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

2. Outline The Gestalt Approach: The Gestalt Approach: Describe problem solving as involving a process called restructuring. Describe problem solving as involving a process called restructuring. The Information-processing Approach: The Information-processing Approach: Describe problem solving as involving search. Describe problem solving as involving search. Analogies: Analogies: A method that combines elements of both restructuring and search. A method that combines elements of both restructuring and search. Experts and nonexperts: Experts and nonexperts: Creative thinking: 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). 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. 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 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. 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 e.g. dealing with relationships or picking a career Think of some problems you have solved or are currently working on. 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 problems are represented in a person’s mind: How people represent a problem in their mind? How people represent a problem in their mind? How solving a problem involves a reorganization or restructuring of this representation. 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. 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? If the length of the radius is r, what is the length of line x?

8. Insight in Problem Solving Associate with restructuring Associate with restructuring A sudden realization of a problem’s solution A sudden realization of a problem’s solution Insight is reflected in the types of problems they posed. 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). 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. 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. 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 Insight problems, noninsight problems, and ‘warmth’ judgments every 15 seconds

10. Insight Problem Triangle Problem Triangle Problem How you can move three of the circles to get the triangle to point to the bottom. How you can move three of the circles to get the triangle to point to the bottom. Chain Problem 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? 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 Algebra problem Slove for x: (1/5)x + 10 = 25 Slove for x: (1/5)x + 10 = 25 Factor 16y 2 – 40 yz + 25 z 2 Factor 16y 2 – 40 yz + 25 z 2

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. 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) Functional fixedness (Jansson & Simth, 1991) Candle Problem (Duncker, 1945) Candle Problem (Duncker, 1945) Two-string problem (Maier, 1931) Two-string problem (Maier, 1931) Situationally produced mental set Situationally produced mental set Water-jug problem (Luchins, 1942) Water-jug problem (Luchins, 1942)

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

15. Adamson (1952) Repeated Duncker’s exepriment 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. 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 Two separate strings that were hanging from the ceiling A chair and a pair of pliers 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 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 B - A – 2C works for all of the problems Fewer steps A + C for problem 7 and A- C for problem 8 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. 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. Design computer program to simulate human problem solving.

21. Newell and Simon’s Approach Initial state: conditions at the beginning of the problem. Initial state: conditions at the beginning of the problem. Goal state: the solution of the problem. Goal state: the solution of the problem. Operators: rules that specify which moves are allowed and which are not. Operators: rules that specify which moves are allowed and which are not. Intermediate state: each step through problem solving. Intermediate state: each step through problem solving. Problem space: initial state, goal state, and all the possible intermediate states for a particular problem. 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 Primary goal: to reduce the difference between the initial and goal states Method: creating intermediate states that are closer to the goal (subgoals). 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. How a problem is stated can affect its difficulty. Acrobat Problem Acrobat Problem Reverse Acrobat Problem Reverse Acrobat Problem

26. Acrobat Problem Kotovsky and Coworkers (1985) 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. 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. An average 9.51 minutes to solve instead of 5.63 minutes in acrobat problem. Reasons for the difficulty 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. 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. 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) Kaplan and Simon (1990) If we eliminate two corners of the checkerboard, can we now cover the remaining squares with 31 dominos? If we eliminate two corners of the checkerboard, can we now cover the remaining squares with 31 dominos?

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

30. Mutilated –Checkerboard Problem (Cont.) Results: Results: The board that emphasized the difference between adjoining squares was easier. 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 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. Solving problem becomes easier when information is provided that helps point people toward the correct representation of the problem.

