“E agora, cinco?”: uma história virtual do conceito para o ensino da tangente no ensino médio

Abstract

This study aims to analyze the contributions of an intentional organization of teaching, grounded in the Logical-Historical Movement and the Guiding Teaching Activity, to the appropriation of the concept of tangent by high school students. It is based on the understanding that Mathematics teaching should provide students with access to the historical conditions that gave rise to concepts, fostering the development of theoretical thinking. The research is characterized as qualitative and was developed through the elaboration and implementation of a Learning Triggering Situation (LTS), which addressed historical elements related to the emergence of the concept of tangent. The activity was organized to engage students through a Virtual History of the Concept, designed to highlight the need for the concept of tangent and enable the investigation of its conceptual nexuses. For the analysis of the empirical material, two analytical axes were established: the understanding of the historical necessity of the concept of tangent and the identification of the conceptual nexuses and students' appropriation of this concept. The results of this research indicate that the articulation between the study of the Logical-Historical Movement of concepts and the organization of teaching through the Guiding Teaching Activity constitutes a powerful approach to the teaching of trigonometry in the school context, insofar as it enables students to approach the conditions that gave rise to mathematical concepts and fosters an understanding of the conceptual relationships that structure them.