1. Chapter 11 Problem Solving and Creativity
University of Utah
Joel Cooper

2. Changes to the syllabus
Next Week Chapters 12 and 13
No supplementary readings
Following week, Lecture on parapsychology
Reading from “why people believe weird things” to be posted online.

3. Problem Solving
A dealer in antique coins got an offer to buy a beautiful bronze coin. The coin had an emperor’s head on one side and the date 544 B.C. on the other. The dealer examined the coin, but instead of buying it, he called the police. Why?
In 544 B.C. Christ had not been born, so a coin from that time would not be marked "B.C." (before Christ).
In 544 B. C. Christ had not been born, so a coin from that time would not be marked "B. C. " (before Christ).

4. More Problems
What is the next letter in the following sequence? O T T F F S S

5. More Problems
You have 10 red socks and 20 brown socks in your bureau drawer. If you reach into it in the dark, how many socks must you take out to be sure of having a pair that matches?

6. Problem Solving Initial State Goal State Obstacles Current situation
Define the problem
Goal State
Desired objective
Obstacles
Choices made about limitations
Strategy choices
Limited resources

7. Problem Representation
The importance of determining what information is relevant and what information is irrelevant is the process of problem representation
People pay attention to the wrong information
People need to focus on the right information

8. Sample Problem
15% of the people in Topeka have unlisted numbers. You select 200 names at random from the Topeka phone book. How many of these people will have unlisted numbers?
Did you say 30?
The correct answer is zero
Students will get this problem wrong if they focus on the math of the problem rather than the meaning of what is said.

9. Sample Problem
A  man wanted to enter an exclusive club but did not know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, "twelve." The member replied, "six " and was let in. A second member came to the door and the doorman said, "six." The member replied, "three" and was let in. The man thought he had heard enough and walked up to the door. The doorman said ,"ten" and the man replied, "five." But he was not let in.
What should have he said?
Three. The doorman lets in those who answer with the number of letters in the word the doorman says.
Students will also get this problem wrong if they focus on the math, rather than a trick. This illustration helps the students to realize how important representing the problem correctly is.
It is also an example of a mental set effect.

10. Strategy Formation Select a strategy to solve the problem Analysis
Breaking into sub goals
Study for exam sub goals
Read textbook & class notes
Identify most relevant topics
Create study questions & answers on note cards
Learn all concepts on note cards
Test self with note cards
Recycle through learning and testing until mastery is achieved

11. Strategy Formation Select a strategy to solve the problem Synthesis
Organize to aid solution
Symbols
Matrixes
Diagrams
Let L = Lucy, S = Sean,
2L=3S, S=10
Mango
Peach
Steak
Alex x
Jarod
Henry

12. Strategy Formation Divergent thinking (Analysis)
Generate multiple solutions to problem
Convergent thinking (Synthesis)
Narrow down to best answer

13. Types of Problems Well-structured problems Ill-structured problems
Clear path to the solution
Math problems
Anagrams
Ill-structured problems
Dimensions of problem are not specified or easy to infer
Finding an apartment
Writing a book

14. Methods for Studying Problem Solving
Error analysis or reaction time
Global measures of performance
Verbal protocols
Participants speak their thoughts out loud while solving problems
Strategies become evident in protocols
Computer simulation
Create models that can recreate human data

15. Strategies to Solve Problems
Algorithms
Systematic procedure guaranteed to find a solution
Heuristics
Useful rule of thumb based on experience
Efficient but does not guarantee a correct solution

16. Heuristics for Problem Solving
Mean-ends analysis
Working forward
Working backward
Generate and test

17. Heuristics for Problem Solving
Mean-ends analysis
Working forward
Working backward
Generate and test
Means-End Analysis
Compare your current state with the goal and choose an action to bring you closer to the goal
Break a problem down into smaller sub goals
Win at Monopoly
You start by buying properties, continue to buy until you get a set, buy houses, then buy hotels, wait for others to land on spaces, etc.
May not work if sub goals cannot be identified  

18. Step 3 A&O or O
Step 2 A&O or A
Step 1 A or O
Apples
Oranges
Apples
&
Oranges
Each box is labeled incorrectly. You may select one fruit from one box. How can you label each box correctly?

19. Working Forward Start at initial state and work to goal state
Heuristics for Problem Solving
Mean-ends analysis
Working forward
Working backward
Generate and test
Working Forward
Start at initial state and work to goal state
Math problems
(2 + 6)/(4 * 1) = ?
Complete the math inside parenthesis first, then divide the quantities to get to solution

20. Heuristics for Problem Solving
Mean-ends analysis
Working forward
Working backward
Generate and test
Working Backward
Figure out the last step needed to reach your goal, then the next-to-the-last step, and so on
You have lost your keys
Try to remember the last time you used them and work backwards
Work backwards from goal state

21. Generate and Test Trial and error strategy
Heuristics for Problem Solving
Mean-ends analysis
Working forward
Working backward
Generate and test
Generate and Test
Trial and error strategy
Create possibilities, test them and discard the ones that are incorrect
Your car will not start
Wait a moment and try again, may be flooded
Check to see if there is gas, if no success
Check to see if the battery is charged… etc.
This may not be the most efficient strategy

