Memory and Cognition

1. Memory and Cognition PSY 324 Topic: Problem Solving Dr. Ellen Campana Arizona State University

2. Outline • The Gestalt Approach: • Describe problem solving as involving a process called restructuring. • The Information-processing Approach: • Describe problem solving as involving search. • Analogies: • A method that combines elements of both restructuring and search. • Experts and nonexperts: • Creative thinking:

3. Gestalt Approach

4. What Is a Problem? • A problem occurs when there is an obstacle between a present state and a goal, and it is not immediately obvious how to get around the obstacle (Lovett, 2002). • Well-defined problems: usually have a correct answer and there are certain procedures that will lead to a solution. • e.g. a math or physics problem • Ill-defined problems: do not necessarily have one “correct” answer and the path to the solution is often unclear. • e.g. dealing with relationships or picking a career • Think of some problems you have solved or are currently working on.

5. Gestalt Approach • How problems are represented in a person’s mind: • How people represent a problem in their mind? • How solving a problem involves a reorganization or restructuring of this representation.

6. Representing a Problem in the Mind The solution is obtained by first perceiving the object and then representing it in a different way. • Restructuring: the process of changing the problem’s representation.

7. Circle Problem • If the length of the radius is r, what is the length of line x?

8. Insight in Problem Solving • Associate with restructuring • A sudden realization of a problem’s solution • Insight is reflected in the types of problems they posed. • The solution involves discovering a crucial element that leads to solution of the problem (Dunbar, 1998).

9. Metcalfe and Wiebe (1987) • Goal: to distinguish between insight problems and noninsight problems. • Starting point: there should be a basic difference between how participants feel they are progressing toward a solution as they are working on an insight problem, and how they feel as they are working on a noninsight problem. • Insight problems, noninsight problems, and ‘warmth’ judgments every 15 seconds

10. Insight Problem • Triangle Problem • How you can move three of the circles to get the triangle to point to the bottom. • Chain Problem • To open a link costs 2 cents and to close a link costs 3 cents. How to join the pieces into a single closed loop of chain with 15 cents?

11. Noninsight Problems • Algebra problem • Slove for x: (1/5)x + 10 = 25 • Factor 16y2 – 40 yz + 25 z2

12. Results

13. Obstacles to Problems Solving • Fixation: people’s tendency to focus on a specific characteristic of the problem that keeps them from arriving at a solution. • Functional fixedness (Jansson & Simth, 1991) • Candle Problem (Duncker, 1945) • Two-string problem (Maier, 1931) • Situationally produced mental set • Water-jug problem (Luchins, 1942)

14. Candle Problem • Some candles, matches in a matchbox, and some tacks • To mount a candle on the corkboard so it will burn without dripping wax on the floor.

15. Adamson (1952) • Repeated Duncker’s exepriment • Participants who were presented with empty boxes were twice as likely to solve the problem as participants who were presented with boxes that were used as containers.

16. Two-string Problem • Two separate strings that were hanging from the ceiling • A chair and a pair of pliers

17. Water-jug Problem • Participants were given three jugs of different capacities and were required to use these jugs to measure out a specific quantity of water • B - A – 2C works for all of the problems • Fewer steps A + C for problem 7 and A- C for problem 8

18. Results

19. Information Processing Approach

20. Modern Research on Problem Solving • Describe problem solving as a search that occurs between the posing of the problem and its solution. • Design computer program to simulate human problem solving.

21. Newell and Simon’s Approach • Initial state: conditions at the beginning of the problem. • Goal state: the solution of the problem. • Operators: rules that specify which moves are allowed and which are not. • Intermediate state: each step through problem solving. • Problem space: initial state, goal state, and all the possible intermediate states for a particular problem.

22. Tower of Hanoi Problem

24. Means-end Analysis • Primary goal: to reduce the difference between the initial and goal states • Method: creating intermediate states that are closer to the goal (subgoals).

25. How a Problem Is Stated • How a problem is stated can affect its difficulty. • Acrobat Problem • Reverse Acrobat Problem

26. Acrobat Problem • Kotovsky and Coworkers (1985)

27. Reverse Acrobat Problem • Same as the acrobat problem, except rule 4 was changed to state that a smaller acrobat could not stand on a larger one. • An average 9.51 minutes to solve instead of 5.63 minutes in acrobat problem. • Reasons for the difficulty • A 400-pound acrobat standing on the shoulders of a 40-pound acrobat is not consistent with our knowledge of the real world. • Visualizing larger acrobats on top of smaller ones would increase the load on the problem-solver’s memory.

28. Mutilated –Checkerboard Problem • Kaplan and Simon (1990) • If we eliminate two corners of the checkerboard, can we now cover the remaining squares with 31 dominos?

