Manipulating maths problems

As an undergraduate at Imperial College, I was one of the many thousands who were taught maths by the great Stan Raimes. As part of his teaching, he taught us “Raimes’s Rules”. These 3 rules were, as it happens, rules for solving differential equations, but apart from rule 1, they had much more general applicability. In this article I wish to consider the second rule. Rule 2 stated “If you already know the answer, you don’t have to work it out”. The point of this rule is that maths is not about just doing a calculation (as so many pupils think it is), it is about manipulating a problem until it is in a soluble form. This is the first bit of solving any maths problem. However, it is the bit that many pupils just don’t get. They look at a maths problem and they can’t see how to solve it immediately and give up. “I can’t do this,” they tell themselves. The part they are missing is an essential part of solving maths problems. It is at this stage that they need to use logic and imagination to convert the problem into an equivalent one that they know how to solve. But, unfortunately, so often, they do not do this. At Puppet Maths we inculcate our pupils with the concept of manipulating the maths problems they get into a form that they can recognise, so that they can solve them. We teach them the process of how to approach maths as well of how to accomplish the mechanics of calculation.