22. Tower of Hanoi
If you are connected to the internet, you can click the blue base bar and open a web page that allows you to try the tower of Hanoi game. The website is Mazeworks at
You may also watch the computer solve the Tower of Hanoi if you like.
Move all the discs from the left peg to the right one. Only one disc may be moved at a time. A disc can be placed either on an empty peg or on top of a larger disc. The goal is to move all the discs using the smallest number of moves possible

23. Recognizing the Isomorphic
From variants of the Hobbit/Orc problem, Reed (1987) found that participants have difficulty recognizing that a past problem’s solution will help them to solve the current problem
Difficulty in recognizing crucial commonalities
Surface features of the problem distract
Current research focuses on factors that help the transfer of solutions
Ross, B. H. (1987). This is like that: The use of earlier problems and the separation of similarity effects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 13,

24. Insight and Problem Solving
Insight is the apparent sudden solution to a problem some time after the problem has been presented
Metcalfe & Weibe (1987)
Participants were given either insight or algebra problems to solve
Insight: A prisoner was attempting escape from a tower. He found in his cell a rope which was half long enough to permit him to reach the ground safely. He divided the rope in half and tied the two parts together and escaped. How could this be?
Algebra: (3x2 + 2x = 10)(3x) = ?
Clip art image from Microsoft.

25. Metcalf & Wiebe (1987) Results
Insight
Metcalf & Wiebe (1987) Results
Participants indicated how close they were to solution every 15 seconds
1 being very cold to 7 being very warm
On the insight problem there is a sudden shift in warmth rating
On the algebra problem there is a consistent getting warmer pattern
Figure from Sternberg text.

26. Gestalt View of Insight
Wertheimer
Sudden rearrangement of elements creates “insight”
Productive thinking goes beyond previously learned associations
Kohler
Animal Model of Insight
Sultan stacked boxes to get banana

27. Insight Current Debate
Is insight a special process or just a normal process in problem solving?

28. Schooler, Ohlsson & Brooks (1993)
Insight
Schooler, Ohlsson & Brooks (1993)
Logic, Insight ≠ Structures
Participants solved insight and logic problems
Half participants verbalized strategies
The control group did not verbalize as they solved the problem

29. Schooler, Ohlsson & Brooks (1993) Results
Insight
Schooler, Ohlsson & Brooks (1993) Results
Performance was decreased in the Insight problem condition when they were forced to use verbal protocol while solving the problems.
One interpretation of this study is that the verbal system is not used to solve these types of problems. Thus, participants had to do “extra verbal work” to describe what they were doing, thus leading to a lower success rate in the verbal condition. This is not the case for the logic problems. Participants simply had to state what they were doing, thus it did not interfere.

30. Insight
Incubation
Time away from a problem provides new insights or otherwise facilitates the problem solving process
Release from a problem solving set, or functional fixedness
Retrieval of new information by changing context
Recovery from fatigue

31. Obstacles to Problem Solving
Mental set
Functional fixedness
Incorrect or incomplete representation of the problem
Lack of domain knowledge

32. Mental Set
Obstacles
Seeing a problem in a particular way instead of other plausible ways due to experience or context
This usually causes you to adopt an ineffective strategy and can prevent problem solving
Make assumptions without realizing it
Difficult to approach the problem in a new way

33. Mental Set?
150’
75’ ?
Two flagpoles, 150’ high. A 150’ rope suspended from each end reaches 75’ from the ground. How far apart are the flagpoles?

34. Functional Fixedness
Obstacles
An inability to assign new functions and roles to elements of a problem
Two string problem
Duncker’s candle problem

35. Problem I Two strings are suspended from the ceiling
Obstacles
Problem I
Two strings are suspended from the ceiling
Goal: Tie the strings together
Problem: Too far apart to hold one and reach for the other
Materials:
Chair
piece of paper
pair of pliers
What is the Solution?

36. Functional Fixedness? Problem II Materials:
Obstacles
Problem II
Functional Fixedness?
Materials:
Box of thumb tacks
Candle
Matches
Objective: Mount candle on wall to make light
What is the Solution?

37. Transfer Negative Transfer Positive Transfer
Obstacles
Negative Transfer
Solving prior problem makes it more difficult to solve later problem
Positive Transfer
Solving earlier problem helps to solve later problem
Gick & Holyoak examine factors contributing to positive transfer

38. Water Jugs Jug A Jug B Jug C Goal 21 127 3 100 14 163 25 99 18 43 10 5
Obstacles
Jug A Jug B Jug C Goal

39. Einstellung phenomena and (or) Negative Transfer
Obstacles
Einstellung phenomena and (or) Negative Transfer
Tendency to solve problems in a particular way when a different approach might have been more productive
Problems 1-5: B-2C-A
Problems 6-8: A-C
Problem 8 can’t be solved B-2C-A
80% who see all 8 problems use B-2C-A
1% of controls use B-2C-A
64% fail to solve #8 vs. 5% of controls

