Tracking knowledge proficiency of students with calibrated Q-matrix

With the emergence of intelligent educational systems, numerous research works are dedicated to Knowledge Tracing (KT), which refers to the issue of diagnosing students' changing knowledge proficiency in exercises. Recent developments in KT have yielded immense success on this task and they mainly use sophisticated and flexible deep neural network-based models to fully exploit the interaction information between students and response logs. However, these models either ignore the significance of Q-matrix associated exercises with knowledge concepts (KCs) or fail to avoid the subjective tendency of experts within the Q-matrix. To tackle these problems, in this paper, we devise a novel Calibrated Q-matrix-based Knowledge Tracing (CQKT) framework to track knowledge proficiency of students dynamically in KT. To be specific, for the original Q-matrix, we primarily strive to capture the high-order connectivity between exercises and KCs to obtain potential KCs of each exercise by utilizing graph convolution network. Then, three Q-matrix calibration methods based on a pairwise Bayesian treatment equipped with potential KCs are adopted to refine and calibrate the raw Q-matrix so that the subjective tendency of the Q-matrix defined by domain experts can be weakened. After that, the embedding of each exercise aggregated the calibrated Q-matrix with historical student interactions is injected into the Long Short-Term Memory (LSTM) network to trace students' knowledge states. Extensive experiments are conducted on three real-world benchmark datasets and the results show the superiority of CQKT. In particular, we demonstrate its practicability via applying it to three fundamental educational tasks, including score prediction, knowledge state estimation, and diagnosis result visualization.