Problem Solving: Applying What We Know

1. Chapter 11 Problem Solving Pt. 1 chap 11 Problem solving

2. Problem Solving Using what we know to apply to new situations. Utilizes Procedural Knowledge - How to do things. Can draw on Semantic and Episodic Knowledge but the result is a representation of “How” to accomplish some goal. chap 11 Problem solving

3. What is a Problem? Initial state: where you currently are. Goal state: where you want to be. • goal-directed or purposeful Obstacles Operators: Allowable actions for moving from the initial to the goal state. How many problems have you solved today? chap 11 Problem solving

4. Research Techniques Think Aloud Protocols Problems with this method? Response Times Systematic Errors (misdirection) Problems set-up in such a way that errors will occur that tell us about the cognitive process that people used. chap 11 Problem solving

5. Steps to Problem Solving 1. Recognizing and identifying a problem. chap 11 Problem solving

6. Water Jug Problem Die Hard 2 A clearer description chap 11 Problem solving

7. Well Defined Problems. - have clear Initial and Goal states - have clear set of operators for obtaining the goal state. Tower of Hanoi Problem chap 11 Problem solving

8. Ill-defined Problems Tend to offer incomplete or uncertain means of solution and often may be effectively solved with a multitude of potential solutions Example: from Wertheimer (1945/82) Two boys of different ages are playing badminton. The older one is a more skilled player, and therefore it is predictable for the outcome of usual matches who will be the winner. After some time and several defeats the younger boy finally loses interest in playing, and the older boy faces a problem, namely that he has no one to play with anymore. chap 11 Problem solving

9. 2. Representing the problem - what are the initial and goal states and possible operators. Form a mental model of the problem space. - mental representation of the Initial and Goal states and the allowable operations. For well defined problems it is possible to diagram as tree diagrams or (search trees) that represent all possible set of operations. chap 11 Problem solving

10. For well-defined problems, the problem space can be diagramed and all possible options can be considered. How we represent the problem space can affect our ability to solve a problem. This diagram corresponds to a partial search tree in the middle of a Tic-Tac-Toe game. chap 11 Problem solving

11. Mutilated Chessboard Problem Suppose a standard 8x8 chessboard has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size 2x1 so as to cover all of these squares? Very difficult problem for computers to solve. chap 11 Problem solving

12. The correct answer is that it is not possible to cover the board in dominos. Consider the board with pink and black squares. Each domino must cover both a black and a pink square. On the mutilated board there are 32 black squares but only 30 pink squares. Therefore, it is not possible to cover the board exactly. chap 11 Problem solving

13. A person who simply tries to visualize placing dominos on the board is likely to run into memory difficulties (758,148 permutations). Very few people solve the problem without assistance. chap 11 Problem solving

14. Kaplan and Simon (1990) four versions of this problem: A board filled with blank squares. A board with pink and black squares A board in which the squares were labeled with the words "pink" and "black", instead of the colors themselves. A board in which the squares were labeled with the words "bread" and "butter". chap 11 Problem solving

15. A better way to represent the problem is to include the exact numbers of black and pink squares, plus the information that a domino will cover one of each. This representation becomes increasingly likely with versions 1 - 4 above. Shifting from a naive representation of the problem to the more sophisticated one can be considered an example of restructuring the problem space. chap 11 Problem solving

16. Functional fixedness Two strings are hanging from the ceiling such that the subject cannot grasp both strings at once. The task is to tie them together using the items in the room. Only 39% of subjects solve this problem in under 10 minutes. chap 11 Problem solving

17. Functional Fixedness Failure to solve a problem because we assume from past experience that a given object (e.g., pliers) has only a limited number of uses. chap 11 Problem solving

18. Developing Solutions: Approaches and Strategies. Associationist Approach Trial and Error – over time we associate successful solutions with problems and then use these solutions to solve new problems. - Works alright for small problem spaces, but with large problem spaces it would take a lot of effort (think of the checkerboard problem). chap 11 Problem solving

19. Gestalt Approach Talk aloud problem protocols show that people use more systematic approaches than trail and error. Insight – restructuring the problem space chap 11 Problem solving

20. Insight Problems Answer occurs suddenly “aha” or not at all. Metcalfe and Wiebe (1987) Study – rated “Warmth” (how close to a solution) every 30 secs. Non-Insight problems -knew when they were close. Insight problems - did not know they were close. chap 11 Problem solving

