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Problem Solving

George Polya identified step-by-step thought process for problem solving.  They can be applied to reference work, modeled for reference service users, and taught as enabling skills.  

1.  Identify the Problem

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 Concentrate on its aim. 

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What do you want? 

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Write the question down -- helps focus the mind. 

2.  Take Stock of What You Have 

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What are the facts?

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What inferences can be reasonably and confidently made? 

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What potential uses can be made of the facts known? 

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What assumptions can you use? 

3. Assess the prospects for success 

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Is there an answer to this question? 

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If there is, can you find it? 

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Is there just one solution, several solutions, no solution 

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Is your idea for solving the problem clear or vague? 

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Is your first hunch likely to work? 

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Is there another hunch that may seem less satisfactory, but may lead in the right direction? 

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Have initial guesses helped clarify assumptions and strategies as productive or unproductive? 

4. If you can't solve the problem directly, look for related problems 

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Look around for an appropriate related problem. 

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See what information you can glean from the question 

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Find questions from the data. 

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See what questions your first examination of information may raise that need clarifying.

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What kind of problem is it? 

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Is it related to any known problem? 

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Is it like any known problem? 

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Do you know a related problem?

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Can you imagine an analogous problem? A more general problem? A more specific problem?

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Make a note of related problems, problems with a similar structure.

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Imagine a similar problem, even a similar problem in a different domain, but preferably one that you could also image a strategy for solving.

5.  Restate the problem and solve it by connecting the stated problem to existing knowledge. 

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This creates a usable piece of knowledge to attack the problem from the outside. 

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Restating the problem may bring in new elements. 

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Consider the analogy of unwinding a heavily knotted parcel by locating a free piece of movable string

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The goal is to jog your mind into potential solutions that may have been overlooked. 

6.  Focus on auxiliary problems. 

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Reduce a difficult problem to several related problems. 

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Investigate the validity of any assumptions.

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Widen or narrow the problem by place it in a larger/smaller context.

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Examine other ideas than the first one that comes to mind

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Review the logical implications of each idea to identify those that are helpful

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Use analogies and metaphors to connect knowledge with the problem at hand.

7. When all else fail, reassess the situation for irrelevant details and side issues.

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Examine the problem in its simplest terms, looking again at the question, the known facts, and the circumstances. 

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Is everything present being considered?

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Are the concepts that are essential to the problem understood?

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Is it appropriate to go back and define terms?
Reassessment is the most important problem solving strategy of all! 

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