Videoanálise e programação no ensino de equações diferenciais na formação de professores: uma experiência didática à luz da aprendizagem significativa

Abstract

This article presents an instructional experience carried out with undergraduate Mathematics students in a Calculus III course, with the aim of analyzing the contributions of integrating experimentation, video analysis, and programming to the learning of Ordinary Differential Equations (ODEs), from the perspective of Meaningful Learning Theory. The activity involved a physical experiment on water outflow from a perforated cylindrical container. The variation in water column height was analyzed through video analysis using Frameskip software and through computational modeling in Python. Based on the experimental data, the least squares method was applied to fit a function to the observed data, which was compared with the theoretical solution of the differential equation modeling the phenomenon. The results indicated strong agreement between the experimental data and the mathematical model. From a didactic-pedagogical perspective, the analysis of students' interactions revealed the anchoring of new concepts in prior knowledge, the overcoming of mechanical learning practices, and the integration of different domains of knowledge, characterizing a meaningful learning process. The findings suggest that the proposed approach enhances conceptual understanding of ODEs and contributes to teacher education guided by an investigative, critical, and reflective perspective.