Didactique des mathématiques et formation des enseignants : le cas de l’Université du Québec à Montréal

Résumé

Les travaux de recherche en didactique qui se sont développés à l’Université du Québec à Montréal (UQAM) ont été dès le départ liés à la formation des enseignants et enseignantes en mathématiques. Cet ancrage particulier a contribué au fil des années à l’enrichissement et à la complexification dans le champ de la didactique des mathématiques de problématiques qui sont venues éclairer, en retour, cette formation. Nous montrerons, à partir de quelques exemples, les orientations prises par les recherches développées par les didacticiens et didacticiennes de l’UQAM, en vertu de cet ancrage original qu’est celui de la formation des enseignants et enseignantes en mathématiques, et préciserons comment s’est opéré leur réinvestissement dans la formation. Cette approche des problèmes didactiques a débouché sur la mise en œuvre graduelle d’un modèle de formation des enseignants et enseignantes en mathématiques au secondaire, dont nous décrirons l’organisation globale et les caractéristiques particulières. Nous illustrerons cette formation en action à partir d’un exemple tiré du cours de didactique de l’algèbre. Cet exemple permettra de faire comprendre les bases théoriques qui président aux choix réalisés par les didacticiens et didacticiennes formateurs, et d’entrevoir le caractère fécond du modèle de formation mis en place sur les apprentissages réalisés par les futurs intervenants et intervenantes.

Abstract

From the outset, the research in teaching methods developed at the Université du Québec à Montréal (UQAM) was linked to the education of pre-service mathematics teachers. This article begins by outlining several determining factors involved in the gradual development of practices for use in the pre-service education program. These factors are key to grasping fundamental features of the program that was gradually worked out by the research team.

Over the years, this particular ‘anchoring’ has served to enrich and complexify a number of mathematics teaching-related problematics and, in turn, to shed light on the pre-service education program itself. Examples are provided of the research orientations adopted by UQAM teaching researchers as a result of this original anchoring in pre-service mathematics education. Specifics are provided of how the findings of this research were then reinvested in pre-service education.

This approach to teaching problems gradually developed into a model for educating future secondary school mathematics teachers. The general framework and specific features of this model are described. An illustration of this educational model is given in the form of an example taken from a course in algebra teaching. In this case, work involved various components of classroom algebra and the new orientations surrounding the teaching of this subject (approaching algebra in a context of generalization, introducing and developing algebra in a context of problem-solving, solving equations, etc.). Various activities are used to illustrate the work of pre-service teachers with respect to teaching situations and the answers, comments, and questions produced by their students. Excerpts from solutions by pre-service teachers and their comments during various situations with which they were faced during their apprenticeship are used to portray the evolution of their potentialities for action and the numerous structuring resources they could draw on for use in structuring interventions among students. In short, this portrait brings out the fruitfulness of the teaching model thus developed on the learning accomplished by these future classroom actors.

What is more, this illustration of pre-service education contained in the example of an algebra teaching course offers insight into the theoretical bases underlying the choices adopted by the teaching researchers/ pre-service teacher educators. On the part of teacher educators, these choices give evidence of a clear epistemological stance with respect to the way they make use of the answers, questions, and comments produced by pre-service teachers. In effect, the teacher education situation is organized as a culture in which certain features are actualized. In particular, this culture fosters explicating and setting off various points of view from one another, opening up and on to a range of solutions, having pre-service teachers validate the solutions’ that are put forward in the classroom, articulating a line of argument with respect to a solution put forward by others, and so on.

As a result, if research by the team contributed to this form of teacher education, it nevertheless remained a background presence. For educators of pre-service teachers, the issue was not one of delivering the findings of their own research or maintaining a form of discourse about the type of intervention that should be enacted in the classroom. Instead, emphasis was placed on involving future classroom actors in a process gradually leading them to construct knowledge that would enable them to grapple with, design, and carry out classroom interventions.