Identifying Mathematical Reasoning Levels in Initial Teacher Training: A GeoGebra-Based Study about conic sections and emphasis on the case of the parabola

This work aims to identify different levels of construction of mathematical reasoning in students of initial formation, in the resolution of a didactic situation about the study of the parabola with the support of GeoGebra.The theoretical support was the Theory of Didactic Situations, considering the levels of mathematical reasoning related to its dialectical movement, together with Didactic Engineering, as a research methodology.The research was carried out undergraduate students at a Brazilian public university.We noticed the strong inclination of students to recognize the parabola only through the perspective of quadratic functions, to the detriment of Analytical Geometry, prioritizing functions as the first alternative solution.The results suggest the need to rethink the parabola approach, aiming at comprehensive teaching, considering it from