150 ❯ Step 4. Review the Knowledge You Need to Score High
Is someone who loves to solve math problems more likely to be a mathematics professor
or a high school student? Although many people immediately reply that it must be the
professor, the correct answer to the problem is the high school student. The total number
of high school students is so much greater than the total number of mathematics profes-
sors that even if only a small fraction of high school students love to solve math problems,
there will be many more of them than mathematics professors. Framing refers to the way
a problem is posed. How an issue is framed can significantly affect people’s perceptions,
decisions, and judgments. We are more likely to buy a product that says it is 90 percent
fat-free, than if it says it contains 10 percent fat. A suggestion can have a powerful effect
on how we respond to a problem. Kahneman and Tversky asked if the length of the
Mississippi River is longer or shorter than some suggested length and then asked how
long the person thinks the river actually is. When the suggested length was 500 miles, the
length guessed was much smaller than when the suggested length was 5,000 miles. The
anchoring effect is this tendency to be influenced by a suggested reference point, pulling
our response toward that point.Biases
Confirmation bias is a tendency to search for and use information that supports our
preconceptions and ignore information that refutes our ideas. To lessen this tendency, we
can consider the opposite. Belief perseverance is a tendency to hold onto a belief after the
basis for the belief is discredited. This is different from belief bias, the tendency for our
preexisting beliefs to distort logical reasoning, making illogical conclusions seem valid or logi-
cal conclusions seem invalid. Hindsight bias is a tendency to falsely report, after the event,
that we correctly predicted the outcome of the event. Finally, the overconfidence bias is a
tendency to underestimate the extent to which our judgments are erroneous. For example,
when reading this section dealing with obstacles to problem solving and errors in decision
making, we tend to think that we make these errors less often than most other people do.Creativity
Creativity is the ability to think about a problem or idea in new and unusual ways, to come
up with unconventional solutions. One way to overcome obstacles to problem solving
and avoid biases in reasoning is to borrow strategies from creative problem solvers.
Convergent thinkers use problem-solving strategies directed toward one correct solution
to a problem, whereas divergent thinkers produce many answers to the same question,
characteristic of creativity. When they feel stuck on a particular problem, creative thinkers
tend to move on to others. Later they come back to those stumpers with a fresh approach.
To combat the confirmation and overconfidence biases, when beginning to solve a prob-
lem, creative problem solvers brainstorm, generating lots of ideas without evaluating them.
After collecting as many ideas as possible, solutions are reviewed and evaluated.