Chapter 11: Problem Solving and Creativity

1
Chapter 11 Problem Solving and Creativity
2
Problem Solving

• A dealer in antique coins got an offer to buy
  a beautiful bronze coin. The coin had an
  emperors 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).

3
Problem Solving

• Initial State
• Current situation
• Define the problem
• Goal State
• Desired objective
• Obstacles
• Choices made about limitations
• Strategy choices
• Limited resources

4
Problem Solving Cycle
Identify Problem
Evaluate success
Define Problem
Monitor Solving
Select Strategy
Allocate Resources
Organize Info
5
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

6
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.

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
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

9
Strategy Formation

• Divergent thinking
• Generate multiple solutions to problem
• Convergent thinking
• Narrow down to best answer

10
Organization of Information

• Organize to aid solution
• Symbols
• Matrixes
• Diagrams

Let L Lucy, S Sean, 2L3S, S10
  Mango Peach Steak
Alex x 0 x
Jarod x x 0
Henry 0 x x
11
Problem Solving Cycle
Identify Problem
Evaluate success
Define Problem
Monitor Solving
Select Strategy
Allocate Resources
Organize Info
12
Types of Problems

• Well-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

13
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 stimulation
• Create models that can recreate human data

14
Newell and Simon (1972)

• Problem space
• All possible actions that can be applied to a
  problem
• Consists of states and operators
• States represent the problem
• Initial-given information prior knowledge
• Goal-desired outcome
• Operators transform one state to another state
• Permitted or selected moves

15
Newell and Simon (1972)

• Use verbal protocol and reproduce using a
  production rule system to create a similar
  representation of the problem
• Created a General Problem Solver (GPS)

16
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

17
Heuristics for Problem Solving

• Mean-ends analysis
• Working forward
• Working backward
• Generate and test

18
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  

19
Working Forward

• Start at initial state and work to goal state
• Math problems
• (2 6)/(4 x 1) ?
• Complete the math inside parenthesis first, then
  divide the quantities to get to solution

20
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
• 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
Transformation Problem

• Hobbits Orcs
• Three hobbits and three orcs come to a river and
  find a boat that holds two. If the Orcs ever
  outnumber the Hobbits on either bank, the Hobbits
  will be eaten.
• How do you get them all to the other side?

23
Tower of Hanoi

• 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.

24
Solution is the same as Forest Burners Forest
Lovers in text
25
Recognizing the Isomorphic

• Reed (1987) found that participants have
  difficulty recognizing that a past problems
  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

26
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) ?

27
Metcalf Wiebe (1987) Results

• Participants indicated how close they were to
  solution every 15 seconds
• 1 being very cold to 7 being very warm
• For insight problems
• Sudden shift in warmth rating
• For algebra problems
• A getting warmer pattern

28
Insight and Brain Activity

• Neural activity associated with insight
• fMRI studies found
• Right hippocampus is active during problem
  solving
• Another found spike in temporal lobe just before
  insight

29
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

30
Three-Process View

• Davis Sternberg (1984)
• Selective-encoding insights
• Sorting relevant from irrelevant
• Selective-comparison insights
• Make connections to previously learned
  information
• Selective-combination insights
• Combine elements in a novel way

31
Insight

• Current Debate
• Is insight a special process or just a normal
  process in problem solving?

32
Schooler, Ohlsson Brooks (1993)

• Proposed that solving insight problems rely on
  different mental structures than solving logical
  transformation problems
• Logical, transformation problems were solved with
  verbal systems, but insight problems were solved
  with nonverbal systems
• Participants were asked to solve a series of
  insight and logic problems
• Half the participants were required to verbalize
  their strategies as they tried to solve the
  problem
• The control group did not verbalize as they
  solved the problem

33
Schooler, Ohlsson Brooks (1993) Results
34
Obstacles to Problem Solving

• Mental set
• Functional fixedness
• Incorrect or incomplete representation of the
  problem
• Lack of domain knowledge

35
Mental Set

• Seeing a problem in a particular way instead of
  other plausible ways due to experience or context
  
• May cause you to adopt an ineffective strategy
  and prevents problem solving
• May make assumptions without realizing it
• May find it hard to approach the problem in a new
  way

36
Luchins (1942) Water Jar Problem

• How would you use 3 jars with the indicated
  capacities to measure out the desired amount of
  water?

