4.1 Writing mathematics

There is more than one purpose to writing your maths clearly and concisely. One is to make your meaning and logic clear to others; in some ways, though, this is not the most important reason. Rather, it is to help you to follow your own logic when problem solving and, hopefully, to help you find the way to the solution. Also, if you review some work in a few weeks’ time, it may not mean anything to you if you haven’t written it down clearly! This idea applies to study in any subject area that you may undertake and especially to university-level study. Often, the new ideas that you study will build on each other and you will need to look back over previous work as a reminder – so it is important that you can understand what you have written.

A couple of ways of helping with this is to ask someone else to read your work, or imagine that you are writing for someone who has little knowledge of the topic and requires a full explanation. This can help you to make sure that you include sufficient detail. At the moment, tell yourself that all your working, however obvious it may seem, should be written down.

Mathematical writing requires skills in using notation and specialist vocabulary. Remember, maths is a language! This skill takes time to develop, so whenever you encounter any maths problems, try to communicate them properly – even if they are just for you. The more you do this, the more like second nature writing your maths correctly will become – and the easier it will be.

The three most important things to remember are as follows:

1. Explain each step in your working clearly.
2. Lay out your explanation clearly.
3. Use correct maths – make sure that what you write is mathematically correct.

See how you get on with spotting what is wrong with the way that the maths has been presented in Activity 7.

Activity 7 What’s wrong with the maths?

Timing: Allow approximately 10 minutes

Consider the following scenario.

You want to pave a patio that’s 4 m long by 3 m wide with paving slabs that are 0.5 m square. The paving slabs cost £6 each. How many will you need, and what will they cost in total?

You go to your local contractor, who says ‘Let me see …’ and scribbles down the following calculation:

Figure 1 Writing mathematics 1

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4 × 3 ÷ 0.5 × 0.5 = 48 × 6 = 288, call it 50 to be safe, so = 50 × 6 = 300

Figure 1 Writing mathematics 1

Can you see the difficulty with the maths and suggest any improvements?

Remember that well-written mathematics is easy to follow and uses correct notation. List any problems or issues you see. Think about how you have seen maths presented in the course so far.

Answer

• You’re going to have great difficulty in checking their work. This could be a problem – you really don’t want to buy more slabs than you need! Nor do you want to purchase too few to finish the job.
• It’s not clear what the answer is. What does that final figure of 300 represent – 300 slabs or £300?
• It’s mathematically incorrect at a number of points. That could lead to some serious miscalculations, such as more or fewer slabs, and overcharging or undercharging. In particular, the contractor misuses the equal sign a few times. You can only use an equal sign if the expression on the left is equivalent – that is, if it gives the same answer – to the expression on the right. If it’s not, this means you need another, separate step.

The next section will help you to see how to make this solution clearer.