cooperative works of participants.

In the whole process the contribution of the francophone authors will be exploited. Welcome to Macau, in a few days!

Maria G. (Mariolina) Bartolini Bussi* and Xuhua Sun**, co-chairs of the ICMI Study 23

*University of Modena and Reggio Emilia (Italy), **University of Macau (China)


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