Environnements Informatisés et Mathématiques: quels usages pour quels apprentissages?

Mathematics, seen as a model of pure science, often conveys the image of a science constructing itself in quite poor technological environments; it nevertheless develops by elaborating (and by exploiting) powerful material and symbolic tools. Actually mathematics teaching is closer to this image of mathematics than to mathematical practice: its goal seems to transmit a form of culture rather than efficient computation tools and theoretical means of their control (Kahane, 2002). This situation is viable if the tools can be held at distance, outside the classroom; it is no longer viable when computation tools (essentially calculators) are imported by students themselves inside the classroom and integrated into their mathematical practice. Thus established conflict between the social legitimacy of these tools and their school illegitimacy (Chevallard, 1992) deeply destabilises mathematics teaching itself. We present here a general framework to think about the integration of the tools in the teaching and learning of mathematics. More precisely, we propose:1A theoretical approach, which allows us to understand the influence of tools on human activity and in particular on professional and school education processes;2An analysis of computerized learning environments, which shows the importance of students' control of their own activity;3Some elements that help to think about the temporal and spatial organization of study in such environments and to guide students' activity;4A reflection about the conception of pedagogical resources, which is all the more necessary if one wants to facilitate an evolution of teachers' practices.