🤖 AI Summary
This study addresses the limitations of conventional temporal segmentation in capturing the dynamic evolution of learning behaviors and identifying intervention windows by proposing a Topological Data Analysis (TDA)-based approach to learning cycle segmentation. Specifically, the method leverages zigzag persistent homology to extract change points in connected components (β0) from transition networks, enabling data-driven segmentation. Its core contribution is reconceptualized as detecting structural behavioral shifts to pinpoint timely interventions, rather than merely enhancing predictive accuracy. Experiments conducted across 22 courses at an open university demonstrate that the proposed approach significantly outperforms traditional time-based baselines. It captures more pronounced inter-period variations and effectively reveals the association between learner behavioral collapse and academic outcomes.
📝 Abstract
Temporal dynamics in learning behavior can be revealed through period segmentation in Transition Network Analysis (TNA). Cristea et al. demonstrated that segmenting courses into halves and quarters reveals how learning strategies evolve and relate to academic performance. Building on this approach, we investigate whether Topological Data Analysis (TDA), specifically connected components ($\beta_0$) change points from Zigzag Persistent Homology, can provide data-driven period boundaries that identify intervention windows. Analyzing 22 courses from the Open University Learning Analytics Dataset, we find that $\beta_0$-based segmentation captures greater between-period variation than time-based segmentation (median variance ratio (VR) = 4.10$\times$; 21/22 courses show VR $>$ 1.1). Permutation tests confirmed significance ($p<0.05$) in 18% of individual courses, with 73% showing positive improvement over random breakpoints. Only one course showed better performance with time-based segmentation. However, analysis of academic outcomes reveals a key insight: final-period behavior shows lower correlation with outcomes in $\beta_0$-based segmentation than in time-based segmentation, reflecting a marked behavioral collapse where engaged learners rapidly disengage. We interpret this as evidence that final-period behavior reflects rather than causes outcomes: students who will pass maintain engagement, while those who will fail disengage. This reframes the value of $\beta_0$: rather than improving prediction, change points identify intervention windows. These are periods where behavioral structure shifts and targeted support may be most effective.