Tecnologias Digitais e Registros de Representação Semiótica no ensino de Sistemas Lineares: uma abordagem integrada

Abstract

The study presented in this dissertation was developed in the Mathematics Education research line and sought to answer the following question: To what extent do different Semiotic Representation Registers enable students to mobilize knowledge in solving tasks involving Linear Systems with the support of Digital Technologies? To this end, the general objective was defined as investigating how a pedagogical approach, based on the assumptions of the Theory of Semiotic Representation Registers and supported by the use of GeoGebra, can contribute to the mobilization of knowledge in solving tasks involving Linear Equation Systems. Three specific objectives were established: 1) To analyze how different Semiotic Representation Registers are mobilized in the content of Linear Systems, present in Mathematics textbooks; 2) To discuss the mathematical knowledge mobilized by students in solving tasks related to Linear Systems of two equations and two variables with and without the support of GeoGebra; 3) To analyze how different Semiotic Representation Registers are mobilized by students in tasks involving systems of three equations and three variables, and how the use of GeoGebra contributes to facilitating conversion between representation registers. The qualitative research involved analyzing three Mathematics textbooks approved by the National Textbook and Teaching Materials Program (2021) and conducting field research in a class of 2nd-grade High School students at a state school in Montes Claros, Minas Gerais, Brazil. The analysis of the textbooks revealed that, although they include different forms of representation, algebraic and natural language prevail, with a greater recurrence of tasks that require processing than those that require conversions. The results of the tasks show that students were able to coordinate at least two registers simultaneously and that GeoGebra proved to be a key tool for performing conversions and treatments in the graphic register. However, difficulties persist in relation to the algebraic resolution of systems — especially in the substitution and scaling methods — and the graphical interpretation of systems with three equations. Overall, the findings point to the relevance of linking the Theory of Semiotic Representation Registers to the use of Digital Technologies, as this combination enables more dynamic experiences and enhances different ways of thinking mathematically