In online intelligent education systems, to offer proactive studying services to students (e.g., learning path recommendation), a crucial demand is to track students’ knowledge mastery levels over time. However, existing works ignore the impact of learning transfer on knowledge tracing and only track knowledge proficiency. Knowledge proficiency alone cannot fully reflect students’ knowledge mastery levels. A student’s knowledge structure (the similarities and differences within knowledge concepts) and abstract principle mastery level (common attributes among knowledge concepts, such as learning methods) also need to be tracked. To this end, we propose a novel multilevel Knowledge Tracing model with Learning Transfer (KTLT) to track students’ knowledge mastery levels. First, we clarify the relationships among abstract principles, knowledge structure, and knowledge proficiency by utilizing the learning transfer theory in educational psychology. Then, we associate each problem with a knowledge vector in which each element represents an explicit knowledge concept by leveraging educational priors (i.e., a Qmatrix). Correspondingly, each student is represented as a knowledge vector (knowledge proficiency) and an abstract principle vector (abstract principle mastery). Given a student’s knowledge and abstract principle vector over time, we use the learning and forgetting curve as priors to capture the student’s knowledge proficiency and abstract principle mastery level over time. Furthermore, we embed the knowledge concept by using a student’s abstract principle mastery level and obtain a personalized knowledge relevance matrix (a student’s knowledge structure) by calculating the cosine similarity among the knowledge embedding results. Finally, we design a probabilistic matrix factorization framework by combining student and problem priors for tracking a student’s knowledge mastery. Extensive experiments on two real-world datasets demonstrate both the effectiveness and explanatory ability of the KTLT.

Knowledge tracing, which is used to predict students’ performance based on their previous practices, has attracted many researchers’ attention. Especially in this rising period of intelligent education, many knowledge tracing methods have been developed. However, most of the existing knowledge tracing methods focus on the personality of practices and knowledge concepts but ignore the contexts related to the studying process. In this paper, we propose a context-based knowledge tracing model, which combines students’ historical performance and their studying contexts during knowledge mastery. To be specific, we first define five studying contexts for performance prediction. The basic context is the current knowledge state of a student, which is described by their practice sequences. Then, a QR-matrix is defined to represent the relationship among questions, knowledge concepts, and responses, which describes the contexts of questions and knowledge. Furthermore, an improved LSTM model is proposed to capture the context of students’ memory and forgetness, and a multi-head attention mechanism is designed to capture the context of students’ behaviors. Finally, based on the captured contexts, the prediction model ContextKT is established. Our prediction model is evaluated on two real educational datasets. The experimental results show our model is effective and efficient in student performance prediction, and it outperforms the other existing methods.

Graph convolutional network (GCN) architecture is the basis of many neural networks and has been widely used in processing graph-structured data. When dealing with large and sparse data, deeper GCN models are often required. However, the models suffer from performance degradation as the number of layers increases. The mainstream attribution of the current research is over-smoothing, and there are also gradient vanishing, training difficulties, etc., so a consensus cannot be reached. In this paper, we theoretically analyze the degradation problem by adopting spectral graph theory to globally consider the propagation and transformation components of the GCN architecture, and conclude that the over-smoothing problem caused by the propagation matrices is not the key factor for performance degradation. Afterwards, in addition to using conventional experimental methods, we proposed an experimental analysis strategy under the guidance of random matrix theory to analyze the singular value distribution of the model weight matrix. We concluded that the key factor leading to the degradation of model performance is the transformation component. In the context of a lack of consensus on the problem of model performance degradation, the paper proposes a systematic analysis strategy, as well as theoretical and empirical evidence.