Contribuições de v. v. davydov para o ensino da metemática: interface entre a teoria do ensino desenvolvimental e a pedagogia histórico-crítica

Abstract

This research investigates theoretical-methodological aspects between two critical theories – the Historical-Critical and the Developmental, in the context of Mathematics Education, specifically in teaching the concept of the division operation. The basic premise was established in the defense that there is a theoretical-philosophical proximity between them. The Theory of Developmental Teaching, proposed by the Russian author V. V. Davydov, has as its basic foundation the assumption that the school must teach the student to think, based on a teaching that boosts psychic development. For this, a program was implemented in school subjects, whose knowledge corresponds to the achievements of science and modern culture. For the fulfillment of this program, the understanding of the teachers about the true function of the school was necessary, since this, in the author's understanding, cannot consist of teaching children a sum of known facts or the empiricism of everyday life, but teaching them to orientate themselves. if for scientific knowledge, for the formation of theoretical thinking. By explaining the real function of schools, Saviani, in his Historical-Critical Pedagogy, states that its role as an institution consists in the socialization of systematized knowledge through scientific knowledge that results in the development of higher psychic functions. In this sense, the teaching of mathematical concepts should prioritize teaching activities of a problematizing nature that mobilize the student to engage in study activity. That is, a teaching that goes beyond pedagogical practices centered on everyday empiricism towards the organization of a teaching that promotes the development of theoretical thinking. Faced with these considerations, we outline the problem of this investigation, which defined the following central question: "What are the manifestations and possibilities of a dialogue between the teaching of the concept of division proposed by Davydov and collaborators in the Theory of Developmental Teaching with Historical-Critical Pedagogy?”. Therefore, the research aimed to analyze the possibilities of an interrelationship with the development of the arithmetic operation division concept for the initial years of elementary school I, between Developmental and Historical-Critical Theories. The study was carried out through bibliographical research based on the philosophical, psychological and didactic-pedagogical foundations between the Theory of Developmental Teaching and Historical-Critical Pedagogy, with the aim of revealing the mode of organization of teaching the concept of division between the two theories. The concept of division, approached by Crestani based on Davydov, has its essence revealed in the 'study tasks', which involve the relationships between magnitudes and their respective measures, based on geometric, algebraic and arithmetic meanings, while the relationship between the logical and the historical in the division process is presented by Duarte, in the organizational movement through the algorithmic process, centered on the decimal numbering system from the abacus instrument. Therefore, in terms of the philosophical conception, there are great approximations between the two theories, however, regarding the way of organizing the teaching of the concept of division, there are considerable differences. The conclusion is that this way of conceiving mathematics teaching based on study tasks, developed by Davydov in the Theory of Developmental Teaching, opens a horizon that expands as an indication in the sense of approximation, to think about the pedagogical practice in Historical-critical Pedagogy.