LEARNING SEQUENCES CONSTRUCTION USING VAN HIELE MODEL AND BAYESIAN NETWORK

南台科技大學資訊管理研究所

LEARNING SEQUENCES

CONSTRUCTION USING VAN HIELE MODEL AND BAYESIAN NETWORK

J. Wey Chen, ProfessorDepartment of Information Management

Southern Taiwan UniversityTainan, Taiwan

南台科技大學資訊管理研究所Outline

Introduction * Motivation * Purpose of the study Theoretical Foundation * Van Hiele Model * The Cognitive Theory * Bayesian network (BN) * General architecture

A Practical Methodology Dignostic test Results and Discussion Conclusion

2

南台科技大學資訊管理研究所On “Programming Teaching and Learning”

1. "Programming" is a complicated business.

2. Dijkstra1 argues that learning to program

is a slow and gradual process of transforming the "novel into the familiar". 3

南台科技大學資訊管理研究所On “Programming Teaching and Learning”

3. programming is not a simple set of discrete skills; the skills form a hierarchy, and a programmer will be using many of them at any point in time. 4. The Educational institutions and businesses are placing more course materials online to supplement classrooms and business training situations.

4

南台科技大學資訊管理研究所Purpose of the Study

The main focus of this study is designed to:

(1) demonstrate a measurement scheme to detect misconceptions employed by the students,

(2) provide a convenient descriptive tool for diagnosing students' programming abilities by representing flaws in the networks.

More specifically, this study will help us

designA complete Java curriculum content and

instructionalsequence. 5


Theoretical Foundation

6

南台科技大學資訊管理研究所Van Hiele Model

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Level 0Visualization

Level 1Analysis

Level 2Informal

Deduction

Level 3Deduction

Level 4Rigor

InformationGuided orientation

ExplicationFree orientation

Integration

南台科技大學資訊管理研究所The Cognitive Theory

8

Bonar and Soloway11 represented and arranged programming knowledge according to its level of difficulty in four cognitive levels:

• Lexical and Syntactic• Semantic• Schematic• Conceptual

南台科技大學資訊管理研究所The Combined Model

9Knowledge structure for each learning node

南台科技大學資訊管理研究所Bayesian network (BN)

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)()()|(

YPYXPYXP

)()|()()|()( YPYXPXPXYPYXP

A Bayesian network (BN) consists of directed acyclic graphs (DAG) and a corresponding set of conditional probability distributions (CPDs). Based on the probabilistic conditional independencies encoded in the DAG, the product of the CPDs is a joint probability distribution.

南台科技大學資訊管理研究所Using Bayesian Networks in

Diagnostic Test

11

Ａ

ＢＣ

Ｄ E

y nＡ 0.9 0.1

A=y A=nC=y 0.8 0.1

C=n 0.2 0.9

A=y A=nB=y 0.6 0.2

B=n 0.4 0.8

B=y B=nE=y 0.7 0.15

E=n 0.3 0.85

B=y B=nD=y 0.3 0.8

D=n 0.7 0.2

Ａ

ＢＣ

Ｄ E

南台科技大學資訊管理研究所Chen’s Implementation (2006)

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Level 2Analysis

Level 3Informal

Deduction

Level 4Deduction

Level 5Rigor

InformationGuided orientation

ExplicationFree orientation

Integration


Level 2Descriptive &

RelationsLevel 3

Implications

Level 4Logic

Modification & Analogy

Level 5Abstraction &

Modeling

南台科技大學資訊管理研究所A Practical Methodology

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1. Hold an expert roundtable discussion to roughly determine a set of knowledge concepts required for a course. 2. Manually construct the course DAG with the aid of the course textbook.3. Develop a diagnostic test to have test questions which cover every cognitive category for every level of understanding in the entire curriculum structure. 4. Extensively conduct the test and collect sufficient Bayesian training data.5. Analyze and use the Bayesian training data to trim the unrelated content and adjust the logical sequence for learning. Once the process is completed, a new course DAG will be produced.6. Group the related knowledge concepts into chapters according to their sequences appearing on the course DAG.

南台科技大學資訊管理研究所1. Hold an expert roundtable discussion to roughly determine a set of knowledge concepts required for a course.

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南台科技大學資訊管理研究所2. Manually construct the course DAG with the aid of the course textbook.

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南台科技大學資訊管理研究所3. Develop a diagnostic test

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CPItem Known NRLN P(NRLN)

CPItemNumber

NRLNNumber P(NRLN | CP_Item)

N2L0 Y N2L10.310344828

48 16 0.333333333

N2L0 N N2L1 10 2 0.2

N2L1 Y N2L20.448275862

18 10 0.555555556

N2L1 N N2L2 40 16 0.4

N2L3 Y N3L00.310344828

6 4 0.666666667

N2L3 N N3L0 52 14 0.269230769

N3L0 Y N3L10.275862069

18 10 0.555555556

N3L0 N N3L1 40 6 0.15

N4L0 Y N4L10.137931034

8 2 0.25

N4L0 N N4L1 50 6 0.12

N4L1 Y N4L20.137931034

8 4 0.5

N4L1 N N4L2 50 4 0.08

N5L1 Y N5L20.448275862

18 16 0.888888889

N5L1 N N5L2 40 10 0.25

N5L2 Y N5L30.344827586

26 16 0.615384615

N5L2 N N5L3 32 4 0.125

N4L3 Y N6L00.724137931

8 6 0.75

N4L3 N N6L0 50 36 0.72

N6L0 Y N6L10.655172414

42 32 0.761904762

N6L0 N N6L1 16 6 0.375

N8L1 Y N8L20.342926863

18 14 0.777777778

N8L1 N N8L2 40 6 0.15

N8L2 Y N8L30.412382567

20 18 0.9

N8L2 N N8L3 38 6 0.157894737


4. Extensively conduct the test and collectsufficient Bayesian training data.

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南台科技大學資訊管理研究所 5. Analyze and use the Bayesian training data to trim the unrelated content and adjust the logical sequence for learning. Once the process is completed, a new course DAG will be produced.

6. Group the related knowledge concepts into chapters according to their sequences appearing on the course DAG. 18


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Dignostic test Results and Discussion

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南台科技大學資訊管理研究所Knowledge Structure for Dignostic Test

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-To move around the levels in a node

Discussion

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南台科技大學資訊管理研究所Discussion

– To move to different learning nodes

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• To determine the learning sequence

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25.0)34|05( LNLNP 75.0)34|06( LNLNP

N4L3

N5L0

N6L0

N4L3

？？N6L0

N5L0


• Diagnosis

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703061866.0735698243.0

655172414.019/15)08(

)35()35|08()08|35(

LNP

LNPLNLNPLNLNP

890555924.0735689243.0

896551724.026/19)08(

)37()37|08()08|37(

LNP

LNPLNLNPLNLNP

N5L3

N7L3

N8L0

？

N7L3

南台科技大學資訊管理研究所Conclusions

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1. The success of this model is attributed to the extensive review of the available literature and to the exploratory interviews with students who participated in the first phase of study.

2. The proposed Modified van Hiele Model for Computer Science Teaching can help unveil the mystery of the “hidden mind” and provide a logical link for students to inductively learn problem-solving and programming skills.

3. The system is able to utilize Bayesian network techniques in modeling the student knowledge based on the proposed knowledge structure.


Thank you for your attention!!

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LEARNING SEQUENCES CONSTRUCTION USING VAN HIELE MODEL AND BAYESIAN NETWORK

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