O uso do geogebra e resoluções visuais no ensino de Matemática

Abstract

This dissertation aims to use GeoGebra software in the Visual Resolution of geometric problems of Basic Education. In this way, it induces a reflection on the various ways to solve a problem, to understand that the Visual Resolution is also a valid solution and can lead to an algebraic solution. Softwares such as GeoGebra allow us to dynamically manipulate objects such as points, lines, segments, among others, allowing a graphical and algebraic visualization of this change of parameters. In the educational scope, besides the aforementioned, the proposal intends to favor the teaching of Mathematics since this methodology can arouse the interest for the discipline, as well as, to allow the student and the teacher to make conjectures. To that end, the teacher’s continuing education is fundamental, he must be attentive to teaching methodologies, guiding students to use the new technologies, favoring the organization of critical thinking. For the research, after a bibliographical survey, we made the option for three problems of the Olimpíada Brasileira de Matemática das Escolas Públicas, which involve area and perimeter. In the first problem, we obtain a non-quadratic continuous function, in which we aim to minimize. In the second, the resulting function is defined by two sentences and it is derivable throughout its domain. Finally, in the third problem, we found a function that is not continuous. Although the problems are of the High School, studying the behavior of these functions is not common in Basic Education. The visual resolution allowed us to conjecture some results and propose the analysis of several others. As for the methodology, the research is classified as exploratory of a qualitative nature, since we intend to unsderstand better the particularities of the proposed problems.