Activités didacticques à caractère vertical pour la construction du concept de limite

Abstract: This paper concerns the activities of a research group in mathematics education about the concept of limit. The main characteristic of this group is that all stages in schooling (primary – 6 to 10 years; middle school – 11 to 13 years, and high school – 14 to 19 years) are represented, both within the group itself and as regards the pupils involved. This vertical cross-section is a resource which is as rare as it is precious. It allows us, indeed, to propose similar activities at different levels, check the evolution of the ideas, techniques and errors of the schoolchildren over time, and observe the effect of the teaching methods on them. With the support of research in mathematics education, we chose some issues, in particular measurement and approximation, which, in our opinion, can favour the gradual early development of the concept of limit. In this context, we would emphasise the importance of approximation as a resource for the long way to build the concept of the limit.