As Organizações Matemáticas e Didáticas na Sala de Aula de Matemática: o caso das equações de segundo grau

Abstract

This article is characterized as an excerpt from a doctoral thesis. It includes an analysis of mathematical organizations (OM) and didactic organizations (OD), proposed in 09 classes, in which students were introduced, by the teacher, to know quadratic equations to an unknown. The notions of OM and OD emerge within the Anthropological Theory of Didactics, proposed by Yves Chevallard, particularly in praxeological analyses. Mathematical organizations concern all mathematical activity that is constructed in the classroom, and this, dialectically, is constituted from the didactic organization. In the article, the analysis of some mathematical compendia that deal with the quadratic equation was included. This analysis allowed us to characterize mathematical organizations. The results of this study indicate that the teacher includes the types of tasks characterized in his teaching actions, with the exception of T4: ax²=0. With regard to techniques, trial and error drew attention, although it was not used frequently among the types of tasks, it appeared in prominent moments. Still on the techniques, among the most powerful and with which the teacher maintains a closer relationship, we highlight the Bhaskara formula. We identified that it was used in the types of tasks (T1, T2 and T3). In relation to didactic moments, in turn, it is possible to see that they were all covered in a non-sequenced, non-individual way (more than one moment acts at the same time in the didactic relationship) and not controlled.