Decision theoretic intelligent tutoring system

DECISION-THEORETIC INTELLIGENT TUTORING SYSTEM PEK PENG KIAT M. Sc. (Distinction), The University of Sheffield M. Eng., National University of Singapore B. Eng. (Second Upper), National University of Singapore A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF INDUSTRIAL & SYSTEMS ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2003 ACKNOWLEDGEMENTS I wish to express my special appreciation to my wife Lian Kuan for her thoughtful and challenging discussions of the ideas in the research, and to my students at Singapore Polytechnic who had volunteered to use iTutor during some of their tutorials. I also wish to express my gratitude to Associate Professor Poh Kim Leng, my research supervisor, for having trusted my ability to carry out the research and his guidance throughout the course of formalizing the ideas. I would like to thank Associate Professors Ong Hoon Liong and Tan Kay Chuan (members of my Thesis Committee) for their very helpful comments during the formative stage of the research. In addition, I wish to thank Ms Ow Lai Chun for her excellent administrative support. Finally, I wish to express my gratitude to Singapore Polytechnic management for having supported the research, without which I would not be able to complete the work. Page i TABLE OF CONTENTS Acknowledgements i Table of Contents . ii List of Figures vii List of Tables . x Summary xii Nomenclature xiv Quote . xvi Chapter 1. Introduction . 1.1 Components of Intelligent Tutoring System 1.2 Current Intelligent Tutoring System 1.2.1 Inadequate Information on Student’s Mastery State . 1.2.2 Making Pedagogical Decision Based on Heuristics 1.2.3 Ineffective Use of Test Items 1.3 Scope of the Research . 1.3.1 Representing Knowledge Structure as Bayesian Networks . 1.3.2 Decision-theoretic Approach to Computerised Tutoring . 1.3.3 Application of Item-Response Model to Tutoring 10 1.3.4 Generating Optimal Tutoring Policy . 11 1.4 iTutor: A Decision-Theoretic Tutoring System 12 1.5 Organisation of this Thesis 17 Page ii Chapter 2. Literature Review . 18 2.1 Construction of Student Model 21 2.1.1 Stereotypes Modelling . 21 2.1.2 Overlay Modelling 23 (a) Expert-Centric Models . 24 (b) Efficiency-Centric Models 26 (c) Data-Centric Models 27 2.1.3 Extended Overlay Modelling . 29 (a) Enumerative Modelling 30 (b) Generative Modelling . 32 (c) Reconstructive Modelling 33 2.2 Diagnosis . 35 2.2.1 Model Tracing . 35 2.2.2 Constraint-Based Modelling . 37 2.3 Learning Theories 39 2.4 Action Selection . 41 2.4.1 Heuristic Approach 41 2.4.2 Decision-Theoretic Approach . 42 2.5 Assessment . 43 2.6 Human-Computer Interaction . 45 2.7 Approach Adopted by This Research 47 Page iii Chapter 3. Student Model 50 3.1 Forms of Knowledge . 51 3.1.1 Online Resource Materials . 51 3.1.2 Learning Objectives . 53 3.1.3 Student Model 55 3.1.4 Buggy Knowledge . 61 3.2 Completion of Probability Tables 63 3.2.1 Prior Probabilities from Expert’s Judgment . 64 3.2.2 Prior Probabilities from Empirical Data . 66 3.2.3 Conditional Probabilities from Expert’s Judgment . 68 3.2.4 Conditional Probabilities from Empirical Data . 70 3.3 Inference . 72 3.3.1 Evidence Collection 72 3.3.2 Linking Evidence to Mastery State . 73 3.3.3 Probabilistic Relevance Among Learning Objectives 74 3.3.4 Posterior Belief of Student’s Mastery State 77 Chapter 4. Modelling of Tutoring Strategy 80 4.1 Making Decisions with Incomplete Information 81 4.2 Learning Values 83 4.3 Action Selection 90 4.4 Item Selection 93 4.5 Tutoring Policy 99 4.5.1 Dynamic Belief Network, DBN 100 4.5.2 Dynamic Decision Network, DDN 102 4.6 Hint Generation . 109 Page iv Chapter 5. Development and Evaluation of iTutor . 111 5.1 Requirements for Applying Decision-Theoretic Approach 113 5.2 Architecture of iTutor 114 5.2.1 Database Management System 114 5.2.2 Human-Computer Interaction . 