Decisões didáticas e contrato didático: interrelações no ensino de um saber algébrico

Abstract

This thesis aimed to develop a theoretical framework for analyzing the interrelationships between didactic decisions and the didactic contract in the teaching of mathematical knowledge belonging to the algebraic field. For that, we anchored ourselves in the theoretical field of Didactic Decisions, a theory that presents the model of the levels of teacher activity, proposed in the literature by (MARGOLINAS, 2002). The second theoretical anchor adopted in this study was the Didactic Contract, due to its relevance in the Theory of Didactic Situations, allowing a look of fundamental importance for the teacher-student-knowledge triangulation in the classroom (BROUSSEAU, 1996). After proposing the theoretical scheme, we conducted an empirical study, with the aim of investigating the adequacy of the proposed model. As research subjects, we selected a teacher from the 8th grade of elementary school in a public school, and his students and, as mathematical knowledge, algebraic expressions and polynomials. The theoretical bases developed in the scheme proposed in this thesis were focused on the interactions that occurred specifically in the planning of classes, in the didactic situation and in the observation of the student in activity (Levels +1, 0 and -1). From the theoretical framework elaborated, the results found pointed out that the didactic decisions that were made in the planning (Level +1) were closely linked with the expectations related to the didactic contract. With regard to teaching practice (Level 0), through our theoretical analysis and with the reflections provided by the teacher and the transcripts of the observed classes, in the empirical analysis, we come to the conclusion that the didactic situations (S0), investigated from the school reality, they evidenced the coexistence and the interrelationship between the Didactic Decisions and the Didactic Contract. Another aspect revealed was that the decision factors, especially the didactic history type, are predominantly part of the interrelations of decision making and the didactic contract. The didactic microdecision of the teacher, when driven by factors of the didactic history type, maintains a close relationship with the didactic contract, since a relation of conformity between both was identified.