Thinking & Problem Solving
Thinking
Thought
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Cognition—mental activities involved in
acquiring, retaining, and using knowledge
Thinking—manipulation of mental
representations to draw inferences and
conclusions.
– Mental processes directed at a goal or purpose.
– 2 kinds of mental representations:
1. Mental image—representation of objects
or events that are not present
2. Concepts – mental category we form to group
objects, events, or situations that share common
characteristics or features.
Mental Image
• Mental Image – mental representation of an object
or event not physically present.
• Mental imaging works similar to actual visual
imaging.
• Mental images are constructed and therefore subject
to error.
• Steven Kosslyn had
people memorize a
map of an island and
then asked them to
imagine specific
areas.
• People took time to
mentally scan their
mental image and
find the different
locations.
• People took the same
amount of time to
mentally scan the
image as they did to
visually scan it.
Concepts
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Concept—mental category we form to group
objects, events, or situations that share common
characteristics or features.
Three Types of Concepts:
1. Formal concept
2. Natural concept
3. Prototype
Examples of Concepts
• Formal concept— rigid rules or features
that define a particular concept.
– All or nothing categorization process
• Categories for solid, liquid, or gas
• A polygon is…
• Natural concept—Eleanor Rosch said these
form from everyday experience and do not
have boundaries that are sharply defined
– Name some mammals…
Concept Hierarchy
• A means to keep mental information
organized from basic concepts to
specific ones
Concept Hierarchy
Prototype
• A typical best example incorporating
the major features of a concept
• The closer a new object is to our
concept prototype the easier it is to
categorize it
• If an object has four wheels and doors
it probably fits our prototype for…
Problem Solving
•Thinking and behavior directed toward attaining a
goal that is not readily available.
•Must understand the problem correctly to
accurately solve it.
Trial & Error
• Trying a variety of solutions and eliminating
those that don’t work.
Algorithms
• A problem solving strategy that
guarantees the solution to the problem
• Not always the most efficient method
y + z = r2
Using an Algorithm
• Pick any month of the year.
• Look at four dates that form a square in that month
and add them together for a total.
• Given this total, how can you determine the four
dates the person chose using an algorithm?
• To find the first date divide the sum by 4 and then
subtract 4.
• To find the second date just add 1 to the date you
got above.
• To find the third date add 7 to the first date.
• To find the fourth date add 8 to the first date.
Heuristics
• A rule-of-thumb problem solving strategy that
makes a solution more likely and efficient but
does not guarantee a solution
• Example: “I” before “E” except after “C”
• They simplify the problem because they let you
reduce the number of possible solutions. (Use the
index to find a topic)
• These can be handy shortcuts, or they can get us
into trouble. (What if topic not in the index?)
Two ways we use Heuristics
• Subgoals – divide the problem into to
smaller more manageable parts
– As you solve each subproblem you get closer to
solving the larger problem.
• Working Backward – determine the steps to
reach your goal starting from the end point.
(i.e. making a budget).
Insight
• The sudden realization of the solution to a
problem
• “Unconscious Problem Solving” – You’re not
aware of the thought process that led you to an
insight.
The solutions to these problems are often characterized by sudden flashes
of insight. Solutions are on page 288 in your textbook.
Intuition
•
Intuition—coming to a conclusion without conscious
awareness of thought processes involved
• Kenneth Bowers explains: New info is combined
with existing info in the long-term memory in a twostage process.
1. Guiding Stage – perceive a pattern in the info but not
consciously. Perception formed from your areas of
expertise.
2. Integrative Stage – the pattern is now in the
consciousness and you try to prove or disprove your
hypothesis.
Obstacles to Solving
Problems
Functional Fixedness
• Type of mental set
• Inability to see an object as having
a function other than its usual one
• Have to unlock the door?
•Use a credit card.
•Tighten a screw without a screwdriver?
–Use scissors
Mounting candle problem
• Using only the objects
present on the right, attach
the candle to the bulletin
board in such a way that the
candle can be lit and will
burn properly
Answer to candle problem
• Most people do not think
of using the box for
anything other than its
normal use (to hold the
tacks)
• To solve the problem,
you have to overcome
functional fixedness
Problem Solving and Computers
Mode Confusion
• Play “Cockpit Confusion” (11:14)
Segment #11 from Scientific
American Frontiers
• Mode Confusion for pilots.