118 5.2.3 Spiral Tutoring Strategy 119 5.3 Items Calibration 120 5.4 Evaluation of iTutor . 124 5.4.1 Evaluation 1: Tutoring Policy . 124 5.4.2 Evaluation 2: Adaptive Tutoring 132 5.4.3 Evaluation 3: System Effectiveness . 136 Chapter 6. Conclusions . 141 6.1 Related Works . 141 6.2 Summary of Contributions 143 6.2.1 Bayesian Network for Modelling Student’s Knowledge Mastery . 144 6.2.2 Decision-Theoretic Approach for Tutoring Action Selection . 144 6.2.3 Item-Response Model for Item Selection 145 6.2.4 Dynamic Decision Network for Tutoring Policy Generation 145 6.3 Future Works 146 6.3.1 Refinement of BNs’ Structure by Learning form Data . 146 6.3.2 Inclusion of Motivation to Learn in Item Response Model . 147 6.3.3 Extending Decision-Theoretic Tutoring to Web-Based Activities . 148 Page v References . 149 Appendices Appendix A. Learning Outcomes for Two Key Concepts ( “Forces” and “Friction and Screw Jack” ) . 169 Appendix B. Set of Bayesian Networks in iTutor . 170 Appendix C. Table of Conditional Probability Values for an Objective with Three Conditions . 174 Appendix D. WINBUG Program on Parameter Estimation 176 Page vi LIST OF FIGURES Fig. 1.1 Interactions of components in intelligent tutoring system. . Fig. 1.2 Process flowchart in computerised adaptive tutoring. Fig. 1.3 Login screen. . 12 Fig. 1.4 An item presented to the student. 13 Fig. 1.5 Topic on “Friction and Screw Jack.” 13 Fig. 1.6 Feedback from iTutor when the student’s answer is incorrect. 14 Fig. 1.7 An item testing “Resolution of Vector.” . 15 Fig. 1.8 User interface for teacher to track student’s progress. 15 Fig. 1.9 Output of a student’s mastery states. 16 Fig. 1.10 A policy with three actions. 16 Fig. 2.1 A classification of Student Model using BN. 24 Fig. 2.2 A dynamic BN modelling the mastery of the student on a single knowledge unit. 27 Fig. 2.3 Extended overlay student model. . 29 Fig. 2.4 A decision tree for a single decision. . 43 Fig. 2.5 Example of a text page with free-form test items and adaptive annotation of links. 46 Fig. 3.1 Problem on “Acceleration of Connected Bodies.” . 52 Fig. 3.2 MathCAD solution. . 52 Fig. 3.3 Interactive graphical display. 53 Fig. 3.4 A generalised BN in the student model. . 56 Fig. 3.5 BN of the key concept on “Forces.” . 59 Fig. 3.6 Relationship between the BNs on “Forces” and “Units & Dimensions.” . 60 Page vii Fig. 3.7 (a) An item testing the LO on “Resultant vector.” (b) Feedback for option (b). (c) Feedback for option (c). (d) Feedback for option (d). . 62 Fig. 3.8 A subset of the BN on “Forces” with the tables of probability values. 64 Fig. 3.9 A solution to item testing “7.5 Angular Motion Formula.” 68 Fig. 3.10 Solution by student #1. . 71 Fig. 3.11 Two alternatives in modelling relationships among the LOs. 75 Fig. 3.12 Initial state of the BN on the topic “Forces” (before observing any evidence). . 78 Fig. 3.13 State of BN after instantiating the node “Vector Addition.” 79 Fig. 4.1 Additive independence of 2-attribute utility function. . 89 Fig. 4.2 (a) Influence diagram for a simple decision problem. (b) Decision tree representation of the simple decision problem. . 91 Fig. 4.3 Decision model for the topic on “Forces.” 93 Fig. 4.4 DDN that incorporates items. . 94 Fig. 4.5 (a) Decision network for LO selection. (b) Selection of an item. 94 Fig. 4.6 Example of item selection for the topic on “Forces.” . 95 Fig. 4.7 Algorithm for computing students’ mastery states for each topic. . 96 Fig. 4.8 Three sample questions. 98 Fig. 4.9 Item-student response matrix. 99 Fig. 4.10 A two-slice fragment of a DBN for monitoring of student’s mastery state. . 101 (a) Generic structure. (b) Specific BN. Fig. 4.11 Dynamic decision network for a tutoring policy {a(1), a(2), …, a(n)}. . 