The notion of partial derivative: expected knowledge levels of students according to prescribed mathematical and didactical organizations

Abstract

We would like to start by presenting our objective, which is to understand the difficulties presented by students in the teaching-learning process of the notion of partial derivative. To do so, we consider as central the theoretical approach defined by Robert, related to the three levels of expected knowledge from the students. We are also supported by the notions of setting according to Douady's definition and Rogalski's point of view, as well as by the elements of the anthropological theory of didactics according to Chevallard and his collaborators. Methodologically, we have used documentary research developed through a grid of analysis according to Dias’s model. The analyzes allow us to advance some considerations on the necessary previous knowledge to learn the notion of partial derivative and its applications, highlighting the importance of the applications in other sciences that need specific attention, since the knowledge associated to these sciences are not developed in the basic education.