El estudio de las integrales triples y de línea mediante aplicaciones físicas experimentales como un recurso didáctico

Abstract

For this research, there were two workshops with experimental activities carried out with an approach from physical applications to cover the study of triple integrals and line integrals in an educational context. These workshops were designed to explore how the application of physical concepts can enrich and facilitate the understanding of advanced mathematical topics. The proposed research is framed as a quantitative laboratory study measured by pre- and post-tests to assess conceptual gain using Hake's method, hypothesis testing, and statistical parameter analysis. In addition to the quantitative assessments, a semantic differential was used to measure aspects related to participants' attitudes toward triple and line integral learning. These measurement tools provided a comprehensive view of the impact of the experimental activities on the students' learning process. The results showed that experimental physics applications can be an effective pedagogical strategy for teaching and learning advanced calculus concepts such as triple and line integrals. In addition, their potential to promote more meaningful and lasting student learning by providing a deeper understanding and greater connection to the real world of physical phenomena was demonstrated. These findings suggest the importance of integrating experimental activities into the mathematics classroom, especially in areas that require a more abstract and theoretical approach.