103 Fig. 4.12 Search tree for part of the DDN in Figure 4.11. . 104 Fig. 4.13 Hint generation based on the targeted LO (shaded node). 110 Fig. 5.1 Architecture of decision-theoretic tutoring system. 114 Fig. 5.2 Data entry by the teacher on prior probability values and path length. 116 Page viii Millán, E., J.L. Pérez-de-la-Cruz and E. Suárez. Adaptive Bayesian Netowrks for Multilevel Student Modelling. In Proc. 5th International Conference on Intelligent Tutoring Systems, June 2000, Montréal, Canada, pp. 534-543. Miller, M. and I. Goldstein. An Automated Consultant for MACSYMA. In Proc. 5th International Joint Conference on Artificial Intelligence, 1977, pp. 789. Milne, S., E. Shiu and J. Cook. Development of a Model of User Attributes and its Implementation within an Adaptive Tutoring System. User Modeling and User-Adapted Interaction, 6, pp. 303-335. 1996. Mislevy, R.J. and D.H. Gitomer. The Role of Probability-Based Inference in an Intelligent Tutoring System, User Modelling and User-Adapted Interaction, 5, pp. 253-282, Kluwer Academic Publishers. 1996. Mitrović, A. Experiences in Implementing Constaint-Based Modeling in SQL-Tutor. In Proc. 4th International Conference on Intelligent Tutoring Systems, August 1998, Texas, USA, pp. 414-423. Mitrović, A., S. Djodjević-Kajan and L. Stoimenov. INSTRUCT: Modeling Students by Asking Questions. User Modeling and User-Adapted Interaction, 6, pp. 273302. Kluwer Academic Publishers. 1996. Monahan G.E. A Survey of Partially Observable Markov Decision Process: Theory, Models, and Algorithms. Management Science. 28(1), pp. 1-16. 1982. Morgan, M.G. and M. Henrion. Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis. Cambridge University Press. 1990. Murray, R.C. and K. VanLehn. DT Tutor: A Decision-Theoretic, Dynamic Approach for Optimal Selection of Tutorial Actions. In Proc. 5th International Conference on Intelligent Tutoring Systems, June 2000, Montréal, Canada, pp. 153-162. References Page 161 Murray, W. An Easily Implemented, Linear-time Algorithm for Bayesian Student Modeling in Multi-level Trees. In Proc. 9th World Conference of Artificial Intelligence and Education, 1999, pp. 413-420. Nathan, M.J. Knowledge and Situational Feedback in a Learning Environment for Algebra Story Problem Solving. Interactive Learning Environments, 5(1), pp. 135-159. 1998. Nelsen, J. Positive Time-out. Prime Publishing. 1999. Nelson, E. W., C.L. Best and W.G. McLean. Schaum’s Electronic Tutor: Engineering Mechanics (Static and Dynamics). Fifth edition, McGraw Hill. 1998. Norsys. Netica Application Reference Manual, version 1.12. Norsys Software Corp. www.norsys.com. 1999a. Norsys. Netica API Programmer’s Library Reference Manual, version 1.06. Norsys Software Corp. On World Wide Web at http://www.norsys.com. 1999b. Oberg, R.J. Introduction to C# Using .NET. Prentice Hall. 2002. Ohlsson, S. Constraint-Based Student Modeling. In Student Modeling: The Key to Individualized Knowledge-Based Instruction, ed by J.E. Greer and G.I. McCalla, pp 167-189. New York: Springer-Verlag. 1994. Ourston, D. and R. Mooney. Theory Refinement Combining Analytical and Empirical Methods. Artificial Intelligence, 66, pp. 311-394. 1994. Patz, R. J. and B.W. Junker. A Straightforward Approach to Markov Chain Monte Carlo Methods for Item Response Models. Ph.D Thesis, Carnegie Mellon University. 1997. References Page 162 Pearl, J. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers, Inc. 1988. Pek, P.K. and K.L. Poh. Using Decision Networks for Adaptive Tutoring. In Proc. 8th International Conference on Computers in Education / International Conference on Computer-Assisted Instruction, Nov 2000, Taipei, Taiwan, pp. 1076-1084. 2000a. Pek, P.K. and K.L. Poh. Framework of a Decision-Theoretic Tutoring System for learning of Mechanics, Journal of Science Education & Technology, 9(4), pp. 343-356. 