As apreensões em geometria : um estudo com professores da educação básica acerca de registros figurais

Abstract

This research, based on the Theory of Registers of Semiotic Representations, by Raymond Duval, was conducted in order to analyze the influence of the type of figural record in perceptual, operative and discursive apprehensions in geometry. As methodological procedures, an extension course for teachers from Basic Education of the public school system was offered, addressing geometry content through figural records: Manipulatives (MM), Geometry Software's (SG) and Graphic Expressions (EG). The course was attended by 30 teachers. In the second stage of the research, a sequence of activities was applied with some volunteers who participated in the extension course - a total of 15 collaborators. The sequence was applied individually and elaborated with the aim of exploring a variety of situations and concepts to identify the aspects of apprehensions provoked on the collaborators by the contact with the figural records. The individual resolutions by the collaborating teachers were analyzed and grouped into a triple analysis: analysis of the understanding, analysis of the reasons and mathematical analysis. This was based on mathematical reasoning exposed by the participants in the form of discursive and non discursive records, and on their oral and written comments along the application as well, considering successes, hesitations and failures in the attempt to solve the tasks. The results of the research show that, by using different figural records to solve geometry problems, factors related to treatments, mobilization of records, apprehensions - whether perceptive, operative or discursive -, and the solving of problems are influenced by the type of figural record available, creating direct consequences in the search for the problem's solution. It was also found that the influence of the type of figural record is associated with the demands of the problem in which the figural record is available. In tasks requiring mathematical deductions (formal language), the EG and SG were the most favorable records, enabling deductive reasoning allied to figural treatment. SG has also provided the movement of figures and figural elements, supporting the understanding of the problems hypothesis and the reasoning for their solution. In tasks that required a figural treatment as part of the problem, MM stood out for enabling empirical attempts - such as cutting, use of ruler, folding - which could help in the solution of the problem.