29. Mutilated –Checkerboard Problem (Cont.) • blank • color • black and pink • bread and butter

30. Mutilated –Checkerboard Problem (Cont.) • Results: • The board that emphasized the difference between adjoining squares was easier. • Participants in the bread-and-butter group solved the problem twice as fast as those in the blank group and required fewer hints • Solving problem becomes easier when information is provided that helps point people toward the correct representation of the problem.

31. Think-Aloud Protocol • Goal: • To determine what information the person is attending to while solving a problem. • To reveal shifts in representation • Procedure • Talk aloud while you solve a problem (just verbalizing what you would normally think) • Analysis of what was said • Russian Marriage Problem

32. Russian Marriage Problem • A “story” version of the mutilated checkerboard problem that makes the answer obvious • 32 bachelors & 32 unmarried women • 2 of the men got into a fight and died • Can matchmakers still arrange all the (hetero) marriages? • When people read this story first they can easily solve the checkerboard problem if they notice there is a connection…

33. Analogies

34. Analogical Problem Solving • Often you can use the solution of one problem to guide the solution of another similar problem • Russian Marriage Problem -> Checkerboard Problem • Analogical Transfer • People try to solve the Target Problem • Some are presented with a Source Problem or Source Story that can help them solve the Target • Russian Marriage (Source) -> Checkerboard (Target)

35. Steps of Analogical Problem Solving • Noticing • Seeing that there is a possible analogy between problems • Most difficult, especially in the real world • Mapping • Connecting elements of the source problem to elements of the target problem • Applying • Using the analogy to generate the solution

36. Improving Analogical Transfer • Two types of features (best when similar) • Structural Features • Surface Features • Analogical Encoding • Strategy for training people to be able to notice and apply analogies • Compare different source problems first, then solve Target

37. Analogical Paradox Lab studies: People use surface features Real World / In Vivo: People use structural features

38. Experts and Non-experts

39. Differences Between Novices and Experts • Experts have more knowledge about their field • More analogies / strategies possible • Experts’ knowledge is organized differently • Deep structural features • physics problem example • Experts spend more time analyzing problems • BUT experts are only experts in their field

40. Creative Problem-Solving

41. A Story • Physics exam question: Describe how the height of a building can be measured using a barometer • Teacher wanted an explanation using principles in class • Compare barometric pressure at the top of the building with barometric pressure at the ground • Equation to find the building’s height

42. A Story • One student’s answers • Lower the barometer to the ground on a piece of string – length of string is height of building • Put barometer in the sun and measure the length of its shadow and the length of the building’s shadow, use proportions to find building height • Give the building superintendent the barometer in exchange for info about building height • These are examples of creative answers

43. What is creativity? • Difficult to define • Involves innovative thinking, generating novel ideas, or making new connections between existing ideas to create something new • Involves divergent thinking

44. Divergent vs. Convergent Thinking • Divergent thinking • Open-ended • Large number of potential “solutions” • No “correct” answer • Associated with ill-defined problems • Convergent thinking • Finding a solution to a specific problem • Thinking converges to the correct solution • Associated with well-defined problems

45. Fixation and Creativity • Earlier we talked about Gestalt psychologists’ research on obstacles to problem-solving • Fixation was one obstacle • Fixation can limit creativity in design • Example: Sony temporarily abandoned work on CD because at the size of a record it would produce 18 hours of music. Realized CDs could be smaller and then resumed research.

46. Jansson and Smith (1991) • Design students • Generate as many designs as possible in 45 minutes • Problem: Design an inexpensive, spill-proof coffee cup • Do NOT include a mouthpiece or straw • Two groups • Fixation group: got a picture of what NOT to do • Control group: no picture

47. Jansson and Smith (1991) • Results: Those who saw pictures of the design with the mouthpiece and straw produced more designs with a mouthpiece and straw • These were forbidden designs • Evidence of design fixation

48. Factors Affecting Creativity • What’s the point of Jansson and Smith (1991)? • Creative problem-solving affected by fixation • Similar to regular problem-solving • Creative problem-solving is also similar to regular problem-solving because analogy can be used • George de Mestral – burrs / velcro (1955) • Insight + 7 years of trial and error

49. Creative Cognition • Ronald Finke developed a technique for training people to think creatively (creative cognition) • Let’s try it! • You’ll need something to write with (and on) • I’ve randomly selected three shapes – take 1 minute to construct an object using the shapes • Don’t make it a familiar object • Don’t worry about what it is used for • You can vary size, position, orientation, material • Wires or tubes can be bent

50. Creative Cognition