Modelación en la enseñanza de temas de Cálculo: Estudio comparativo al desarrollar un problema de optimización

[Objective] The study aimed to analyze the modeling process carried out by university students when solving a problem involving the notion of function optimization. [Methodology] Mathematical modeling is approached from the perspective known as models and modeling, utilizing the modeling cycles of Blum, Leiß, and Borromeo-Ferri, as well as the extended cycle for the use of digital technologies, to describe the processes students undertake during their resolution. The research design is an instrumental case study. The work of two second-semester students from the Business Administration program at a university in Lima, Peru, enrolled in the Calculus course during the first semester of 2022, is reported. Data collection was carried out through worksheets, GeoGebra files, and semi-structured interviews. [Results] The results show that the students developed skills in three areas: in the real world, by understanding that the cost of wiring varies according to the length and type of cable; in the mathematical world, by creating and using a mathematical model to optimize a function by applying prior knowledge of calculus; and in the computational world, by using GeoGebra to apply these concepts. [Conclusions] It is concluded that GeoGebra is a solid tool for developing modeling problems since its interface allows connecting the numerical, algebraic, geometric, and variational fields, providing a better interpretation of the phenomenon of change underlying an optimization problem.