1 EPISTEMIC AND COGNITIVE ANALYSIS OF AN ARITHMETIC – ALGEBRAIC PROBLEM SOLUTION1

We analyze the solution of a problem proposed on the context of a mathematics methods course for in-training primary teachers, by applying some notions of the “onto-semiotic approach ” to mathematics knowledge. The generalization of the arithmetic statement given to students involves the use of algebraic reasoning, giving way to the study of the relations between arithmetic and algebra, as well as the relations between empirical and deductive argumentation. The solution of elementary problems and the epistemic-cognitive reflection on the objects and meanings used during the solution is proposed as a means to overcome a limited students ’ conception on the nature of mathematics, usually reduced to its conceptual and procedural aspects. 1. INTRODUCCTION To train future primary teachers on mathematics and its didactics it is necessary to select problems whose solution put into effect competences on different subject matter knowledge fields (arithmetic, geometry, measure, stochastic, algebraic thinking) and that promote the articulation among the competences of mathematic and didactic type. On the other hand, the design and implementation of the study processes ask for the teacher to develop analytical competences of the mathematic objects and processes used during the solution o