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MODELLING OF EDUCATION AND LEARNING SYSTEMS WITH APPLICATIONS

by

A. CHANDRAMOULI

Electrical Engineering Department

Submitted

in fulfilment of the requirements of the degree of

DOCTOR OF PHILOSOPHY

oiLs%

to the

INDIAN INSTITUTE OF TECHNOLOGY, DELHI

February 1994

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Dedicated to

All "THOSE" who "LIVE" for "OTHERS"

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CERTIFICATE

This is to certify that the thesis entitled Modelling of Education and Learning Systems with Applications which is being submitted by Mr. A. Chandramouli to the Indian Institute of Technology, Delhi for the award of the degree of Doctor of Philosophy in Electrical Engineering, is a record of bona fide work carried out by him. He has worked under my guidance and supervision and has fulfilled the requirements for the submission of this thesis, which has attained the standard required for a Ph.D. degree of the Institute. The results presented in this thesis have not been submitted elsewhere for the award of any other degree or diploma.

p s ___c- l/f

(P.S. SATSANGII/

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Acknowledgements

To start off on the journey of research is simple; however, to complete it successfully is a tough job. During this journey a researcher needs guidance, support, encouragement, monitoring and, at the same time, freedom of thought to choose research topic. In general, a research student expects his/her supervisor to fulfill all his/her needs. From the very beginning of this research work all my above mentioned needs were taken care of by a single person, Professor P.S. Satsangi. Though a hard task master, he is basically a kind hearted person with lot of innovative and fresh ideas. He was always the source of inspiration for me. I simply have no words to thank him adequately and express my sense of gratitude for all that he has done for me.

During the course of my research journey I came across a number of delightful and helpful personalities who made my journey pleasant and helped me reach the destination. Prof. B.P. Singh initiated me into this field when I joined the CD cell of the EE Department at IIT Delhi in the year 1986. He continued to encourage me, in various ways, till the last stages of this work. Prof. S.I. Ahson enlightened me about the usage of computer as a tool for planning through simulation. Prof. M. Gopal's advice at crucial stages and Prof. K.S. Prakasa Rao's helpful attitude made my life simpler. Wide ranging discussions with Dr. M.C. Mathur were also helpful. I gratefully acknowledge their help.

My research voyage, which started at IIT Delhi in 1987, came to an end at IIT Kanpur after going round different places and organizations. At IIT Kanpur, where I worked on a DST sponsored project, I received all kinds of help from the coordinators of the project, Prof. P.K. Kalra and Prof. S.C. Srivastava. I wish to place on record my indebtedness to both. I also wish to thank Prof, Sachchidanand who readily allowed me to take the final printout of this thesis on his laboratory printer.

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The credit for neat figures goes to Mr. T. Srinivas Rao, who really struggled with computer to bring out the figures as neatly as possible. Also Mr. D.M. Vinod Kumar helped me in several ways in the preparation of this thesis. I can not forget the help rendered by them. I am thankful to Dr. V.P. Pyara of Dayalbagh Educational Institute for going through the entire manuscript and suggesting corrections wherever necessary. I also acknowledge pleasant atmosphere of Dayalbagh and helpful nature of its people in the completion of this work.

This thesis would not have seen the light of the day without the love and unflinching support of my wife Mrs. K. Durga Bhavani. She was always there, by my side, as a friend sharing with me all the ups and downs of this long journey. The affection shown by my loving children, Deepu and Bharat and at times their innocent queries such as "Ph.D Kyoon Karna Hai?" (Why do Ph.D?) went a long way towards making this task of writing pleasant.

Finally, I acknowledge one and all who helped me, directly or indirectly, during the course of my investigation leading finally to this stage.

tJJ'' t L-6C)2ACI Li

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Abstract

Without education, no society could have progressed much. Education paves the way for innovations and inventions of new technologies. Though the contribution of education to the society is rich / big, its fruits would not have been so ripe and sweet unless it is properly cultivated / managed. As time passes and situation / society changes, both the education and management components have to adapt / learn to come up to the new / changed situation. These three components have quite complex causal relationships with the economic system / set up prevalent in a society. Thus the thesis work is a study on the education system and learning system with a management perspective so as to improve the performance of a system through intervention at the highest policy making / design level.

