An exploratory study about the errors and difficulties of high school students regarding the concept of derivative

The errors that students make when solving a mathematical problem are a powerful tool to detect difficulties in the learning of this discipline. Their diagnosis allows the development of teaching techniques that avoid or rectify their commission. This article presents the results of an exploratory study which aims at analyzing the errors that students make when studying the concept of derivative of a function. To this end, the errors made by 27 high school students during the resolution of a series of exercises are examined. The results allow to identify those categories in which students make a higher number of errors when studying the derivative. The analysis also reveals difficulties caused by poor learning of prior knowledge. The later invites to reflect on the need to promote a logical and coherent analysis of concepts, language and solutions, when solving mathematical problems.