Análisis de errores en tareas sobre el concepto de derivada: una mirada desde la teoría APOE (Acción, Proceso, Objeto, y Esquema)

The present study focuses on the visible, that is, on analyzing errors that students make to identify possible causes. The framework proposed by the APOE (Action, Process, Object, and Schema) theory is applied through the definition of 27 variables based on mathematical elements involved in three tasks that conform a questionnaire on the concept of derivative. The participants are 103 first-year engineering students. The data gathered consist of students’ answers to the questionnaire collected during the first semester of the year 2021. The results show that there are difficulties associated with the construction of the reversal of processes as revealed by the great number of errors associated with the use variables obtained from logical equivalences. It is concluded that encapsulating the derivative as a cognitive object, corresponding to its function, is difficult to achieve.