Benjamin Keep, PhD, JD | The Essentials of Problem Solving @benjaminkeep | Uploaded January 2024 | Updated October 2024, 45 minutes ago.
An introduction to the psychology of problem solving. Featured problems: the towers of Hanoi, the Chinese ring puzzle, the Wason 4-card selection task, the candle problem, Roman matchstick problems, and toothpick shape problems.
00:00 A quick note
00:47 The problem state space and the towers of Hanoi
4:45 Problems of representation and the Chinese ring puzzle
6:42 Context and variations of the Wason 4-card selection task
9:42 Introduction to insight problems: the candle problem
11:05 Differences between insight and incremental problems
12:15 Barriers to insight: Roman matchstick problems
17:30 Insight problems: too big of a distinction?
19:08 Well-structured and ill-structured problems
21:11 Representation and argument
23:34 Becoming a better problem solver: toothpick problems
26:45 Domain-specific knowledge and strategy change
30:55 What transfers across problem-solving domains?
Sign up to my newsletter here: http://www.benjaminkeep.com.
ACKNOWLEDGEMENTS
The towers of Hanoi footage comes from Math Playground's version of the towers.
The Chinese ring puzzle footage comes from Youtuber @Jojikiba, here youtube.com/watch?v=nydIl2VO12I
The candle problem visuals: youtube.com/watch?v=PEvThYxtnFQ. If you made it or you know who did, please let me know. The link above seems to be the oldest and most complete version.
Paul Zeitz photo: imo-official.org/advisory.aspx?year=2019
Math and STEP problems: imo-official.org/problems/IMO2022SL.pdf and usmle.org/sites/default/files/2021-10/Step_1_Sample_Items.pdf, respectively.
Physics problems: Badeau, R., White, D. R., Ibrahim, B., Ding, L., & Heckler, A. F. (2017). What works with worked examples: Extending self-explanation and analogical comparison to synthesis problems. Physical Review Physics Education Research, 13(2), 020112. doi.org/10.1103/PhysRevPhysEducRes.13.020112
Visit eternagame.org for more info on Eterna.
The Chess explanation clip: @BetterChessTraining.
The Starcraft 2 clip: an @ESChamp video, here: youtube.com/watch?v=4okBbHaCQ98
The go examples come from Sensei’s library: senseis.xmp.net/?CornersThenSidesThenCenter
Starcraft 2 map: news.blizzard.com/en-us/starcraft2/23223597/new-ladder-maps-for-2019-season-4
Parity example: artofproblemsolving.com/wiki/index.php?title=Parity
The free body diagram is from a Math and Science video: youtube.com/watch?v=mI11vHsRnC8
The map of Easter Island: en.wikipedia.org/wiki/File:Easter_Island_map-en.svg
The cashflow statement: en.wikipedia.org/wiki/Cash_flow_statement#cite_note-21, but is originally from Epstein, Barry J.; Eva K. Jermakowicz (2007). Interpretation and Application of International Financial Reporting Standards. John Wiley & Sons. pp. 91–97. ISBN 978-0-471-79823-1.
REFERENCES
Simon, H. A., & Newell, A. (1971). Human problem solving: The state of the theory in 1970. American psychologist, 26(2), 145.
The tower of Hanoi state space was adapted from Zhang, J., & Norman, D. A. (1994). Representations in distributed cognitive tasks. Cognitive science, 18(1), 87-122.
The Chinese Ring puzzle state space (for 5 rings) is adapted from Kotovsky, K. & Simon, H. A. (1990). What Makes Some Problems Really hard: Explorations in the Problem Space of Difficulty. Cognitive Psychology, 22(2), 143–183.
The “underage drinking” example of the Wason 4-card task comes from this classic:
Griggs, R. A., & Cox, J. R. (1982). The elusive thematic‐materials effect in Wason's selection task. British journal of psychology, 73(3), 407-420.
A short meta-analysis on the Wason 4-card task: Ragni, M., Kola, I., & Johnson-Laird, P. (2017). The Wason Selection task: A Meta-Analysis. In CogSci. researchgate.net/profile/Ilir-Kola/publication/322682384_The_Wason_Selection_Task_A_Meta-Analysis/links/5a688e6f4585156abdffd541/The-Wason-Selection-Task-A-Meta-Analysis.pdf
On the insight experience: Webb, M. E., Little, D. R., & Cropper, S. J. (2016). Insight Is Not in the Problem: Investigating Insight in Problem Solving across Task Types. Frontiers in Psychology, 7. frontiersin.org/articles/10.3389/fpsyg.2016.01424
The Matchstick Roman numeral problems and the discussion of constraints and chunks come from: Öllinger, M., Jones, G., & Knoblich, G. (2008). Investigating the Effect of Mental Set on Insight Problem Solving. Experimental Psychology, 55(4), 269–282. doi.org/10.1027/1618-3169.55.4.269
On strategic change, see: Siegler, R. S. (2002). Microgenetic studies of self-explanation. Microdevelopment: Transition processes in development and learning, 31, 58.
On the importance of representations in ill-structured domains, see: Chandrasekharan, S., & Nersessian, N. J. (2011). Building cognition: the construction of external representations for discovery. In Proceedings of the Annual Meeting of the Cognitive Science Society (Vol. 33, No. 33).
