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An Experiment in Students’ Acquisition of Problem Solving Skill from Goal-Oriented Instructions

An Experiment in Students’ Acquisition of Problem Solving Skill from Goal-Oriented Instructions. Matej Guid 1 , Jana Krivec 2 , Ivan Bratko 1. Artificial Intelligence Laboratory Faculty of Computer and Information Science , University of Ljubljana, Slovenia and

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An Experiment in Students’ Acquisition of Problem Solving Skill from Goal-Oriented Instructions

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  1. An Experiment in Students’ Acquisition of Problem Solving Skill fromGoal-Oriented Instructions Matej Guid1, Jana Krivec2, Ivan Bratko1 Artificial Intelligence Laboratory Faculty of Computer and Information Science, University of Ljubljana, Slovenia and DepartmentofIntelligentSystems Jožef Stefan Institute, Ljubljana, Slovenia COGNITIVE 2012

  2. Outline Part I Chunks in declarative knowledge vs Chunks in procedural knowledge Part II Conceptualization of domain knowledge: how the goal-oriented instructions were obtained Part III The experiment in students’ acquisition of problem solving skill from goal-oriented Instructions

  3. Chunks in Declarative Knowledge • CHUNKS IN DECLARATIVE KNOWLEDGE • completed units of logically related information clusters • facilitate retrieval and use • better utilization of limited working memory capacity pioneer works of De Groot, Simon, Chase, Gobet etc. used chess as a domain of choice... real-game position randomly shuffled pieces reconstructing chess positions Gobet et al. (2001) Seedetails in GobetF. et al. Chunkingmechanisms in human learning .Trends in CognitiveSciences, 2001.

  4. Chunks in Declarative Knowledge • CHUNKS IN DECLARATIVE KNOWLEDGE • completed units of logically related information clusters • facilitate retrieval and use • better utilization of limited working memory capacity • COMMONLY ACCEPTED pioneer works of De Groot, Simon, Chase, Gobet etc. used chess as a domain of choice... LETTERS OR WORDS? chunks in declarativeknowledge egdelwonkevitaralced ni sknuhc CHREST (Chunk Hierarchy and Retrieval STructures) & domain of chess familiar placements of groups of pieces Seedetails in GobetF. et al. Chunkingmechanisms in human learning .Trends in CognitiveSciences, 2001.

  5. What About Chunks in Procedural Knowledge? • CHUNKS IN PROCEDURAL KNOWLEDGE • We attempt to: • show the existence of chunks in procedural knowledge, • define chunks in procedural knowledge – “procedural chunks” • see how they are incorporated in ones memory. X LITTLE KNOWN People learn procedural knowledge by (sub-consciously) constructing meaningful units of procedural knowledge. Our previous study:reconstructing chess gamesKrivec, Guid & Bratko (2001) Current work: chess beginners were playing chess games against a computer • A PROCEDURAL CHUNK IN CHESS • a sequence ofchess moves that all together belong to a chess concept • memorized by a player as a whole. Krivec J., Guid M. & Bratko I. Identification and Characteristic Descriptions of Procedural Chunks. COGNITIVE 2009.

  6. How Could a World Champion Blunder a Mate in one? Deep Fritz – Kramnik Man vsMachine, Bonn 27.11.2006 A rare pattern with white knight on f8 and black king on h8? • If the last two moves were 1.Ng6-f8++ Kh7-h8, • wouldn’t it be “impossible” not to see 2.Qe4-h7#? position after 34... Qa7-e3, allowing 35.Qe4-h7# Kramnik in the press conference: "It was actually not only about the last move.I was calculating this line very long in advance, and then recalculating. ........ I was feeling well, I was playing well, I think I was pretty much better. I calculated the line many, many times, rechecking myself... It's just very strange, I cannot explain it." Chessbase.com: How could Kramnik overlook the mate? http://www.chessbase.com/newsdetail.asp?newsid=3512

  7. The Mechanism of “Einstellung” Effect EXAMPLE: THE EINSTELLUNG EFFECT IN CHESS EXPERTS Bilalić, McLoud, Gobet (2010) expert chess players were asked to find the shortest solution: 1st solution: smothered mate (5 moves) 2nd solution: less familiar (3 moves) smothered mate (before: 1st solution) not possible anymore! Bilalić B. etal. TheMechanismofEinstellung (Set) Effect. CurrentDirectionsofPsychologicalScience, 2010.

