Banca de QUALIFICAÇÃO: FRANCISCO NETO LIMA DE SOUZA

AL-BIRUNI AND HIS LETTER ABOUT THE RELATIONSHIPS BETWEEN SIDES AND ANGLES OF SPHERICAL AND PLANE TRIANGLES: A DIGITAL TEACHING GUIDE DIRECTED TO THE TRAINING OF MATHEMATICS TEACHERS

History of Islamic Mathematics in the 11th century. Al-Biruni's letter to Abu Said. Geometric knowledge. Historic-activities-with-technology. Interface between history and teaching.

Focused on the study of the history of mathematics (HM), more precisely on the history of Islamic mathematics in the medieval period, this work was based on a letter, written by al-Biruni in the 11th 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, we turn to the proposition of an interface between history and teaching through the alliance between HM and digital technologies (DT) via mathematical investigation (IM). Therefore, the present dissertation was guided by the following question: what knowledge can be mobilized from a historical-activity-with-technology elaborated based on the didactic potentialities of a letter written by al-Biruni in the 11th century and conceived through the articulation between history and teaching? Aiming to answer this question, our general objective is to propose an articulation between history and teaching via an alliance between HM, TD and IM, aimed at the training of mathematics teachers and, for that, we established three specific objectives closely related, they are: to study aspects related to al-Biruni, his production and the context in which he and his work are inserted; establish connections between the histories of mathematics present in the treaty with the historical-activities-with-technologies of Sousa (2020) in the perspective of the interface between history and teaching of Saito (2013) and; to elaborate and apply a Didactic Guide, aimed at the formation of the mathematics teacher, involving historical-mathematical aspects of the letter. We emphasize that we combined methodological procedures and different instruments to compose the analyzed data, they are: bibliographic research, documentary research, semi-structured questionnaires, photographs, field diary, filming, recordings and records of participants in the activities proposed with the Educational Product. As a result, we present an Educational Product prototype, whose main structure is in the final stage of development. This, in turn, will be applied in the opportunity of an extension course.