Language, notation and formulas
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# 5 Approaches to problem solving

You should not expect always to be able to read a problem and then just write down the answer. When you are faced with a written mathematical question or problem to solve, read it carefully. It is important that you get to grips with the question in two ways: first, that you absorb the information given; and second, that you find out what the question is really asking. Your solution will link the two. This method can be summarised by the following questions.

- What do I know?

- What do I want?

Try to decide not only what you know from the question itself, but also what you know from past experience which is at all relevant to the problem.

When you consider what you want, first decide whether you have to (a) find an answer or (b) show that something is true.

In order to get to grips with what a question is really about, it can often be helpful to begin by drawing a diagram.

If you are stuck, it may help to review your work. Try to write out your thoughts as clearly as possible so that you can easily see each step and the ideas they are based on.

You may need to leave the problem for a while and then come back to it, in order to see it more clearly. In this case, it is vital that you have written down what you have done so far. It may also be a good idea to talk to someone about it. The act of describing a problem to someone can often be enough to help you see what you should do to arrive at a solution. If there is nobody to talk to, try ‘talking to yourself’.

Always consider whether the answer you have come up with ‘makes sense’; that is, step back a bit and see whether it fits in with the other information that you have.

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