Integração do software GeoGebra na resolução de problemas da olímpicos: uma abordagem baseada na Teoria das Situações Didáticas

The presence of mathematics in student education is essential, contributing to their intellectual and professional development and fostering reasoning skills crucial for tackling daily challenges. However, mastering this subject requires a level of reasoning that many students struggle to attain due to various factors, as evidenced by results from external assessments such as the Program for International Student Assessment (PISA). Using the Theory of Didactical Situations, this study looks into what happens when you use GeoGebra in a math Olympiad-based teaching situation involving a geometric problem from the 2023 Brazilian Math Olympiad for Public and Private Schools (OBMEP). Based on reports from the Institute for Pure and Applied Mathematics (IMPA), it is found that the mathematical education of teachers reveals significant gaps, directly impacting teaching quality. We used the four stages of Didactical Engineering as a research method to create a teaching session that uses GeoGebra to help students see shapes more clearly while solving Olympiad problems. This made it easier for them to understand geometry. The results indicated substantial progress in understanding geometric concepts, despite some identified didactical obstacles. Moreover, we highlight the importance of visualizing and manipulating geometric figures to solve complex problems, illustrating how GeoGebra can be a powerful tool for developing geometric thinking. Improvements that are being considered include slowly adding technological tools and creating activities that link pictures and ideas that aren't concrete.