Discrete Mathematics in Relation to Learning and Teaching Proof and Modelling

The article presents the bases of a research aimed in the long run towards the construction of an « ambient environment » for discrete mathematics, a construction which would not only facilitate a first acquaintance to this mathematical field, but would also provide an alternative approach to some transversal concepts, such as proof and modelization. First, we give some results of our study about their status and role in pupils’curricula and manuals : we show that this mathematical field is in fact most often approached in a casual and unofficial manner, in combination with other mathematical knowledge and thus diverted from its real significance. We then develop our thesis on possibilities offered by discrete mathematics as a tool for learning proof and modelization. In order to support our thesis, we investigate some specificities of proof practice in discrete mathematics, especially from the viewpoint of truth checking and validation. These investigations are led from two points of view, a theoretical one and an experimental one.