Propuesta metodológica para la enseñanza y aprendizaje de las derivadas a través de la resolución de problemas

Abstract

In the context of the study and learning of mathematics, the understanding of derivatives has proven to be a persistent challenge for both learners and teachers. Therefore, the objective of this research was to conduct a comprehensive examination of the topic of derivatives to design a referential document that contemplates a methodological proposal through problem-solving for the teaching of derivatives. The methodology of this work was approached under a non-interactive qualitative approach with a descriptive scope, using a documentary research design. Through these three methodological aspects, a referential document was designed, focusing on problem-solving within the domain of derivatives which encompasses the two fundamental outcomes of this study. Firstly, it entails the development of an innovative methodological proposal for the study of derivatives through problem-solving, comprising four distinct phases: reading and understanding the topic, searching and studying mathematical tools, construction of the solution, and finally, verification of results. Secondly, the study resulted in the creation of contextualized problems related to the topic of derivatives through the application of these four new phases, serving as an exemplification of the methodological proposal. Thus, it was concluded that through the use of the referential document, it is possible to contribute to the development of critical thinking skills, alongside logical and creative reasoning on the subject of derivatives, which serve as the foundational basis for the exploration of differential calculus.