1. Does Conjunctive Knowledge Tracing Provide Leverage to the Temporal and Location Heuristics in Error Attribution? Adaeze Nwaigwe University of Maryland University College August 4, 2012

2. Introduction Previously, we proposed, implemented and evaluated four computational models for making error attributions in Intelligent Tutoring Systems (Nwaigwe et al., 2007).  two location-based models and  two temporal-based models Basis for the models  whether the attribution was driven by interface location and whether or not the student model in the Intelligent Tutor was used.  whether the attribution was driven by the temporal ordering of events and again, and whether or not the student model in the Intelligent Tutor was used.

3. Error Attribution Heuristics EA Heuristics Location-basedTemporal-based SM used SM not usedSM used SM not used

4. Doing Error Attribution.. In applying each heuristic on an error transaction our simplified approach was to uniformly apportion blame to all knowledge components (KCs) needed to generate a successful outcome. However, not all KCs may have been to blame. In the Andes log, for a significant proportion of time, multiple KCs are needed to generate a single correct step

5. Current Research Simplified approach (Standard Knowledge Tracing) may cause problem selection thrashing in an Intelligent Tutor where multiple KCs are required to produce a single response for difficult problems (Koedinger et al., 2011). Conjunctive Knowledge Tracing (CKT) in blame assignment has shown promise (Koedinger et al., 2011) in  reducing problem selection thrashing in a Geometry Cognitive Tutor and  in improving future task selection, therefore saving students' time

6. Our Goals…1 To investigate whether the four heuristics initially proposed will gain leverage when combined with CKT in terms of the quality of their cognitive models.

7. Our Goals….2 Since our previous study showed the simple location heuristic to be superior, we wish to see if use of CKT + the simple location heuristic will make better use of the student’s time and  will result in an improved inference procedure update of the student model,  Better future task selection and  enhanced student learning,  Versus using the simple location heuristic solely. We intend to conduct our study in a Physics Intelligent Tutor.

8. Standard Knowledge Tracing P(Know-KC 1 |Error) = P(Error|Know-KC 1 * P(Know-KC 1 ) = S * K 1 /[K 1 * S + (1-k 1 ) * (1-G )] ……. (1) K 1 (Know-KC 1 ) = prob of knowing KC 1 G = prob that student is correct when they do not know the KC S = prob that a student will be incorrect even though they know the KC Eq (1) derives from conditional probability: P(A|B) = P(B|A)* P(A) / P(B) SKT blames all KCs equally as seen from eq. (1). Approach too simplistic (Koedinger et al., 2011) P(Error)

9. Conjunctive Knowledge Tracing P(Error|Know-KC 1 ) = S 1 + K 2 S 2 +(1 – K 2 )(1 – G 2 ) – [S 1 ][K 2 S 2 + (1 – K 2 )(1 – G 2 )… (2) P(Error ) = 1-P(Correct) = 1 – [K 1 (1-S 1 ) + (1-K 1 )G 1 ][K 2 (1- S 2 ) + (1 – K 2 )G 2 ]…. (3) Thus, P(Know-KC 1 | Error ) = S 1 + K 2 S 2 +(1 – K 2 )(1 – G 2 ) – [S 1 ][K 2 S 2 + (1 – K 2 )(1 – G 2 ) * P(Know-KC1)] / 1 – [K 1 (1-S 1 ) + (1-K 1 )G 1 ][K 2 (1- S 2 ) + (1 – K 2 )G 2 ]…….. (4) CKT uses eq (4) and considers the fact that the student may have made an error in executing “both” KC 1 and KC 2. Eq (4) can be generalized to more than 2 KCs

10. What we intend to do…. We will use CKT to compute KC probabilities Use probabilities to assign blame Measure quality of  resulting cognitive model  inference procedure update of the student model,  future task selection and  student learning.

11. Thank you!! Questions???