21. Kounios & Beeman (2009) have identified where Insight flashes come from. In the seconds before the insight appears, a brain area in the right temporal lobe (shown here) shows a spike in activity. This region of the ‘right brain’ in particular excels in drawing together distantly related information – exactly what is needed when working on a hard creative problem. This is known as Divergent Thinking chap 11 Problem solving

22. Remote Associates - Tests divergent thinkingCome up with one word that goes with each of words in the following sets. • Falling, Actor, Dust • Coin, Quick, Spoon • Cracker, Union, Rabbit • Rock, Times, Steel chap 11 Problem solving

23. Insight seems effortless and automatic. Analytic problem solving is effected by dual task procedure - but not insight problems (Lavric et al., 2000) Individual differences in WM correlate with analytic problem solving – but not insight problems (Fleck, 2008) People with less focused attention sometimes perform better on tests of insight and creative problem solving (Bowden et al. 2005) chap 11 Problem solving

24. The cheap-necklace problem experiment (Silveira, 1971) “You are given four separate pieces of chain that are each three links in length.  It costs 2¢ to open a link and 3¢ to close a link.  All links are closed at the beginning of the problem.  Your goal is to join all 12 links of chain into a single circle at a cost of no more than 15¢.” chap 11 Problem solving

25. Insight problems are often solved more successfully after taking a break. Incubation effects Each group worked a total of ½ an hour Group 1 - no break: 55% solved the problem. Group 2 - 30 min break: 64% solved the problem Group 3 - 4 hour break: 85% solved the problem chap 11 Problem solving

26. Incubation – taking a break • Sio & Ormerod (2009). Meta-analysis • There is an small but significant incubation effect • Better with divergent thinking tasks. • Longer preparation periods gave a greater effect • Surprisingly, low cognitive demand tasks • yielded a stronger incubation effect than • did rest during an incubation period. chap 11 Problem solving

27. Three ways to restructure a problem • Selective encoding – previously irrelevant information is now seen as relevant. • Selective combination – a new framework is identified (new way of looking at the problem). • Selective comparisons – seeing a nonobvious connection between the current and previous problems. chap 11 Problem solving

28. Negative Transfer Past experience with problems can lead to putting restraints on a problem that do not apply in the current situation. chap 11 Problem solving

29. Nine Dot Problem Draw four straight lines to join all the dots without taking the pen off the page

30. Solution: you can go beyond the borders of the nine dots ’

31. Restructuring often involves relaxing constraints that we have put on a problem space that do not apply in the current situation (e.g., the nine dot problem). Video chap 11 Problem solving

32. The riddle A father and his son are out driving and are involved in a terrible accident. The father is killed instantly, and the son is in critical condition. The son is rushed to the hospital and prepared for an operation that could save his life. The surgeon comes in, sees the patient, and exclaims, “I can’t operate, that boy is my son!” Who is the surgeon? Kids vs. Adults - Who Best Knows the Answer to the Surgeon Riddle? chap 11 Problem solving

33. Chi & Snyder (2012) participants who received tDCS (stimulation) of their anterior temporal lobes were better able to solve the puzzle than those who had ‘sham’ stimulation. They conclude that this effect was “due to inhibiting brain networks associated with top down imposition of prior knowledge, knowledge that inclines us to join the dots up within the square.” chap 11 Problem solving

34. Can brain trauma cause cognitive enhancement? Reverberi et al. (2008) Patients with lateral Frontal Cortex damage solved 82% of "insight"-based task problems (math problems arranged in toothpicks) compared to 43% for healthy controls. Lateral Frontal lobe plays role in imposing constraints. chap 11 Problem solving

35. Can Insight be improved? • Training – but little transfer to real life problems. • Positive mood • Context cues Slepian et al. (2010) 73 college students watched as words were flashed across a computer screen. They viewed 10 words associated with insight — such as create, conceive, and envision —10 other words and 20 non-words. They were then asked to respond as quickly and as accurately as possible if what they were shown was a word or non-word. chap 11 Problem solving

36. The students had either a bare, unshaded incandescent 25-Watt light bulb or an overhead fluorescent light turned on in the room. Volunteers exposed to the light bulb responded quicker to words linked to insight than other words, supporting the notion that light bulbs were indeed connected to insight in their minds. chap 11 Problem solving

