Uma Proposta para a Compreensão do Objeto Função a Partir da Teoria dos Registros de Representação Semiótica

Abstract

This research aims to understand the mathematical object Functions by employing Raymond Duval's Theory of Registers of Semiotic Representations and using a teaching sequence for this. For that, the theoretical knowledge about Functions was taken up, a bibliographic and analytical study on the Theory of Registers of Semiotic Representations was carried out and a teaching sequence was finally elaborated. Therefore, we approached the object functions, specifically that would provide the conversion of records, the determination and variation of the coefficients of the real function of a real variable, the analysis of the behavior of the function in its domain and the exploitation of GeoGebra software as a potential in the teaching of functions. The methodology of this work is based on a qualitative research through a bibliographical review. The teaching sequence considers Duval's Theory of Registers of Semiotic Representations and uses as teaching-learning-evaluation methodology the Problem Solving Methodology proposed by Onuchic and Allevato. When this methodology is used, occurs the investigation activity that can be done by the teacher or by the students or both. In this way, four lesson plans were organized, we first studied the case of existence or non existence of a Function considering a problem situation, and then another situation was proposed with the objective of exploring the behavior of the function variables. In the second lesson, we discussed the variation of the parameters and the construction of the graphs, using GeoGebra software. In the third lesson the transformations (conversion and treatment) between the registers of semiotic representation are discussed and the identification of quantities is explored. And in the last lesson, through the use of situations-problems, we tried to work the different registers of semiotic representation. It is thus considered that the proposed sequence of teaching based on the Duval‟s theory, which uses the transformations of registers (treatment and conversion) in a contextualized way can enhance the understanding of the mathematical object Functions, in this case, the linear and quadratic functions were studied.