The aim of this article is to combine the different practices and researches which made the teaching of mathematics a place where rigor and passion walk together, where « follow the program » walk together with the enrichment of every one. For that, it seems to me necessary to mutually refer to the works of the Commission inter-IREM (Institute of research for the teaching of mathematics) « Epistemology and history of mathematics », the Commission inter-IREM « First cycle » (pupils 10-15years old), the works of didactic in the irem, the philosophic ideas on learning, as well as psychoanalytic research conducted in the departments of sciences of education.