2000b. Pek, P.K. and K.L. Poh. Formulation of Tutoring Policy for Maximizing Students’ Learning through Decision-Theoretic Approach. International Journal of Engineering Education, 18(6), pp. 652-666. 2002. Quinlan, J.R. Introduction of Decision Trees. Machine Learning, 1, pp. 81-106. 1986. Raiffa H. Decision Analysis. Addison-Wesley. 1968. Reckase, M. D. The Difficulty of Test Items that Measure More Than One Ability, Applied Psychological Measurement, 9(4), pp. 401-412. 1985. Regian, J.W. and V.J. Shute. Basic Research on the Pedagogy of Automated Instruction. In Simulation-Based Experiential Learning, ed by D.M. Towne, T. de Jong and H. Spada. pp. 121-132. Berlin: Springer-Verlag. 1993. Reye, J. A belief Net Backbone for Student Modeling, In Proc. 3rd International Conference on Intelligent Tutoring Systems, June 1996, Montréal, Canada, pp. 596-604. References Page 163 Reye, J. Two-Phase Updating of Student Models Based on Dynamic Belief Network. In Proc. 4th International Conference on Intelligent Tutoring Systems, August 1998, Texas, USA, pp. 274-283. Rich, E. Users are Individuals: Individualizing User Models. International Journal of Man-Machine Studies, 18, pp. 199-214. 1983. Rissanen, J. Stochastic Complexity and Modeling. Annals of Statistics, vol. 14, pp. 1080-1100. 1986. Rubin, D.B. Estimation in Parallel Randomized Experiments, Journal of Educational Statistics, 6, pp. 377-400. 1981. Rubin, D.B. Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician, Annual Statistics, 12, pp. 1151-1172. 1984. Russell S. and P. Norvig. Artificial Intelligence: A Modern Approach. Prentice Hall. 1995. Sammut, C. and R.B. Benerji. Learning Concepts by Asking Questions. Machine Learning: An Artificial Intelligence Approach, Volume II. Morgon Kaufmann, San Mateo, CA. 1986. Savage L. The Foundations of Statistics. Wiley. 1954. Schank, R.C. and C. Cleary. Engines for Education. Hillsdale, N.J.: Lawrence Erlbaum. 1995. Schum, D.A. The Evidential Foundations of Probabilistic Reasoning. New York: Wiley. 1994. References Page 164 Seidel, R.J., and R.S. Perez. An Evaluation Model for Investigating the Impact of Innovative Educational Technology. In Technology Assessment in Software Applications, ed by H.F. O’Neil and E.L. Baker. pp. 177-208. Los Angeles, Calif.: Graduate School of Education and Information Studies, University of California, Los Angeles. 1994. Self, J.A. Bypassing the Intractable Problem of Student Modeling. In Intelligent Tutoring Systems: At the Crossroads of Artificial Intelligence and Education, ed by C. Frasson and G. Gauthier. pp. 107-123, Ablex Publishing Corporation. 1990. Shachter R.D. Evaluating Influence Diagrams, Operations Research, 33(6), pp. 871882. 1986. Shelby, R., K. Schulze, D. Treacy, M. Wintersgill, K. VanLehn and A. Weinstein. An Assessment of the ANDES Tutor. In Proc. Physics Education Research Conference, July 2001, New York, USA. Shortliffe, E.H. Computer-Based Medical Consultations: MYCIN. Elsevier. 1976. Shute, V.J. My Knowledge of Knowledge. In Proc. 4th International Conference on Intelligent Tutoring Systems, August 1998, Texas, USA, pp. 4. Simon H.A. The New Science of Management Decisions. New York: Harper & Row. 1960. Skinner, B. Science and Human Behavior. New York: Macmillan. 1953. Sleeman, D., H. Hirsh, I. Ellery and I. Kim. Extending Domain Theories: Two Case Studies in Student Modeling. Machine Learning, 28, pp. 11-37. 1990. References Page 165 Soloway, E. and W. Johnson. Remembrance of Blunders Past: a Retrospective on the Development of PROUST. In Proc. 6th Annual Conference of the Cognitive Science Society, August 1984, pp. 57. Spetzler, C.S. and C.A. Stael von Holstein. Probability Encoding in Decision Analysis. Management Science, 22, pp.340-352. 1975. Stiggins, R. Student-centered Classroom Assessment. 