Interactive Calculus Learning: merging Cognitive Roots, Documentational Genesis, and GeoGebra

Resumo

This article aims to contribute to Calculus teaching regarding the selection of teaching resources that take learning difficulties into consideration. We advocate choosing appropriate resources that reflect the results of theories and the advantages of using technology. Theoretical constructs proposed by David Tall (1941-2024), such as cognitive root and local straightness, as well as documentational genesis, introduced by Gueudet and Trouche, are used to support our approach to the concepts of derivative and differential equation. Examples such as the blancmange function and the use of GeoGebra are discussed as tools that foster the understanding of complex concepts through interactive and dynamic visualizations. This study emphasizes the importance of combining theory and practice in the use of technologies to facilitate meaningful Calculus learning, which highlights the relevance of these approaches to the field of Mathematics Education.