Margaret W. Matlin, Cognition, 8e
Outline Chapter 11
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CHAPTER 11
Problem Solving and Creativity
CHAPTER INTRODUCTION
problem solving
 used when you want to reach a certain goal, but the solution is not
immediately obvious
 missing information and/or obstacles block the path
 initial state
 goal state
 obstacles
thinking—requires you to go beyond the information you were given, so
you can reach a goal
UNDERSTANDING THE PROBLEM
understanding the problem
 construct a well-organized mental representation of the problem
 based on the information provided in the problem and previous
experience
Paying Attention to Important Information
identifying and attending to the most relevant information
Bransford and Stein (1984)
 algebra story problems
 distracting negative thoughts
Effective problem solvers read the description of a problem very
carefully, paying particular attention to inconsistencies.
©2013 John Wiley & Sons, Inc.
Margaret W. Matlin, Cognition, 8e
Outline Chapter 11
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Methods of Representing the Problem
problem representation
working-memory capacity
Symbols
algebra
translating words into symbols
oversimplification
misremembering the problem
Matrices
matrix—grid showing all possible combinations of items
Demonstration 11.3: Hospital Room Problem
most useful for complex, stable, categorical information
Diagrams
instructions for assembling objects
Novick and Morse (2000)
 origami
 more accurate with both a verbal description and a step-by-step diagram
rather than only a verbal description
represent abstract information in a concrete fashion
reduce large amount of complicated information into a concrete form
hierarchical tree diagram
graphs
Visual Images
escape boundaries of traditional concrete representations
good visual-imagery skills provide advantage
©2013 John Wiley & Sons, Inc.
Margaret W. Matlin, Cognition, 8e
Outline Chapter 11
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Situated Cognition, Embodied Cognition, and Problem Solving
situated-cognition approach—We often use helpful information in our
immediate environment to create spatial representations; importance of
external situation/context.
embodied cognition approach—We often use our own body and our
own motor actions, in order to express our abstract thoughts and
knowledge; importance of own body as context.
Situated Cognition
boys selling candy in Brazil; calculating ratio comparisons
 Our ability to solve a problem is tied into the specific physical and social
context in which we learned to solve that problem.
 An abstract intelligence test often fails to reveal how competent a person
would be in solving problems in real-life settings.
 Problem solving does not only take place inside a person's head.
 Real life provides information needed to solve complicated problems.
 Other people also provide information.
implications for education
ecological validity
Embodied Cognition
People solve certain kinds of problems more quickly or more accurately if
allowed to move parts of their bodies.
mental-rotation tasks
swinging rope problem
movement of gears problem
©2013 John Wiley & Sons, Inc.
Margaret W. Matlin, Cognition, 8e
Outline Chapter 11
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PROBLEM-SOLVING STRATEGIES
algorithm—always produces a solution; sometimes inefficient
exhaustive search—try all possible answers
heuristic—general rule; strategy in which you ignore some alternatives
and explore only those alternatives that seem especially likely to produce
a solution
weighing costs and benefits of using heuristics
The Analogy Approach
analogy approach—using a solution to a similar, earlier problem to help
in solving a new problem
engineers
cross-cultural research
creative breakthroughs
The Structure of the Analogy Approach
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determining the real problem
problem isomorphs
surface features
structural features
Example: tracking college applications
failure to see analogies
solving a problem in a new setting
Factors Encouraging Appropriate Use of Analogies
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overcoming the influence of context
trying several structurally similar problems before the target problem
training to sort problems into categories based on structural similarities
©2013 John Wiley & Sons, Inc.
Margaret W. Matlin, Cognition, 8e
Outline Chapter 11
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The Means-Ends Heuristic
means-ends heuristic
 divide the problem into subproblems
 try to reduce the difference between the initial state and the goal state for each
of the subproblems
 identify the "ends" you want and then figure out the "means" to reach them
 one of the most effective and flexible problem-solving strategies
Research on the Means-Ends Heuristic
Demonstration 11.5: Elves and Goblins (Greeno,1974)
 People pause at points in the problem when they begin to tackle a subproblem
and need to organize a sequence of moves.
 Working memory is active during planning.
 Sometimes the correct solution requires moving backward, temporarily
increasing the distance to the goal.
 People are reluctant to move away from goal state.
Computer Simulation
computer simulation
 computer program that will perform a task the same way that a human
would
 includes false starts
 should be no better (or worse) at solving the problem than a human would
be
 test by comparing program with the steps humans would take in solving
the problem
Newell and Simon's General Problem Solver (GPS)
 participants talk out loud while working on a relevant problem
 narrative used to create computer simulations
 uses means-ends analysis strategy; difference-reduction strategy
 generality not as great as researchers had wished
 real-life problems not so clear cut
Anderson's ACT-R theory
 computer simulations for problem solving (like Elves-and-Goblins),
algebra, geometry, computer science
 developed to learn more about how people acquire skills in problem
solving
 developed "cognitive tutors" for use in mathematics classes
©2013 John Wiley & Sons, Inc.
