
In this paper a transversal study is presented, from a cognitive outlook, about the solving frameworks used by (N=264) students faced to two mathematical problems at school. Johnson-Laird's Theory of Mental Models (1983,1990a, 1990b, 1996) is used as a reference, to explain students' cognitive operation with relation to the representations they use and the way they do it. The arithmetic and algebraic solutions carried out by students according to the level they belong are described. They are interpreted as the performance of mental models linked to each of those frameworks. The results show that a high percentage of students of each level build mental models to understand and solve the problems posed.