Soluções de equações quadráticas por 'Abd al Hamid Ibn Turk na formação inicial do professor de matemática: uma perspectiva orientada pela história da matemática

Abstract

The present work deals with the presentation of a notebook of activities that aims at the integration between the History of Mathematics (HM) and the Digital Technologies of Information and Communication (TDIC) through Mathematical Research (IM) for the teaching of geometric algebra in Teaching Superior, notably, in the mathematics degree. Regarding the historical topic, we decided to study solutions of quadratic equations from the perspective of Abd Al-Hamid Ibn Turk, an Islamic mathematician who lived in the 9th century. From bibliographic research, the first phase of this study, we found that the main work on Ibn Turk is by Sayili (1962), entitled Logical Necessities in Mixed Equations by 'Abd al Hamid Ibn Turk and the Algebra of His Time, in Portuguese, Necessidades Logics in Mixed Equations: 'Abd al Hamid Ibn Turk and the Algebra of His Time. Thus, this document is our main reference, dealing with the resolution of polynomial equations of the 2nd degree from a geometric reasoning. The bibliographic research resulted in the second phase of this work, the elaboration of the activity booklet, which brings the possibility for students to carry out historical investigations, with the support of the Geogebra software, establishing relations between algebra and geometry. This activity book was applied to a class of Didactics of Mathematics I (MAT1516) of the degree course in mathematics at UFRN in 2019.2. Such an application showed that technologies assist in the process of (re) construction of mathematical discoveries as students optimize the time to elaborate constructions, thus leaving more time to make investigations inspired by the problems of the History of Mathematics. In addition, these activities caused interest in studying the mathematical concepts covered and provided active participation of students in the construction / development of knowledge. It is noteworthy that all this qualitative research resulted in an educational product developed based on the above, available to teachers who want to use it in their classes.