[Submitted on 1 Oct 2026 (v1), last revised 14 Oct 2026 (this version, v2)]
Abstract:Asynchronous online learning offers temporal flexibility at a structural cost: learning communities tend to fragment rather than cohere. $beta_0$, the number of disconnected behavioral clusters from Zigzag Persistent Homology, serves as a cohort-level indicator of this structure. Two questions remained unverified at scale: (1) does apparent $beta_0$ convergence reflect genuine behavioral alignment or learner dropout? and (2) do assessment deadlines produce reproducible fragmentation-convergence cycles? We address both across all 22 OULAD courses (N > 22,000; 857 week-pairs). Changes in $beta_0$ strongly co-vary with active learner changes (pooled r = 0.387; median per-course r_delta = 0.459, 20/22 courses), identifying $beta_0$ as a participation-sensitive indicator: $beta_0$ and active learner counts co-respond to deadline events rather than one causing the other. Deadlines produced fragmentation in 82.6% of assessments and the full Fragment First, Converge Later (FFCL) cycle in 60.2%. 3-phase analysis confirmed structural fragmentation as the dominant long-term trajectory (90.9% of courses), moderated by curriculum structure. These findings establish $beta_0$ as a participation-sensitive structural indicator with direct implications for AI-augmented learning analytics design.
Submission history
From: Hitoshi Inoue [view email]
[v1] Thu, 1 Oct 2026 14:10:36 UTC (340 KB)
[v2] Wed, 14 Oct 2026 11:25:52 UTC (888 KB)
