O software GeoGebra como instrumento no ensino de geometria analítica: uma perspectiva a partir da atividade orientadora de ensino

Abstract

Based on the assumptions of the Teaching-Orienteering Activity and the didactic principles for the organization of teaching proposed by Davýdov (1982), this research sought to identify potentialities and limitations of the use of GeoGebra as an instrument for the elaboration of a teaching situation of Analytical Geometry, intended for the High School stage. In order to achieve the objective proposed in this work, studies were initially carried out on the Teaching-Orienteering Activity, didactic principles, the GeoGebra software and the historical aspects of analytical geometry. Subsequently, analyzes of the perspectives of other researchers were carried out regarding the potentialities and limitations presented by the use of GeoGebra in the teaching of analytical geometry, classifying them into four categories, related to: the tools that the software presents; the student’s interest in the study of mathematics; the process of learning the concepts of analytical geometry; and the conscious use of GeoGebra, both by the teacher and the student. In addition, from the elaboration of a triggering situation for learning, called “Knowing the tourist attractions of Curitiba”, the potential and limitations of the software were analyzed. The situation elaborated proposes to explore some conceptual nexuses of analytic geometry, such as distances, angles and relative positions between straight circles. A proposal for organizing teaching using the situation was based on the organization of a book in GeoGebra, composed of three chapters: 1) Introduction to the use of GeoGebra; 2) Knowing the tourist attractions of Curitiba: the triggering problem of learning; and 3) Knowing the tourist attractions of Curitiba: reflections and summaries. With the analyzes carried out, among the potentialities of using GeoGebra, the possibility of simultaneously visualizing different representations of mathematical objects, identifying their algebraic and geometric characteristics, in addition to arousing greater interest in the student in mathematics and allowing the teacher to the development of interactive teaching materials. The limitations identified are related to the lack of tools in the software that allow performing calculations related to constructions, which can limit student learning if used without the support of other resources. It was also found that, in isolation, the triggering situation of learning and the manipulation of GeoGebra tools are not enough to guarantee the manifestation of the principles proposed by Davýdov. This depends on the interaction between the subjects involved, as well as their actions in the teaching and learning processes.