Praxeologias do Professor: análise comparativa do livro didático no ensino de equações polinomiais do primeiro grau

The aim of this paper was to analyze, comparatively, praxeologies in didactic books and praxeologies carried out by teachers in their teaching practice, concerning the teaching of first-degree polynomial equations, investigating the relations of conformity between them. This study is based on the view of the Anthropological Didactic Theory (ATD), proposed by Yves Chevallard. The methodology consisted of a qualitative approach, in which we analyzed the mathematical and didactic organizations of three teachers, comparing them with those of reference books. The results indicate that there is a certain conformity between the praxeologies proposed by textbooks’ the authors to be taught and the praxeologies effectively taught by the teachers in the classroom. Teachers were the organizers of the tasks, techniques, and technology of increasing complexity, made the routine and problematized in the classroom. The first-degree polynomial equation of the type c b ax   was the common point among the three teachers, although two of them worked with the equation type 2 2 1 1 b x a b x a    .