Obstacles to Problem Solving

259
Problem Solving
■ What did the researcher find?
Bradshaw found several factors that might have contributed to the Wright brothers’
success. First, as bachelors, they had a lot of spare time to work on their designs. Second, they owned a bicycle shop, so they were familiar with lightweight, but sturdy,
structures. Third, they were brothers who had a good working relationship. And finally,
as mechanics, they were good with their hands. Were any of these features directly
responsible for their successful invention of the airplane?
Perhaps, but Bradshaw’s use of the comparative case study method revealed that
everyone else working on the problem of flight shared at least one of these features
with the Wright brothers. For instance, an engineer named Octave Chanute was good
with his hands and familiar with lightweight, sturdy structures. And two other pairs of
brothers had worked together to try to invent a flying machine.
However, Bradshaw found one feature that was unique to the Wright brothers’
approach. Of all the inventors working on the problem, only the Wrights spent considerable time and energy testing aircraft components before field-testing complete
machines. This feature was important because even the best designs of the day flew for
only a few seconds—far too briefly to reveal what was working and what was not. As
a result, inventors had to guess about what to fix and often ended up with an
“improved” model that was worse than the previous one.
■ What do the results mean?
Bradshaw’s comparative case study method suggested that the problem-solving strategy of decomposition was the basis for the Wright brothers’ success. By testing components, they were able to collect the information they needed to develop an efficient
propeller, improve the shape of the wings for maximum lift, and refine other vital components of their aircraft.
■ What do we still need to know?
Decomposition is a strategy often seen in the laboratory, and as demonstrated by
the case of the Wright brothers, it is a potentially important aspect of major inventions and discoveries beyond the laboratory. But is decomposition, or means-end
analysis, used in other real-world settings as well? To find out, researchers will need
to conduct additional studies of people’s mental strategies as they attempt to solve
problems ranging from how to install a new computer to how to efficiently search
the Internet.
Obstacles to Problem Solving
The failure of the Wright brothers’ competitors to use decomposition is just one example of the obstacles that face problem solvers every day. Difficulties frequently occur at
the start, during the diagnosis stage, when a person forms and then tests hypotheses
about a problem.
As a case in point, consider this true story: In September 1998, John Gatiss was in
the kitchen of his rented house in Cheltenham, England, when he heard a faint
“meowing” sound. Worried that a kitten had become trapped somewhere, he called
for the fire brigade to rescue the animal. The sound seemed to be coming from the
electric stove, so the rescuers dismantled it, disconnecting the power cord in the
process. The sound stopped, but everyone assumed that wherever the kitten was, it
was now too frightened to meow. The search was reluctantly abandoned, and the
stove was reconnected; four days later, however, the meowing began anew. This time,
Gatiss and his landlord called the Royal Society for the Prevention of Cruelty to Animals (RSPCA), whose inspectors heard the kitten in distress and asked the fire brigade
260
FIGURE
Chapter 7 Thought, Language, and Intelligence
7.5
The Jar Problem
The task here is to come up
with the number of quarts of
by
water shown in the first column by using jars with the capacities
shown in the next three columns. Each line
represents a different problem, and you
have an unlimited supply of water for
each one. Try to solve all seven problems
without looking at the answers in the text.
doing
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learn
Quantity
1.
2.
3.
4.
5.
6.
7.
21
10
19
21
18
6
15
quarts
quarts
quarts
quarts
quarts
quarts
quarts
Jar A
8
6
5
20
8
7
12
Jar B
35
18
32
57
40
17
33
Jar C
3
1
4
8
7
2
3
to come back. They spent the next three days searching for the cat. First, they dismantled parts of the kitchen walls and ripped up the floorboards. Next, they called
in plumbing and drainage specialists, who used cables tipped with fiber-optic cameras to search remote cavities where a kitten might hide. Rescuers then brought in a
disaster search team, which tried to find the kitten with acoustic and ultrasonic
equipment normally used to locate victims trapped under earthquake debris. Not a
sound was heard. Increasingly concerned about how much longer the kitten could
survive, the fire brigade tried to coax it from hiding with the finest-quality fish, but
to no avail. Suddenly, there was a burst of “purring” that, to everyone’s surprise (and
the landlord’s dismay), was traced by the ultrasonic equipment to the clock in the
electric stove! Later, the landlord commented that everyone assumed Gatiss’s original hypothesis was correct—that the “meowing” came from a cat trapped in the kitchen.
“I just let them carry on. If there is an animal in there, you have to do what it takes.
The funniest thing was that it seemed to reply when we called out to it” (London Daily
Telegraph, 1998).
