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Knowledge tracing (KT) has recently been an active research area of computational pedagogy. The task is to model students' mastery level of knowledge based on their responses to the questions in the past, as well as predict the probabilities that they correctly answer subsequent questions in the future. A good KT model can not only make students timely aware of their knowledge states, but also help teachers develop better personalized teaching plans for students. KT tasks were historically solved using statistical modeling methods such as Bayesian inference and factor analysis, but recent advances in deep learning have led to the successive proposals that leverage deep neural networks, including long short-term memory networks, memory-augmented networks and self-attention networks. While those deep models demonstrate superior performance over the traditional approaches, they all neglect more or less the impact on knowledge states of the most recent questions answered by students. The forgetting curve theory states that human memory retention declines over time, therefore knowledge states should be mostly affected by the recent questions. Based on this observation, we propose a Convolutional Knowledge Tracing (CKT) model in this paper. In addition to modeling the long-term effect of the entire question-answer sequence, CKT also strengthens the short-term effect of recent questions using 3D convolutions, thereby effectively modeling the forgetting curve in the learning process. Extensive experiments show that CKT achieves the new state-of-the-art in predicting students' performance compared with existing models. Using CKT, we gain 1.55 and 2.03 improvements in terms of AUC over DKT and DKVMN respectively, on the AS-SISTments2009 dataset. And on the ASSISTments2015 dataset, the corresponding improvements are 1.01 and 1.96 respectively.

Knowledge tracing (KT) models students' mastery level of knowledge concepts based on their responses to the questions in the past and predicts the probability that they correctly answer subsequent questions in the future. Recent KT models are mostly developed with deep neural networks and have demonstrated superior performance over traditional approaches. However, they ignore the explicit modeling of the learning curve theory, which generally says that more practices on the same knowledge concept enhance one's mastery level of the concept. Based on this theory, we propose a Convolution-Augmented Knowledge Tracing (CAKT) model and a Capsule-Enhanced CAKT (CECAKT) model to enable learning curve modeling. In particular, when predicting a student's response to the next question associated with a specific knowledge concept, CAKT uses a module built with three-dimensional convolutional neural networks to learn the student's recent experience on that concept, and CECAKT improves CAKT by replacing the global average pooling layer with capsule networks to prevent information loss. Moreover, the two models employ LSTM networks to learn the overall knowledge state, which is fused with the feature learned by the convolutional/capsule module. As such, the two models can learn the student's overall knowledge state as well as the knowledge state of the concept in the next question. Experimental results on four real-life datasets show that CAKT and CECAKT both achieve better performance compared to existing deep KT models.

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