Design principles for a system to teach problem solving by modelling

This paper presents an approach to the design of a learning environment in a mathematical domain (elementary combinatorics) where problem solving is based more on modelling than on deduction or calculation. In this approach, we want to provide the student with a presentation which is close to the natural language formulations that she tends to give spontaneously, while ensuring a rigorous mathematical reasoning. To do so, we have introduced three modelling levels : first a mathematical formalisation of the students' intuitive process, then a conceptual and computational model allowing mathematical reasoning as well as communication with the student, and finally a presentation consisting in several interfaces, each one grouping problems of some class. These interfaces are viewed as nondeterministic "machines" that the student uses to build a configuration satisfying some constraints.