Conhecimentos matemáticos para o ensino de geometria na Educação Básica

Abstract

In this thesis, we present and problematize the results of a research in which we investigated mathematical knowledge for teaching, with regard to working with geometry in elementary school. The discussion about what can be constituted as a set of relevant geometry knowledge to be treated in the Teachers Education, for us, is related to the specificity of teaching practice in this area of Mathematics. Therefore, the question that gave direction to this investigation was the following: What mathematical knowledge for teaching Geometry - therefore, relevant to be dealt with in the Teachers Education - are unveiled in elementary school Mathematics classes? Based on this question, this research aims to identify and problematize mathematical knowledge for teaching, regarding to teaching geometry in elementary school, aiming at a discussion about the relevance of this knowledge for the Mathematics Teachers Education. The theoretical inspiration for the constitution of the thesis was formed from the articulation of works on the theme of the specific knowledge of Mathematics teacher’s for teaching in Basic Education and on School Mathematics. To achieve the research objective, it was analyzed, under an interpretative perspective, a set of real geometry classroom situations, in the final years of elementary school, in which questions that were asked to the participating teachers demanded knowledge that proved to be specific to teaching geometry, either these knowledge having been used or not by the research teachers during the observed teaching. The analyzed data were located, during their discussion, in specific literature on issues of teaching geometry in Basic Education. Some issues pointed out in specific literature stood out in the observations of the teachers’ classes, which suggested that they should be analyzed from the perspective of geometric knowledge for teaching. Among them, we highlight issues related to the use of visualization, as a component of the teaching of polyhedra and nonpolyhedra and flat shapes, and the use of argumentation and proof when working with the similarity of triangles and the Pythagorean Theorem. Our analyzes converge to a conclusion that specific mathematical knowledge for teaching geometry, or geometric knowledge for teaching, involves multiple knowledge attached to the teaching processes themselves, and also attached in theories of Mathematics Education and Fundamentals of Mathematics. We consider as an implication of the thesis for the Mathematics Teachers Education the possibility of building a curriculum for these majors that includes the study of geometric knowledge for teaching, which may provide elements that in fact meet the training needs of teachers.