Una actividad para promover el desarrollo del pensamiento variacional de profesores de bachillerato

Abstract

In mathematics courses, it is common to study concepts and algorithms presented in a decontextualized and abstract way, which does not necessarily allow students to develop the skills required to use mathematics in solving problems. For this reason, it is increasingly promoted to pay attention to so-called mathematical thinking, a way of reasoning that gives rise to the use of mathematics in solving both intra- and extra-mathematical problems. In the case of engineering, it is particularly important to develop Variational Thinking.

Reviewing educational mathematics research reports in this regard, we found that even in traditional Calculus courses some difficulties are reported in their teaching, since formalism and techniques are privileged, focusing on algorithms or mechanizations, which, although are necessary, it is recommended that it be addressed through the problems of variation and accumulation. The objective of this work is a proposal for teaching Calculus through the study of Variational Thinking, where the study of variation in real contexts of interest to students is privileged. Under this approach, the design of an activity is presented with data from the Department of Scientific and Technological Research of the University of Sonora (DICTUS) on the growth of a microalgae that serves as food for crustaceans, in an aquaculture farm in Bahía de Kino Sonora. In this activity, students carried out the study focusing on What changes? How does it change? and, How much does it change? which allows the elements of the Calculus to emerge, such as: the magnitudes involved in the variation, increasing and/or decreasing periods, the rate of change, among others. The use of this approach provides great benefits in the study of variation, since students develop the elements of calculus naturally when facing problems in professional contexts.