Problem Solving Techniques

In addition to general sense-making, metacognition tips that apply to problem solving in general (see the link for Pólya), there are some specific problem solving techniques of which to be aware. Not all will work on any given problem, but each one is useful enough in a variety of cases to justify including it here. E-mail me with any suggested additions.

1. Make a physical model.
2. Draw a graph.
3. Draw a picture (somewhere in between 1 and 2).
4. Organize data in a table or chart.
5. Look for a pattern (visual or in data).
6. Work backwards from the solution, if you know it.
7. Solve a special case or related simpler problem first.
8. Divide the problem into cases.
9. Argue by contradiction.
10. Estimate, and then refine your guesses.