Margaret W. Matlin, Cognition, 8e
Outline Chapter 11
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The Hill-Climbing Heuristic
hill-climbing heuristic
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When you reach a choice point, choose the alternative that seems to lead most
directly toward your goal.
useful when only the immediate next step can be seen; not enough information
about alternatives
the less direct alternative may have greater long-term benefits
doesn't guarantee the goal will be reached
encourages short-term goals, rather than long-term solutions
FACTORS THAT INFLUENCE PROBLEM SOLVING
bottom-up processing—emphasizes stimulus information
top-down processing—emphasizes our concepts, expectations, memory,
and prior knowledge
Expertise
expertise
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consistent exceptional skill and performance on representative tasks for a
particular area
not necessarily related to years of experience
Experts have developed top-down processes that allow them to perform well
on many different components of problem solving in their particular area.
Expertise in one area does not necessarily transfer to other areas.
Knowledge Base
knowledge
schemas
training in variety of relevant settings
training with immediate feedback
Memory
memory skills of experts tend to be very specific
Chess experts' memory is better only if the information fits a particular schema.
Experts are only slightly better than novices at remembering random
arrangements of chess pieces.
©2013 John Wiley & Sons, Inc.
Margaret W. Matlin, Cognition, 8e
Outline Chapter 11
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Expertise (continued)
Problem-Solving Strategies
Experts:
 are more likely to use the means-ends heuristic effectively on a novel
problem
 approach problems systematically
 are more likely to emphasize structural features when using the analogy
approach
Speed and Accuracy
problem-solving operations become more automatic
parallel processing
serial processing
Metacognitive Skills
Experts better than novices at monitoring their own problem solving.
Experts also better at: judging the difficulty of the problem, allocating time,
monitoring the usefulness of ideas, recovering from errors
Experts underestimate the amount of time novices will require to solve a problem
in the experts' area of specialization.
Mental Set
mental set
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using the same solution from previous problems, even though the problem
could be solved by a different, easier method
close mind prematurely; stop thinking
breaking mental set associated with greater change in event-related brain
potentials (ERPs)
overactive top-down processing
Demonstration 11.6A: Luchin's water-jar problem
fixed mindset
growth mindset
©2013 John Wiley & Sons, Inc.
Margaret W. Matlin, Cognition, 8e
Outline Chapter 11
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Functional Fixedness
functional fixedness
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assign stable uses to an object
fail to think about the features of the object that might be useful in helping
solve a problem
overactive top-down processing
Duncker's candle problem
emergencies
cross-cultural studies
In Depth: Gender Stereotypes and Math Problem Solving
Another example of overactive top-down processes: Our stereotypes can
influence our beliefs about our own abilities.
gender stereotypes
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beliefs and opinions associated with females and males
generally not supported by research when it comes to problem solving skills
consistent gender similarities on standardized math tests for students of all
ages
gender similarities on solving complex math problems
Females earn higher grades in math courses than males, beginning with
elementary school and continuing up through college.
Many women, even women math majors, do not associate themselves with
mathematics.
The Nature of Stereotype Threat
Struggling with a popular stereotype may cause additional anxiety that may lead
to less effective problem solving.
stereotype threat—If you belong to a group that is hampered by a negative
stereotype—and you think about your membership in that group—your
performance may suffer.
©2013 John Wiley & Sons, Inc.
Margaret W. Matlin, Cognition, 8e
Outline Chapter 11
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In Depth: Gender Stereotypes and Math Problem Solving
(continued)
Research with Asian American Females
Shih and coauthors (1999)—compare the effects of two competing stereotypes
using three groups of Asian American women
1. Ethnicity-emphasis condition: One group of participants were asked to
indicate their ethnicity and then answer several questions about their ethnic
identity. Then they took a challenging math test. These women answered 54%
of the questions correctly.
2. Control-group condition: A second group of participants did not answer any
questions beforehand. They simply took the challenging math test. These
women answered 49% of the questions correctly.
3. Gender-emphasis condition: A third group of participants were asked to
indicate their gender and then answer several questions about their gender
identity. Then they took the challenging math test. These women answered
only 43% of the questions correctly.
When Asian American women are reminded of their ethnicity, they perform
relatively well.
When Asian American women are reminded of their gender, they may experience
stereotype threat, and their problem-solving ability can decline.
