发表机构
Nakamura Gakuen University; Hiroshima University（中村学园大学; 广岛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用拓扑数据分析中的连通分量变化点对转换网络分析进行周期分割，在开放大学22门课程中验证了其优于时间分割的变异捕获能力，并揭示最后阶段行为反映而非导致学业结果，从而将变化点定位为干预窗口而非预测工具。
AI 中文摘要
学习行为中的时间动态可以通过转换网络分析（TNA）中的周期分割来揭示。Cristea等人证明了将课程分割为半段和四分之一段可以揭示学习策略如何演变及其与学业表现的关系。基于这种方法，我们研究拓扑数据分析（TDA），特别是从之字形持续同调中得到的连通分量（$\eta_0$）变化点，是否能够提供数据驱动的周期边界，以识别干预窗口。通过分析开放大学学习分析数据集中的22门课程，我们发现基于$\eta_0$的分割比基于时间的分割捕获了更大的周期间变异（中位方差比（VR）= 4.10倍；22门课程中有21门课程的VR > 1.1）。置换检验确认了显著性（$p < 0.05$）在18%的个别课程中，73%的课程显示出相对于随机断点的正向改进。只有一门课程在基于时间的分割中表现更好。然而，对学业结果的分析揭示了一个关键见解：在基于$\eta_0$的分割中，最后阶段的行为与结果的相关性低于基于时间的分割，这反映了一种显著的行为崩溃，即参与的学习者迅速脱离。我们将此解释为最后阶段行为反映而非导致结果的证据：将通过的学生保持参与，而将失败的学生则脱离。这重新定义了$\eta_0$的价值：变化点并非用于改进预测，而是识别干预窗口。这些是行为结构转变的时期，针对性的支持可能最为有效。
英文摘要
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 ($β_0$) 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 $β_0$-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 $β_0$-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 $β_0$: rather than improving prediction, change points identify intervention windows. These are periods where behavioral structure shifts and targeted support may be most effective.
Journal refInnovations in Analytics of Learning Dynamics (TNA 2026), CCIS vol. 3079, pp. 62-74, Springer, 2026
DOI：10.1007/978-3-032-34157-0_5
