Using Bayesian networks to manage uncertainty in student modeling

When a tutoring system aims to provide students with interactive help, it needs to know what knowledge the student has and what goals the student is currently trying to achieve. That is, it must do both assessment and plan recognition. These modeling tasks involve a high level of uncertainty when students are allowed to follow various lines of reasoning and are not required to show all their reasoning explicitly. We use Bayesian networks as a comprehensive, sound formalism to handle this uncertainty. Using Bayesian networks, we have devised the probabilistic student models for Andes, a tutoring system for Newtonian physics whose philosophy is to maximize student initiative and freedom during the pedagogical interaction. Andes' models provide long-term knowledge assessment, plan recognition, and prediction of students' actions during problem solving, as well as assessment of students' knowledge and understanding as students read and explain worked out examples. In this paper, we describe the basic mechanisms that allow Andes' student models to soundly perform assessment and plan recognition, as well as the Bayesian network solutions to issues that arose in scaling up the model to a full-scale, field evaluated application. We also summarize the results of several evaluations of Andes which provide evidence on the accuracy of its student models.