1. Personalized Interactive Tutoring in Chess
Department of Computational and Cognitive Networks
Academy of Sciences of Armenia
Institute for Informatics and Automation Problems
Personalized Interactive Tutoring in Chess
Edward Pogossian
Sedrak Grigoryan

2. 1.Why Tutoring and what we did

3. Actuality:
- basic knowledge is passed to descendents only first hand
- students learn in different ways
- unordinary students: require personalized approach
Premises:
- advances in computer sciences => make possible
personalized interactive tutoring and examining
- certain types of exams can be interpreted as game problems
Questions
How to provide experts with adequate computer tutoring tools?
How to examine the acquisition of knowledge ?

4. What we did: 1. We provide experts with a computer tutoring tool based on solvers of chess-like games 2. The adequacy of our models rely on consistency of knowledge presentation and processing with ones in English and experiments in tutoring chess endgames

5. 3. Effectiveness of learning by tool is measured in scales and by methodology consistent with ones of experts 4. Solvers of chess like games can be a base for effective tutoring 5. Tutoring tools have to be developed in close cooperation of all parties involved in education and cognitive modeling

6. How we did. 1. RGT Problems 2. RGT Solvers 3. Modeling Tutoring 4
How we did? 1. RGT Problems 2. RGT Solvers 3. Modeling Tutoring 4. Adequacy of Models of Tutoring 5.Conclusion

7. 1. RGT Problems

8. Unsolved combinatorial problemsկ
Unsolved combinatorial problems
Unsolved problems
RGT
Tutoring
Solving by Modeling Human
Approaches
Interpreting unsolved problems by solved ones
Solved problems

9. RGT Problems Meet the Following Requirements
Game Tree
There are Interacting Actors 2.
Actors may perform actions
Action1
Action2 1. 3.
There are specified types of situations
Situation1
Situation2
Some situations are selected as Goals 4.
Situation1
Situation2
Actors’ Actions transform Situations 5.
Sit1
Sit2
Sit3
Action2
Action1
Soric araj berel RGT dasi masin 2 slide

10. Anomalies detection in computations Defense of Military Units
RGT Class of Problems
RGT
Intrusion Protection
Problems of Testing
Chess
Kernel
Management
Anomalies detection in computations
Defense of Military Units

11. 2. RGT Solvers

12. Strategy Search in RGT Solvers
Input Situation
Actions
Goals
Goal1
G1/A
G1/B
G1/C

13. RGT Solvers Controller Store of Abstracts, Goals, Plans Store of
T-Prints
Graph of Abstracts
Abstract Matcher
GUI
Abstracts Acquirer
Matching Visualizer
T-Prints Perceiver
Problem Manager A1 A2 A3 A5
A41 A6
Abstracts
Sub1
Sub2
Classifier
Method,
[0/1], Name
List of Attributes
T-Print
PPIT
CPMU GP
RHP
Acquirer
Knowledge Revealer
Actions by Moves

14. 3. Modeling Tutoring

15. How Experts Are Tutoring ?
1. Student has certain level of knowledge (e.g. knows chess basic rules)
2. Teaches for unknown chess concepts required for the solution
3. Teaches for the plan to play (e.g. Push king to an edge, make opposition and put mate)
Level i+1
CheckMate
Level i
King can’t escape
King under check
King has no defense

16. Personalized Interactive Tutoring Environment Based on RGT Solver
RGT Knowledge models Adequate to Expert
Strategy Search Algorithms Adequate to Expert Approach
Adequate to
Tutoring by RGT expert
RGT Expert

17. Tutoring Environment
Student has background of understanding chess, figures, colors (black and white), board, moves
Tutoring for Chess Concepts
Tutoring for Strategies
1. Explanation of Chess Concepts
1. Explanation of Plans and Goals
2. Providing examples of chess concepts
2. Providing examples of performances of plans
Թվարկում ենք էն մինիմալ գաղափարները որոնք որ պետք է պարտադիր իմանա ուսանողը
Մենք ընդունում ենք որ I մակարդակը գիտի եւ անցնում ենք i+1 մակարդակ
Պետք է նշել ուսուցչի ուսուցման եղանակը՝ էսօրվա դասը՝ ուսուցիչը անցնում է I մակարդակից i+1 մակարդակ: Նա համոզվում է որ ուսանողը ունի I մակարդակը նոր անցնում է էդ մակարդակ,
3. Testing of understanding

18. RGT Solvers in Tutoring
Tutoring Environment
Interfaces for
Integration of RGT problems
Feedback provision mechanisms to identify bad described RGT knowledge (for improvement purposes)
Testing of RGT knowledge
Tutoring Protocol
RGT Solver
Generation of Testing Situations
Chess Tutoring Interface
Tool for measuring the progress of students
Explanations of Classifiers and Strategies
Generation of Examples
Future Steps
Partially completed
Completed

