Four points for this lecture

1
Four points for this lecture

• Role of problem solving in history of cognition.
• Theories about problem
• Theories about solvers knowledge
• Theories about process.

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Role of problem solving in history of Cognition

• Young turks vs. Behaviourist establishment
• Challenge to model some high level behaviour
• Availability of computers as a metaphor
• Virtue of programme as model
• Explicit
• You can tell whether it works

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GPS Newell Simon

• Newell Simon pointed out that...
• Mental processes (MPs) are knowable
• MPs can be seen as a sequence of steps
• Computer programs show human-like behaviour
• Computer programs make every step explicit
• Programs are therefore ideal as models of human
  mental function.

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(Global modellers) sometimes seem to be
marching to a different drummer than scholars in
psychologys strong empirical tradition. Creative
thinking about what would constitute an adequate
comprehension theory is as important to most of
them as doing experiments to devise one. Anderson
(1976) for example, has argued convincingly for
the value of rational experiments, in which the
data are everyday facts of life and logical
proofs rather than systematic observations from
the laboratory. These strategies are an
unanticipated, and sometimes unappealing,
development for some strict laboratory
scientists. (p. 459) Lachman, Lachman,
Butterfield (1979)
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The dilemma

• L, L, B were saying that we may have to choose
  do we want to do experimental work? Or do we
  want to study complex behaviours such as problem
  solving?
• Cognitive psychologists split into 2 schools on
  these issues, one led by Herbert Simon and Alan
  Newell, one led by Daniel Kahneman and Amos
  Tversky

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The dilemma

• Simon and colleagues came out of the battle with
  Behaviourism both sides wanted convincing
  models of complex human behaviours (for Skinner,
  language for Simon, problem-solving.)
• Simon always argued that verbal reports were
  needed to study what really matters.

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The dilemma

• Kahneman and his colleagues were younger. They
  came out of cognitive psychology. They focused on
  the kinds of representations and processes that
  other cognitive psychologists worked on. These
  are not available to introspection, but are
  studied through ingenious experimental methods.

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The dilemma

• Newell died in the early 90s, Tversky in the mid
  90s, and Simon in 2002. Both Simon (1979) and
  Kahneman (2002) were awarded Nobel Prizes in
  Economics for their work on problem solving and
  decision making.
• This is some of what they learned on the way

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The problem, the solver, the process

• Types of problems (Greeno, 1978)
• Inducing structure (e.g., analogies)
• Discovery of a pattern relating elements of a
  problem to each other.
• Transformation (e.g., water jar problem)
• Manipulation of objects or symbols while
  following certain rules.

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The problem, the solver, the process

• Arrangement (e.g., anagrams, seating guests)
• All the elements are given, and the task is to
  re-arrange them.
• Any problem could be in more than one category.

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The problem, the solver, the process

• Some characteristics of the solver will be
  discussed in the chapter on expertise.
• Here, well talk about characteristics that
  interfere with problem-solving
• Functional fixedness
• Negative set

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The problem, the solver, the process

• Gestalt psychology Perception is in your head.
• Tau effect Kappa effect
• Principles that govern perception in humans
• Good form, good continuation, proximity,
  similarity
• Perception important in problem-solving.

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The problem, the solver, the process

• X X X G G G G G G G
• X X X
• X X X
• X X X G G G G G G G
• Are these columns or rows?
• Theyre both but we see the Xs as columns and
  Gs as rows, because of Proximity.

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The problem, the solver, the process

• Gestalt psychologists studied how our biases as
  perceivers influenced our problem-solving.
• Functional fixedness fix a candle to the wall.
  Youre given
• A table
• A candle
• A box of matches
• A box of tacks.

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The problem, the solver, the process

• Subjects are better at candle task if the matches
  and the tacks are on the table, not in the box.
• It is easier to think of empty boxes as something
  other than containers to overcome functional
  fixedness.
• Other examples panty-hose can be used to make a
  fan belt

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The problem, the solver, the process

• Mental set
• Set is a preference for certain operators (things
  you can do, actions you can take to solve a
  problem).
• Luchins and the water jar problem
• Einstellung (mechanization of thought) people
  kept using a strategy that worked even when a
  better one was available

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The problem, the solver, the process

• Humans are, nonetheless, very good at
  problem-solving. We are the great problem-solvers
  of the world.
• We are good at solving individual problems.
• Animals solve problems through evolution.
• Humans solve problems much faster.
• We keep solving new problems.
• We go out of our way to find new problems

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The problem, the solver, the process

• 3 stages of problem solving (Hunt Ellis, 1993).
• 1. Understanding the problem
• This is about representation how do you
  represent the problem?
• Gestalt psychologists said, this is a question of
  perception (see lawyer joke).

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The problem, the solver, the process

• 2. Generating solutions. You could
• Generate all possible solutions (e.g., chess)
• Generate solutions randomly
• Use a strategy such as a heuristic

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Some heuristics for producing solutions

• A heuristic is a rule of thumb, a simple
  strategy that works often, but not always. (In
  contrast, algorithms always work, but not always
  available, and can be unworkable when available.)
• A. Generate-test method
• very slow if lots of possible solutions exist

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Some heuristics for producing solutions

• B. Means-ends analysis
• must know what the ends are you seek
• must know the means available
• Current state
• Goal state
• Difference between them
• Operators

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Some heuristics for producing solutions

• C. Working backwards
• Start by figuring out what the solution to your
  problem looks like.
• Move backward from that goal to your current
  state.
• This defines a path that leads to goal
• E.g., I want to get into a graduate programme
  in cognitive psychology.

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The problem, the solver, the process

• 3. Evaluating solutions
• How do you know when youve solved your problem?
• A problem for psychotherapists how do you know
  when youre finished, when your client doesnt
  need you any more?

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The problem, the solver, the process

• Hunt Ellis suggested that there are
  general-purpose operations applicable to a
  variety of problems.
• That invites an attempt to create a
  problem-solving program that uses general purpose
  operations.
• Newell Simons GPS is the most important such
  program.

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The problem, the solver, the process

• GPS used means-ends analysis.
• Assess the difference between current state and
  goal state.
• Find and apply an operator that can reduce that
  difference.
• Assess the difference again. If no difference,
  exit if difference still, find an operator.

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The problem, the solver, the process

• General Problem Solver (GPS)
• For complex problems, GPS model suggests two ways
  we can go wrong
• If we cant figure out most important difference
• If we dont have a relevant operator.

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The problem, the solver, the process

• Finding the most important difference
• Sub-goaling set up a series of sub-goals before
  you begin the problem-solving process.
• E.g., if you want to go to medical school,
  youll need some chemistry courses. Do you have a
  chemistry course? If not, look for an operator
  (take a chemistry course).

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The problem, the solver, the process

• Finding a relevant operator
• One way of obtaining new operators is through
  formal education or training.
• A second way is through analogy seeing how a
  different problem is similar to the current one.
  This may let you adapt operators that worked with
  that problem (Gick Holyoak, 1980).

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The problem, the solver, the process

• Using analogy to find a relevant operator
• One thing that gets in the way of seeing
  analogies is focus on the surface form of a
  problem.
• A major difference between novices and experts
  in any area is that experts are less likely to
  focus on the surface form. They see the
  underlying structure of problems in the domain.
• Well come back to this point soon