On-Line Student Modeling for Coached Problem Solving Using Bayesian Networks

This paper describes the student modeling component of Andes , an Intelligent Tutoring System for Newtonian physics. Andes ’ student model uses a Bayesian network to do long-term knowledge assessment, plan recognition and prediction of students’ actions d

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1 Intelligent Systems Program, University of Pittsburgh, PA, U.S.A. Leaming Research and Development Center, University of Pittsburgh, PA, U.S.A. 3 Department of Information Science, University of Pittsburgh, PA, U.S.A.

Abstract. This paper describes the student modeling component of ANDES, an Intelligent Tutoring System for Newtonian physics. ANDES' student model uses a Bayesian network to do long-term knowledge assessment, plan recognition and prediction of students' actions during problern solving. The network is updated in real time, using an approximate anytime algorithm based on stochastic sampling, as a student solves problems with ANDES. The information in the student model is used by ANDES' Help system to tailor its support when the student reaches impasses in the problern solving process. In this paper, we describe the knowledge structures represented in the studentmodeland discuss the implementation of the Bayesian network assessor. We also present a preliminary evaluation of the time performance of stochastic sampling algorithms to update the network.

1 Introduction AN DES is an Intelligent Tutoring System that teaches Newtonian physics via coached problern solving (VanLehn, 1996), a method of teaching cognitive skills in which the tutor and the student collaborate to solve problems. In coached problern solving, the initiative in the student-tutor interaction changes according to the progress being made. As long as the student proceeds along a correct solution, the tutor merely indicates agreement with each step. When the student stumbles on a certain part of the problem, the tutor helps the student overcome the impasse by providing tailored hints that Iead the student back to the correct solution path. In this setting, the critical problern for the tutor is to interpret the student's actions and the line of reasoning that the student is following. To perform this task the tutor needs a student model that performs plan recognition (Charniak and Goldman, 1993; Genesereth, 1982; Huber et al., 1994; Pynadath and Wellman, 1995). Inferring an agent's plan from a partial sequence of observable actions is a task that involves inherent uncertainty since often the same observable actions can belong to different plans. In coached problern solving, two additional sources of uncertainty increase the difficulty of the plan recognition task. Firstly, coached problern solving often involves interactions in which most of * This research is supported by AFOSR under grant number F49620-96-1-0180. by ONR's Cognitive Sci-

ence Division under grant N00014-96-1-0260 and by DARPA's Computer Aided Education and Training Initiative under grant N66001-95-C-8367. In addition, Dr. Druzdzel was supported by the National Science Foundation under Faculty Early Career Development (CAREER) Program, grant IRI-9624629. We would like to thank Zhendong Niu and Yan Lin for programming support. A. Jameson et al. (eds.), User Modeling © Springer-Verlag Wien 1997

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the important reasoning is hidden from the coach's vie