2nd Ed. Upper Saddle River, NJ:Prentice Hall. 1997. Stone, C.A. Monte Carlo Based Null Distribution for an Alternative Goodness-of-Fit Test Statistic in IRT Models, Journal of Educational Measurement, No. 1, pp. 58-75. 2000. Tang Y., KCC Chan, A. Wu and P. Winoto. A Fuzzy-Based Assessment for Perl Tutoring System. Proc. 8th International Conference on Computers in Education / International Conference on Computer-Assisted Instruction, June 2000, Taipei, Taiwan, pp. 1068-1075. Tatman, J. A. and R.D. Shachter. Dynamic Programming and Influence Diagrams. IEEE Transactions on Systems, Man and Cybernetics, 20(2), pp. 365-379. 1990. Terwilliger, J. Semantics, Psychometrics, and Assessment Reform: A Close Look at “Authentic Assessments”. Educational Research, 26, pp. 24-27. 1997. Tyler, R. Basic Principles of Curriculum and Instruction. pp. 46. Chicago: University of Chicago Press. 1950. Van Lehn, K. Student Modeling. In Foundations of Intelligent Tutoring Systems, ed by M.C. Polson, J.J. Richardson and N.J. Hillsdale. Lawrence Erlbaum. 1988. References Page 166 VanLehn, K. and J. Martin. Evaluation of an Assessment System Based on Bayesian Student Modeling, International Journal of Artificial Intelligence and Education, 8, pp.179-221. 1998. VanLehn K, Z. Niu, S. Siler and AS. Gertner. Student Modelling from Conventional Test Data: A Bayesian Approach Without Priors. In Proc. 4th International Conference on Intelligent Tutoring Systems, August 1998, Texas, USA, pp. 434-443. Veermans, K. and W.R.V. Joolingen. Using Induction to Generate Feedback in Simulation Based Discovery Learning Environments. In Proc. 4th International Conference on Intelligent Tutoring Systems, August 1998, Texas, USA, pp. 196–205. Wainer, H., N.J. Dorans, R. Flaugher, B.F. Green, R.J. Mislevy, L. Steinberg and D. Thissen. Computerized Adaptive Testing: A Primer. Lawrence Erlbaum Associates, Inc. 1990. Walker, J. The Psychology of Learning: Principles and Processes. Upper Saddle River, NJ: Prentice Hall. 1996. Wang, H. and M.J. Druzdzel. User Interface Tools for Navigation in Conditional Probability Tables and Elicitation of Probabilities in Bayesian Networks. In Proceedings of the Sixteenth Annual Conference on Uncertainty in Artificial Intelligence (UAI-2000), pp. 617-625. 2000. Also on World Wide Web at http://www.pitt.edu/~druzdzel/abstracts/uai00c.html. Webb G., B. Chiu and M. Kuzmycz. Comparative Evaluation of Alternative Induction Engines for Feature Based Modelling. International Journal of Artificial Intelligence in Education, 8, pp. 97-115. 1997. References Page 167 Weber, G. and M. Specht. User Modelling and Adaptive Navigation Support in WWW-based Tutoring Systems. Retrieve from http://www.psychologie.unitrier.de:8000 /projects/ELM/Papers/UM97-WEBER.html. 1997. Wenger, E. Artificial Intelligence and Tutoring Systems: Computational and Cognitive Approaches to the Communication of Knowledge. Chapter 16. Morgan Kaufmann Publishers, Inc. 1987. Winterfeldt, D. V. and W. Edwards. Decision Analysis and Behavioral Research. Cambridge University Press. 1986. Woolf, B.P. and W. Hall. Multimedia Pedagogues: Interactive Systems for Teaching and Learning. IEEE Computer (Special Issue on Multimedia). 28(5), pp. 7480. 1995. Zachary, W., J. Cannon-Bowers, J. Burns, P. Bilazarian and D. Krecker. An Advanced Embedded Training System (AETS) for Tactical Team Training. In Proc. 4th International Conference on Intelligent Tutoring Systems, August 1998, Texas, USA, pp. 544-553. Zweig G. and S. Russell. Compositional Modeling with DPNs, Report No. UCB/USD97-970, September 1997, Computer Science Division (EECS), University of California, Berkeley. 