Epistemological Analysis and Design of Research Situations in Discrete Mathematics: Method and Examples 

Résumé En

In France and more widely in French-speaking countries, the theory of didactic situations is one of the theoretical reference frameworks for the construction of teaching and learning situations, with a focus on didactic engineering as a research methodology. Epistemological or mathematical analysis is an essential phase in the design of such engineering to support research for mathematical situations. In particular, those that make it possible to mobilise the essential components of research activity in mathematics linked, for example, to experimentation, the formulation of conjectures or proof. Moreover, current research shows that the field of discrete mathematics is conducive to the design of situations, at all levels of teaching, which mobilise these components. Consequently, a 'generic' method will be proposed for carrying out this type of analysis, based on examples of problems from current research in discrete mathematics.