Slope of tangent line: element of connection of the derivative as a limit or rate of change mediated by GeoGebra

García-Cuéllar D.J.; Martínez-Miraval M.A. · RISTI - Revista Iberica de Sistemas e Tecnologias de Informacao (2023)

Resumen

The study aims to report how university students connect various notions related to the concept of derivative by mobilizing the notion of slope of tangent line mediated by GeoGebra. The derivative as slope, limit or rate of change, are notions that are connected by performing transformations between their representations, and by using GeoGebra, schemes for using this artifact can be identified that help this process; therefore, aspects of the Theory of Semiotic Representation Records and the Instrumental Approach are considered. In the experimental part, the students made conversions between the representations of the derivative as the limit of a quotient of variations and as an instantaneous rate of change, connected from the notion of slope of tangent line. It is concluded that the design of applets with sliders, linked to points, lines and slope values, makes it possible to understand the derivative as a dynamic process.

Instituciones: Pontificia Universidad Católica del Perú; Universidad Antonio Ruiz de Montoya