Integration of Definitions and Exploration of Semiotic Representations of Conics Using Computational Resources

Abstract

This article aims to investigate how the articulation of different semiotic representation registers of conic sections—especially the algebraic, graphical, and spatial-figural ones—helps overcome the traditional fragmentation found in the teaching of Analytic Geometry. To this end, it draws on the Theory of Semiotic Representation Registers and introduces the Conics 3D computational environment, specifically developed to enable the simultaneous and dynamic exploration of these registers. The analysis shows that, by allowing students to interactively manipulate algebraic, graphical, and spatial-figural representations, the software not only promotes a more unified understanding of conic sections but also fosters the development of reasoning and visualization skills. It is concluded that the adoption of such a computational tool strengthens the dialogue between theory and practice, expanding the possibilities for more meaningful mathematics education, both in basic education and in teacher training.

Keywords
Theory of Registers of Semiotic Representations; Conics; Geometry; Spatial Figural Representation; Dynamic Semiotic Register