Beyond Descriptive Statistics: Analysis of Time Series of Student Interactions in Engineering Courses Through the Lens of Modern Mathematical Methods

This study examines the effectiveness of Universal Design for Learning (UDL) tools in engineering courses by analyzing student interaction time series data through statistical and machine learning methods. The primary objectives are to determine (1) whether student engagement with UDL tools is self-informative and (2) to assess whether these interactions can be used to detect engagement changes. Two key UDL components are studied: (a) digital forms, which facilitate non-graded participation and formative feedback, and (b) multimedia tools that provide accessible, self-paced learning opportunities. Student interactions are analyzed using auto-regressive models, including ARIMA, SARIMA, and advanced machine learning methods like GRU and CatBoost. The study also employs Pruned Exact Linear Time (PELT) to detect significant engagement shifts. Findings suggest that student interaction data predicts future engagement, with GRU performing best in minimizing absolute errors and ARIMA excelling in proportional error estimation. Segmentation using PELT enhances predictive accuracy by identifying behavioral shifts. This study shows that classroom-based interactions provide more stable metrics than outside-classroom activities. Ultimately, these methods can help educators improve course accessibility, personalize interventions, and optimize UDL strategies at scale.