Naturally enough, Problem Solving is about solving problems.
And we’ll restrict ourselves to thinking about mathematical problems here even though Problem Solving in school has a wider goal.
This is useful to show others what they have done and it is also helpful in finding errors should the right answer not be found.
At this point many children, especially mathematically able ones, will stop.
On the other hand, we use "answer" to mean a number, quantity or some other entity that the problem is asking for. It is frequently the case that children move backwards and forwards between and across the steps.
Finally, a "solution" is the whole process of solving a problem, including the method of obtaining an answer and the answer itself.method answer = solution But how do we do Problem Solving? Pólya enunciated these in 1945 but all of them were known and used well before then. The Ancient Greek mathematicians like Euclid and Pythagoras certainly knew how it was done. In fact the diagram below is much more like what happens in practice There is no chance of being able to solve a problem unless you are can first understand it.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.By "method" we mean the means used to get an answer.This will generally involve one or more Problem Solving Strategies. Although we have listed the Four Stages of Problem Solving in order, for difficult problems it may not be possible to simply move through them consecutively to produce an answer.These include the basic arithmetical processes and the algorithms that go with them.They include algebra in all its levels as well as sophisticated areas such as the calculus.This exploratory phase will also help them to understand the problem better and may make them aware of some piece of information that they had neglected after the first reading.Having explored the problem and decided on a plan of attack, the third problem-solving step, solve the problem, can be taken.Hopefully now the problem will be solved and an answer obtained.During this phase it is important for the children to keep a track of what they are doing.