Ambady and coauthors (2001)—similar pattern among Asian American girls
Research with European American Females
O'Brien and Crandall (2003)
 college women taking difficult math test
 math test identified as "known to show higher scores for men than for
women" vs. "known to show no gender differences"
 Women performed worse on the test identified as "known to show higher
scores for men than for women."
Thoman and colleagues (2008)
 provided "male ability" vs. "males try harder" explanation for supposed
score differences
 Women in the "try harder" condition answered significantly greater
percentage of questions correctly.
©2013 John Wiley & Sons, Inc.
Margaret W. Matlin, Cognition, 8e
Outline Chapter 11
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In Depth: Gender Stereotypes and Math Problem Solving
(continued)
Potential Explanations
Stereotype threat can produce high arousal; high arousal is likely to interfere with
working memory.
Thought suppression may reduce working memory capacity.
Quinn and Spencer (2001)
 Arousal and reduced working memory decrease the ability to construct
problem-solving strategies.
 stereotype threat experiment using word problems vs. numerical equations
 Men performed better than women on word-problems test; no differences
on the numerical test.
In general, research shows gender-similarities in problem-solving skills.
Female students may earn lower scores if they receive messages that
females are less competent than males in mathematics.
Insight Versus Noninsight Problems
insight problem—seems impossible until sudden solution appears; light bulb,
"aha"
noninsight problem—gradual solution
The Nature of Insight
gestalt psychologists vs. behaviorists
begin with inappropriate assumptions that need to be discarded
inappropriate use of top-down processing
Metacognition During Problem Solving
Janet Metcalfe (1986)—People's confidence builds gradually for noninsight
problems, but shows a sudden leap in solving insight problems.
ancient coin problem
"feeling-of-warmth" scale
Figure 11.3: Results
Problem solvers typically report a dramatic increase in their confidence when they
believe they have located the correct solution to an insight problem.
©2013 John Wiley & Sons, Inc.
Margaret W. Matlin, Cognition, 8e
Outline Chapter 11
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Insight Versus Noninsight Problems (continued)
Advice About Problem Solving
Think about previous experience with similar problems.
Consider whether the problem might require insight.
If problem seems to be an insight problem:
 try to represent the problem in a different way
 think about a different meaning for an ambiguous word
 draw sketches, work with physical objects, use gestures
 be willing to think "outside the box"
CREATIVITY
creativity—finding solutions that are novel and useful
Psychologists disagree as to whether creativity involves ordinary thinking
or exceptional people.
Guilford's Classic Approach to Creativity
divergent production—measure creativity in terms of the number of
different responses made to a test item
Demonstration 11.8: Divergent Production Tests
 moderate correlations between divergent production test scores and
other judgments of creativity
 number of solutions doesn't indicate novelty and/or usefulness
The Nature of Creativity
1. Creativity includes convergent thinking, as well as divergent
thinking.
2. Creativity is associated with many regions within the left
hemisphere, as well as many regions within the right brain.
3. Creativity can occur when we use focused attention (conscious
attention) as well as defocused attention (altered states of
consciousness).
©2013 John Wiley & Sons, Inc.
Margaret W. Matlin, Cognition, 8e
Outline Chapter 11
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The Relationship Between Extrinsic Motivation and Creativity
extrinsic motivation—desire to work on a task to earn a promised reward
People often produce less creative projects if they are working on these
projects for external reasons.
Creativity can actually be enhanced if the extrinsic factors provide useful
feedback.
Individual Differences: The Relationship Between Intrinsic
Motivation and Creativity
intrinsic motivation—motivation to work on a task for its own sake,
because you find it interesting, exciting, or personally challenging
People are more likely to be creative when they are working on a task
that they truly enjoy.
Ruscio and coauthors (1998)
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students rate level of interest in writing, art and problem solving
later perform tasks in the three areas
judges rate projects
high intrinsic motivation related to judged creativity of projects
Prabhu, Sutton, and Sauser (2008)
 personality traits, intrinsic motivation, and creativity
 self-efficacy, perseverance
Results
1. The students with high scores on intrinsic motivation tended to earn high
scores on creativity. If you are working on a project because you find it
interesting, your work is more likely to be creative.
2. The students with high scores on extrinsic motivation tended to earn low
scores on creativity. As we discussed earlier, if you are working on a
project because you want some kind of reward, your work is less likely to
be creative.
3. Self-efficacy was closely correlated with creativity. The correlation could
be explained by the students' intrinsic motivation. When students are high
in self-efficacy, they tend to have high intrinsic motivation, and this high
intrinsic motivation encourages their creativity.
4. Persistence was not consistently correlated with creativity. However, these
results could be due to the use of self-report.
©2013 John Wiley & Sons, Inc.