Problem Solving

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2. Outline. How problem solving worksProblem solving as restructuringProblem solving as searchProblem solving through analogiesHow experts solve problemsCreative cognitionProblem solving and the brain. . 3. What is an analogy?. Analogies occur when there are parallels between two different situationsAnalogical problem solving is a way to restructure a problem in a parallel fashionUse solution to one problem to solve another.

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Problem Solving

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1. 1 Problem Solving

2. 2 Outline How problem solving works Problem solving as restructuring Problem solving as search Problem solving through analogies How experts solve problems Creative cognition Problem solving and the brain

3. 3 What is an analogy? Analogies occur when there are parallels between two different situations Analogical problem solving is a way to restructure a problem in a parallel fashion Use solution to one problem to solve another

4. 4 The importance of how a problem is stated Sometimes, figuring out where to start is the toughest Kaplan & Simon (1990) - Mutilated checkerboard problem

5. 5 Mutilated Checkerboards A checkerboard consists of 64 squares. These squares can be completely covered by placing 32 dominos on the board so each covers two squares. If we eliminate two opposing corners, can we cover the remaining squares with 31 dominos? What do you think the answer is?What do you think the answer is?

6. 6 Kaplan & Simon Methods 4 groups, each receive different condition

7. 7 Goal: Parity Representation Insight: Laying down a domino must cover different squares (black & pink, never black & black) When you remove two corners, you remove two like squares The answer? No, 31 dominos will not cover the board

8. 8 How most people do this Started with 64 squares, took 2 away. 62 / 2 = 31, so 31 dominos should do it. Then when they try it on paper, it doesn’t work. Try utilizing the words on the paper Notice domino covers bread and butter Also notice two breads were removed Come to the correct conclusion

9. 9 Kaplan & Simon Results Bread & butter group solved the problem twice as fast as blank group Bread & butter group: 1 hint Blank group: 3.14 hints Color and pink & black groups: In between blank and bread & butter

10. 10 What does this show? The Gestalt idea of restructuring a problem - Insight! This can also be achieved through analogy…

11. 11 Telling an analogous story In a small village, there were 32 bachelors and 32 unmarried women. The matchmaker succeeded in arranging 32 satisfactory marriages. Then one drunken night, two bachelors, in a test of strength, killed each other. Can the matchmaker come up with 31 heterosexual marriages among the 62 survivors?

12. 12 Duncker’s Radiation Problem Malignant Tumor with ray to destroy it Ray of proper intensity to destroy tumor will also destroy healthy tissue Ray of intensity to not destroy healthy tissue will not destroy tumor What do you do?

13. 13 Did you solve it? What about a story called “The General”?

14. 14 How about now? Figure 11.16b (p. 409) (b) Solution to the radiation problem. Bombarding the tumor, shown in the center, with a number of low-intensity rays from different directions destroys the tumor without damaging the tissue it passes through.Figure 11.16b (p. 409)(b) Solution to the radiation problem. Bombarding the tumor, shown in the center, with a number of low-intensity rays from different directions destroys the tumor without damaging the tissue it passes through.

15. 15 This is actually how it’s done! Figure 11.16c (p. 409) (c) Radiosurgery, a modern medical technique for irradiating brain tumors with a number of beams of gamma rays, uses the same principle. The actual technique uses 2001 gamma-ray beams.Figure 11.16c (p. 409)(c) Radiosurgery, a modern medical technique for irradiating brain tumors with a number of beams of gamma rays, uses the same principle. The actual technique uses 2001 gamma-ray beams.

16. 16 The General’s Radiation Problem The stories are analogous Source problem: The General Source because you were given the solution Target problem: Radiation problem Fits in with idea of restructuring

17. 17 Gick & Holyoak (1980) Did a study with the radiation problem and The General story Only 10% could solve the radiation problem with no help After hearing “The General”, another 30% could solve it When hinted that two stories were related, 75% of people got the answer

18. 18 Hearing the story is not enough Three steps to understand analogy between problems Noticing the analogous relationship Mapping the correspondence between source and target problems Applying the mapping to generate a parallel solution

19. 19 Schemas and analogies Can you induce subjects to create a “problem schema”? They could activate it - a process called “schema induction” Gick & Holyoak tested this process

20. 20 Gick & Holyoak (1983) Methods Participants read two of four stories The General The Fire Chief Two others Then asked to describe their similarities Finally asked to solve the radiation problem

21. 21 Schema classification: Good Both stories used the same concept to solve a problem, which was to use many small forces applied together to add up to one large force necessary to destroy the object. 21%

22. 22 Schema classification: Intermediate and Poor Intermediate: In both cases, many small forces were used. 20% Poor: In both stories, the hero was rewarded for his efforts. 59%

23. 23 Gick & Holyoak Results Figure 11.18 (p. 413) Results of Gick and Holyoak’s (1983) schema-induction experiment, showing that participants who developed good schemas by reading two stories, were more likely to solve a target problem than those who did not develop good schemas.Figure 11.18 (p. 413)Results of Gick and Holyoak’s (1983) schema-induction experiment, showing that participants who developed good schemas by reading two stories, were more likely to solve a target problem than those who did not develop good schemas.

