Teoria histórico-cultural e o cálculo de área de figuras planas

Abstract

In this work, we present the perspective of Vygotsky and Davydov's historical-cultural theory to address the issue of calculating the area of flat figures. We present the main concepts of this theory with the purpose of applying them in the logical movement of calculating areas of flat figures. Davydov states several times that in class the teacher, in his teaching planning, must consider the possibility of the student following the path taken by scientists in determining the object, in this case, the calculation of areas. By doing so, the student has the concrete possibility of appropriating the scientific concept. To this end, the teacher must escape the commonplace of traditional teaching that focuses its efforts on transmitting empirical knowledge, that which characterizes the superficiality of the object of study, based on sensitive data. An important type of knowledge, but not sufficient to determine the internality of the object. Davydov strongly advises that the teacher carries out teaching focused on scientific aspects, seeking to carry out a movement that shows the essence of the object, the refined ways that determined it, showing the student its relationship with social and cultural contexts, that is, its applicability. In this sense, we propose the need for a basic unit of measurement as the essence of the concept of area, showing that this notion allows us to calculate any type of flat area and that this procedure leads us to the generalized area calculation, that is, to the concept of integral, a revolutionary concept in Mathematics. In this discussion, we present the deductive methods of Mathematics, as creative ways in determining concepts and which also shows the conceptual links in the calculation of areas.