1. Knowledge Tracing
Parameters can be learned with the EM algorithm!
Modeling or measuring learning requires modeling knowledge
Knowledge Tracing used to model learning
Parameters
(probability of learning)
(guess/slip)
(prior)
P(Skill: 0 → 1)
P(Skill: 0 → 1) S S S
Latent
(skill knowledge)
(dichotomous)
P(correct| Skill = 0)
P(incorrect| Skill = 1)
Observables
(question answers)
incorrect
correct
correct

2. 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
Learning rate between opportunities are the same regardless of which problem the student saw
Forgetting is always set at 0
0.12
0.12
Item Effect Model (Pardos, Heffernan 2009)
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.
0.11
0.15

3. Item Order Model (Pardos, Heffernan 2009)
The six sequence permutations are modeled with shared Bayesian parameters
Also 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