Abstract
In Costa Rica, as well as in France, it has become customary to include lists of abilities and/or competencies within the study plans. For instance, the ability to use a given theorem or concept to solve problems in various contexts. What is exactly the range of such an indeterminate objective? In which types of problems are the students supposed to use the considered mathematical piece of knowledge? Is it possible to define a scale of complexity, relevant to differentiate the problems, in order to design a problem solving progressive path and to evaluate students’ learning. To deal with these issues, we propose tools from two theories developed in the French mathematics education field of researches, the Anthropological Theory of Didactics (Chevallard) and the theory of the Double Approach of students’ and teachers’ practices (Robert). We illustrate our propositions with examples from the unit about similitude and Thales theorem from the Costa Rica Grade 8 Mathematics Program.