Descriptive visualization and justification of surface area formulas in a dynamic geometry environment with undergraduate students

Abstract

This research analyzes the process that students of the Bachelor's Degree in Teaching and Learning of Mathematics in Secondary Education follow when they justify surface area formulas of polygons in a dynamic geometry environment with GeoGebra software. A didactic engineering approach was applied with 23 fourth-semester students through nine didactic guides centered on the construction of quadrilaterals, triangles, and regular polygons. The study reports how participants move from the geometric rigidity of pencil and paper toward dragging, animation, and the identification of invariants. The results show that dynamic visualization contributes elements for the construction of mathematical arguments about area formulas, the recognition of geometric properties, and the generalization of procedures. The work concludes that dynamic geometry, articulated with didactic guides designed for specific purposes, favors the construction of geometric reasoning in initial teacher education.