Polya's problem-solving phases

In the late 1940s, a mathematician named George Polya outlined a set of problem-solving "phases" as follows:
  1. Understand the problem.
  2. Devise a plan for solving the problem.
  3. Carry out the plan.
  4. Evaluate the solution for accuracy and for its potential as a tool in solving other problems.
These shouldn't be understood as steps to be followed. They are phases that will be completed some time during the problem-solving process.

As well, these are not to be understood as a sequence. In particular, phase 2 can proceed before phase 1 is complete, and phase 4 can be applied to the plan of phase 2 or to preliminary portions of phase 3 (thus happening before phase 3 is complete). In fact, in the "ages problem" exercise we did in lecture, one could argue that the piano clue was not understood (phase 1) until the time at which we solved the problem, near the end of the "carry out the plan" operation (phase 3).

Also note that this is an analysis of how problems are solved, not of an ideal. It would be nice if we could always come up with correct algorithms and correct programs. However, we can't. The evaluation phase is essential.

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