Olimpíada Internacional de Matemática: situações didáticas olímpicas no ensino de geometria plana

Abstract

This paper presents a didactic proposal based on the use of Olympic Problems, specifically the International Mathematical Olympiad, in a complementary way, with the Didactic Situation Theory for the teaching of plane geometry. Thus, its main objective is to investigate whether the Olympic Didactic Situations work the processes of plane geometry teaching with the help of GeoGebra software in a classroom context with international mathematics issues. The investigation was aligned to the Didactic Engineering research methodology, with the use of GeoGebra software to aid in teacher training and student Olympic preparation. The Experimentation phase took place in a state school in Ceará and was organized in four meetings, with a study team formed by eight student Olympiad coaches. First, the description and application of the three Olympic Teaching Situations were performed, by the web conference virtual platform, remotely, besides the instant messaging application, which helped in the resolutions, by the students, and in the elaborations, by the researcher, with the GeoGebra software, which meets the new strategies of the teaching and learning processes of the geometry, algebra, calculus and statistics contents, allowing the interested parties the possibility of exploring, conjecturing, investigating such contents in the construction of the mathematical knowledge of the Olympic Situation. Data were collected remotely, viewing the students' performance in preparation, recorded by writing, photos and audios, based on the four stages proposed in the Theory of Didactic Situations: Action, Formulation, Validation and Institutionalization, validating internally by confronting the phases of Didactic Engineering, which are Preliminary or Prior Analysis, Design and a priori Analysis, Experimentation, a posteriori Analysis and (internal) Validation. We analyzed some dissertations from the repository of the Professional Masters in Mathematics in National Network with the topics incenter and circumcenter applied in Olympic competitions. In this situation, it was identified that there is little research that uses Olympic problems using GeoGebra. Finally, there is the Educational Product constituted by the data collected through this research, which includes five teaching situations that were elaborated, explore the concept of geometry and were mediated by a GeoGebra Calculator Suite application and a website with videos and application suggestions for the high school teacher.