Researching (Algebraic) Problem Solving from the Perspective of Local Theoretical Models

Concepts such as Local Theoretical Model, Mathematical Sign System, logico-semiotic outline, analytical reading, and formal competence model, elaborated within long term research programs developed in Mexico and Spain, are presented. Empirical data from a study carried out in Spain with students of a teacher training school are analyzed using this theoretical framework. The cases analyzed show to which extent the logico-semiotic outline determines the arithmetic or algebraic nature of the entire problem solving process, even in the case of pupils which had been instructed in general problem solving heuristics, management and control, including the explicit training in changing the plan of solution when facing difficulties.