Motivation Leads to Success

Mathematics as a school subject is notorious for inducing real anxiety in many pupils and undermining the confidence of many more. Students often arrive in secondary school from primary, full of enthusiasm, having enjoyed maths in primary school – but then, their new work is harder, the explanations are more obscure, they can no longer 'see the point' of what they are doing - and their confidence drains away.

This is especially a problem in mathematics because so many topics depend on previous topics. If you miss out on the geography of London you may not be much handicapped when you come to the geography of the Midlands. If you were absent when the class did the history of the French revolution, you will not be seriously handicapped when you get to the First World War. But if you fall behind on basic algebra, then you may find that you are handicapped for ever more, getting further and further behind and more and more lost.

The other side of that coin is that positive steps to increase motivation can increase confidence and greatly reduce anxiety even if they do not totally banish it. A vicious circle can become a beneficent circle in which a bit more confidence in the short run leads to much greater confidence in the long term.

Unfortunately, textbooks often leave pupils in the dark by failing to tell them why topics are important and why they are on the syllabus in the first place. Many topics, for example, are closely connected to science: quadratic equations are linked to the fascinating history of Galileo and the flight of projectiles. Amazingly, textbooks will occasionally present, for example, the equation of a ball bearing rolling down a chute – another of Galileo's ingenious experiments – without identifying it. The teacher recognises it at once, but the students are left in the dark.

This also sometimes has the result – laughable if it were not so absurd – that students will do some mathematical topic in their science lessons, because it is needed, without their maths teacher even being aware that they have met it.

Sine and cosine curves also illustrate the many connections between maths and science: they are used to describe many types of oscillations in physics, chemistry and in biology. Yet such links between maths and science are few and far between in the official mathematics syllabuses and in textbooks.

Some students are not bothered by this lack of connection. They start by being highly motivated and are perfectly happy to lap up as best they can whatever food is put in front of them.

'What's the point of exponentials? Don't tell me, just show me how to 'do' them. Oh, I see, OK, yes, I get that, I can remember that,' and they're off.

Other students, however, do stop to wonder 'What's the point of quadratics, Miss?' or 'Why do we have to do polygons, Sir?' If such inquisitive pupils are not given satisfying answers, their motivation suffers and if they meet with difficulties they are more likely to be confused and less likely to persevere.

Many teachers will respond to such criticism by saying that, well, yes, of course it would be nice if there were time to make all these connections but, frankly, the exam syllabuses are just too crowded, time is too short, so let's forget about context and meaning and just focus on technique.

As I have said, this approach works for some students, but for many it does not, and it is not true that putting topics in context is time-consuming. In the long run, by increasing understanding and motivation, time is saved and students benefit. They can 'fit the pieces of the jigsaw together' which not only raises their confidence, but also makes their work easier to remember.

Learning in a void is never a good idea. Mathematics-in-context is easier to understand and easier to master – and it's more enjoyable.