When you think about it, the whole aim of education is to equip children to solve problems.
In the Mathematics Curriculum therefore, Problem Solving contributes to the generic skill of problem solving in the New Zealand Curriculum Framework.
Third, in looking back and thinking a little more about the problem, children are often able to see another way of solving the problem.
This new solution may be a nicer solution than the original and may give more insight into what is really going on.
But Problem Solving also contributes to mathematics itself.
It is part of one whole area of the subject that, until fairly recently, has largely passed unnoticed in schools around the world. The skills are things that we are all familiar with.
Pólya’s second stage of finding a strategy tends to suggest that it is a fairly simple matter to think of an appropriate strategy.
However, there are certainly problems where children may find it necessary to play around with the information before they are able to think of a strategy that might produce a solution.
But it is worth getting them into the habit of looking back over what they have done. First of all it is good practice for them to check their working and make sure that they have not made any errors.
Second, it is vital to make sure that the answer they obtained is in fact the answer to the problem and not to the problem that they thought was being asked.