mathematics, seen as a parangon of pure sciences, often give the image of science built in poor technological environments; however, they have developed by forging powerful material and symbolic tools for themselves (or by exploiting them). Mathematics teaching is generally more in line with the image of mathematics than with the reality of their practice: the aim seems to be to transmit a general form of culture rather than to propose effective calculation tools and the theoretical means of their control (Kahane 2002). This is viable as long as the tools can be kept remotely, outside the classroom; it is no longer the case when computing tools (mainly calculators) are imported by the pupils themselves into the classroom and integrated into their school practices. The resulting conflict between the social legitimacy of these tools and their illegitimate school system (Chevallard 1992) deeply destabilises education in the context of which we will present a general framework for thinking about the integration of tools in the learning and teaching of mathematics. More specifically, we proposerons:1.Une a theoretical approach, making it possible to understand the influence of tools for human activity and in particular for training, vocational or school processes; 2.An analysis of the characteristics of computerised learning environments, highlighting the importance of students’ control of their own instrumented activity; 3.Elements to think about the organisation of the time and space of the study in these environments and to guide students’ activity; 4.Reflecting on the design of the teaching resources needed to facilitate the necessary development of professional practices.