Problem solving
Problem Solving: 3 Types of Problems
Jim Greeno (1978)
• Inducing structure
• Arrangement problems
• Transformation problems
Inducing structure
– to discover relations among
numbers, words, symbols, or ideas
– Series completion and analogy
problems
Merchant : Sell :: Customer : _____
Lawer : Client :: Doctor : ______
Arrangement problems
– arrange the parts of a problem
in a way that satisfies some
criterion
– often solved by insight, a
sudden discovery of the
correct solution following
incorrect attempts based
primarily on trial and error
– String problem and Anagrams RWAET
KEROJ
Transformation problems
– carrying out a
sequence of
transformations in
order to reach a
specific goal
– Hobbits and orcs
problem
– Water jar problem
Effective Problem Solving
• Well defined vs. ill defined problems
– the initial state, the goal state, and the
constraints are clearly specified
– Most real world problems are ill defined
Creativity
• Strernberg’s five components
–Expertise
–Imaginative thinking skills
–Adventuresome personality
–Intrinsic motivation
–A creative environment
Barriers to Effective Problem Solving
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Irrelevant Information
Confirmation Bias
Functional Fixedness
Mental Set (people persist in using problem-solving
strategies that have worked in the past)
• Unnecessary Constraints
Barriers to Effective Problem Solving
– Functional fixedness is the tendency to view
objects as functioning only in their usual or
customary way
– Mental set is the tendency to persist in solving
problems with solutions that have worked in the
past
Obstacles to Problem Solving
• arrange six matches to
form four equilateral
triangles
• Attach the candle to the
wall in a way that wax
will not drop onto the
table below
Obstacles to Problem Solving
Approaches to Problem Solving
• Algorithms (methodical step by step)
• Heuristics (guiding principles)
Approaches to Problem Solving
• Algorithms (methodical step by step)
– Systematic trial-and-error
– Trying all possible alternatives
– Guaranteed solution
Algorithmic Problem Solving
Figure 8.12 The tower of Hanoi problem
Approaches to Problem Solving
• Heuristics (guiding principles) “rule of thumb”
– Shortcuts
– No guaranteed solution
• Forming subgoals to solve one part
• Working backward from a specified endpoint
• Searching for analogies from previous problem to solve a
current one
• Changing the representation of a problem
Figure 8.16 Representing the bird and train problem
Making Decisions and
Forming Judgments
Using and Misusing Heuristics
Decisions Involving Uncertainty:
Estimating the Probability of Events
– We tend to rely on 2 rule-of-thumb strategies to
help us estimate the likelihood of events
1. The availability heuristic is a strategy in which the
likelihood of an event is estimated on the basis of
how readily available other instances of the event
are in memory. The less accurately our memory of
an event reflects the actual frequency of the event,
the less accurate our estimate of the event’s
likelihood will be
The Availability Heuristic
Solving Problems and Making
Decisions
2. The representativeness heuristic is a strategy in
which the likelihood of an event is estimated by
comparing how similar it is to our prototype of the
event. This strategy can produce faulty estimates if
• We fail to consider possible variations from the
prototype, or
• We fail to consider the approximate number of
prototypes that actually exist
The Representative Heuristic
Solving Problems and Making
Decisions
Four obstacles to logical thinking can account for
much of the persistence of unwarranted beliefs in
pseudosciences or other areas
• The belief-bias effect occurs when people accept only
the evidence that conforms to their belief, rejecting or
ignoring any evidence that does not
• Confirmation bias is the strong tendency to search for
info or evidence that confirms a belief, while making
little or no effort to search for info that might disprove
the belief
Solving Problems and Making
Decisions
• The fallacy of positive instances is the tendency to
remember uncommon events that seem to confirm our
beliefs and to forget events that disconfirm our beliefs
• The tendency to overestimate the rarity of events is
referred to as the overestimation effect
Overconfidence
Culture, Cognitive Style,
and Problem Solving
• Field dependence – relying on external frames
of reference
• Field independence – relying on internal
frames of reference
– Western cultures inspire field independence
– Cultural influence based in ecological demands
• Holistic vs. analytic cognitive styles
Decision Making:
Evaluating Alternatives and Making Choices
• Simon (1957) – theory of bounded rationality
• Making Choices
– Additive strategies
– Elimination by aspects
– Risky decision making
• Expected value
• Subjective utility
• Subjective probability
Table 8.3 Application of the additive model to choosing an apartment
Heuristics in Judging Probabilities
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The availability heuristic
The representativeness heuristic
The tendency to ignore base rates
The conjunction fallacy
The alternative outcomes effect
Figure 8.18 The conjunction fallacy
Understanding Pitfalls in Reasoning
About Decisions
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The gambler’s fallacy
Overestimating the improbable
Confirmation bias and belief perseverance
The overconfidence effect
Framing
Evolutionary Analyses: Flaws in Decision Making and
Fast and Frugal Heuristics
• Cosmides and Tooby (1996)
– Unrealistic standard of rationality
– Decision making evolved to handle real-world
adaptive problems
– Problem solving research based on contrived,
artificial problems
• Gigerenzer (2000)
– Quick and dirty heuristics
– Less than perfect but adaptive