1. Intelligent Tutoring System based on Belief networks Maomi Ueno Nagaoka University of Technology

2. Advantages of ITS in probabilistic approaches Mathematical analysis of the system behaviors. Mathematical approximation for convenient calculation

3. Decision making approaches to describe a teachers behavior Assumption A Teacher behaves to maximizes the following expected utility. Expected Utility = ΣUtility×Probability

4. Probability model to describe human behaviors Tversky A. and Kahneman,D. 3 Tversky A. and Kahneman,D. 4 Tversky A. and Kahneman,D. 83 Simon H.A. and etc. It is impossible to describe human behaviors by using Probabilistic approaches.

5. Rationality Human is Rational.(probabilistic approaches) vs. Human is not Rational.(has pointed out, and seems right.)

6. Purposes of this study What is the utility of a teachers behavior? This paper tries to describe a teachers behavior as a simple function.

7. Relational works Reye, J. (1986)A belief net backbone for student modeling, Proc of Intelligent Tutoring System, pp.274- 283. R. Charles Murray and Kurt VanLehn (2000) DD Tutor:A decision-Theoretic, Dynamic approach for Optimal Selection of Tutorial Actions, Proc of Intelligent Tutoring System, pp. 153-162.

8. Unique features of this paper A simple utility function: Changes of the predictive student model Teachers Prior knowledge An exact parameterization of Bayesian student modeling : Predictive distribution of Bayesian networks.

9. Student model Bayesian Belief networks

10. Prior distribution as a Prior Knowledge Dirichret distribution,which is a conjecture distribution of the Bayesian networks

11. Predictive distribution as a student model

12. Teachers actions Instruction corresponding to the js node. Ask a question corresponding to the js node.

13. Select the action to maximize utility function Expected Value of Instruction Information (EVII)

14. Stopping rule EVII < 0.0001 Probability propagation Given Instruction frame j P(x j ) p(x j =1 | x 1 =1, x 2 =1, x j-1 =1)=1 Given question frame j P(x j ) x j =1 :right answer 0:wrong answer

15. Examples Data: 248 Junior high school students test data

16. Prior parameter n 1 <n 0 P(root) = 0.0 When a teacher know that the student knowledge is poor

17. Strategy Bottom Up strategy (from the easy material to the difficult material) Instruction frames

18. Prior parameter n 1 >n 0 P(top)=1 When a teacher know that the student knowledge is excellent, Top down strategy The system presents the difficult question. If the student provides wrong answer, then the system presents more easy question and instruction.

19. Prior parameter n 1 =n 0 When a teacher have no knowledge about the student knowledge Flexible strategies

21. Strategy Diagnose the student knowledge states Then, the system instructs knowledge which student can not understand by using the bottom-up strategy.

22. Conclusions The prior knowledge for the student Prediction of students knowledge A simple utility function: How can the teacher change the students predicted knowledge states.

23. Future tasks We are developing large scale ITS based on this study. How can we evaluate the behaviors of the system? Good or bad?