O uso da história da matemática e do GeoGebra para o ensino e aprendizado da geometria analítica com ênfase no estudo de retas

Abstract

This thesis aims to analyze and understand strategies that graduates in mathematics from the State University of Mato Grosso use from the experience with the History of Mathematics and with the software GeoGebra to solve certain problems that can make possible a better understanding or resignification of the concepts of point, coordinates and equation of the line. In articulating this question we made use of the History of Mathematics, treated as a pedagogical resource for the teaching of Mathematics. For this, we perform a historical resumption of the coordinate system, the point and equation of the line and the use of the technologies. The question that we seek to answer with this research is: What strategies do students use from their experience with the History of Mathematics and GeoGebra to solve certain problems involving coordinates, point and equation of the line? The methodology used was qualitative, with an experimental method and data analysis from the semiotic representation registers of Duval (2011) and the Boero, Pedemonte and Gadotti (1997) Voices and Echo Games theory. The data produced allow us to affirm that the strategies used by the students present different semiotic representations in the resolutions of the proposed problems and activities, which were mediated through the use of software and historical knowledge of Analytical Geometry. We found a posture of independence presented by the students during this process and in the production of "resonant echoes". We conclude that the History of Mathematics inserted in the teaching of Analytical Geometry and the use of GeoGebra software enabled the student to develop problem solving strategies that contribute to the re - signification of basic concepts, both Geometry and Algebra.