Problem Jar A Jar B Jar C Desired
1 29 3 2 20
2 21 127 3 100
3 14 163 25 99
4 18 43 10 5
5 9 42 6 21
6 20 59 4 31
7 23 49 3 20
8 15 39 3 18
9 28 76 3 25
37
Bar Problem

• A man walked into a bar and asked for a drink.
  The man behind the bar pulled out a gun and shot
  the man. Why should that be so?
• Solution The man behind the bar wasnt a
  bartender. He was a robber.

38
Functional Fixedness

• An inability to assign new functions and roles to
  elements of a problem
• Two string problem
• Dunckers candle problem

39
Transfer

• 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

40
Gick Holyoak (1980)

• Give participants one problem to read with a
  solution
• Give same participants a second problem which can
  be solved using a similar solution

41
Gick Holyoak (1980)

• Analogous General/Fortress problem
• A dictator ruled a small country from a
  fortress. The fortress was situated in the middle
  of the country and many roads radiated outward
  from it, like spokes on a wheel. A great general
  vowed to capture the fortress and free the
  country from the dictator. The general knew that
  if his entire army could attack the fortress at
  once it could be captured. But a spy reported
  that the dictator had planted mines on each of
  the roads. The mines were set so that small
  bodies of men could pass over them safely, since
  the dictator needed to be able to move troops and
  workers about, however, any large force would
  detonate the mines. Not only would this blow up
  the road, but the dictator would destroy many
  villages in retaliation. A full-scale direct
  attack on the fortress therefore seemed
  impossible.

42
Gick Holyoak (1980)

• Solution to general problem
• The general, however, was undaunted. He divided
  his army up into small groups and dispatched each
  group to the head of a different road. When all
  was ready he gave the signal, and each group
  charged down a different road. All of the small
  groups passed safely over the mines, and the army
  then attacked the fortress in full strength. In
  this way the general was able to capture the
  fortress.

43
Ask Participants to Solve this Problem
0

• Radiation problem
• Given a human being with an inoperable stomach
  tumor, and rays that destroy organic tissue at
  sufficient intensity, by what procedure can one
  free him of the tumor by these rays and at the
  same time avoid destroying the healthy tissue
  that surrounds it?

44
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

45
Gick Holyoak (1980) Results
46
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

47
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

48
Neuropsychology of Planning

• Frontal lobe active in problem solving
• Prefrontal cortex active in planning

49
Expertise

• Not a general ability
• Experts have extensive knowledge that is used to
  organize, represent, and interpret information
• Thus affecting their abilities to remember,
  reason, and solve problems

50
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

51
Experts vs. Beginners Under what condition did
the experts remember more?
52
Results

• 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

53
Beer Study

• Valentin, Chollet, Beal Patris (2007)
• Beer experts
• Two year beer training program in France
• Beer Novices
• No prior training
• Tasted a series of 8 different beers

54
Beer Study

• Assessed memory of beers between experts and
  novices
• Experts remembered more

55
Experts Differ From Novices

• 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

56
Innate Talent vs. Acquired Skill

• Clear that expertise requires acquired skill BUT
  some performance is not explainable by knowledge
  level alone

57
Creativity

• Process of creating something that is original
  and worthwhile

58
Creativity

• May refer to
• The product
• The person\personality creating the product
• The process
• Steps followed to create the product
• The environment
• A synthesis of all of the above

59
Psychometric View

• Emphasis is on the measure of the product a
  person createscreativity test scores
• Guilford (1950)
• Torrance (1988)

60
The Process Approach

• Weisberg (1988)
• Nothing innately special about people
• Hard work and dedication leads to creativity

61
Personality Approach

• Baron (1988)
• Way of looking at things
• Amabile (1996)
• Intrinsic motivation is important

62
Environment Approach

• Csikszentmihalyi (1996)
• Must examine historical and social context in
  which product is made
• When one achieves balance with context, one
  achieves flow
• Flow is the enjoyment we experience when we are
  engaged in mental and physical challenges that
  absorb us

63
A Synthesis

• Gardner (1993)
• Examined case studies of creative people
• Albert Einstein (logical-mathematical),
• Pablo Picasso (spatial)
• T. S. Elliot (linguistic)
• Mohandas Gandhi (interpersonal)
• Most of these individuals had strengths in more
  than one intelligence (confluence), and had
  noticeable weaknesses in others
• Identified internal and external influences
• First become a master then creativity is possible

64
Sternberg, Kaufman, Pretz (2002)

• 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

65
Neuroscience of Creativity

• Prefrontal regions are active
• Brodmanns area 39 is active

66
Sternbergs Propulsion Model of Creative
Contributions

• Replication
• Redefinition
• Forward Incrementation
• Advance forward incrementation
• Redirection
• Reconstruction-redirection
• Reinitiation
• Integration