Função modular quadrática: um estudo a partir da interpretação global figural

Abstract

This master’s thesis presents a study on the quadratic modular function, based on Raymond Duval’s Theory of Semiotic Representation Registers, specifically the Global Figural Interpretation approach. This approach enables the exploration of functions through correlations between significant visual units and significant algebraic units. These correlations arise from the development of the semiotic operations of treatment and conversion. In this regard, the master’s thesis highlights the importance of conceptual understanding of these operations, since, according to Duval, mathematical learning occurs primarily through them, especially through conversions between registers. Thus, the objective of the master’s thesis is to conduct a qualitative investigation into the sketches of the quadratic modular function’s curve, analyzing the correspondences between semiotic representations in the graphical register and their algebraic representations. This analysis considers the quadratic function in both its complete and incomplete forms. The research utilizes GeoGebra as a tool for observing the transformations that occur within the semiotic representations of the quadratic modular function. As a result, the Global Figural Interpretation may enhance the teaching of the quadratic modular function by exploring the operations of treatment and conversion, allowing for a broader and more qualitative perspective on curve sketching and its correlation with the algebraic expression.