ICMI

Bulletin No. 46

June 1999

On the 16^{th} day of June 1998, Claude Janvier passed away after a long struggle with illness, leaving his family, colleagues, and numerous friends across the world struck with consternation. This text is a homage to a teacher-educator deeply engaged in his work and an internationally renowned researcher in the field of mathematics education who contributed in many ways to the improvement and understanding of mathematics teaching and learning.

After completing a baccalaureate and master degree in applied mathematics at McGill University in Montréal, Claude Janvier received in 1978 a doctorate in education from the University of Nottingham in England with a thesis on *The interpretation of complex Cartesian graphs representing situation, studies and teaching experiments*. He became a leader in Québec in the creation of programs for the preparation and development of teachers of mathematics. For Claude, the problems of preparing teachers and of research in mathematical thinking and teaching were closely linked, one domain of activity drawing profound inspiration from the other. From as early as 1970, Claude Janvier was actively engaged in an innovative program of in-service teacher training, PERMAMA (Perfectionnement des maîtres en mathématiques). His involvement in the conception of courses for in-service training led to the production of still up-to-date audiovisual scenarios and didactical material regarding, for example, the teaching of statistics or functions. The topic of functions eventually became one of his preferred subjects and his research in the domain is well known internationally. The students in his courses on the teaching of variables and functions recognized his particular expertise in the field, as is witnessed by the affectionate nickname they gave him, "Monsieur Fonction".

Claude Janvier was involved in the conception and implementation of numerous courses for prospective mathematics teachers: mathematics courses on geometry or modeling in mathematics and sciences; mathematics education courses on the concepts of proportional reasoning, of measure, of variable and function or on the teaching of volume. He regularly supervised the students’ practicum, being convinced of the importance of such an involvement for all teacher educators. He contributed to the preparation of numerous researchers in mathematics education, supervising theses in a variety of domains which testify to the richness of his expertise (the use of analogies in the teaching of electricity, conceptions of probability, the role of films in the teaching of mathematics, the utilization of transitory symbolism, problems of representation in the learning and teaching of mathematics, etc.). He was also interested by post-secondary education, as is attested by his study on the contextualisation of reasoning by electro-technicians. He played an important role in the onset of the CIRADE (Centre Interdisciplinaire de Recherche sur l'Apprentissage et le Développement en Éducation) at the Université du Québec à Montréal (UQAM), serving as the director of the center for many years.

Claude Janvier had numerous activities at the international level, in addition to acting as a referee for various research journals on the didactic of mathematics and sciences (Didaskalia, Journal for Research in Mathematics Education, Recherche en didactique des mathématiques,…). From 1987 to 1993, he was in charge of a cooperation project with the École Normale Supérieure de Marrakech, in Morocco, on the preparation of teacher educators in mathematics and sciences. He was actively engaged in the CIEAEM (Commission Internationale pour l'Étude et l'Amélioration de l'Enseignement des Mathématiques) and was a founding member of PME (The International Group for the Psychology Mathematics Education), serving on its international committee from 1979 to 1983 and as the Secretary from 1980 to 1982. From 1989, he played an important role in the PME Working Group on Representations, and accepted in 1994 to co-chair this group with Gérard Vergnaud. Near the end of his life, he continued his activity by planning and co-editing two special issues of the *Journal of Mathematical Behavior* dedicated to "Representations and the Psychology of Mathematics Education" (vol. 17, Nos. 1 and 2). Sadly, he did not live long enough to see the results of this labor.

In 1996, he was awarded the Prix Abel-Gauthier of the Association mathématique du Québec. The mention recognized his contribution to the improvement of the quality of the teaching of mathematics and stressed the originality, the utility, and the value of his written works (Pallascio, 1997).

A wonderful French expression sums up the frame of mind of Claude Janvier: *la mathématique qui se fait plutôt que la mathématique toute faite* (roughly translated, ‘mathematics that is developing rather than mathematics that is all done’). In addition, Claude always took an interdisciplinary perspective. As he said, "It was always my idea to incorporate other subjects into mathematics, and mathematics into other subjects. This is the foundation of my ideas." (Gattuso, 1997)

Claude was for us a mentor, a companion, and a colleague. We will remember his intellectual contributions but still more we will recall his warmth, humanity, and dear and irreplaceable friendship. Claude is still present, and will continue to be among us.

L. Gattuso (1997) "À bâtons rompus : Claude Janvier répond aux interrogations de jeunes enseignants."* Bulletin AMQ* (Association mathématique du Québec)* *XXXVII (3) 20-26.* *

Pallascio, R. (1997) "AMQ en action : Présentation du lauréat 1996 du prix Abel-Gauthier." *Bulletin AMQ *(Association mathématique du Québec)* *XXXVII (4) 20-22.

On teacher training:

"Teachers training in mathematics education in a constructivist perspective." In: L.P. Steffe and P. Nesher (eds.) *Theories of mathematical learning*. Erlbaum, 1996.

On the role of representation in mathematics education:

C. Janvier (ed.) *Problems of representation in the teaching and learning of mathematics.* Erlbaum, 1987.

On the role of context in mathematics and science education:

C. Janvier, M. Baril and C. Mary (1993) "Contextualized reasoning of electrical technicians." In: M. Caillot (ed.) *Learning electricity or electronics with advanced educational technology*. Springer-Verlag, NATO ASI Series F, 115, p. 157-169.

On the concept of variable and function:

C. Janvier (1993) "Les graphes cartésiens: des traductions aux chroniques." *Les sciences de l'éducation pour l'ère nouvelle* 1 (3) 17-39.

**Linda Gattuso and Nadine Bednarz**

Département de mathématiques et CIRADE

Université du Québec à Montréal

C.P. 8888, Succursale Centre ville

Montréal H3C 3P8 CANADA

gattuso.linda@uqam.ca, descamps-bednarz.nadine@uqam.ca