Ensino de probabilidade : um olhar sobre os obstáculos didáticos a partir da análise da relação contratual entre professor-aluno-saber

Abstract

The present research aimed to analyze how the contractual relationship can influence the emergence of didactic obstacles in the teaching of Probability in the Final Years of Elementary School, more specifically in the 9th Grade. Therefore, we used as a theoretical contribution of this work, two theoretical notions developed by Guy Brousseau, the Didactic Contract and the Didactic Obstacle. The Didactic Contract refers to the clauses established, especially implicitly, from the relationship between teacher and student in the face of knowledge belonging to the didactic situation. The Didactic Obstacle, in turn, concerns the teacher's choices when leading to the didactic situation, reflected in their actions, speeches and gestures, which have the potential to create barriers in the appropriation of knowledge. The mathematical knowledge that intertwined the research was Probability, a mathematical field governed by indeterminism that has chance as its object of study. The research is exploratory and had the participation of four Mathematics teachers from a public school in the municipality of São Lourenço da Mata, Mata Norte region of Pernambuco. Methodologically, the construction of their data occurred from three stages: mapping of didactic obstacles in Probability; semi-structured interviews; class observation. The results indicate that the emergence of obstacle factors occurs mainly from the didactic contractual element called negotiation, but that they can also emerge in other elements of the Didactic Contract such as expectation, rule and rupture. In addition, the study points out that there are some types of didactic situations in the face of the emergence of these obstacles: those that already favor the emergence of obstacles because they are already inadequately idealized; those that, in theory, would not favor the didactic obstacles, but the way the teacher negotiates it, makes the situation obstacle.