Mathematical Models for Personalized Learning in Virtual Environments

Abstract

The digital transformation of education has promoted the development of mathematical models aimed at personalizing learning within virtual environments. These models make it possible to analyze students’ academic behavior through predictive algorithms, artificial intelligence, machine learning, and educational analytics, fostering more adaptive, flexible, and student-centered learning processes. This article aims to analyze, through a narrative literature review, the main mathematical models used for personalized learning in virtual platforms, considering their pedagogical applications, benefits, limitations, and challenges in the contemporary educational context. The study was conducted under a qualitative-documentary approach through the critical and interpretive review of scientific literature published between 2019 and 2026 in academic databases such as Scopus, Web of Science, ERIC, and Google Scholar. The analyzed literature shows that models based on machine learning, Bayesian networks, fuzzy logic, predictive algorithms, and educational recommendation systems contribute to strengthening academic monitoring, immediate feedback, student motivation, and pedagogical decision-making. Likewise, several challenges are identified, including data quality, technological infrastructure, teacher training, information privacy, and potential algorithmic bias. It is concluded that mathematical models constitute relevant tools for consolidating personalized and intelligent learning systems, provided that their implementation is aligned with pedagogical, ethical, and inclusive criteria.