Conversões entre os registros algébrico e gráfico em livros de matemática do 1° ano do Ensino Médio: uma análise do capítulo de função afim

Abstract

This article presents the results of a study that aimed to analyze, in light of the Theory of Semiotic Representational Registers, the conversions between algebraic and graphical registers—particularly in the graphical-algebraic direction—within the content on linear functions in three high school freshman-level mathematics textbooks. This is a qualitative study conducted using content analysis, in which categories were defined related to approaches to constructing the graph’s plot (point-by-point, plot extension, and overall interpretation of figurative properties) and to the transformations between these records (treatments and conversions). The results showed a predominance of the algebraic representation over the graphical one, as well as a low incidence of activities involving conversion between these representations, especially from graphical to algebraic. The conversion from algebraic to graphical notation occurs predominantly through point-by-point and line extension approaches, while conversion in the graphical-to-algebraic direction is limited and rarely used. It can be concluded that the approaches adopted in the analyzed textbooks may hinder conceptual understanding of the linear function, particularly with regard to conversions between algebraic and graphical representations (in both directions), as they do not promote the integration of these two modes of representation, indicating the need for practices that prioritize the holistic interpretation of graphical properties.