Advanced mathematical cognition and the development of abstract thinking in higher education: A didactic and epistemological analysis

Abstract

In current higher education, advanced mathematical cognition is positioned as a key component for the development of abstract thinking, integrating complex cognitive processes such as generalization, formalization, modeling, and deductive reasoning. From a didactic perspective, it is necessary to move beyond traditional, procedure-centered models, promoting strategies that foster the meaningful construction of knowledge through problem-solving, the use of multiple representations, and mathematical argumentation. Within this framework, the study aimed to analyze, from didactic and epistemological perspectives, the influence of advanced mathematical cognition on university students, identifying both the cognitive processes involved and the existing learning difficulties and pedagogical limitations. To this end, a systematic review based on the PRISMA method was employed, allowing for the collection and analysis of relevant scientific evidence on the topic. The results indicated that the development of skills such as abstraction, generalization, and logical reasoning promotes a deep understanding of complex mathematical content, positively impacting academic performance, problem-solving, and the ability to transfer knowledge to diverse contexts.