Uso de GeoGebra para la comprensión geométrica de la derivada en estudiantes de tercer año de bachillerato. Un estudio de caso

Abstract

Abstract: This research examines the use of GeoGebra for developing a geometric understanding of the derivative, both before and after the implementation of a GeoGebra-mediated instructional sequence. The study was conducted with third-year high school students at the Manuel Gonzalo Albán Rumazo Educational Unit, located in the Aláquez parish, Latacunga canton, Cotopaxi province. A quantitative approach was adopted, utilizing a pre-experimental design with a single group of 30 students, who were assessed both before and after the intervention (pretest-posttest). The pretest results showed a mean score of 4.60 points. Following this, an intervention mediated by GeoGebra structured according to the ERCA model (Experience, Reflection, Conceptualization, and Application) was implemented, focusing primarily on activities involving the exploration, visualization, and analysis of dynamic representations. After the intervention, the mean score on the posttest increased to 7.07 points. Statistical analysis using the Wilcoxon signed-rank test revealed statistically significant differences between the two assessments (p < 0.001). Furthermore, the effect size was large (r = 0.76), and Hake s normalized gain reached a value of 0.46, indicating a medium gain. The results obtained from the participating group demonstrate an improvement in the geometric understanding of the derivative following the GeoGebra-based intervention, supporting the use of this software as an effective instructional resource for teaching differential calculus at the high school level.