Um estudo das relações entre os lados e os ângulos de um triângulo, inseridas em uma carta escrita por al-Biruni, com direcionamentos à formação do professor de matemática

Abstract

Centered on the study of the history of mathematics (HM), precisely on the history of Islamic mathematics in the medieval period, this work was based on a document written by al-Biruni in the eleventh century, which carries at its core an initial greeting, five demonstrations on some relations between sides and angles in triangles on the sphere and in the plane, and a final salutation. From the study of this document and the selection of our research object that corresponds to the first demonstration of the letter, we considered the proposition of an interface between history and teaching through the alliance between HM and digital technologies (DT) via mathematical investigation (MI) . The present dissertation was guided by the following question: how can the mathematical knowledge mobilized by the analysis of al-Biruni's letter be used for an articulation between HM and teaching via alliance in teacher education? Aiming to answer this question, our general objective is to develop an articulation between the history of mathematics and teaching aimed at the training of mathematics teachers. We emphasize that in the context of this research, methodological procedures and different collection instruments were combined to compose the data, they are: bibliographical research, documentary research, action research, semi-structured questionnaires, photographs, field diary, filming, recordings and records of the participants in the proposed activities with the Educational Product. As a result, we present a refined Educational Product, based on an application that was carried out within the curricular component Didactics of Mathematics I of the degree course in Mathematics at the Federal University of Rio Grande do Norte.