Complementation Between Usage Schemes and Mental Actions in an Approach to the Definite Integral Using GeoGebra

Abstract

In the process of approximating the area of a region by means of Riemann sums a relationship between different variables that change simultaneously takes place, and although digital technologies help to visualize the process, it is important to understand how an individual reasons with the software. This study aimed to analyze how the interaction between usage schemes and mental actions of an individual occurs when solving an assignment about the definite integral study using GeoGebra. Theoretical approaches of both covariational reasoning and instrumental approach were used in qualitative research using action research as a method. Students mobilized their usages schemes related to variation, summation, and limit notions, which were run using the GeoGebra commands slider and RectangleSum, these commands were used in order to represent and coordinate the changes in the values of the variables: number of rectangles and sum of their areas; this allowed identifying a complementation between these usage schemes and mental actions, strengthening the analysis of the information. Finally, it is concluded that the complementation of two theoretical approximations provides elements that are essential when analyzing the phenomenon studied, in order to understand how a student reasons covariationally when using GeoGebra during the learning process.