The rapid development of the technologies for online learning provides students with extensive resources for self-learning and brings new opportunities for data-driven research on educational management. An important issue of online learning is to diagnose the knowledge proficiency (i.e., the mastery level of a certain knowledge concept) of each student. Considering that it is a common case that students inevitably learn and forget knowledge from time to time, it is necessary to track the change of their knowledge proficiency during the learning process. Existing approaches either relied on static scenarios or ignored the interpretability of diagnosis results. To address these problems, in this article, we present a focused study on diagnosing the knowledge proficiency of students, where the goal is to track and explain their evolutions simultaneously. Specifically, we first devise an explanatory probabilistic matrix factorization model, Knowledge Proficiency Tracing (KPT), by leveraging educational priors. KPT model first associates each exercise with a knowledge vector in which each element represents a specific knowledge concept with the help of Q -matrix. Correspondingly, at each time, each student can be represented as a proficiency vector in the same knowledge space. Then, our KPT model jointly applies two classical educational theories (i.e., learning curve and forgetting curve ) to capture the change of students’ proficiency level on concepts over time. Furthermore, for improving the predictive performance, we develop an improved version of KPT, named Exercise-correlated Knowledge Proficiency Tracing (EKPT), by considering the connectivity among exercises with the same knowledge concepts. Finally, we apply our KPT and EKPT models to three important diagnostic tasks, including knowledge estimation, score prediction, and diagnosis result visualization. Extensive experiments on four real-world datasets demonstrate that both of our models could track the knowledge proficiency of students effectively and interpretatively.

中文翻译：

---

学习还是遗忘？一种跟踪学生知识熟练度的动态方法

在线学习技术的快速发展为学生提供了广泛的自主学习资源，也为数据驱动的教育管理研究带来了新的机遇。在线学习的一个重要问题是诊断每个学生的知识熟练程度（即对某个知识概念的掌握程度）。考虑到学生难免不时学习和忘记知识是一种常见的情况，因此有必要在学习过程中跟踪他们的知识熟练程度的变化。现有方法要么依赖于静态场景，要么忽略了诊断结果的可解释性。为了解决这些问题，在本文中，我们提出了一项关于诊断学生知识能力的重点研究，其目标是追踪和解释他们的进化同时进行。具体来说，我们首先设计了一个解释性概率矩阵分解模型，知识能力追踪(KPT)，通过利用教育先验。KPT 模型首先将每个练习与一个知识向量相关联，其中每个元素在问-矩阵。相应地，在每个时间，每个学生都可以表示为同一知识空间中的一个熟练度向量。然后，我们的 KPT 模型联合应用了两种经典的教育理论（即，学习曲线和遗忘曲线) 以捕捉学生对概念的熟练程度随时间的变化。此外，为了提高预测性能，我们开发了 KPT 的改进版本，命名为运动相关知识能力追踪（EKPT），通过考虑具有相同知识概念的练习之间的连接性。最后，我们将我们的 KPT 和 EKPT 模型应用于三个重要的诊断任务，包括知识估计、分数预测和诊断结果可视化。对四个真实世界数据集的广泛实验表明，我们的两个模型都可以有效地和解释性地跟踪学生的知识熟练程度。