Use of mathematical modeling as a methodological proposal for the development of cognitive competences in the subject of differential equations

This study proposes to integrate mathematical modeling as an active methodology with a pedagogical approach oriented toward competency development. The objective is to use modeling activities as a bridge that connects problem-solving with the strengthening of cognitive competencies. The model contrasts with traditional methods, which typically focus on the execution of algorithms and the memorization of theorems and formulas, limiting mathematical learning to obtaining results without exploring their application to engineering problems or practical contexts. The research is conducted in an educational environment, where students could analyze, describe, formulate hypotheses, contrast them, reflect, argue, and communicate their ideas. The research design is quasi-experimental, descriptive-correlational, and the research employs scientific, inductive-deductive, and analytical-synthetic methods, basing the methodology on problem-solving in accordance with the progress of the Differential Equations course syllabus. To evaluate the proposal, techniques such as direct observation, teamwork, multiple-choice tests, and feedback were used with second-semester students. The results show that methodology promotes greater development of cognitive skills compared to the traditional approach based on mechanical problem-solving. It can be concluded that mathematical modeling allows students to develop cognitive skills such as critical thinking, creativity, and problem-solving through the analysis, synthesis, and evaluation of information.