Guía didáctica para la enseñanza de las aplicaciones de las derivadas: tasas de variación y problemas de optimización

Abstract

The teaching of derivative applications is generally not properly addressed by teachers, since they choose to explain this topic superficially due to lack of didactic resources and time constraints. Consequently, it is taught merely as a set of mechanical processes and formulas, without exploring its multiple real-world applications. This approach negatively impacts students' meaningful learning by hindering their ability to visualize the applications of derivatives in their environment. Therefore, this work aims to develop a didactic guide focused on constructing mathematical models for teaching derivative applications (such as rates of change and optimization problems). The primary goal is to design an educational resource for teachers, which will facilitate a more interactive and dynamic teaching approach, based in constructivist principles.