An education system might be modelled at various (hierarchical) levels, viz.

global / regional level, local / institute level and micro / component level. At global level the scope of the education system would be to consider it as a subsystem of a larger socioeconomic system. At the local level each educational institute would be a subsystem of a larger regional education system. And at the micro level the individual component subsystems such as students, personnel, physical facilities would need to be considered. However, in this thesis, the modelling applications at two of the three levels i.e., regional and local levels have been addressed in the field of higher technical education.

The crux of the issue of the education system modelling is having a control over the education system process by manipulating student intake for instance. To handle this problem the education system at regional level, in the thesis, is modelled as technical manpower planning which is captured through a dynamic education - employment process model. Further, the technical manpower planning is viewed at two levels, one at the aggregate level and the other at the disaggregate or discipline- wise level. Different policy options and their individual effects in terms of sensitivity

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on the system behavior have been studied through simulation of a system dynamics model. An illustrative case study for the state of Uttar Pradesh, India, is presented.

Education system at the local / institute level has been modelled to study how the internal dynamics of the educational institute affects its own growth as well as its output to the outside environment. An example of development of alternate profiles of evolution of dynamics of the Indian Institute of Technology, Delhi at the macroscopic level during the VIII five year plan period (1990-95) has been illustrated through direct and transformed system dynamics model simulations.

A model of learning system, Knowledge Automaton, developed in the thesis subsumes most of the existing models of learning as special cases. This model is applied, conceptually, to both technical manpower planning and educational institute planning studies.

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CONTENTS

Certificate i

Acknowledgements ii

Abstract iv

Contents vi

List of Figures x

List of Tables xiv

Chapter 1 Introduction 1

1.1 Introduction to the problem 1

1.2 Modelling and Simulation 4

1.2.1 Concepts / Terms 4

1.2.2 Why Modelling and Simulation? 9

1.3 Methodologies 11

1.3.1 Over View of Methodologies 11 1.3.2 Methodologies for the Problem(s) Handled 13 1.3.3 Why System Dynamics Methodology? 14 1.3.4 Why Physical System Theoretic Methodology? 16

1.3.5 Why Learning Automata? 18

1.4 Scope of the Thesis 20

1.4.1 Education System Modelling at the Regional Level 22 1.4.2 Education System Modelling at the Local/Institute Level 23 1,4.3 Learning System Modelling 24

1.4.4 Applications 25

1.5 Thesis Organization 26

Chapter 2 Modelling of Education System at the Regional Level 28 2.1 Introduction

2.1.1 Objectives of the Model 30

2.2 Education - Employment Process: A Model for Manpower

Planning 31

2.2.1 Causal Loop Diagram 32

2.3 Regional Technical Manpower Planning 34

2.3.1 Causal Loop Diagram 35

2.3.2 Flow Diagram for Technical Manpower Planning 38 2.3.3 System Dynamic Equations 40

2.3.4 Aggregate Model 42

2.3.5 Disaggregate / Discipline-wise Model 43

2.4 Policy Options 43

2.4.1 Sensitivity of Policies 44

2.4.2 Policy Sets / Future Scenarios 45

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2.5 Simulation Results and Structural Validity of the Model 46

