Methodological foundations of the teaching and learning process of mathematical concepts and theorems in higher education

Abstract

Learning Differential Calculus theorems in the Computer Science program at Agostinho Neto University shows limitations due to traditional approaches prioritizing rote memorization of formal proofs, disconnected from professional practice. Objective: To propose a didactic alternative to improve the quality of theorem learning within the Mathematical Analysis II course. Metodología y métodos: This research is theoretically grounded in the Onto-Semiotic Approach and contemporary problem-solving frameworks. Using didactic modeling, a proposal structured around three dimensions was designed: configurational, heuristic mediation, and rhetorical institutionalization, operationalizing the subprocesses of derivation, proof, evaluation, and application. Results: A didactic alternative was developed and applied to Fermat’s and Lagrange’s theorems, contextualized to the computer science profile (resource optimization and data transfer rates). Its feasibility and relevance were validated through expert judgment, achieving a high level of consensus.