19. Chess concepts explanation
1. Different levels of explanations
CheckMate
King can’t escape
King under check
King has no defense
Field under check
Field under check of Knight
Field under check of Knight1
King
Field
Figure
King Type
White or Black
Not empty type X Y
Figure Type
Figure Color

20. RGT Solvers provide: - Models of RGT knowledge -Strategy search algorithms -Tutoring protocols
Tutoring is
Personalized
Interactive
level by level explanation,
testing, feedback provision and correction,
assessment of the progress of students.

21. Explanation of plans and goals
Abstract1
Plan1
Precondition
Goal2
Abstract2
Postcondition
Goal4
Goal1
Evaluator

22. Providing an example of performances of plans
Goal2
Precondition
Plan1
Postcondition
Goal2
Goal4
Evaluator
Goal1
Goal1
Precondition
Actions
Postcondition
Evaluator

23. Testing of Acquisition
RGT Solver
Plan
Plan
Action 1
Action 1
Correct
Action 2
Action 4
Wrong, Explain
Action 3
Action 3
Correct

24. 4.Adequacy of Models of Tutoring

25. Knowledge-based Solvers have Effectiveness and Efficiency (EE) comparable with experts
minimax Solvers provide the idea of max Effectivenes, but not acceptable joint EE
minimax Solvers with parametric evaluation functions
Knowledge Based Solvers
Search by minimax, parametric
evaluation function
Solving by Modeling Human
Approaches, Expert Systems
Botvinnik, Pitrat, Wilkins: Parametric methods are not adequate for combinatorial problems

26. Categories of English Verbs
“Have, Be, Do” (HBD) knowledge presentation in English and in the model are consistent
Have,
Possess,
Own,… Do
English Verbs
Be, Exist,…
Categories of english verbs
Be, exist
Have, possess, own Do

27. HBD model is consistent with OOP
4. Is inherited from another abstract
1. Abstract Name
2. Has attributes
3. Does actions

28. Advantages of HBD Models
Property
OOP
Ont.
Pr.S.
HBD
Represent different type of knowledge + -
Opacity
Reuse
Polymorphism
Inheritance
Matching data to the entities (rules, classes etc.)
Dynamically change class hierarchies
Dynamically generate/integrate new entities

29. Personalized Planning and Integrated Testing (PPIT) 2007
RGT Solvers are able to process complex knowledge in solving RGT Problems
Reti etude: draw
Nadareishvilli etude: winning
Botvinnik suggested tests for measuring the program’s quality: the Reti and Nodareishvili chess etudes
Personalized Planning and Integrated Testing (PPIT) 2007

30. By exhaustive search Nadareishvili etude can be solved only with the depth of 36 in the game tree search while experts and RGT Solver solve it analyzing about 500 positions

31. Tutoring Rock vs. King
Explanation of the winning strategy in Rock against King endgames:
Put mate
Avoid stalemate
Escape rook from attack
Push king to the edge (without putting rook under attack)
Make a waiting move when preOpposition appears
Bring white king closer to the opponent king

32. The Plan of Rook vs King :
Put mate
Avoid stalemate
Escape rook from attack
Push king to the edge (without putting rook under attack)
Make a waiting move when preOpposition appears
Bring white king closer to the opponent king

33. 1st step: Explanation of Goals:
RGT Solver
Explain
Plan 1 =
1. “mate” concept 2
2. “stalemate” concept 3
3. “rook under attack”
4. “edge”, “push king to the edge” 4
5. “Pre Opposition”, “waiting move” concepts 5
6. “Opposition” 6

34. 3. Escape Rook from the Attack
Rook under attack
Rook
Field under attack
Field under attack of King
Field under attack of Knight
Field under attack of King1
Field under attack of King8

35. 4. Push King to the edge (without putting Rook under Attack)
EdgeVertical
EdgeHoirzontal
1. King is maximal close to edge
2. King has less moves

36. 5. Make a waiting move when pre Opposition appears
1. Rook distance is maximal by the vertical/horizontal

37. 6. Bring white King closer to the black King (avoid opposition)
Oppostion
Oppostion by vertical
Oppostion by horizontal
Oppostion by horizontal 1
Oppostion by horizontal 2
1. Distance between kings is minimal

38. 2nd step: Example of Execution of Plans:
RGT Solver
Plan 1 = 2
1. Put Mate
2. Avoid Stalemate 3
3. Escape rook from attack 4
4. Push king to the edge
Move R g5 selected 5 6
Similarly next situations are processed and explained