2.5.1 Parameter Estimation 46

2.5.2 National Technical Manpower Information System (NTMIS) 47

2.5.3 Aggregate Model Results 48

2.5.4 Discipline-wise Model Results 50

2.5.5 Model Validation 56

2.5.6 Sensitivity Results 58

2.5.7 Scenario Generation 63

2.6 Discussion and Conclusions 68

Chapter 3 Modelling of Education System at the Local/Institute

Level 74

3.1 Introduction 74

3.1.1 Objectives of the Modelling 76 3.2 Direct System Dynamics Model of an Educational Institute 77

3.2.1 Causal Loop Diagram 77

3,2.2 Flow Diagram 82

3.2.3 System Dynamic Equations 82

3.2.4 Policy Options 85

3.3 PST Based Network Model of an Educational Institute 87

3.3.1 Component Models 88

3.3.2 System Graph 101

3.3.3 System State Equations 103

3.4 Transformation of Network Model to

System Dynamics Model 106

3.4.1 Transformation Procedure 108 3.4.2 Transformed System Dynamics Model

(TSDM) Flow Diagram 111

3.4.3 System Dynamics Equations 112

3.4.4 Policy Options 116

3.5 Simulation Results 118

3.5.1 Indian Institute of Technology, Delhi (IITD) - System 118

3.5.2 Results of Direct SDM 122

3,5.3 Results of Transformed Flow SDM 122 3.5.4 Results of Transformed Cost SDM 122 3.5.5 Results of Sensitivity Analysis 126 3.5.6 Generation of Scenarios / Alternate Profiles of

Growth of the Institution 137

3.6 Discussion and Conclusions 146

Chapter 4 Modelling of a Learning System 153

4.1 Introduction 153

vii

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4.2 Basic Model of Learning Automaton (LA) 155

4.2.1 The Environment 155

4.2.2 The Automaton 156

4.2.3 Learning Schemes 157

4.3 Other Models of Learning 158

4.3.1 Learning Model in Psychology (LMP) 158 4.3.2 Learning Model in Artificial Intelligence (LMAI) 163 4.3.3 Learning in Artificial Neural Networks (LANN) 167

4.4 Knowledge Automaton (KA) 169

4.4.1 Need for Knowledge Automaton 170 4.4.2 Structure of Knowledge Automaton 171 4.4.3 Behavior of Knowledge Automaton 176 4.4.4 Performance / Learning Improvement Algorithms 178 4.5 Conceptualizing Different Learning Models from KA 179 4.5.1 Learning Automaton from KA 179 4.5.2 Learning Model of Psychology from KA 180 4.5.3 Learning Model in AI from KA 182 4.5.4 Learning in Artificial Neural Networks from KA 182

4.6 Simulation Results 184

4.7 Discussion and Conclusions 185

Chapter 5 Applications of Knowledge Automaton 188

5.1 Introduction 188

5.2 Embedding Knowledge Automaton 191 5.2.1 What Does Embedding of Knowledge Automaton Mean? 191 5.2.2 How to Embed Knowledge Automaton? 192 5.3 Problem Formulation for Application of KA 194 5.3.1 Cases of Problem Formulation 194 5.3.2 Generic Problem Formulation for Application of KA 196 5.3.3 Policy Element / Performance Updation 198 5.4 KA Application to Education System at Regional Level 201

5.4.1 Model of an Education System at Regional Level with

Embedded Knowledge Automaton (MESRELEKA) 201 5.4.2 MESRELEKA Formulation with a Set of Control Actions 203 5.4.3 MESRELEKA Formulation with a Set of Scenarios 204 5.4.4 MESRELEKA Formulation with a Set of Policy Elements 205 5.5 KA Application to Education System

at Local / Institute Level 205 5.5.1 Model of Education System at Institute Level

with Embedded Knowledge Automaton (MESINLEKA)

for Direct SDM Formulation 206 5.5.2 Model of Education System at Institute Level

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with Embedded Knowledge Automaton (MESINLEKA)

for Transformed SDM Formulation 207

5.6 Simulation Results 208

5.6.1 Results of MESRELEKA 209

5.6.2 Results of MESINLEKA 211

5.7 Discussion and Conclusions 213

Chapter 6 6.1

6.2

6.2.1 6.2.2 6.2.3 6.2.4 6.3

6.3.1 6.3.2 6.3.3 6.3.4 6.3.5

References

Conclusions Introduction

Highlights of the Work Done

Education System Modelling (at Regional Level) Educational Institute Modelling

Modelling of a Learning System Applications of Knowledge Automaton Future Scope of Research

Future Scope of Education System Modelling (at Regional Level)

Future Scope of Educational Institute Modelling Future Scope of Learning System Modelling

Future Scope of Applications of Knowledge Automaton Future Scope of Subject Domain of

Education and Learning System

220 220 220 220 222 224 224 225 225 225 226 227 227 228 Appendix-A System Dynamics Methodology 239 Appendix-B Physical System Theoretic Approach 253 Appendix-C Learning Automaton Paradigm 262

List of Publication s from this work Curriculum Vitae

ix

References

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