Student mistakes are often not random but, rather, reflect thoughtful yet incorrect strategies. In order for educational technologies to make full use of students' performance data to estimate the knowledge of a student, it is important to model not only the conceptions but also the misconceptions that a student's particular pattern of successes and errors may indicate. The student models that drive the 'outer loop' of Intelligent Tutoring Systems typically only track positive skills and conceptions, not misconceptions. Here, we present a method of representing misconceptions in the kinds of Knowledge Component models, or Q-Matrices, that are used by student models to estimate latent knowledge. We show, in a case study on a fraction arithmetic dataset, that incorporating a misconception into the Knowledge Component model dramatically improves model fit. We also derive qualitative insights from comparing predicted learning curves across models that incorporate varying misconception-related parameters. Finally, we show that the inclusion of a misconception in a Knowledge Component model can yield individual student estimates of misconception strength. These estimates are significantly correlated with out-of-tutor individual measures of student errors indicative of the misconception.
: Ran Liu, Rony Patel and Kenneth R. Koedinger (2016). "Modeling Common Misconceptions in Learning Process Data". In Proceedings of the Sixth International Conference on Learning Analytics & Knowledge (LAK '16). ACM, New York.