Aliança entre história da matemática e tecnologias digitais via octante reflexivo dos irmãos Hadley para o ensino de geometria na formação de professores

Abstract

This dissertation proposes a historical-mathematical study supported by the alliance between History of Mathematics and Digital Technologies through the use of the Reflective Octant instrument, which results in an Educational Product directed to teacher training. In this way, it is linked to the research line Teaching and Learning of Natural Sciences and Mathematics of the PPGECNM-UFRN and seeks to answer the focus question: How can the alliance between HM and DT contribute to the production/elaboration of the Educational Product, Reflective Octant, for the training of mathematics teachers about the teaching of geometry? In this perspective, the objective of the research is to develop a historical-mathematical study around the use of the Octante based on the alliance between History of Mathematics and Digital Technologies for teacher training for the production of a EP. For this, we used a methodological approach that is characterized by qualitative research, with bibliographic and documentary procedures and also experimental. To clarify, a survey of data was carried out on the Octante and the Hadley brothers, with the intention of contextualizing the period in which the instrument was developed and understanding the mathematical knowledge behind its use. To this end, bibliographic and documentary data were used in order to catalog the sources and carry out a historical-mathematical study. From this characterization, an Educational Product was produced, which sought to enable the understanding of the influences of the Hadley brothers and The Royal Society in the development of the Octant, as well as to understand how the double reflection works, which depends on the structure of the instrument and knowledge of a mathematical nature to happen, allowing angles and distances to be taken and to direct navigation. In addition, in an experimental procedure, the application of the Educational Product was carried out in a class of Mathematics Undergraduates. During the application in the initial training of teachers, it was possible to perceive some points that could be improved in the EP, such as typing errors and reformulation of the questions for better understanding, as well as the possible relationships that arise from the alliance between HM and DT with connections for the use of the Octant Reflexivo instrument, thus validating and refining it. Furthermore, data extracted from instruments such as questionnaires, field diaries, photos and others showed us that the undergraduate students perceived a possibility of using HM in conjunction with DT; understood that the construction and manipulation of the Digital Octante allowed the mobilization of concepts such as point, line, semi-line, relationship between internal and external angles of triangles, bisectors, perpendicular lines, and others; they also indicated that the EP can be used in undergraduate, basic education; among other points that we consider the results of this research. Thus, this study sought to contribute to the initial training of teachers, as well as to research within the scope of the alliance between HM and DT and the use of Mathematical Instruments.