40. Gick & Holyoak (1980)
Obstacles
Give participants one problem to read, with a solution
Then give them a second problem, which can be solved using a similar solution

41. Gick & Holyoak (1980) 3 groups of participants
Obstacles
Gick & Holyoak (1980)
3 groups of participants
Control group that only tried to solve the radiation problem
A group previously given the analogous General/Fortress problem & solution
A group given the General/Fortress problem and told that its solution would help in solving the radiation problem

42. Gick & Holyoak (1980) Results
Obstacles
Gick & Holyoak (1980) Results

43. Transfer Recap Negative Transfer Positive Transfer
Obstacles
Negative Transfer
Solving prior problem makes it more difficult to solve later problem
Positive Transfer
Solving earlier problem helps to solve later problem
Gick & Holyoak examine factors contributing to positive transfer

44. Factors Affecting Use of Analogies
Obstacles
Factors Affecting Use of Analogies
Similarity
Number of examples exposed to
Gick and Holyoak conducted a study in which the dictator story was just one of three other stories participants heard before radiation problem
Only 20% got the problem correct
Whether schema for problem is activated
If the two problems are separated by a delay or if they are presented in different contexts, almost none of the participants use the analogy

45. Expertise Not a general ability
Have an extensive knowledge that they use to organize, represent, and interpret information in their environment
This affects their abilities to remember, reason, and solve problems

46. Chase & Simon (1973) & DeGroot (1965)
Expertise
Chase & Simon (1973) & DeGroot (1965)
Participants were chess masters and beginning chess players
Studied a chess board that had the pieces randomly displayed or a chess board with pieces in the middle of a game.
Beginners and experts had to recall as many pieces as they could

47. Expertise
Experts vs. Beginners
Under what condition did the experts remember more?
Check student’s understanding of the graph by having them look at graphs and explain the results found.

48. Results
Expertise
Master chess players and beginning players recalled a similar number of pieces from the random board
Master chess players remember significantly more chess pieces from the game board in play than did the beginning chess players

49. Experts Differ From Novices
Expertise
Better schemas
Well organized knowledge in specific domain
Less time to set up problem
Select more appropriate strategies
Faster at solving problems
Are more accurate

50. Creativity
Process of creating something that is original and worthwhile
Multiple views which emphasize
The product
The person\personality creating the product
The creative process; the steps that the creative person followed to create the product
The creative environment
A synthesis of all of the above

51. Boost your creativity for inspiring ideas and innovation
Are you seeking inspiration for a project? Do you want help 'thinking outside of the box'? Do you need to get over a creative block? True creativity seems to happen by itself because it is a product of the unconscious mind, that 'back part' of the mind that incubates ideas until they are ready for the light of day. Hypnosis can help you take your conscious fingers out of the creativity process and leave your unconscious mind to come up with the sorts of ideas, solutions and innovations that it is so good at. Creativity is such a great advantage in all sorts of situations:
for humor in social situations
for innovation in business
for art, music and writing
for originality in public speaking
Get the Creativity Booster today, sit back, relax, and watch the ideas come flooding in.

52. Psychometric View
Creativity
Emphasis is on the measure of the product a person creates—creativity test scores
Guilford (1950)
Torrance (1988)

53. Breaking Functional Fixedness
Creativity
Breaking Functional Fixedness
Coat hanger creativity test
You have 2 minutes, write down all possible uses for a coat hanger.
Think outside the box
STOP
START

54. The Process Approach Weisberg (1988)
Creativity
The Process Approach
Weisberg (1988)
Nothing innately special about people
Hard work and dedication leads to creativity

55. Personality Approach Baron (1988) Amabile (1996)
Creativity
Baron (1988)
Way of looking at things
Amabile (1996)
Intrinsic motivation is important

56. Environment Csikszentmihalyi (1996)
Creativity
Csikszentmihalyi (1996)
Historical and social context critical
Contextual balance begets “flow”
Flow = enjoyment when absorbed

57. A Synthesis Gardner (1993) Examined case studies of creative people
Creativity
Gardner (1993)
Examined case studies of creative people
Strengths and weakness’
internal and external
First became a master, then creative works cameth forth

58. Sternberg, Kaufman, & Pretz (2002)
Creativity
Creativity is not a monolithic ability
Confluence of six main resources are necessary for creativity
intellectual abilities, knowledge, styles of thinking, personality, motivation, and environment
Three intellectual abilities are especially important:
Synthetic ability
To see problems using novel perspectives and not be bound by conventional thinking
Analytic ability
To recognize the importance of ideas and focus energy on those worth pursuing
Practical-contextual
To be able to convey and sell the importance of the ideas to others
Sternberg, R. J., Kaufman, J. C., & Pretz, J. E. (2002). The creativity conundrum. New York: Psychology Press.

59. How to Improve Your Problem Solving
Follow a systematic plan
Draw inferences
Develop sub-goals
Work backwards
Search for contradictions

60. How to Improve Your Problem Solving
Search for relations among problems
Reformulate problems
Represent problems graphically
Define boundary conditions