How could fifteen fire-rescue workers, three RSPCA inspectors, four drainage workers, and two acoustics experts waste eight days and cause nearly $2,000 in damage to
a house in pursuit of a nonexistent kitten? The answer lies in the fact that they, like the
rest of us, were prone to four main obstacles to efficient problem solving, described in
the following sections.
mental set The tendency for old
patterns of problem solving to persist.
functional fixedness The tendency to
think about familiar objects in familiar
ways.
Multiple Hypotheses Often, we begin to solve a problem with only a hazy notion
of which hypotheses to test. Suppose you heard a strange sound in your kitchen. It
could be caused by several different things, but which hypotheses should you test, and
in what order?
People have a difficult time working with more than two or three hypotheses at
a time (Mehle, 1982). The limited capacity of short-term memory may be part of
the reason (Halford et al., 2005). As discussed in the memory chapter, a person can
hold only about seven chunks of information in short-term memory. Because a
single hypothesis, let alone two or three, might include more than seven chunks, it
may be difficult or impossible to keep them all in mind at once. Further, the availability and representativeness heuristics may lead people to choose the hypothesis
that comes most easily to mind and seems most likely to fit the circumstances (Tversky
& Kahneman, 1974). That hypothesis may be wrong, though, meaning that the
correct hypothesis is never considered. Mr. Gatiss diagnosed what he heard as
distressed meowing because it sounded more like a kitten than a clock and because
it was easier to imagine an animal trapped behind the stove than a suddenly faulty
clock inside it.
261
Problem Solving
FIGURE
7.6
The Nine-Dot Problem
The problem is to draw no
more than four straight lines
by
that run through all nine dots
on the page without lifting your pencil
from the paper. Figure 7.8 shows two ways
of going beyond mental sets to solve this
problem.
doing
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learn
Mental Sets Sometimes people are so blinded by one hypothesis or strategy that
they stick with it even when better alternatives should be obvious. This is a clear case
of the anchoring heuristic at work. Once Gatiss reported hearing a “trapped kitten,” his
description created an assumption that everyone else accepted and that no one challenged. Figure 7.5 shows a problem-solving situation in which such errors often appear.
The first problem in the figure is to come up with 21 quarts of liquid by
learn using 3 jars that have capacities of 8, 35, and 3 quarts, respectively. Before
by
doing you read any further, try to solve this problem and all the others listed in
Figure 7.5.
How did you do? You probably figured out that the solution to the first problem is
to fill Jar B to its capacity of 35 quarts, and then use its contents to fill Jar A to its
capacity of 8 quarts, leaving 27 quarts in Jar B. Finally, you pour from Jar B to fill Jar
C twice, leaving 21 quarts in Jar B [27 (2 3) = 21]. You probably found that a
similar solution worked for each problem. In fact, by the time you reached Problem 7,
you might have developed a mental set, a tendency for old patterns of problem solving
to persist (Luchins, 1942; Sweller & Gee, 1978). If so, your mental set probably caused
you to use the same old formula (B A 2C) even though a simpler one (A C)
would have worked just as well. Figures 7.6 and 7.8 show another way in which mental sets can restrict our perception of the possible solutions to a problem.
Another restriction on problem solving may come from experience with objects.
Once people become familiar with using an object for one purpose, they may be
blinded to other ways of using it. Long experience may produce functional fixedness,
a tendency to use familiar objects in familiar, rather than creative, ways (German &
Barrett, 2005). Figure 7.7 provides an example. An incubation strategy often helps to
break mental sets.
2
Ignoring Negative Evidence On September 26, 1983, Lt. Col. Stanislav Petrov was
in command of a secret facility that analyzed information from Russian early-warning
satellites. Suddenly, alarms went off as computers found evidence of five U.S. missiles
being launched toward Russia. Tension between the two countries was high at the time,
so, based on the availability heuristic, Petrov hypothesized that a nuclear attack was
FIGURE
7.7
An Example of Functional
Fixedness
Before reading further, look at
this drawing and ask yourself
how you would fasten together two strings that are hanging from
the ceiling but are out of reach of each
other. Several tools are available, yet most
people don’t think of attaching, say, a pair
of pliers to one string and swinging it like
a pendulum until it can be reached while
holding the other string. This solution is
not obvious because we tend to fixate on
the function of pliers as a tool rather than
as a weight. People are more likely to
solve this problem if the tools are scattered around the room. When the pliers
are in a toolbox, their function as a tool is
emphasized, and functional fixedness becomes nearly impossible to break.
doing
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learn
by