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

32. Russian Marriage Problem A “story” version of the mutilated checkerboard problem that makes the answer obvious A “story” version of the mutilated checkerboard problem that makes the answer obvious 32 bachelors & 32 unmarried women 32 bachelors & 32 unmarried women 2 of the men got into a fight and died 2 of the men got into a fight and died Can matchmakers still arrange all the (hetero) marriages? 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… 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 Often you can use the solution of one problem to guide the solution of another similar problem Russian Marriage Problem -> Checkerboard Problem Russian Marriage Problem -> Checkerboard Problem Analogical Transfer Analogical Transfer People try to solve the Target Problem People try to solve the Target Problem Some are presented with a Source Problem or Source Story that can help them solve the Target Some are presented with a Source Problem or Source Story that can help them solve the Target Russian Marriage (Source) -> Checkerboard (Target) Russian Marriage (Source) -> Checkerboard (Target)

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

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

37. Analogical Paradox Lab studies: People use surface features Lab studies: People use surface features Real World / In Vivo: People use structural 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 Experts have more knowledge about their field More analogies / strategies possible More analogies / strategies possible Experts’ knowledge is organized differently Experts’ knowledge is organized differently Deep structural features Deep structural features physics problem example physics problem example Experts spend more time analyzing problems Experts spend more time analyzing problems BUT experts are only experts in their field 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 Physics exam question: Describe how the height of a building can be measured using a barometer Teacher wanted an explanation using principles in class Teacher wanted an explanation using principles in class Compare barometric pressure at the top of the building with barometric pressure at the ground Compare barometric pressure at the top of the building with barometric pressure at the ground Equation to find the building’s height Equation to find the building’s height

42. A Story One student’s answers One student’s answers Lower the barometer to the ground on a piece of string – length of string is height of building 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 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 Give the building superintendent the barometer in exchange for info about building height These are examples of creative answers These are examples of creative answers

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

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

45. Fixation and Creativity Earlier we talked about Gestalt psychologists’ research on obstacles to problem-solving Earlier we talked about Gestalt psychologists’ research on obstacles to problem-solving Fixation was one obstacle Fixation was one obstacle Fixation can limit creativity in design 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. 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 Design students Generate as many designs as possible in 45 minutes Generate as many designs as possible in 45 minutes Problem: Design an inexpensive, spill-proof coffee cup Problem: Design an inexpensive, spill-proof coffee cup Do NOT include a mouthpiece or straw Do NOT include a mouthpiece or straw Two groups Two groups Fixation group: got a picture of what NOT to do Fixation group: got a picture of what NOT to do Control group: no picture 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 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 These were forbidden designs Evidence of design fixation Evidence of design fixation

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

49. Creative Cognition Ronald Finke developed a technique for training people to think creatively (creative cognition) Ronald Finke developed a technique for training people to think creatively (creative cognition) Let’s try it! Let’s try it! You’ll need something to write with (and on) 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 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 make it a familiar object Don’t worry about what it is used for Don’t worry about what it is used for You can vary size, position, orientation, material You can vary size, position, orientation, material Wires or tubes can be bent Wires or tubes can be bent

50. Creative Cognition

51. The next step is to interpret how these objects could be used The next step is to interpret how these objects could be used I’ll give you a category and you’ll have 1 minute to interpret your object as an item in that category I’ll give you a category and you’ll have 1 minute to interpret your object as an item in that category Decide what your object could be used for Decide what your object could be used for Decide how it would work Decide how it would work CATEGORY: Tools and Utensils You’ve just created a preinventive form You’ve just created a preinventive form

52. Creative Cognition People generated 360 preinventive forms People generated 360 preinventive forms 120 rated as being “practical” 120 rated as being “practical” 65 rated as being “creative” AND “practical” 65 rated as being “creative” AND “practical”

53. Creative Cognition The points of Finke, 1995 The points of Finke, 1995 People generated creative solutions even though People generated creative solutions even though They were not told to be creative They were not told to be creative They were not screened for creativity They were not screened for creativity They were not trained in how to be creative They were not trained in how to be creative Creative problem-solving similar to regular problem- solving Creative problem-solving similar to regular problem- solving People were more likely to find creative uses for forms they generated People were more likely to find creative uses for forms they generated Technique lessened fixation issues Technique lessened fixation issues

54. THE END Don’t forget to read “Something to Consider”