An introduction to the psychology of problem solving. Featured problems: the towers of Hanoi, the Chinese ring puzzle, the Wason 4-card selection task, the candle problem, Roman matchstick problems, and toothpick shape problems.
00:00 A quick note
00:47 The problem state space and the towers of Hanoi
4:45 Problems of representation and the Chinese ring puzzle
6:42 Context and variations of the Wason 4-card selection task
9:42 Introduction to insight problems: the candle problem
11:05 Differences between insight and incremental problems
12:15 Barriers to insight: Roman matchstick problems
17:30 Insight problems: too big of a distinction?
19:08 Well-structured and ill-structured problems
21:11 Representation and argument
23:34 Becoming a better problem solver: toothpick problems
26:45 Domain-specific knowledge and strategy change
30:55 What transfers across problem-solving domains?
Sign up to my newsletter here: http://www.benjaminkeep.com.
ACKNOWLEDGEMENTS
The towers of Hanoi footage comes from Math Playground's version of the towers.
The Chinese ring puzzle footage comes from Youtuber @Jojikiba, here youtube.com/watch?v=nydIl2VO12I
The candle problem visuals: youtube.com/watch?v=PEvThYxtnFQ. If you made it or you know who did, please let me know. The link above seems to be the oldest and most complete version.
Paul Zeitz photo: imo-official.org/advisory.aspx?year=2019
Math and STEP problems: imo-official.org/problems/IMO2022SL.pdf and usmle.org/sites/default/files/2021-10/Step_1_Sample_Items.pdf, respectively.
Physics problems: Badeau, R., White, D. R., Ibrahim, B., Ding, L., & Heckler, A. F. (2017). What works with worked examples: Extending self-explanation and analogical comparison to synthesis problems. Physical Review Physics Education Research, 13(2), 020112. doi.org/10.1103/PhysRevPhysEducRes.13.020112
Visit eternagame.org for more info on Eterna.
The Chess explanation clip: @BetterChessTraining.
The Starcraft 2 clip: an @ESChamp video, here: youtube.com/watch?v=4okBbHaCQ98
The go examples come from Sensei’s library: senseis.xmp.net/?CornersThenSidesThenCenter
Starcraft 2 map: news.blizzard.com/en-us/starcraft2/23223597/new-ladder-maps-for-2019-season-4
Parity example: artofproblemsolving.com/wiki/index.php?title=Parity
The free body diagram is from a Math and Science video: youtube.com/watch?v=mI11vHsRnC8
The map of Easter Island: en.wikipedia.org/wiki/File:Easter_Island_map-en.svg
The cashflow statement: en.wikipedia.org/wiki/Cash_flow_statement#cite_note-21, but is originally from Epstein, Barry J.; Eva K. Jermakowicz (2007). Interpretation and Application of International Financial Reporting Standards. John Wiley & Sons. pp. 91–97. ISBN 978-0-471-79823-1.
REFERENCES
Simon, H. A., & Newell, A. (1971). Human problem solving: The state of the theory in 1970. American psychologist, 26(2), 145.
The tower of Hanoi state space was adapted from Zhang, J., & Norman, D. A. (1994). Representations in distributed cognitive tasks. Cognitive science, 18(1), 87-122.
The Chinese Ring puzzle state space (for 5 rings) is adapted from Kotovsky, K. & Simon, H. A. (1990). What Makes Some Problems Really hard: Explorations in the Problem Space of Difficulty. Cognitive Psychology, 22(2), 143–183.
The “underage drinking” example of the Wason 4-card task comes from this classic:
Griggs, R. A., & Cox, J. R. (1982). The elusive thematic‐materials effect in Wason's selection task. British journal of psychology, 73(3), 407-420.
A short meta-analysis on the Wason 4-card task: Ragni, M., Kola, I., & Johnson-Laird, P. (2017). The Wason Selection task: A Meta-Analysis. In CogSci. researchgate.net/profile/Ilir-Kola/publication/322682384_The_Wason_Selection_Task_A_Meta-Analysis/links/5a688e6f4585156abdffd541/The-Wason-Selection-Task-A-Meta-Analysis.pdf
On the insight experience: Webb, M. E., Little, D. R., & Cropper, S. J. (2016). Insight Is Not in the Problem: Investigating Insight in Problem Solving across Task Types. Frontiers in Psychology, 7. frontiersin.org/articles/10.3389/fpsyg.2016.01424
The Matchstick Roman numeral problems and the discussion of constraints and chunks come from: Öllinger, M., Jones, G., & Knoblich, G. (2008). Investigating the Effect of Mental Set on Insight Problem Solving. Experimental Psychology, 55(4), 269–282. doi.org/10.1027/1618-3169.55.4.269
On strategic change, see: Siegler, R. S. (2002). Microgenetic studies of self-explanation. Microdevelopment: Transition processes in development and learning, 31, 58.
On the importance of representations in ill-structured domains, see: Chandrasekharan, S., & Nersessian, N. J. (2011). Building cognition: the construction of external representations for discovery. In Proceedings of the Annual Meeting of the Cognitive Science Society (Vol. 33, No. 33).
