PSGY1010
Cognitive Psychology 1
Thinking I:
Problem Solving
Dr Chung Kai Li
KaiLi.Chung@nottingham.edu.my
Thinking lectures
Eysenck & Keane
▪ Lecture 1: Problem solving
▪ Lecture 2: Reasoning
▪ Lecture 3: Decision-making
Chapter 12, 13, & 14
(pp.573-711)
Today’s lecture
Learning objectives:
▪ Distinguish between Gestalt and Behaviourist approaches to problem solving,
providing examples
▪ Describe Wallas’ stage theory of problem solving
▪ Define and describe evidence for the existence of incubation in problem solving
▪ Describe different barriers to problem solving, using experimental evidence
▪ Describe feelings-of-knowing with feelings-of-warmth
3
What is a problem?
▪ “A problem arises when a living organism has a goal, but does not
know how this goal is to be reached” (Duncker, 1945)
▪ A problem could therefore be said to have three crucial elements:
Starting state
A set of processes (usually called operators)
that can transform the starting state into the
goal state
Goal state
4
Two historical approaches
The Behaviourist Approach
The Gestalt Approach
• Problem solving occurs through
an incremental process of trialand-error.
• Problem solving occurs through
a process of restructuring and
insight.
5
The Behaviourist approach
▪ Behaviours are learned from interactions with the environment.
▪ All behaviour can be reduced to simple stimulus-response behaviours.
▪ A specific, predictable response occurs to a given stimulus.
▪ Behaviourism is primarily concerned with observable behaviours (as
opposed to internal events like thinking and emotion).
▪ Behaviour should be studied scientifically using experiments
6
Edward Lee Thorndike (1874-1949)
▪ Prior to Charles Darwin, animal and human
minds were thought to be fundamentally
different
▪ Darwin argued, on the basis of shared
evolutionary ancestry, that there’s a continuity
between human brains and the brains of other
animals
▪ Thorndike was concerned with problem solving
and other complex cognitive functions in animals
7
Thorndike’s Puzzle Box (1898)
▪ Thorndike placed cats in a puzzle box with a
clasp to hold the door shut
▪ The door could not be opened without the
cat performing a sequence of actions
▪ Cats were repeatedly exposed to the
problem and the time taken to solve it was
recorded and plotted
▪ Did they develop ‘insight’?
8
Thorndike’s Puzzle Box (1898)
▪ If the cats developed insight, the following results could be expected:
Did this happen?
→ No!
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Thorndike’s Puzzle Box (1898)
▪ The cats learn to escape from the puzzle box by a process of trial and
error, eventually pulling the correct string
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Thorndike’s Puzzle Box (1898)
▪ Although the initial escape is initially by chance behaviour, future
escapes become progressively faster as the connection between
behaviour and reward is learned.
▪ Problem solving was incremental (trial-and-error) rather than
insightful.
▪ Thorndike proposed the ‘Law of Effect’:
▪ Any behaviour that is followed by pleasant consequences is likely
to be repeated
▪ Any behaviour followed by unpleasant consequence is likely to be
stopped.
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The Gestalt approach
▪ After the work of Thorndike many scientists thought that animals could
only learn through trial-and-error.
▪ Gestalt psychologists reacted against the view. They drew a
distinction between:
▪ Reproductive thinking: involving re-use of previous experience
▪ Productive thinking: involving a novel restructuring of the problem
▪ Insight occurs during productive thinking when the problem is
suddenly restructured, and the solution becomes clear.
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Wolfgang Köhler (1925)
▪ Köhler (1925) was a German Gestalt psychologist trapped on Tenerife
during WW1.
▪ Found a colony of chimpanzees and spent time observing their
problem-solving behavior
▪ He believed that animal thought was more complex than most people
imagined
▪ The puzzle box experiment was not ideal because the responses
required by the cat were so unfamiliar, the cat could not perceive a
mechanism
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Köhler (1925)
▪ Of these chimpanzees, Sultan was Köhler’s favourite subject
▪ Sultan was given the problem of getting some bananas that were
outside his cage and beyond the reach of his arms.
▪ If he was given two sticks that were both too short to reach the
bananas on their own, he would first give up and sulk.
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Köhler (1925): Sultan’s insight
▪ After a period of time, he
suddenly went to the sticks and
placed one inside the other
creating a stick long enough to
reach the bananas.
▪ He restructured the problem
and had a moment of insight.
15
Köhler (1925)
▪ Problem solving is viewed to be the result of sudden insight rather
than incremental trial and error.
▪ The moment the correct solution is found, performance is perfect.
▪ Why the difference between Thorndike’s cats and Köhler’s chimps?
▪ Thorndike’s cats were hungry and distressed whereas Köhler’s
chimps were well-fed and cared.
▪ Birch (1945) found that apes raised in captivity did not show this
same level of insight.
16
Wallas (1926): Four stages of creative thinking
▪ The importance of insight has been formalised into accounts of
creative thinking:
1. Preparation: A problem is formulated, and initial attempts are
made to solve the problem.
2. Incubation: The problem is set aside, and no conscious work is
done on it.
3. Illumination: A sudden inspiration provides a new insight into the
way in which the problem might be solved.
4. Verification: Conscious work on the problem develops and tests
the inspiration to provide a full solution to the problem.