• When we rely too much on computers
Mental Set
• A tendency to approach a problem in
a particular way
• A well-established habit of
perception or thought
• The set may or may not be helpful in
solving a new problem
Nine dots problem
• Without lifting your
pencil or re-tracing
any line, draw four
straight lines that
connect all nine dots
Nine dots mental set
• Most people will not
draw lines that extend
from the square formed
by the nine dots
• To solve the problem,
you have to break your
mental set
Fixation
• A mental set that hinders the solution
of a problem
• One needs to think beyond the mental
set to solve the new problem
Can you
measure out
the amount of
water in the
right-hand
column, using
any of the
three jars (A,
B, and C) with
volumes as
shown in the
middle
column?
Problems 1 through 7 can all
be solved by filling Jar B,
then pouring off enough
water to fill Jar A once and
Jar C twice
desired volume = B - A - 2C
Problem 6 can be solved
with a simpler formula (A C), and so can Problem 7 (A
+ C). Many people miss
these easy solutions
because the mental set from
the first several problems
becomes fixated. Did your
thinking stay flexible?
Problems 1 through 7 can all
be solved by filling Jar B,
then pouring off enough
water to fill Jar A once and
Jar C twice
desired volume = B - A - 2C
Problem 6 can be solved
with a simpler formula (A C), and so can Problem 7 (A
+ C). Many people miss
these easy solutions
because the mental set from
the first several problems
becomes fixated. Did your
thinking stay flexible?
Decision Making
Decision Making
• Single feature model—make a decision by
focusing on only one feature
–Do you use this model in making decisions?
–Ever choose a date based on looks?
–Go see a movie because a friend told you it was
good?
–Choose a restaurant based on price?
•Choose a class based on how easy you heard it was?
Additive Model
• Systematically evaluate the important
features of each alternative.
• First create a list of factors that are
important to you.
• Then rate each alternative on each factor.
• What factors do you consider when
choosing a college? (See transparency
chart)
Elimination-by-Aspects
• Rate choices based on features.
• Evaluate each alternative one characteristic at a
time staring with the one you think is most
important.
• Eliminate those that do not meet the desired
criteria even if they have other desirable
characteristics.
• Over time your alternatives will be narrowed
down.
• We often use this to get our options to a few and
then use the additive model to make the final
decision.
Decisions Involving Uncertainty
Availability Heuristic
• Uses information from our memory to
judge the likelihood of events
• When instances of an event are easily
recalled we consider that event more
likely to reoccur.
• Can be correct or incorrect
•Rare events can cause us to
overestimate the likelihood of
reoccurrence. (i.e plane crashes)
Availability Heuristic
• Judge probability of an event by how easily you
can recall previous occurrences of that event
• Most will overestimate deaths from natural disasters
because disasters are frequently on TV
• Most will underestimate deaths from asthma
because they don’t make the local news
Representative Heuristic
• Estimate the likelihood of an event by comparing how similar
its essential features are to our prototype of the event.
• Example: Because Ken is 6‘6“, people often mistakenly
assume that he must be a member of his college's basketball
team
• Can be false if…
– We fail to consider possible variations from the prototype.
– Fail to consider approximate number of prototypes that actually exist.
• Most will overuse this strategy
Bias Effects
• Confirmation bias—only search for information
confirming one’s belief.
• Belief bias—accept only information that
conforms to beliefs
• Fallacy of positive instances—remember
uncommon events that confirm our beliefs
• Overestimation—tendency to overestimate
rarity of events
Overconfidence
• The tendency to be more confident
than correct when estimating the
accuracy of one’s beliefs and
judgments
• How well do you know your info for
this test?
Framing
• The way an issue is worded or presented
• Can influence decisions and judgments
– Do you think it is OK to kill unborn
children?
– Do you believe that abortion is an
appropriate option for those with
unwanted pregnancies?
Belief Perseverance
• The tendency for our preexisting opinions
to distort our sense of whether a particular
conclusion is logically valid
• Clinging to one’s initial beliefs even after
new information discredits the basis on
which they were formed
• the best advice to give people who want to
avoid belief perseverance is: “Consider
the Opposite”
Strategies for solving problems
1. Break mental sets – be creative! (see next slide)
2. Find useful analogy
3. Represent information efficiently
4. Find shortcuts
5. Establish sub-goals
6. Turn ill-defined problems into well-defined
problems
Be Creative! (pg. 313-314)
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Choose the goal of creativity
Reinforce creative behavior
Engage in problem finding
Acquire relevant knowledge
Try different approaches
Exert effort and expect setbacks
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