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The diagram at the left shows solution paths that result from using a concept based approach to problem solving. There may be several possible concepts which respond to the question asked. These lead to different paths through solution space and draw on different concepts in knowledge space. A solution path consists of continuous, logically connected steps.

A particular path may provide alternatives as one proceeds along the solution path. By choosing different paths and branches the solutions and the concepts that support it can be explored . There is much, though, that is common to the different paths. By such exploration an understanding of the problem, its solution and the concepts can evolve. The most elegant solution can be discovered.

It is much like traveling from one place to another. One can choose different routes and different modes of transportation. In this way one can have experiences that others have not had and see things others have not seen. Travel the less traveled paths in exploring a problem solution. You will find many special places.

The diagram at the right above is the result of not using a concept based approach to problem solving. No satisfaction or enjoyment is available from the approach shown in that diagram.

Introductory physics textbooks and teaching materials generally present problem solutions in the manner depicted in the right-hand diagram. The resulting lack of logical structure makes the material unduly difficult to learn. The material presented here will help those interested in making the transition to a coherent concept-based approach to problem solving as represented by the left diagram.

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Copyright 1995. Howard C. McAllister