A Journey into the van der Pol Equation and Haar Wavelet through Engaging Didactic Situations

Abstract

This qualitative study explores the impact of a didactic sequence based on the theory of didactic situations on the learning of the van der Pol equation and its solution using the Haar wavelet method among undergraduate students in Mathematics and Physics at the Technological University of Pereira. The study objectives focus on identifying students’ strengths and challenges, assessing collaborative and individual competencies, and evaluating proficiency in applying the Haar wavelet method to solve the equation. A sample of five students actively participated in all phases of the Didactic Situation, which included action, formulation, validation, and institutionalization. The results indicate that the carefully structured didactic sequence significantly improved students’ understanding and engagement with the van der Pol equation and Haar wavelet method. The inclusion of real-world applications and interactive approaches facilitated effective learning strategies. Overall, this study highlights the effectiveness of the theory of didactic situations-based didactic sequence in fostering a deeper appreciation and comprehension of complex mathematical concepts among Mathematics and Physics undergraduates. This research contributes to the enrichment of the academic journey, creating a captivating realm of mathematical beauty and scientific wonder for both students and educators. Keywords: didactic sequence, the van der Pol equation, the Haar wavelet method, problem-solving. https://doi.org/10.55463/issn.1674-2974.50.7.19