354 • CHAPTER 12 Problem Solving
CHAPTER SUMMARY
- A problem occurs when there is an obstacle between a
present state and a goal and it is not immediately obvi-
ous how to get around the obstacle. - The Gestalt psychologists focused on how people repre-
sent a problem in their mind. They devised a number of
problems to illustrate how solving a problem involves a
restructuring of this representation and to demonstrate
factors that pose obstacles to problem solving. - The Gestalt psychologists introduced the idea that
reorganization is associated with insight—a sudden
realization of a problem’s solution. Insight has been dem-
onstrated experimentally by tracking how close people
feel they are to solving insight and noninsight problems. - Functional fixedness is an obstacle to problem solv-
ing that is illustrated by Duncker’s candle problem and
Maier’s two-string problem. Luchins’ water-jug problem
illustrates the mental set created while solving a problem. - Alan Newell and Herbert Simon were early proponents
of the information-processing approach to problem solv-
ing. They saw problem solving as the searching of a prob-
lem space to find the path between the statement of the
problem (the initial state) and the solution to the problem
(the goal state). This search is governed by operators and
is usually accomplished by setting subgoals. The Tower of
Hanoi problem has been used to illustrate this process. - The acrobat problem and the reverse acrobat problem
illustrate that how the problem is presented can influence
problem difficulty. Research on the mutilated checker-
board problem also illustrates the importance of how a
problem is presented. - Newell and Simon developed the technique of think-
aloud protocols to study participants’ thought process as
they are solving a problem. - Analogical problem solving occurs when experience with
a previously solved source problem or a source story is
used to help solve a new target problem. Research involv-
ing Duncker’s radiation problem has shown that even
when people are exposed to analogous source problems or
stories, most people do not make the connection between
the source problem or story and the target problem.- Analogical problem solving is facilitated when hints
are given regarding the relevance of the source prob-
lem, when the source and target problems have similar
surface features, and when structural features are made
more obvious. Analogical encoding is a process that
helps people discover similar structural features. - The analogical paradox is that participants in psycho-
logical experiments tend to focus on surface features
in analogy problems, whereas people in the real world
frequently focus on deeper, more structural features. In
vivo problem-solving research has shown that analogical
problem solving is often used in real-world settings. - Experts are better than novices at solving problems in
their field of expertise. They have more knowledge of
the field, organize this knowledge based more on deep
structure than on surface features, and spend more time
analyzing a problem when it is first presented. - Creative problem solving is associated with divergent
thinking rather than with convergent thinking. We have
only a limited understanding of the processes involved in
creative problem solving and creativity in general. There
is evidence that fixation can inhibit creative problem
solving, and that using analogical thinking can enhance
it. A technique called creative cognition has been used to
train people to think creatively. - Mathematics problem-solving performance is affected by
working memory capacity. High working memory capac-
ity is associated with better performance than low work-
ing memory capacity under low-stress conditions, but
this advantage disappears under high-stress conditions. - Pick a problem you have had to deal with, and ana-
lyze the process of solving it into subgoals, as is done in
means-end analysis. - Have you ever experienced a situation in which you were
trying to solve a problem, but stopped working on it
because you couldn’t come up with the answer? Then,
after a while, when you returned to the problem, you
got the answer right away? What do you think might be
behind this process? - On August 14, 2003, a power failure caused millions of
people in the northeastern and midwestern United States
and in eastern Canada to lose their electricity. A few days
later, after most people had their electricity restored,
experts still did not know why the power failure had
occurred and said it would take weeks to determine the
cause. Imagine that you are a member of a special com-
mission that has the task of solving this problem, or some
other major problem. How could the processes described
in this chapter be applied to finding a solution? What
would the shortcomings of these processes be for solving
this kind of problem?- Think of some examples of situations in which you over-
came functional fixedness and found a new use for an
object.
Think ABOUT IT
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