1997. References Page 168 Appendix A. Learning Outcomes for Two Key Concepts Learning Outcomes for “Forces” General learning objective (GLO): • Understand the concept of “Forces” Specific learning objectives (SLO): • Know the SI units and dimensions for force and its multiples • Define a vector quantity • Use triangle or parallelogram method of vector addition to find the resultant force • Resolve a force into two components analytically • Determine analytically the resultant (in terms of magnitude, angle and direction) of several forces using rectangular components Learning Outcomes for “Friction and Screw Jack” General learning objective (GLO): • Understand friction on horizontal and inclined planes, and in screw threads Specific learning objectives (SLO): • Define the force of “friction” • Sketch the free body diagram of a block moving or tendering to move on a horizontal surface • Define normal reaction, coefficient of static friction, coefficient of kinetic friction, total reaction, angle of friction, and angle of repose • Determine the force required to move a body along a horizontal or inclined plane • Identify screw jack with square threads as an inclined plane problem • Define the pitch, helix angle, no. of starts and lead of a square threaded screw • Determine the torque or effort required to operate tools using square threads Note: The above learning outcomes are used for illustrations in the thesis. Learning outcomes for other key concepts may be obtained from the author upon request at pekpk@sp.edu.sg. The Bayesian networks for all the nine key concepts are shown in page 169 to 172. Appendix A. Learning Outcomes for Two Key Concepts Page 169 Appendix B. Set of Bayesian Networks in iTutor 1. Bayesian Network on “Units and Dimensions” Topic 1: Units & Dimensions L1_1 Engr Quantity L1_3 Significant Figures L1_2 Conversion G1 Units & Dimensions 2. Bayesian Network on “Forces” Topic 2: Forces L2_1 Vector L2_4 Resolution L2_2 Vector Addition *G1 Units & Dimensions L2_5 Direction L2_3 Resultant Vector L2_6 Angle G2 Forces L2_7 Magnitude 3. Bayesian Network on “Moments of a Force” Topic 3: moment of a Force *G2 Forces L3_4 Perpendicular Distance L3_3 Moments L3_2 Moments Addition L3_1 Couples G3 Moment of Force Appendix B. Set of Bayesian Networks in iTutor Page 170 4. Bayesian Network on “Free Body Diagram” Topic 4: Free Body Diagram L4_6 Frictionless Rollers L4_7 Smooth Surfaces L4_9 Cables L4_10 Built-in Support L4_13 Known Line of Action L4_2 Dimensions L4_8 Hinged Support L4_12 Rough Surfaces L4_11 Pulleys L4_14 Unknown Line of Action L4_3 Reactions L4_4 Applied Force L4_1 Outline L4_5 Labels G4 Free Body Diagram 5. Bayesian Network on “Equilibrium Conditions” Topic 5: Equilibrium Conditions *G2 Forces L5_1 Equilibrant Force L5_2 Equations for CCFS L5_3 Equations for NonCFS L5_5 CCFS L5_4 Moment Arm *G4 Free Body Diagram L5_6 NonCFS G5 Equilibrium Conditions Appendix B. Set of Bayesian Networks in iTutor Page 171 6. Bayesian Network on “Friction and Screw Jack” Topic 6: Friction & Screw Jack L6_2 Friction L6_15 Num of Starts L6_14 Helix Angle L6_3 Normal Reaction L6_16 Lead L6_13 Pitch L6_4 Coefficient of Static Friction L6_17 Effort L6_10 Horizontal Plane L6_5 Coefficient of Kinetic Friction L6_12 Screw Thread L6_1 Definition L6_6 Total Reaction L6_9 Rough Surface *G2 Forces L6_7 Angle of Friction *G4 Free Body Diagram L6_11 Inclined Plane L6_8 Angle of Repose G6 Friction and Screw Jack 7. Bayesian Network on “Kinematics” Topic 7: Kinematics L7_3 Linear D-T Graph L7_4 Linear V-T Graph L7_5 Linear A-T Graph L7_2 LM Equations L7_7 AM Equations L7_8 Angular D-T Graph L7_6 Angular Motion L7_1 Linear Motion L7_11 Combined Motion L7_9 Angular V-T Graph L7_10 Angular A-T Graph G7 Kinematics Appendix B. Set of Bayesian Networks in iTutor Page 172 8. Bayesian Network on “Newton’s Laws of Motion” Topic 8: Newton’s Laws of Motion L8_2 Acceleration L8_1 Inertia L8_3 Second Law *G2 Forces L8_4 One Body L8_8 Kinematics