# Calibrated Q-Matrix-Enhanced Deep Knowledge Tracing with Relational Attention Mechanism
###### Abstract  
With the development of online educational platforms, numerous research works have focused on the _knowledge tracing_ task, which relates to the problem of diagnosing the changing knowledge proficiency of learners. Deep-neural-network-based models are used to explore the interaction information between students and their answer logs in the current field of knowledge tracing studies. However, those models ignore the impact of previous interactions, including the exercise relation, forget factor, and student behaviors (the slipping factor and the guessing factor). Those models also do not consider the importance of the Q-matrix, which relates exercises to knowledge points. In this paper, we propose a novel relational attention knowledge tracing (RAKT) to track the students' knowledge proficiency in exercises. Specifically, the RAKT model incorporates the students' performance data with corresponding interaction information, such as the context of exercises and the different time intervals between exercises. The RAKT model also takes into account the students' interaction behaviors, including the slipping factor and the guessing factor. Moreover, consider the relationship between exercise sets and knowledge sets and the relationship between different knowledge points in the same exercise. An extension model of RAKT is called the Calibrated Q-matrix relational attention knowledge tracing model (QRAKT), which was developed using a Q-matrix calibration method based on the hierarchical knowledge levels. Experiments were conducted on two public educational datasets, ASSISTment2012 and Eedi. The results of the experiments indicated that the RAKT model and the QRAKT model outperformed the four baseline models. knowledge tracing; attention mechanism; relation modeling; calibrated Q-matrix  
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Knowledge tracing is the core of personalized exercise and is defined as the task of estimating how students master many knowledge points. Specifically, a student selects some exercises from problem sets (e.g., e\({}_{1}\), e\({}_{2}\), e\({}_{3}\), e\({}_{4}\)) to learn some knowledge concepts (KCs) and leaves his/her response logs (e.g., right or wrong); see Figure 1. Knowledge tracing is then performed using his/her previous practice attempts and exercise-KC interactions to indicate the student's own latent knowledge state on each KC [7]. The interactions from past exercises have a distinctive effect on the target KC and determine the mastery of a certain KC. Additionally, the impact varies depending on the situation. Generally, the effect of past interactions is determined by four factors. The first factor is the exercise relation. The closer the association between past interactions and current practice, the better the performance in the knowledge tracing task will be. The second factor is the time intervals between current practice and past interactions (e.g., e\({}_{1}\), e\({}_{2}\), e\({}_{3}\), e\({}_{4}\)). When considering the forgetting behavior of learners, the degree of mastery of skills for students decays with time. Therefore, the shorter the time interval between the past interaction and the current interaction, the greater the probability that the students will answer the current exercise correctly. The third factor is the students' interaction behaviors, including the guessing factor and the slipping factor. When students choose to guess the answer correctly or answer the question very carelessly, resulting in incorrect answers, the student's mastery of the knowledge point will be worse. The last factor is the learning resource modeling. Cross-mapping between practices and KCs can be characterized as a Q-matrix, whose rows and columns reflect exercises and KCs, respectively. The Q-matrix is considered as the source of information about the exercise knowledge concept [5] with binary elements, in which \"1\" presents this KC, which is covered by an exercise, and \"0\" presents a non-association between the exercise and this KC.