The Essentials of Problem Solving

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?

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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    • Chinese Ring Puzzle (Baguenaudier) --...  

The candle problem visuals:    • The Candle Problem - Legendado  . 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: https://www.imo-official.org/advisory...

Math and STEP problems: https://www.imo-official.org/problems... and https://www.usmle.org/sites/default/f..., 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. https://doi.org/10.1103/PhysRevPhysEd...

Visit www.eternagame.org for more info on Eterna.

The Chess explanation clip: @BetterChessTraining.

The Starcraft 2 clip: an @ESChamp video, here:    • The Science To The Perfect Wall-Off i...  

The go examples come from Sensei’s library: https://senseis.xmp.net/?CornersThenS...

Starcraft 2 map: https://news.blizzard.com/en-us/starc...

Parity example: https://artofproblemsolving.com/wiki/...

The free body diagram is from a Math and Science video:    • Master It!  Free Body Diagrams in Phy...  

The map of Easter Island: https://en.wikipedia.org/wiki/File:Ea...

The cashflow statement: https://en.wikipedia.org/wiki/Cash_fl..., 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. https://www.researchgate.net/profile/...

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. https://www.frontiersin.org/articles/...

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. https://doi.org/10.1027/1618-3169.55....

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).