Bayesian knowledge tracing
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Bayesian knowledge tracing is an algorithm used in many intelligent tutoring systems to model each learner's mastery of the knowledge being tutored. It models student knowledge in a hidden Markov model as a latent variable, updated by observing the correctness of each student's interaction in which they apply the skill in question. BKT assumes that student knowledge is represented as a set of binary variables, one per skill, where the skill is either mastered by the student or not. Observations in BKT are also binary: a student gets a problem/step either right or wrong. Intelligent tutoring systems often use BKT for mastery learning and problem sequencing. In its most common implementation, BKT has only skill-specific parameters.
Bayesian knowledge tracing is an algorithm used in many intelligent tutoring systems to model each learner's mastery of the knowledge being tutored. It models student knowledge in a hidden Markov model as a latent variable, updated by observing the correctness of each student's interaction in which they apply the skill in question. BKT assumes that student knowledge is represented as a set of binary variables, one per skill, where the skill is either mastered by the student or not. Observations in BKT are also binary: a student gets a problem/step either right or wrong. Intelligent tutoring systems often use BKT for mastery learning and problem sequencing. In its most common implementation, BKT has only skill-specific parameters. p(L_1)^k_u=p(L_0)^k Equation (b): p(L_t \mid \text{obs}=\text{correct})^k_u=\frac{p(L_t)^k_u\cdot(1-p(S)^k)}{p(L_t)^k_u\cdot(1-p(S)^k)+(1-p(L_t)^k_u)\cdot p(G)^k} Equation (c): p(L_t\mid \text{obs}= \text{wrong})^k_u=\frac{p(L_t)^k_u\cdot p(S)^k}{p(L_t)^k_u\cdot p(S)^k+(1-p(L_t)^k_u) \cdot (1-p(G)^k)} Equation (d): p(L_{t+1})^k_u=p(L_t\mid \text{obs})^k_u+(1-p(L_t\mid \text{obs})^k_u)\cdot p(T)^k Equation (e): p(C_{t+1})^k_u=p(L_{t+1})^k_u\cdot(1-p(S)^k)+(1-p(L_{t+1})^k_u)\cdot p(G)^k
See also
Computerized adaptive testing Item response theory Knowledge space theory Latent growth modeling
References
Further reading
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