Understanding the problem

The first task to address when faced with a problem is to understand that problem. What exactly is being asked? In everyday life, all too often the wrong problem is addressed because people do not take this step (politicians are particularly bad offenders here). But not just in everyday life. All too often pupils will not read a question properly and will rush off and do pages of maths and not produce the answer that was required of them, simply because they have not taken the time to understand the question (with school children this is forgivable, they are learning still, whereas with politicians there can be no such mercy).
Puppet Maths teaches that understanding the problem is the first step in the process of mathematics.

How does one go about understanding the problem? It contains 3 elements: where are we now? where are we trying to get to? and how might we get there? For pupils of maths the second is usually set out pretty explicity in the questions they are set, this leaves just the first and the third to be addressed. Very often the first is straightforward, but not always. Sometimes the scenario set out in the question is complex and requires a diagram to be drawn to make it more comprehensable. Puppet Maths teaches pupils to draw diagrams, after all why hold all that information in your head when you can put it down on paper. But what if the problem isn't easily drawn? Puppet Maths teaches its pupils to think analogously, to use their imagination so that they can represent complex scenarios simply and understanably.
The third question is the one that most find the most difficult. How might we get from the initial problem to the final solution? Notice the wording here... it's "how might" not "how do". Often pupils think that there is one correct route to get a solution, and if they do not know it at the start of the question, then they are lost and there is no opportunity of solving the problem. It is a tragedy that so many pupils think like this, and it is a consequence of the way in which they have been taught maths in school. Maths is about the application of logic and reason, a maths problem is an adventure in which the pupils explore various paths through it in an attempt to come out the other side. Sometimes they will make a wrong turning and have to stop and go back. Sometimes they will go off in completely the wrong direction and have to start again. Sometimes they will recognise a path, something they have seen before, and consequently know the way out of the maze. If more pupils thought of maths in these terms then more pupils would find maths easy, more pupils would find maths fun. At Puppet Maths, we inculcate this view of maths, because we want to make maths easy and make maths fun.