Solving types of problems and identifying obstacles in learning derivatives

Calculus courses form the basis for other mathematics courses in higher education. However, students often encounter obstacles in this course, which results in a poor command of calculus. This research focused on the evaluation of performance in application problems and the characterization of the obstacles presented by students in learning the concept of the derivative of a real variable function, in the Mathematics Pedagogy programs at two universities in Chile. The research methodology was qualitative/descriptive and exploratory, with quantitative data analysis. The study included a test of open-ended mathematical problems, differentiated according to their nature into routine and non-routine problems, and according to the context in which the problems are formulated, classified as real, realistic, fantasy and purely mathematical, in addition to a student opinion questionnaire regarding the types of obstacles students face in calculus in understanding the notion of the derivative. In terms of problem solving, greater knowledge was found in only two types, both routine purely mathematical context and fantasy context; in relation to the types of obstacles that hinder the learning of derivatives, from the students' point of view, didactic obstacles were identified more than ontogenetic and epistemological ones.