A aprendizagem da função afim por meio de uma abordagem qualitativa e global com uso da plataforma Desmos

Abstract

The object of this dissertation was the learning of the affine function, mediated by the Desmos platform, subsidised by the main aspects of algebra learning, according to Raymond Duval’s theory of Semiotic Representation Registers. This study seeks to highlight the intellectual gestures required and the cognitive phenomena mobilised for understanding and learning the affine function in the final years of primary school. The question that guided the research was: To what extent can the Desmos platform contribute to a global and qualitative approach to the learning of the affine function by 9th grade students? In view of this question, the general objective was to investigate to what extent, in the light of the theory of Semiotic Representation Registers, the Desmos platform can contribute to a global and qualitative approach to the learning of the affine function by 9th grade students. Data collection was carried out through the application of a didactic sequence, for a group of students from the 9th year of Elementary School of a public school in the municipality of Remanso – Bahia. For the organisation, treatment and analysis of data, Bardin’s Content Analysis (2021) was used. The data were organised into four categories: (i) – Participants’ initial perceptions of the Desmos platform; (ii) – Correspondence between the units of meaning of two semiotic representations of the affine function, using the Desmos Graphing Calculator; (iii) – Study of the sign of the affine function, using the Desmos Graphing Calculator; and (iv) – Cognitive conversion operations, in both directions, between graph and equation. The results indicate that the use of the Desmos platform proved to be positive because it is an accessible and easy-to-interact resource, which favoured the visualisation and exploration of the significant symbolic units of the algebraic expression and the visual variables of the graphical representation, in addition to instigating the curiosity of the participants in the search for new learning. It is concluded that the use of the Desmos platform enhances the exploration of transformations by conversion between the graphic and algebraic representations of the affine function, in both directions, providing understanding and learning of this mathematical object in a global and qualitative way.