A construção de uma prova visual em trigonometria – o modelo RBC+C e o GeoGebra

Résumé fourni par la source

This study analyses how two first-year students enrolled in a Higher Professional Technical Course construct a visual proof of the trigonometric identity for the sine of the sum of two angles. The AiC and RBC+C models are adopted, using GeoGebra. A qualitative interpretative study was conducted with two students in the context of a Mathematics lesson. The empirical data include the students’ written and oral productions, dialogues between the students and the teacher, and the teacher’s written records. The epistemic actions mobilised were analysed, supported by subcategories developed for the study in accordance with the mathematical content and the required visual proof. The results show that the R, B and C actions evolved in an integrated manner, leading to the emergence of action C. Action R fostered the abstraction process, while the articulation between R and B constituted the central axis of the construction. GeoGebra supported the construction of the visual proof.