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 epogossi@aua.am Sedrak Grigoryan addressforsd@gmail.com

1.Why Tutoring and what we did

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 ?

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

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

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

1. RGT Problems

Unsolved combinatorial problems կ Unsolved combinatorial problems Unsolved problems RGT Tutoring Solving by Modeling Human Approaches Interpreting unsolved problems by solved ones Solved problems

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

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

2. RGT Solvers

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

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

3. Modeling Tutoring

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

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

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

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

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

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.

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

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

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

4.Adequacy of Models of Tutoring

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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

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

5. Conclusion

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 3. 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

Thank You !

4. Advances in RGT Solutions

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

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

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

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 .

Stilman B., USA

Modeling Chess Tutoring by RGT Solver

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

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?

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

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.

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

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

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.