In the context of learning analytics, predicting and enhancing student engagement is critical, particularly within mathematics programmes where structured learning activities and rigorous assessment schedules prevail. While advanced machine learning models have been widely applied to forecast student behaviours, a notable gap exists in leveraging parsimonious and interpretable methods for initial predictive benchmarks. This study addresses the research challenge by investigating the applicability of the homogeneous Poisson process (HPP) to model time-stamped student engagement events, such as assignment submissions, problem-solving sessions, and interactive forum posts, in mathematics courses. Adopting a robust quantitative methodology, we analysed extensive engagement data from mathematics programmes using the HPP framework, which posits that events occur independently at a constant average rate. Our simulation studies and empirical evaluations reveal that the constant event rate estimated by the HPP serves as a reliable predictor of overall student activity and engagement trends. While machine learning techniques often deliver high predictive accuracy, the HPP offers the advantage of interpretability, providing clear and actionable insights that are easily communicated to educational practitioners. Key results indicate that the HPP effectively identifies periods of heightened engagement that align with critical academic milestones in mathematics curricula, such as examination preparation and project deadlines. Based on these findings, we recommend that educational researchers and practitioners incorporate the homogeneous Poisson process as a foundational predictive tool within their learning analytics toolkit. Its simplicity and clarity not only enable the establishment of baseline benchmarks for student engagement but also facilitate the development of data-driven interventions tailored to the unique dynamics of mathematics education.

Keywords: Homogeneous Poisson Process, Predictive Learning Analytics, University Mathematics, Teaching Programme, Time-stamped Student Engagement Events.