Active Methodologies and Educational Technology for the Development of Mathematical Competencies in Higher Education: A Systematic Review

This article presents a qualitative, integrative systematic review of the communication between active methodologies and educational technology in the development of mathematical competencies in higher education. The study draws on 20 specific documentary sources, including articles from journals cited in Scopus and Web of Science, international conference proceedings, and Ibero-American journals, and constructs a critical discussion of the following conceptual categories: conceptual understanding mediated by digital tools; the presence of meta-analytic evidence on the flipped classroom and gamification; the reconfiguration of student-centered active methodologies; teachers' technological-pedagogical-content knowledge (TPACK); and, finally, mathematical modeling as a new conceptual category. The results suggest that the literature shows some convergence on the pedagogical value of dynamic visualization tools and active learning as a method coupled with appropriate teacher training, while remaining divided between meta-analyses reporting more mixed and sometimes undermined effects of the flipped classroom in higher education and more positive documentation in case studies using active learning methods and technology. A gap is noted in long-term learning retention between Anglophone and Latin American literature, and a lack of reflection on the redesign of assessment. The research introduced a three-layer conception of the realms of infrastructure, teacher knowledge, and situated methodological design, and highlights future possibilities for empirical research.