Parameters L8_7 First Law L8_5 Two Bodies L8_6 Body on Inclined Plane L8_9 Third Law G8 Newton Laws of Motion 9. Bayesian Network on “Torque and Moment of Inertia” Topic 9: Torque and Moment of Inertia L9_2 Ring L9_3 Disc L9_1 Lamp Mass *G7 Kinematics *G3 Moment of Force L9_4 Cylinder L9_5 Radius of Gyration L9_6 Moment of Inertia G9 Torque and Moment of Inertia Appendix B. Set of Bayesian Networks in iTutor *G4 Free Body Diagram Page 173 Appendix C. Table of Conditional Probability Values for an Objective with Three Conditions If the states of nq and pa(nq) are similar, then Pr( n q | pa ( n q )) = else Pr( nq | pa (nq )) = ∑ ( w p ,q − (c − 1)κ ) pa ( nq ) ∑κ pa ( n q ) where c is the number of states, is a constant, wp,q is the weight of parent node p to the child node q, and ≤ wp,q ≤ 1. Let κ be 0.005, w1,4 be 0.5, w2,4 be 0.3, and w3,4 be 0.2. The conditional probability values of LO4 are: LO1 LO2 LO3 NM NM NM NM NM NM NM NM NM PM PM PM PM PM PM PM PM PM M M M M M M M M M NM NM NM PM PM PM M M M NM NM NM PM PM PM M M M NM NM NM PM PM PM M M M NM PM M NM PM M NM PM M NM PM M NM PM M NM PM M NM PM M NM PM M NM PM M NM 0.970 0.785 0.785 0.685 0.500 0.500 0.685 0.500 0.500 0.485 0.300 0.300 0.200 0.015 0.015 0.200 0.015 0.015 0.485 0.300 0.300 0.200 0.015 0.015 0.200 0.015 0.015 LO4 PM 0.015 0.200 0.015 0.300 0.485 0.300 0.015 0.200 0.015 0.500 0.685 0.500 0.785 0.970 0.785 0.500 0.685 0.500 0.015 0.200 0.015 0.300 0.485 0.300 0.015 0.200 0.015 M 0.015 0.015 0.200 0.015 0.015 0.200 0.300 0.300 0.485 0.015 0.015 0.200 0.015 0.015 0.200 0.300 0.300 0.485 0.500 0.500 0.685 0.500 0.500 0.685 0.785 0.785 0.970 Appendix C. Table of Conditional Probability Values for an Objective with Three Conditions Page 174 Formula coded in column Pr(LO4 = "NM") = (W1-0.01)*IF(LO1="NM",1,0) + (W2-0.01)*IF(LO2="NM",1,0) + (W3-0.01)*IF(LO3="NM",1,0) + 0.005*IF(LO1="NM",0,1) + 0.005*IF(LO2="NM",0,1) + 0.005*IF(LO3="NM",0,1) Formula coded in column Pr(LO4 = "PM") = (W1-0.01)*IF(LO1="PM",1,0) + (W2-0.01)*IF(LO2="PM",1,0) + (W3-0.01)*IF(LO3="PM",1,0) + 0.005*IF(LO1="PM",0,1) + 0.005*IF(LO2="PM",0,1) + 0.005*IF(LO3="PM",0,1) Formula coded in column Pr(LO4 = "M") = (W1-0.01)*IF(LO1="M",1,0) + (W2-0.01)*IF(LO2="M",1,0) + (W3-0.01)*IF(LO3="M",1,0) + 0.005*IF(LO1="M",0,1) + 0.005*IF(LO2="M",0,1) + 0.005*IF(LO3="M",0,1) Appendix C. Table of Conditional Probability Values for an Objective with Three Conditions Page 175 Appendix D. WINBUG Program on Parameter Estimation # paraEst.odc # To estimate parameters for item difficulty # x[j,i] denotes the jth student’s response to ith item # n denotes number of items # N denotes number of students # item difficulty is measured by beta, while student’s mastery level is measured by theta model { beta.tau ~ dnorm (0.0, 10) I(0,) theta.tau ~ dnorm (0.0, 10) I(0,) for (i in 1:n) { beta.mu[i] ~ dnorm (0, 1) I(0,1) beta[i] ~ dnorm (beta.mu[i], beta.tau) I(0,1) } for (j in 1:N) { theta.mu[j] ~ dnorm (0, 1) I(0,1) theta[j] ~ dnorm (theta.mu[j], theta.tau) I(0,1) for (i in 1:n) { logit(p[j,i]) [...]... the readiness to leave the tutoring session is constructed This ensures that the policy can be generated in polynomial time and yet personalised to the student’s needs Chapter 1 Introduction Page 11 1.4 iTutor: A Decision- Theoretic Tutoring System The ideas formalised in this research have been applied to the development of a functional decision- theoretic intelligent tutoring system called iTutor iTutor... utility functions in tutoring are not based on risk attitude of the decision- maker (teacher) Similarly, the expected utility that is based on dollar equivalent is not useful in tutoring context Decision- theoretic approach in a computerised tutoring system aims to provide optimal action selection which maximises student learning and is defensible Pedagogy can be