Classificació de superfı́cies compactes i la seva aplicació didàctica a l’aula de batxillerat

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Sergi Muria Maldonado ; [en] In this work, we present a complete characterization of the classification of compact surfaces from a topological point of view with the main goal of contextualizing the design of a didactic proposal whose objective is to bring topology closer to high school students. This work is divided into two parts. The first one, in which we study the classification of both bordered and unbordered surfaces from a theoretical perspective, includes an alternative proof to the classical one for the Classification Theorem for Compact Surfaces. In the second one, where the didactic proposal is presented, we use experiential and manipulative mathematics as a bridge between students and mathematical abstraction, and we analyze the proposal’s implementation at Barcelona’s INS Pedralbes.