The exponential functional form of the BKT Markov chain calls into question the popular practice of fitting that model form to student data¶

Claim · All claims
Evidence · 1 study · theoretical r3 · q1
Currency · newest study 2013 · not yet checked against its sources · not reviewed by a person · overdue for a recheck since 2016: tool and model accuracy changes quickly

Subclaims¶

q1 i? Because the Markov-chain form of BKT (which predicts the student-averaged probability of a correct application) has the functional form of an exponential, while some studies report individual learning better described by a power law, the article argues these results call into question fitting the Markov model form of BKT to student data. → Brett Van de Sande 2013

Evidence¶

Brett Van de Sande 2013¶

Van de Sande, B. (2013). Properties of the Bayesian Knowledge Tracing Model. Journal of Educational Data Mining, 5(2). doi:10.5281/zenodo.3554629

q1 · i? · theoretical · r3

Authors' interpretation in the conclusion (type e), weighing the analytical exponential solution for the BKT Markov chain (the hidden Markov model form is analysed separately, by fixed-point analysis) against Heathcote et al.'s exponential account and Chi et al.'s finding that student learning of physics skills was better explained by a power law even for individual students. No new data are analyzed here.

"Together, these results call into question the popular practice of fitting the Markov model form of BKT to student data. Perhaps a model that has power law behavior would work better?"

Discussion¶

Related Claims¶

• The survey states that deep learning knowledge tracing models exhibit superior performance to Bayesian and logistic models but have significant room for improvement in interpretability. — the general claim this finding bears on, with the studies behind it
• The HMM form of BKT, solved analytically, is a three-parameter exponential in opportunity number — related
• The identifiability problem of the BKT HMM arises because combinations of P(G) and P(L0) with the same product A give identical functional forms — related
• Semi-Markov models fit the writing-process data better than continuous-time Markov chain models — related
• A Hidden Markov Model over knowledge states identifies Analytical Thinking (A5) as the learning bottleneck with the lowest forward transition probability — related
• Individualized Knowledge Tracing parameters fit student data significantly better and change mastery-learning practice decisions for many students — related
• The Knowledge Tracing Algorithm does not suffer the identifiability problem: all four parameters affect its behavior separately — related