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In 1957 Newell and Simon developed the General Problem Solver, a computer program that used means-ends analysis to find solutions to a range of - problems that have clear paths (if not easy ones) to a goal state.
A description of these studies, with photographs, can be found here.
The Gestalt psychologists described several aspects of thought that acted as barriers to successful problem solving.
Another barrier to problem solving is functional fixedness, whereby individuals fail to recognize that objects can be used for a purpose other than that they were designed for.
Maier (1930) illustrated this with his two string problem.
Like difference reduction, the means-ends analysis heuristic looks for the action that will lead to the greatest reduction in difference between the current state and goal state, but also specifies what to do if that action cannot be taken.
Means-ends analysis can be specified as follows The application of means-ends analysis can be illustrated with the Tower of Hanoi problem.
In particular, in the process of thinking about a problem individuals sometimes "restructured" their representation of the problem, leading to a flash of insight that enabled them to reach a solution.
In (1915) Wolfgang Köhler described a series of studies with apes in which the animals appeared to demonstrate insight in problem solving situations.
At no point on either side of the river can orcs outnumber hobbits (or the orcs would eat the outnumbered hobbits).
The problem, then, is to find a method of transporting all six creatures across the river without the hobbits ever being outnumbered.