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.So a problem about three pigs may be changed into one which has any number of pigs. The answer to this problem will contain the answer to the previous three questions.There we were asked for the number of towers of height one, two and three.This is the side of mathematics that enables us to use the skills in a wide variety of situations.Before we get too far into the discussion of Problem Solving, it is worth pointing out that we find it useful to distinguish between the three words "method", "answer" and "solution".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.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.