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Incubation followed by Illumination
▪ Anecdotal evidence from some scientific discoveries:
▪ The physiologist and physicist Helmholtz described how “happy
ideas come unexpectedly, without effort, like an inspiration.”
▪ The mathematician Hadamard (best known for his proof of prime
number theory) wrote “unconscious activity often plays a decisive
part in discovery; that periods of ineffective effort are often
followed, after intervals of rest or distraction, by moments of
sudden illumination.”
▪ Is there experimental evidence that incubation is really useful?
18
Silveira (1971)
▪ Starting State: You are given four chains, each
consisting of three links.
▪ It costs 2¢ to open a link and 3¢ to close a link.
▪ All links are closed at the beginning of the
problem.
▪ Goal State: Your goal is to join all 12 links of chain
into a single circle at a cost of no more than 15¢.”
▪ Solve the problem: Find the set of processes that
transform the goal state into the starting state.
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Silveira (1971): The cheap necklace problem
▪ Control Group: Worked on the problem for half an hour.
▪ 55% solved the problem
▪ Experimental Group 1: Worked for half an hour and then
interrupted by a half-hour break during which other activities were
performed
▪ 64% solved the problem
▪ Experimental Group 2: Worked for half
an hour and then interrupted by a fourhour break during which other
activities were performed
▪ 85% solved the problem
20
Murray & Denny (1969): When is Incubation
necessary?
▪ Participants were divided into high and low ability groups on the basis
of their performance on a ‘use of objects test’ of creativity.
▪ Participants were then given 20 minutes to solve a complex practical
problem (moving steel balls into a metal cylinder without getting within
8 feet of the cylinder).
▪ Interpolated Activity or ‘Incubation’ Group: Given a 5-minute break
▪ Continuous Activity or ‘Control’ Group: Not given a 5-minute break
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Murray & Denny (1969)
▪ For the high ability participants the break acted as a distraction from the
problem at hand & interfered with performance.
▪ The low ability participants for whom the problem was relatively hard were
aided by the break– they required a period of incubation.
▪ Individual differences in problem-solving ability determine whether an
incubation period is effective.
22
What are some barriers to successful problem
solving?
▪ Functional fixedness
▪ People fixate one a property/function of an object that can be used
to solve the problem and cannot think about it in a different way.
▪ The Einstellung Effect
▪ Learn a particular strategy for solving a problem which has
produced success in the past but continue to use it even when
inappropriate.
23
Duncker (1945): Functional fixedness
▪ “Support the candle on the wall so that it doesn’t drip on the table
below”
24
Duncker (1945): Functional fixedness
▪ Participants often tried to nail the candle to the
wall or glue the candle with wax.
▪ The task becomes easier when the box of
nails is emptied onto the table.
▪ Participants are no longer fixated on the
box’s normal function of holder nails.
▪ Instead, they can re-conceptualise it as a
candle holder.
25
Overcoming Fixedness: The Nine Dot Problem
▪ Draw four continuous straight lines connecting all the dots without lifting your pen
from the paper (Scheerer, 1963)
▪ According to Scheerer most people cannot solve this because they assume (are
fixated) in believing they must stay within the square.
▪ To solve the problem, you must draw outside the square!
▪ Weisberg & Alba (1981) found that about 20% of people can solve the problem
when told to draw outside the box
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Luchins (1942): The Water Jug Problem
▪ Each problem specifies the capacities of jugs A, B, and C, and a final
desired quantity.
▪ The task is to work out how to use the jugs to measure out the final
required quantity.
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Three jug solution
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Luchins (1942): The Einstellung Effect
▪ The Einstellung Effect
▪ The negative effect of previous experience when solving new
problems.
▪ People become biased by previous experience to use all three jugs
to solve all problems.
▪ The most efficient solution to problems 7 is to use just two jugs.
29
Brown & McNeill (1966): Feeling of Knowing
▪ Even when we cannot solve a problem immediately, we sometimes
feel closer to the solution than at other times.
▪ A classic example is the “tip-of-the-tongue phenomenon”
▪ Brown & McNeill (1966): What is the word for “a navigational
instrument used in measuring angular distances, especially the
altitude of the sun, moon and stars at sea?”
▪ When people claim the answer is “on the tip of their tongue” they
are 57% correct in identifying the first letter of the word.
▪ The correct word is a ‘sextant’
30
Metcalfe (1986): Feeling of Warmth
▪ Feelings-of-warmth sometimes predict how close to solution you are.
▪ Metcalfe (1986) compared feelings-of-warmth for incremental and insight
problems.
▪ This seems to be the case when incremental solutions are required rather than
insight solutions.
▪ Feelings of warmth predicted performance on Incremental Problems (e.g.,
Tower of Hanoi)
▪ Feelings of warmth did not predict performance on Insight Problems (e.g.,
Reversing Triangle problem)
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Summary
▪ The Behavioural approach suggests problem solving occurs through the process
of trial-and-error, whereas the Gestalt approach suggests it occurs through a
moment of insight.
▪ Wallas’ four stages of creative thinking highlight the importance of incubation in
problem solving.
▪ There is anecdotal evidence for this
▪ There is some experimental evidence for this
▪ Individual differences influence the efficacy of an incubation period
▪ Functional Fixedness and the Einstellung Effect are two barriers to problem
solving.
▪ Feelings-of-warmth predict performance on incremental but not insight problems.
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Thank you
Any questions?