The HMM form of BKT, solved analytically, is a three-parameter exponential in opportunity number¶

Claim · All claims
Evidence · 1 study · theoretical r3 · q2
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¶

q2 i? The probability of a correct response P(Cj) under the HMM form of BKT has the functional form of an exponential and depends on only three parameters: P(S), P(T), and the combined constant A. → 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

q2 · i? · theoretical · r3

Analytical derivation (Section 2): the recursion for P(Lj) is solved exactly, giving P(Cj) = 1 − P(S) − A·e^(−βj), so 'P (Cj) is an exponential' as shown in Fig. 1. No data are fit; this is a closed-form result under the model.

"Note that the form of P (Cj), as a function of j, depends on only three parameters: P (S), P (T ), and (1−P (S)−P (G)) (1−P (L0))."

Discussion¶

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