Online learning has amplified the need to understand how student engagement patterns influence learning outcomes, particularly given the flexibility of technology-mediated environments. To address this, we propose a Bayesian nonparametric dynamic item response theory (IRT) framework that tracks within-individual ability trajectories across instructional units. The proposed model integrates B-spline basis expansions to capture nonlinear effects of engagement behaviors on ability drift, alongside a Mixture-of-Finite-Mixtures (MFM) prior to automatically determine the number of latent learner clusters. This framework overcomes three limitations in the existing literature: (1) rigid linearity assumptions in engagement-ability relationships, (2) dependence on pre-specified cluster counts, and (3) the inability to track longitudinal ability dynamics. We apply the model to longitudinal data from 198 undergraduates completing a 9-chapter introductory statistics course on CourseKata. The model automatically identified four distinct learner profiles: struggling-declining (11\%), low-stable (23\%), mainstream-stable (55\%), and high-improving (12\%). Results indicate that ability trajectories remained remarkably stable across chapters, and engagement quantity metrics did not significantly predict ability drift. These findings suggest that in introductory online statistics education, academic ability primarily reflects a stable pre-existing characteristic rather than a dynamically malleable course outcome. Ultimately, this framework offers a flexible tool for learner profiling to inform adaptive instructional design.

翻译：在线学习强化了理解学生参与模式如何影响学习成果的需求，特别是在技术中介环境的灵活性背景下。为应对这一挑战，我们提出了一种贝叶斯非参数动态项目反应理论（IRT）框架，用于追踪跨教学单元的个体内能力轨迹。该模型整合了B样条基函数展开，以捕捉参与行为对能力漂移的非线性影响，并采用有限混合混合（MFM）先验自动确定潜在学习者聚类数量。本框架克服了现有文献中的三个局限性：（1）参与-能力关系的刚性线性假设，（2）对预设聚类数量的依赖，以及（3）无法追踪纵向能力动态。我们将该模型应用于198名本科生完成CourseKata平台上一门9章节入门统计学课程的纵向数据。模型自动识别出四种独特的学习者轮廓：挣扎下降型（11%）、低稳定型（23%）、主流稳定型（55%）和高进步型（12%）。结果表明，能力轨迹在章节间保持高度稳定，且参与数量指标未能显著预测能力漂移。这些发现表明，在入门级在线统计教育中，学术能力主要反映一种稳定的固有特征，而非动态可变的课程成果。最终，本框架为学习者画像提供了灵活工具，以支持自适应教学设计。