Problem Solving
PERTEMUAN 10
9.1 Early research on problemsolving
• A cat placed in a box with a trapdoor was
not observed to show behaviour
approximating thinking, but instead
performed all kinds of behaviours until the
appropriate response was made
accidentally, the trapdoor would then open
and food was available as a reward
Scheerer (1963): nine-dot problem
9.2 Gestalt problem solving
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Representation
Set
Incubation
Insight
Insight
• Wolfgang Köhler (1925), on the island of
Tenerife.
– He founded a colony of chimpanzees and studied
their problem-solving behaviour.
– one chimp named Sultan was able to use a stick to
obtain some bananas that were placed on the outside
of his cage.
– When provided with two poles, neither of which was
long enough to reach the bananas, the ape first
‘sulked’, then eventually put one pole inside the other
to create a longer pole  Insight
• Gestalt psychologists saw problem solving as
the ‘closure’ of a problem, achieved by the
representation of the problem in an appropriate
way.
• In analogy with Gestalt theories of perception, a
problem is only a problem because it is
incomplete; the solution makes it complete, and
finding the solution ‘closes’ the incompleteness.
• Closure is accompanied by the flash of insight or
‘aha!’ experience.
Incubation
• Incubation: three general findings
– ONLY after much time and effort are already invested
– burst of insight (the “aha!” feeling)
– not in final form
• Five hypotheses about why incubation works
– decrease fatigue
– forget inappropriate sets and directions
– added practice - divided attention with part of your mind still
working on the problem
– change occurrence of an external event that triggers a new
association
• e.g. waffle iron and running shoes
– unconscious processing - run automatized search strategies
• Incubation results in
– innovation - synthesis of ideas
– insight - pieces come together
• Maier (1930, 1931) investigated the ‘twostring’ problem
Functional fixedness
• functional fixedness: the inability to use
an object appropriately in a given situation
because of prior experience of using the
object in a different way.
• Functional fixedness is a good example of
stereotypical thinking and is a ‘block’ to
problem solution
• Duncker (1945) concerns a problem where
subjects are handed a candle, a box of
nails and other objects
Problem-solving set
• Another potential ‘block’ to problemsolving is referred to as ‘set’ which is the
rote application of learned rules.
• Luchins (1942) experiment:
– demonstrates that some problems cannot be
solved through reproductive thinking
– and that our past experience can hinder
problem solution
An example of the water jug
problem
9.3 Problem space theory of
problem solving
Newell and Simon (1960s)
1. Representing the problem—a problem space is constructed which
includes both the initial state and the goal state, the instructions
and the constraints on the problem and all relevant information
retrieved from long-term memory. To assist such representation,
symbols, lists, matrices, tree diagrams, graphs and visual imagery
can all be used.
2. Selection of operators—operators are actions that will achieve a
goal, and are used for transforming the initial state
3.
Implementation of the selected operators—this results in a new
current state within the problem space.
4. Evaluation of the current state—if it corresponds to the goal, a
solution is reached.
Tower of Hanoi Problem
Problem-solving strategies
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Heuristics,
State-action tree.
Problem reduction
Means-end analysis
9.4 Problem solving and knowledge
• Expertise
• Problem-solving by analogy
9.5 Problem solving and reasoning
deficits
• Impairments in attention
• Impairments in abstract and conceptual
thinking
• Impairments in cognitive estimation
• Impaired strategy formation
• Deficits in everyday higher order
planning
Card sorting task
Improving Your Problem Solving
• Try
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novel or atypical associations
working backwards
solving a similar but easier problem
diagramming the problem
visualization
brainstorming (withhold evaluation)
analogies
evaluating other people’s solution to other problems
• read biographies
– breaking the problem into sub goals
• Techniques for systematizing your search
– inferences - what else applies
• consciously draw as many inferences as possible from the
goals, given, and actions
– classification of action sequences
• record all actions tried
• organize equivalence classes I.e. inverse actions
– state evaluation
• define a “quantitative” evaluation for all momentary outcomes
• choose actions that have evaluations closest to goals
– contradictions
• derive inferences from the given that are inconsistent with the
goal
• avoid actions that lead to inconsistent subgoals