  Recently, we have seen a rapid rise in usage of online educational platforms.
The personalized education became crucially important in future learning
environments. Knowledge tracing (KT) refers to the detection of students'
knowledge states and predict future performance given their past outcomes for
providing adaptive solution to Intelligent Tutoring Systems (ITS). Bayesian
Knowledge Tracing (BKT) is a model to capture mastery level of each skill with
psychologically meaningful parameters and widely used in successful tutoring
systems. However, it is unable to detect learning transfer across skills
because each skill model is learned independently and shows lower efficiency in
student performance prediction. While recent KT models based on deep neural
networks shows impressive predictive power but it came with a price. Ten of
thousands of parameters in neural networks are unable to provide
psychologically meaningful interpretation that reflect to cognitive theory. In
this paper, we proposed an efficient student model called BKT-LSTM. It contains
three meaningful components: individual \textit{skill mastery} assessed by BKT,
\textit{ability profile} (learning transfer across skills) detected by k-means
clustering and \textit{problem difficulty}. All these components are taken into
account in student's future performance prediction by leveraging predictive
power of LSTM. BKT-LSTM outperforms state-of-the-art student models in
student's performance prediction by considering these meaningful features
instead of using binary values of student's past interaction in DKT. We also
conduct ablation studies on each of BKT-LSTM model components to examine their
value and each component shows significant contribution in student's
performance prediction. Thus, it has potential for providing adaptive and
personalized instruction in real-world educational systems.