24. 24 So what can we say? Note how only 21% of people created good schemas We’re still not fully aware of what happens during problem solving But we understand how to make it better Through practice and training

25. 25 Outline How problem solving works Problem solving as restructuring Problem solving as search Problem solving through analogies How experts solve problems Creative cognition Problem solving and the brain

26. 26 Experts are good at solving problems Experts: People who, through intensive study, have become acknowledged as being knowledgeable about their field They solve problems in their field better and faster than novices Why?

27. 27 Experts Possess More Knowledge About Their Fields Chase & Simons chess chunking study Experts can chunk common game pieces together Able to remember more chess pieces NOT if chess pieces are randomized Novices cannot chunk Could not remember many chess pieces

28. 28 Chess experts vs. novices Chess experts (more than 10,000 hours of play) 50,000 chess patterns in memory Chess novices 1,000 chess patterns in play Poor players Few or none

29. 29 Experts’ Knowledge is Organized Differently Chi et al. (1982) - Give 24 physics problems to experts (professors) and novices (students with one semester of physics) Ask each group to organize them

30. 30 Chi et al. Results

31. 31 Experts Spend More Time Analyzing Problems An expert will try to understand the problem and underlying concepts before diving in Example: Drawing a picture before writing equations

32. 32 Experts Are No Better Outside of their Domain Voss et al. (1983) - Gave a problem involving Soviet agriculture to 3 groups Expert political scientists Novice political scientists Expert chemists Only the expert political scientists solved the problem well

33. 33 Experts do not always know best Younger scientists are often responsible for revolutionary discoveries (Kuhn, 1970; Simonton, 1984) Experts are worse than novices at situations that require flexible thinking (Frensch & Sternberg, 1989) Good news for me!

34. 34 Outline How problem solving works Problem solving as restructuring Problem solving as search Problem solving through analogies How experts solve problems Creative cognition Problem solving and the brain

35. 35 Creativity is important to PS The basics of creativity is not well-studied How do you study it? But some research has shown how good we are at it

36. 36 Finke’s Object Creation Task Pick three numbers

37. 37 Now create your object Construct a new object using these three parts Should be interesting and possibly useful Should NOT correspond to a familiar object Vary size, position, orientation, and materials of the parts NOT the shape (except for wire and tube) When you’re ready, draw a picture of it

38. 38 You’ve made a preinventive form Now, for each of these categories, imagine how your object could be used Furniture Transportation Toys and games Personal items

39. 39 An example from a subject

40. 40 Finke Results A panel of judges rated 360 created objects 120 were rated as “practical inventions” 65 were rated as “creative inventions” Anyone can be creative - you don’t need training or even practice

41. 41 Divergence & Creativity Divergent thinking - Open-ended, no “correct” answer Convergent thinking - One “correct” answer to a problem

42. 42 Divergent Thinking Creativity tests employ divergent thinking Asking participants to determine as many uses as possible for familiar objects like bricks Correlation between tasks claiming to measure creativity are modest (Guilford, 1967)

43. 43 Outline How problem solving works Problem solving as restructuring Problem solving as search Problem solving through analogies How experts solve problems Creative cognition Problem solving and the brain

44. 44 Imaging the brain during chess Nichelli et al. (1994) Asked questions like “Can the white knight capture the black rook?”

45. 45 Playing Chess & the Brain

46. 46 Wow, that’s a lot of brain It’s not surprising that complex problem solving needs a lot of the brain But what’s new is the planning and executing strategies This requires the prefrontal cortex

47. 47 Prefrontal Cortex, eh? Damage to the PFC causes perseveration Patients cannot switch from one pattern of behavior to another Wisconsin Card Sorting Task

48. 48 WCST Example

49. 49 What’s the catch? The sorting rules change after some number of trials So first it’s color, and then it’s color for the next 15 cards But then it switches to shape The research question: How long does it take someone to switch?

50. 50 Common WCST Results Normal people: Takes 2-3 tries to figure out the new rule People with PFC damage: Is often unable to figure out the new rule Usually stick with the old rule Unable to change previous behavioral pattern

51. 51 The Prefrontal Cortex is used in Control of strategies Planning Reasoning Integrating information Dorsolateral Prefrontal Cortex (DLPFC) Is it the central executive? Hmmm…

52. 52 The Prefrontal Cortex is used in Personality and emotional regulation Ability to delay gratification Other parts of the PFC (orbitofrontal cortex) used in emotional regulation Phineas Gage

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