37. To see if light bulbs could actually promote insights, Slepian et al. next gave college students spatial, math and verbal problems to solve and had either a bare light bulb or an overhead fluorescent light turned on in the room partway into the problem. The volunteers either solved the problems faster or more often with the light bulb than with the fluorescent light. chap 11 Problem solving

38. Mental Set The tendency to approach situations in a certain way because that method worked in the past. chap 11 Problem solving

39. Luchins’ water-jug experiment (Lurchin 1942, 1959) - Mental Set The subject is given a set of jugs of various stated capacities, and is asked to measure out a desired quantity of water. chap 11 Problem solving

40. All problems except 8 can be solved by B - 2C - A. For problems 1 through 5 this solution is simplest. For problem 7 and 9 the simpler solution is A + C. Problem 8 cannot be solved by B - 2C - A, but can be solved by A - C. Problems 6 and 10 can be solved more simply as A - C. chap 11 Problem solving

41. Subjects who worked through all problems in order: • 83% used B- 2C - A on problems 6 and 7. • 64% failed to solve problem 8. • 79% used B - 2C - A on problems 9 and 10. • Subjects who saw only last 5 problems. • Fewer than 1% used B - 2C - A. • Only 5% failed to solve problem 8. • Past solutions can blind us to better solutions. chap 11 Problem solving

42. Mental Set and the Incubation Effect. Why does taking a break work? Are people working on the problem at some subconscious level without knowing it? Talk aloud protocols (Simon, 1966) After break did not come back with a solution. Instead when they returned to problem after a break, they tended to try new solutions/ Taking a break counteracted mental set effects. chap 11 Problem solving

43. Positive Transfer – enhanced problem solving due to past experience with analogous problems. Using analogies – similarities between past and current problems. chap 11 Problem solving

44. The tumor problem (Duncker, 1945): A doctor wants to destroy a tumor inside a patient's body without damaging the surrounding healthy tissue. There is a device for delivering rays that can destroy the tumor, but at the intensity needed these rays also destroy the surrounding healthy tissue. What should the doctor do? chap 11 Problem solving

45. Reasoning By Analogy Gick & Holyoak’s study on the Tumor and the Fortress problems. The fortress story (Gick & Holyoak, 1980) helps subjects solve the tumor problem. •   Without hearing the fortress story, about 10% of college students solve the tumor problem. • After hearing the fortress story, about 75% of college students solve the tumor problem. chap 11 Problem solving

46. Effectiveness of analogy use. In Gick Holyoaks’s study, the analogy was helpful only when people were explicitly told that the two problems might be related. Context similarity Structural similarity chap 11 Problem solving

47. Context vs. Structural Similarities Students given a set of math word problems and helped to work through the solutions. New problems given (child is told that earlier examples will help). Children often tried to use procedures that applied to problems with similar context (problems about apples) rather than problems with similar form (addition or subtraction). chap 11 Problem solving

48. The Disposable Spill-Proof Coffee Cup Problem (Adapted From Jansson & Smith, 1991) Suppose you are asked to construct an inexpensive, disposable, spill-proof coffee cup. You should construct as many designs as possible, write comments with each design, and number each individual design. There are no constraints in the materials you may want to use. The problems to be addressed are: 1. Leaking of the cup if it tips over 2. Leaking of the cup when squeezed 3. Hot liquid burning the user’s mouth chap 11 Problem solving

49. Can giving examples decrease problem solving? Chrysikou & Weisberg, (2005) Participants were instructed to “think aloud” and were assigned to 1 of 3 conditions: • control (standard instructions), (b) fixation (inclusion of a problematic example, describing its problematic elements), or (c) defixation (inclusion of a problematic example, with instructions to avoid using problematic elements). chap 11 Problem solving

50. This is an example of a present day disposable, spill-proof coffee cup. It is a Styrofoam cup, with a mouthpiece and a straw. The problems in this case are that the straw will leak if the cup tips over and if it is rotated 90° from the angle shown in the diagram; the cup will also leak if it is squeezed, another negative characteristic; finally, the hot liquid emerging uncooled from the straw shown in the example would burn one’s mouth. In your designs TRY TO AVOID: 1. Using straws 2. Using mouthpieces 3. Using an overflow device chap 11 Problem solving