GeoGebra applets for teaching the derivative: Characteristics and influence of the derivative schema

Abstract

The aim of this work is to identify the main characteristics of GeoGebra resources for teaching the derivative. For this purpose, 76 applets were analyzed according to five variables (derivative schema, mathematical element, representation systems, actions and interactivity) and the influence of the levels of the derivative schema on the rest of the variables was also examined. The data reveal that most applets address the intra- and inter-levels of the derivative schema, and that the graphical and algebraic representation systems are the most frequently used. Furthermore, at the inter-level of the derivative schema, applets address more global properties of the derivative and employ additional representation systems, enabling a greater variety of actions than at the intra-level. However, the results suggest that GeoGebra offers few resources for working at the highest (trans-) level of the derivative schema. The inter-level requires more extensive engagement with the remaining variables, and Fisher’s exact test was used to examine the influence of the level of the derivative schema.