Behaviorist psychologists thought problems were solved by trial & error and reproducing past responses.

Cognitive psychologists were convinced problem-solving wasn't random but that there was a series of mental processes involved.

The types of problems studied:

- Problems of Arrangement
- Problems of Transformation
- The Missionaries and Cannibals
- The Tower of Hanoi
- The Water Problem
- More recently: Computer Programming, Mine Clearing, Target Ranging, etc.

Three areas of problem-solving to be discussed:

A theory for solving transformation type problems: Newell & Simon's General Problem Solver

- This type of theory is called a
*production system*-- It produces states of knowledge

- Long-Term Memory
- Contains
*Procedural Knowledge*-- knowledge of the different types of operators that can be performed.

- Contains
- Short-Term Memory -- Limited Capacity (also called the
*Problem Space*). Contains:- Current State
- Goal State (Multiple Goals may be held)
- Sub-Goals may be held
- Operators are applied

The key difficulty in solving any transformation type problem is determining which operators to apply and when to apply them.

- Example

(These are called

- Create Subgoals -- Create an intermediate goal state that is closer to the final goal state. Try to find an operator that creates subgoal from current state.
- Means-End Analysis -- Strategy in which the operator that most greatly reduces the
difference between the current state and goal state is selected. To do this, you must:
- Note the difference between the current state and the Goal state.
- Either
- Test all the operators and choose the one that most greatly reduces this difference.
- Choose an operator that provides a substantial reduction, regardless of whether it provides the greatest reduction or not.

- Work Backwards -- Try to apply operators to the goal state to achieve the current state. Once this is accomplished, simply apply these in reverse order to the current state.

Expertise & Problem-Solving

Anderson (1988) suggested that there are two different types of problem-solving procedures used. These differentiate between novices and experts.

- Novices use
*weak-method*procedures.- These procedures are domain-independent. (They can be applied to any domain.)
- These require substantial mental effort to perform.
- These are virtually identical to Newell & Simon's model.

- Experts use
*domain-specific*procedures.- These are combinations of
*specific*problem-solving situations and a series of compiled actions leading to solutions. - These solutions are relatively automatically triggered.
- These procedures are created by successful repetitions.

- These are combinations of

Examples:

- Driving home.
- Flying a plane
- Playing video games

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- Seeing that the basic structure of the two problems as similar.
- Inferring the appropriate solution for the current problem from the analogous problem.

Gick & Holyoak (1980)

- S's attempted to solve Duncker's Radiation problem.
- Three groups of S's were run:
- A control group that only tried to solve this problem.
- A group previously given the analogous General/Fortress problem.
- A group given the General/Fortress problem and told that its solution would help in solving the radiation problem.

What factors determine whether an analogy is seen as appropriate?

- Time: If extra time is introduced between hearing an analogous problem and solving
the current problem, use of the analogy goes down.

- Similarity: The more similar the features of the analogous problem, the more likely it is
used.

- Abstraction: The more the person has thought about the underlying ideas of the analogous
problem(s), the more likely it is used.
- This is related to the "abstraction of schemas".
- Gick & Holyoak (1983) showed that if you gave S's multiple analogies and you forced them
to infer the
*general, underlying pattern*of all the analogies, S's were more likely to use the analogies.

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Schooler, Ohlsson & Brooks (1993) have recently suggested that solving insight based problems rely on different mental systems (structures) than solving logical, transformation problems.

They suggested that logical, transformation problems were solved with Verbal systems, but insight problems were solved with Nonverbal systems.

Experiment:

- S's solved a series of insight and logic problems.
- Half the S's were required to verbalize their strategies as they tried to solve the problem. The other half of the subjects (Control group) did not.

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