39. 3rd step: Examining Understanding of Plans:
RGT Solver
Plan 1 = 2
1. Put Mate
Plan
2. Avoid Stalemate 3
3. Escape rook from attack
K e3 move is performed by student
4. Push king to the edge 4
5. Make a waiting move 5
6. Bring king closer to opponent 6
Selected K e3 move is correct
Similarly next situations are checked, if wrong, corrected and explained as in (1,2 steps)

40. Measuring Progress of Students
Knowledge-Based Solvers against Knowledge-Based Solvers
Knowledge-Based Solvers against Experts (students)
Experts (students) against Experts (students)

42. Chess ratings based scales and methodlogy of the quality of RGT Solvers are developed Strong measurement of quality of modifications of RGT Solvers and their constituents

43. 5. Conclusion

44. 1. We provide experts with a computer tutoring tool based on the RGT Solvers 2. The adequacy of model of tutoring to one of experts was successfully examined Adequate scales and methodology were developed to measure the effectiveness of tutoring 4. RGT Solvers are the base for effective models of tutoring 5. Development of effective tutoring tools needs close cooperation of educators and cognitive modelers

45. Thank You !

46. 4. Advances in RGT Solutions

47. Confirming Adequacy of Models of RGT Knowledge and Matching Algorithms
It was confirmed for:
Chess
Marketing
Intrusion Protection

48. Advances in RGT Solutions
Strongly specified RGT class of problems
Chess ratings based scales of the quality of RGT Solvers
Advances in solving particular RGT problems are interpretable for RGT class: unified Solvers can be constructed
Knowledge-based Solvers can provide EE comparable with human experts (Botvinnik: Parametric methods are not adequate for combinatorial problems)
Knowledge consist of Strategies (regularities), Classifiers of situations, Goals and Plans
RGT Knowledge is constructive and can be simulated

49. RGT Knowledge-Based Solvers overcome RGT minimax Sovlers by EE.
IGAF1 and IGAF2 RGT Solvers Based on Common Planning vs Minimax Solvers Diagram (in Intrusion Protection)
Number of nodes searched by the IGAF2 algorithm compared with the IGAF1 algorithm and the minimax

50. Single Ownship Against Air Threats
Ownship and air threats as actors
Situation with ownship and threads in certain distance range.
Ownship goal: to defend, air threats goal: to make damage
Actions of ownship : A. launch a long range surface-air missile (SAM), B. shoot the medium range gun C. shoot the short range gun.
Actions for threats: an anti-ship missile .

51. Stilman B., USA

52. Modeling Chess Tutoring by RGT Solver

53. Personalized Interactive Tutoring by RGT Solvers
Actuality of Personalized Tutoring
RGT Solver based Tutoring
Tutoring Environment:
Tutoring for classifiers
Tutoring for strategies
Measuring the progress of students
Confirmation of Adequacy of Tutoring
Applications գրել, տուտոռինգը տալ վերջում, ստեղ չտալ

54. Questions Actuality: - students learn in different ways
- unordinary students:
require personalized approach (e.g. autistic children)
Premises:
- advances in computer sciences => make possible
personalized interactive tutoring and testing
- certain types of exams can be interpreted as RGT problems
Questions
How to provide tutoring of classifiers and strategies adequate to experts ?
How to examine acquisition of knowledge adequate to experts?

55. Personalized Interactive Tutoring Environment Based on RGT Solver
RGT Knowledge models Adequate to Expert
Strategy Search Algorithms Adequate to Expert Approach
Adequate to
Tutoring by RGT expert
RGT Expert

56. RGT Solver In Tutoring RGT Solvers provide Tutoring is Personalized
Models of RGT knowledge
Strategy search algorithms
Tutoring protocols
Tutoring is
Personalized
Interactive
level by level explanation,
testing, feedback provision and correction,
assessment of the progress of students.

57. RGT Solvers In Tutoring
Tutoring Environment
Interfaces for
Integration of RGT problems
Feedback provision mechanisms to identify bad described RGT knowledge (for improvement purposes)
Testing of RGT knowledge
Tutoring Protocol
RGT Solver
Generation of Testing Situations
Chess Tutoring interface
Tools for Measuring the Progress of Student
Explanations of Classifiers and Strategies
Generation of Example

58. Tutoring for concepts
Tutoring for strategies
Examples for knowledge
Testing of knowledge

59. Conclusion
Methods and software for tutoring to chess are developed within RGT Solver. The approach gives the following advantages:
The mechanism of tutoring is personalized for each student.
Level by level tutoring, testing are provided in the interactive environment.
Students’ performance measurement means are provided in the developed interface tool.