Intelligent Tutoring Intelligent Tutoring System based on Belief System based on Belief

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Maomi Ueno

Nagaoka University of Technology

Advantages of ITS in probabilistic approaches

Mathematical analysis of the system behaviors.

Mathematical approximation for convenient calculation

Decision making approachesto describe a teacher’s behavior

Assumption

A Teacher behaves to maximizes the following expected utility.

Expected Utility = ΣUtility×Probability

Probability model to describe human behaviors

Tversky、 A.　 and Kahneman,D. １９７ 3 Tversky、 A.　 and Kahneman,D. １９７ 4 Tversky、 A.　 and Kahneman,D. １９ 83 Simon， H.A.　１９７４ and etc.

↓

It is impossible to describe human behaviors by using Probabilistic approaches.

Rationality

Human is Rational.(probabilistic approaches)

vs. Human is not Rational.(has pointed out,

and seems right.)

Purposes of this study

What is the utility of a teacher’s behavior? This paper tries to describe a teacher’s

behavior as a simple function.

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.

Unique features of this paper

A simple utility function:

Changes of the predictive student model Teacher’s Prior knowledge An exact parameterization of Bayesian

student modeling :

Predictive distribution of Bayesian networks.

Student model

Bayesian Belief networks

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8 9

1011

12

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15 application problem

ax + b =cx + d type

ax + bx = c type

ax + b= c type

x + a = b type

substituion representation of equation

ax = b type

division

multiplication

positive and negative number

addition

subtraction

literal representation

Figiure 1. An example of the student model

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},,,{ 21 iqi xxx ix },,,{ 21 iqxxx ix .i

Prior distribution as a Prior Knowledge

Dirichret distribution ,which is a conjecture distribution of the Bayesian networks

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Predictive distribution as a student model

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Teacher’s actions

Instruction corresponding to the j’s node. Ask a question corresponding to the j’s

node.

Select the action to maximize utility function

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actionxxpactionxxpEVII

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Expected Value of Instruction Information

(EVII)

Stopping rule

EVII < 0.0001

Probability propagationGiven Instruction frame j

P(xj) →p(xj=1 | x1=1, x2=1, xj-1=1)=1

Given question frame j

P(xj) → xj =1 :right answer

0:wrong answer

Examples

Data: 248 Junior high school students test data

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8 9

1011

12

13

14

15 application problem

ax + b =cx + d type

ax + bx = c type

ax + b= c type

x + a = b type

substituion representation of equation

ax = b type

division

multiplication

positive and negative number

addition

subtraction

literal representation

Figiure 1. An example of the student model

Prior parameter n1’ <n0’P(root) = 0.0

When a teacher know that the student knowledge is poor

Strategy

Bottom Up strategy

(from the easy material to the difficult material)

Instruction frames

Prior parameter n1’ >n0’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.

Prior parameter n1’ =n0’

When a teacher have no knowledge about the student knowledge

Flexible strategies

Quesion Frame 15

Question Frame 12

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0.90.9

0.90.80.60.40.40.20.10.0 0.0

0.80.7

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0.90.90.50.30.00.00.0

0.8QuestionFrame 9

0.1

0.80.7

0.70.6

0.90.9

1.00.90.50.30.00.10.1

0.9 QuestionFrame 3

0.1

10.9

0.90.8

0.90.9

1.00.90.60.40.00.10.1

1

QuestionFrame 11

0.1

10.9

0.90.9

0.90.9

1.00.90.91.00.00.10.1

1 Instruction Frame 12

0.1

10.9

0.90.9

0.90.9

1.00.90.91.01.00.60.4

Instruction Frame 13

0.7

10.9

0.90.9

0.90.9

1.00.90.91.01.01.00.8

Instruction Frame 14

0.8

10.9

0.90.9

0.90.9

1.00.90.91.01.01.01.0

Instruction Frame 15

1.0

10.9

0.90.9

0.90.9

1.00.90.91.01.01.01.0

Strategy

Diagnose the student knowledge states Then, the system instructs knowledge

which student can not understand by using the bottom-up strategy.

Conclusions

The prior knowledge for the student Prediction of student’s knowledge A simple utility function:

How can the teacher change the student’s predicted knowledge states.

Future tasks

We are developing large scale ITS based on this study.

How can we evaluate the behaviors of the system? Good or bad?