incorporated into decision analysis to... of tutoring actions can be assured that are consistent with students’ responses The scope of this research is summarised in Section 1.3 In Section 1.4, a fully functional ITS, calls iTutor, which is used to demonstrate decision- theoretic tutoring is introduced, while a guide to the rest of the thesis is discussed in Section 1.5 Chapter 1 Introduction Page 2 1.1 Components of Intelligent Tutoring System. .. decision- maker who goes through the decision- analytical processes For example, the decision- analytic approach highlights the distinction between a good decision and a good outcome Heckerman (1991) defines a good decision is one that is consistent with the preferences and complete information of a decision- maker; while a good outcome is desirable Unlike decision- theoretic (Raiffa, 1968) model in most... relationships 1.3.2 Decision- theoretic Approach to Computerised Tutoring Probability theory describes what an agent should believe on the basis of evidence; utility theory describes what an agent wants, and decision theory puts the two together to describe what an agent should do Chapter 1 Introduction Decision analysis provides a philosophy that Page 9 emphasises the insights that can be gained by a decision- maker... prototype decision- theoretic intelligent tutoring system known as iTutor has been developed, which possesses knowledge associated with first year Engineering Mechanics that is taught at Singapore Polytechnic Simulated students are used to evaluate iTutor because it can cover wide spectrum of abilities and responses effectively and efficiently The evaluations show that iTutor is able to generate tutoring. .. elaborated The formal approach of achieving optimal tutoring policy in polynomial time is formalised in Chapter Four In Chapter Five, the development of iTutor and evaluation of its effectiveness and efficiency is presented Finally, in Chapter Six, the lessons that we can derive from this work and the further directions in decision- theoretic intelligent tutoring system are provided Chapter 1 Introduction Page... sound probabilistic reasoning, decision theory, and item-response model Although decision- theoretic technique has been around for some time, its application in education, especially in computer-based tutoring is uncommon The scope of this research is presented in the following subsections: 1.3.1 Representing Knowledge Structure as Bayesian Networks It is known from expert systems development that knowledge... standard for the tutoring decisions can be achieved After an action is decided, other consequential actions such as which learnable unit to present and which item to use can be determined The utility functions that are formulated according to the learning value for each tutoring action will be discussed in Chapter Four 1.3.3 Application of Item-Response Model to Tutoring For adaptive tutoring to work,... research has been reported in the development of computer programs for effectively teaching students These programs are called Intelligent Tutoring Systems (ITSs) The desire to build ITSs stems from observations of the effectiveness of one-to-one tutoring Presently, one-to-one tutoring is not feasible because the number of students greatly outweighs the number of teachers With the advent of affordable . 1.1 Components of Intelligent Tutoring System 3 1.2 Current Intelligent Tutoring System 5 1.2.1 Inadequate Information on Student’s Mastery State 7 1.2.2 Making Pedagogical Decision Based on. 1.3.2 Decision- theoretic Approach to Computerised Tutoring 9 1.3.3 Application of Item-Response Model to Tutoring 10 1.3.4 Generating Optimal Tutoring Policy 11 1.4 iTutor: A Decision- Theoretic. DECISION- THEORETIC INTELLIGENT TUTORING SYSTEM PEK PENG KIAT M. Sc. (Distinction), The University