Mathematical modeling in calculus: two technological approaches to an optimization problem
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| Autors: | , , , |
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| Format: | artículo original |
| Estat: | Versión publicada |
| Data de publicació: | 2025 |
| Descripció: | [Objective] The study aimed to analyze the modeling process conducted 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 from Blum, Leiß, and Borromeo-Ferri, as well as the extended cycle for the use of digital technologies, to describe the processes students conduct during their resolution. The research design is an instrumental multiple case study. The paper reports 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. Data was collected using worksheets, GeoGebra files, and semi-structured interviews. [Results] Results show that 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 on 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. |
| Pais: | Portal de Revistas UNA |
| Institution: | Universidad Nacional de Costa Rica |
| Repositorio: | Portal de Revistas UNA |
| Idioma: | Español |
| OAI Identifier: | oai:www.revistas.una.ac.cr:article/20473 |
| Accés en línia: | https://www.revistas.una.ac.cr/index.php/uniciencia/article/view/20473 |
| Paraula clau: | mathematical modeling modeling cycles optimization GeoGebra economic functions derivation criteria mathematics education modelización matemática ciclos de modelización optimización funciones económicas criterios de derivación matemática educativa modelagem matemática ciclos de modelagem otimização funções económicas critérios de derivação matemática educacional |