Praxeological analysis of derivative as rate of change at Calculus textbooks

Abstract

Most of difficulties of Calculus learning get complicated when textbooks, used as reference in the course, lack of theoretical support, insomuch as definitions or theorems are enunciated without being demonstrated, generating a confusion between students’ intuitive ideas and formal definition of mathematical concepts. The objective of this article is to show a comparative analysis of three textbooks, which are consulted at undergraduated programs, regarding the way derivative rate of change is approached. We consider as theoretical support the Anthropological Theory of Didactics by Yves Chevallard, whose fundamental principle is that all human activity could be described as a unique model, called praxeology, based on “know-how” and “knowledge”, analyzing the type of problems and techniques that are used to solve them as well as the used justifications.