# 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?