Faculty Advisor

Ryan S.J.d Baker

Faculty Advisor

Neil T. Heffernan

Faculty Advisor

Sonia Chernova


In the field of Artificial Intelligence in Education, many contributions have been made toward estimating student proficiency in Intelligent Tutoring Systems (cf. Corbett & Anderson, 1995). Although the community is increasingly capable of estimating how much a student knows, this does not shed much light on when the knowledge was acquired. In recent research (Baker, Goldstein, & Heffernan, 2010), we created a model that attempts to answer that exact question. We call the model P(J), for the probability that a student just learned from the last problem they answered. We demonstrated an analysis of changes in P(J) that we call “spikiness", defined as the maximum value of P(J) for a student/knowledge component (KC) pair, divided by the average value of P(J) for that same student/KC pair. Spikiness is directly correlated with final student knowledge, meaning that spikes can be an early predictor of success. It has been shown that both over-practice and under-practice can be detrimental to student learning, so using this model can potentially help bias tutors toward ideal practice schedules. After demonstrating the validity of the P(J) model in both CMU's Cognitive Tutor and WPI's ASSISTments Tutoring System, we conducted a pilot study to test the utility of our model. The experiment included a balanced pre/post-test and three conditions for proficiency assessment tested across 6 knowledge components. In the first condition, students are considered to have mastered a KC after correctly answering 3 questions in a row. The second condition uses Bayesian Knowledge Tracing and accepts a student as proficient once they earn a current knowledge probability (Ln) of 0.95 or higher. Finally, we test P(J), which accepts mastery if a student's P(J) value spikes from one problem and the next first response is correct. In this work, we will discuss the details of deriving P(J), our experiment and its results, as well as potential ways this model could be utilized to improve the effectiveness of cognitive mastery learning.


Worcester Polytechnic Institute

Degree Name



Computer Science

Project Type


Date Accepted





machine learning, knowledge tracing, intelligent tutoring systems, educational data mining