Problem solving strategies

Solving a problem means ...

finding a way out of a difficulty,

a way around an obstacle,

attaining an aim that was not immediately attainable.

Georg Pólya

Framework for problem solving described by G. Pólya

How is it possible to invent a solution? Pólya's answer is to study heuristics - the science of problem-solving. He describes four steps to work through when attacking a problem.

Understanding the problem

  • Carefully read the problem.
  • Decide what you are trying to do.
  • Identify the important data.

Devising a plan

Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution.

Consider some possible actions:

  • look for a pattern;
  • draw a sketch;
  • make an organised list;
  • simplify the problem;
  • quess and check;
  • make a table;
  • write a number sentence;
  • act out the problem;
  • identify a sub-task; and
  • check the validity of given information.

Carrying out the plan

Carrying out your plan of the solution, check each step.

  • Can you see clearly that the step is correct?
  • Can you prove that it is correct?

Looking back

Examine the solution obtained.

  • Can you check the result? Can you check the argument?
  • Can you derive the solution differently? Can you see it at a glance?
  • Can you use the result, or the method, for some other problem?