Enseñanza del teorema de Thales basada en procesos de argumentación

Abstract

This research in mathematical education focused on analyzing the argumentative processes of students during the learning of Thales' theorem, incorporating communicative elements throughout a teaching proposal designed for this purpose. The intention of this research centered on several key aspects. First, the construction of adapted argumentation levels for implementation in a mathematical education teaching sequence was addressed. These levels provided a clear and progressive framework that guided students from initial responses to the consolidation of solid and well-founded arguments. The designed teaching proposal focused on the learning of Thales' theorem and was implemented with the goal of promoting argumentation as an integral part of the educational process. Through this proposal, students had the opportunity to strengthen and formalize their prior knowledge, using it as a foundation for the construction of new mathematical knowledge. Furthermore, a deeper and more detailed understanding of how and why mathematical methods work was achieved, surpassing mere memorization of formulas and procedures. One of the key findings of this research was the need to actively promote argumentation in the mathematics classroom. It was identified that students were not accustomed to providing reasoned solutions, which poses a challenge to their educational development. Therefore, the importance of paying greater attention in the classroom to communicative skills was emphasized, fostering a pedagogical approach that encourages active participation, argumentative reasoning, and the application of mathematical concepts in diverse contexts. In conclusion, this research underscores the relevance of argumentation as a fundamental tool in mathematical education. It also highlights the need for teacher training that promotes meaningful mathematical learning, oriented towards deep understanding and practical application in students' everyday lives.