Applications of Bayesian Decision Theory to Intelligent Tutoring Systems

The purpose of this paper is to consider some applications of Bayesian decision theory to intelligent tutoring systems. In particular, it will be indicated how the problem of adapting the appropriate amount of instruction to the changing nature of student's capabilities during the learning process can be situated within the general framework of Bayesian decision theory. Two basic elements of this approach will be used to improve instructional decision making in intelligent tutoring systems. First, it is argued that in many decision-making situations the linear loss model is a realistic representation of the losses actually incurred. Second, it is shown that the psychometric model relating observed test scores to the true level of functioning can be represented by Kelley's regression line from classical test theory. Optimal decision rules will be derived using these two features. During the last 2 decades, adaptive instructional systems have been studied by many researchers (e.g., Atkinson, 1976; De Diana & Vos, 1988; Gegg-Harrison, 1992; Hambleton, 1974; Hansen, Ross, & Rakow, 1977; Holland, 1977; Vos, 1990, 1991, 1992, 1993, 1994a; Vos & De Diana, 1987). Although different authors have defined the term "adaptive instruction" in a different way, most agree that it denotes the use of strategies to adapt instructional treatments to the changing nature of student abilities and characteristics during the learning process (see, e.g., Landa, 1976). In the context of computer-based instruction (CBI), adaptive instructional programs are often qualified as intelligent tutoring systems (ITSs). Examples of such Requests for repr ints should be addressed to Hans J. Vos, Univers i ty of Twente, Depa r tmen t of Education, P.O. Box 217, 7500 AE Enschede, The Netherlands. E-mail: VOS @EDTE.UTWENTE.NL