Using Item Response Theory to Refine Knowledge Tracing.
Yanbo Xu, Jack Mostow · 2013
Previous work on knowledge tracing has fit parameters per skill (ignoring differences between students), per student (ignoring differences between skills), or independently for each pair (risking sparse training data and overfitting, and undergeneralizing by ignoring overlap of students or skills across pairs). To address these limitations, we first use a higher order Item Response Theory (IRT) model that approximates students ’ initial knowledge as their one-dimensional (or low-dimensional) overall proficiency, and combines it with the estimated difficulty and discrimination of each skill to estimate the probability knew of knowing a skill before practicing it. We then fit skill-specific knowledge tracing probabilities for learn, guess, and slip. Using synthetic data, we show that Markov Chain Monte Carlo (MCMC) can recover the parameters of this Higher-Order Knowledge Tracing (HO-KT) model. Using real data, we show that HO-KT predicts performance in an algebra tutors significantly better than fitting knowledge tracing parameters per student or per skill.