  8. Procedural Chunks in Chess A “simple” solution...

  9. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Nf7+ Kg8 3. Nh6++ Kh8 4. Qg8+ Rxg8 5. Nf7#

  10. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Nf7+ Kg8 3. Nh6++ Kh8 4. Qg8+ Rxg8 5. Nf7#

  11. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Nf7+ Kg8 3. Nh6++ Kh8 4. Qg8+ Rxg8 5. Nf7#

  12. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Nf7+ Kg8 3. Nh6++ Kh8 4. Qg8+ Rxg8 5. Nf7#

  13. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Nf7+ Kg8 3. Nh6++ Kh8 4. Qg8+ Rxg8 5. Nf7#

  14. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Nf7+ Kg8 3. Nh6++ Kh8 4. Qg8+ Rxg8 5. Nf7#

  15. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Nf7+ Kg8 3. Nh6++ Kh8 4. Qg8+ Rxg8 5. Nf7#

  16. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Nf7+ Kg8 3. Nh6++ Kh8 4. Qg8+ Rxg8 5. Nf7#

  17. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Nf7+ Kg8 3. Nh6++ Kh8 4. Qg8+ Rxg8 5. Nf7#

  18. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Nf7+ Kg8 3. Nh6++ Kh8 4. Qg8+ Rxg8 5. Nf7#

  19. Procedural Chunks in Chess … and a “difficult” solution

  20. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Qh6

  21. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Qh6

  22. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Qh6

  23. Procedural Chunks in Chess 1. Qe6+ Kh8 2. Qh6

  24. Procedural Chunks in Chess Whatmakesthedifference in cognitivedifficultyoffindingthetwosolutions? “easy” “difficult”

  25. Conceptualization of Procedural Knowledge path: requires excessive computation, difficult to memorize ORIGINAL THEORY • ....................................................................... PROBLEM SOLUTION axioms laws formulas rules of the game … CONCEPTUALIZEDDOMAIN THEORY DECLARATIVE KNOWLEDGE PROCEDURAL KNOWLEDGE WHAT? HOW? basic domain knowledge goal-oriented rules Možina M. et al. Goal-oriented conceptualization of procedural knowledge. Conference on Intelligent Tutoring Systems, 2012.

  26. Conceptualization of Procedural Knowledge path: requires excessive computation, difficult to memorize ORIGINAL THEORY • ....................................................................... PROBLEM SOLUTION axioms laws formulas rules of the game … CONCEPTUALIZEDDOMAIN THEORY DECLARATIVE KNOWLEDGE PROCEDURAL KNOWLEDGE WHAT? HOW? basic domain knowledge goal-oriented rules Možina M. et al. Goal-oriented conceptualization of procedural knowledge. Conference on Intelligent Tutoring Systems, 2012.

  27. Conceptualization of Procedural Knowledge path: requires excessive computation, difficult to memorize ORIGINAL THEORY • ....................................................................... PROBLEM SOLUTION axioms laws formulas rules of the game … CONCEPTUALIZEDDOMAIN THEORY DECLARATIVE KNOWLEDGE PROCEDURAL KNOWLEDGE basic rules of chess piece movements the 50-move rule … the “right” corner concept basic strategy … • procedures: IF-THEN rules • simple and compact rules • easy to memorize • … • intuitive knowledge • intermediate goals • … Možina M. et al. Goal-oriented conceptualization of procedural knowledge. Conference on Intelligent Tutoring Systems, 2012.

  28. Problem State Space start node . . . . . . (too) long solution path : : : : : : . . . goal nodes

  29. Learning Intermediate Goals start nodes of intermediate goals . . . . . . goal nodes of intermediate goals : : : : : : . . .

  30. Conceptualization of Domain Knowledge: Chess Endgame KBNK – the most difficult of elementary chess endgames: several recorded cases when even grandmasters failed to win the result of conceptualization: Hierarchy of (only) 11 GOALS http://www.ailab.si/matej/KBNK/ example games with goal-oriented instructions goal-oriented instructions

  31. Teaching Materials (1): Textbook Instructions

  32. Teaching Materials (2): Example Games with Goals

  33. A Grandmaster Failed to Win ... A grandmaster of chess failed to win the following endgame…

  34. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001 “wrong corner” “right corner”

  35. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  36. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  37. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  38. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  39. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  40. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  41. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  42. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  43. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  44. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  45. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  46. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  47. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  48. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  49. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

  50. A Grandmaster Failed to Win ... GM Kempinski (white) – GM Epishin (black), Bundesliga2001

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