Uma sequência didática para o ensino e aprendizagem da função afim com o uso da robótica estrutural

Abstract

The present dissertation aimed to investigate possibilities of using structural robotics in the process of teaching mathematics as a means of promoting learning and the perception of the connection between it and other areas of knowledge. The theoretical references used were elements of Rabardel's Instrumental Genesis as a means of instrumentalization of robotics, and of Duval's Theory of Registers of Semiotic Representations as a means of evaluating the learning of taught concepts. To guide the research, the following question was formulated: Structural robotics has possibilities of instrumentalizing, according to Rabardel's conceptualization, the process of teaching mathematical concepts such as the Affine Function, in order to favor the learning process in connection with concepts of related areas? For this, we used a didactic sequence aimed at teaching the Affine Function. This sequence was applied to students in the second year of high school, from a public state school in the metropolitan region of São Paulo, and the methodological procedures were guided by the phases of didactic engineering with the experimentation developed in the period of six classes, two per week. In the phase of systematization of the studied concepts, the GeoGebra software was used. The data indicated that the specificities of structural robotics emphasize and value the structural stage of its use, unlike the others, whose central objective is programming. This material is anchored in the possibility of the rods being fitted by connectors, which are distinguished by their open angles and colors, which allows the teacher to create conditions for the instrumentalization of the teaching process. In addition, this technology allows exploring the relationship of a mathematical concept with concepts from related areas. The data also revealed, in the confrontation between the a priori and a posteriori analysis, evolution of knowledge of basic concepts, of improvement of the abstraction conditions of the students identified when they related constructions with robotics materials and mathematical, physical and engineering concepts. There was an evolution of understanding of the Affine Function, because at different times it was referenced in its different representations, without this bringing confusion of understanding. The confrontation between the a priori and a posteriori analyzes also made it possible to identify an evolution in the students' conceptions of mathematics, since they were able to attribute to mathematical concepts the understanding of concepts of physics and engineering