Differential modeling of learning-forgetting dynamics in learning analytics with a predictive approach

Resumen

The present study is guided by the following scientific question: How can the evolution of knowledge over time be modeled through differential equations by deriving predictive metrics within learning analytics? Based on this inquiry, the general objective is to model the evolution of knowledge over time using differential equations in order to derive predictive metrics in learning analytics. The study follows a quantitative approach with a non-experimental, longitudinal design. The sample consisted of a cohort of 59 students enrolled in the course Linear Algebra and Analytic Geometry. A total of 22 assessment activities recorded in Moodle were normalized to the [0,1] scale and organized into six weekly blocks to construct a temporal series of academic performance. Using these data, a differential learning–forgetting model was fitted, integrating a learning rate and a forgetting rate. The estimated parameters (a = 0.42; b = 0.15) allowed the projection of an equilibrium level consistent with the final observed performance (0.73) and the derivation of predictive metrics, such as convergence half-life and the projected time horizon for crossing academic proficiency thresholds. The findings confirm the dynamic nature of learning and demonstrate the relevance of the model as a tool to support data-informed pedagogical decision-making.