Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Chapter 11: Problem
Solving and Creativity
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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).
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Problem Solving
• Initial State
– Current situation
– Define the problem
• Goal State
– Desired objective
• Obstacles
– Choices made about limitations
– Strategy choices
– Limited resources
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Problem Solving Cycle
Evaluate
success
Identify
Problem
Define
Problem
Monitor
Solving
Allocate
Resources
Select
Strategy
Organize
Info
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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.
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Strategy Formation
•Divergent thinking
– Generate multiple solutions to problem
•Convergent thinking
– Narrow down to best answer
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Organization of Information
• Organize to aid solution
– Symbols
– Matrixes
– Diagrams
Let L = Lucy, S = Sean,
2L=3S, S=10
Mango Peach
Alex
Jarod
Henry
x
x
0
0
x
x
Steak
x
0
x
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Problem Solving Cycle
Evaluate
success
Identify
Problem
Define
Problem
Monitor
Solving
Allocate
Resources
Select
Strategy
Organize
Info
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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)
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Heuristics for Problem Solving
• Mean-ends analysis
• Working forward
• Working backward
• Generate and test
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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?
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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.
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Solution is the same as Forest Burners &
Forest Lovers in text
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Recognizing the Isomorphic
• 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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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) = ?
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Insight
• Current Debate
– Is insight a special process or just a
normal process in problem solving?
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Schooler, Ohlsson & Brooks (1993)
Results
90
Verbal
80
Control
70
60
50
40
30
20
10
0
Insight
Logic
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Obstacles to Problem Solving
• Mental set
• Functional fixedness
• Incorrect or incomplete representation
of the problem
• Lack of domain knowledge
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Luchins (1942) Water Jar Problem
How would you use 3 jars with the indicated capacities to
measure out the desired amount of water?
Problem
1
2
Jar A
29
21
Jar B
3
127
Jar C
2
3
Desired
20
100
3
4
5
6
14
18
9
20
163
43
42
59
25
10
6
4
99
5
21
31
7
8
9
23
15
28
49
39
76
3
3
3
20
18
25
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
wasn’t a bartender. He was a robber.
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Functional Fixedness
• An inability to assign new functions
and roles to elements of a problem
– Two string problem
– Duncker’s candle problem
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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.
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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.
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Ask Participants to Solve this
Problem
• 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?
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Gick & Holyoak (1980) Results
100
90
80
70
60
50
40
30
20
10
0
Control
Analogy
Analogy & Hint
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Neuropsychology of Planning
• Frontal lobe active in problem solving
• Prefrontal cortex active in planning
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Experts vs. Beginners
Under what condition did
the experts remember
more?
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Beer Study
• Assessed memory of beers between
experts and novices
– Experts remembered more
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Innate Talent vs. Acquired Skill
• Clear that expertise requires acquired
skill BUT some performance is not
explainable by knowledge level alone
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Creativity
•
Process of creating something that is
original and worthwhile
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Psychometric View
• Emphasis is on the measure of the
product a person creates—creativity
test scores
• Guilford (1950)
• Torrance (1988)
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
The Process Approach
• Weisberg (1988)
– Nothing innately special about people
– Hard work and dedication leads to
creativity
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Personality Approach
• Baron (1988)
– Way of looking at things
• Amabile (1996)
– Intrinsic motivation is important
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
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
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Neuroscience of Creativity
• Prefrontal regions are active
• Brodmann’s area 39 is active
Cognitive Psychology, Fifth Edition, Robert J. Sternberg
Chapter 11
Sternberg’s Propulsion Model of Creative
Contributions
• Replication
• Redefinition
• Forward Incrementation
• Advance forward incrementation
• Redirection
• Reconstruction-redirection
• Reinitiation
• Integration