Knowledge TracingModeling or measuring learning requires modeling knowledge

• Knowledge Tracing used to model learning

incorrect correct correct

Observables(question answers)

SLatent(skill knowledge)(dichotomous)

S S

P(Skill: 0 → 1) P(Skill: 0 → 1)Parameters(probability of learning)(guess/slip)(prior)

P(correct| Skill = 0)P(incorrect| Skill = 1)

Parameters can be learned with the EM algorithm!

1

Assumption of Knowledge Tracing• Knowledge tracing assumes that learning rate is the same between each opportunity• Our model associates the learning rate with the particular problem that was encountered

Knowledge Tracing

0.12 0.12

• Learning rate between opportunities are the same regardless of which problem the student saw• Forgetting is always set at 0

Item Effect Model (Pardos, Heffernan 2009)

0.11 0.15

• Learning rates are attributes of specific problems• In implementing the model, learning rates must be associated with their respective problem for all sequence orders (permutations)S.

Item Order Model(Pardos, Heffernan 2009)

3

The six sequence permutations are modeled with shared Bayesian parametersAlso known as Equivalence classes of CPTs (conditional probability tables )

- Implementation harnesses the power of randomization to help estimate accurate parameters using all response data- Permutation Analysis of Randomized Dichotomous Sequences