How to Learn Mathematics Effectively
Ask most people what subject they found hardest to learn, and they’ll say mathematics. One problem is, it’s so unforgiving. Set any student to paint a picture or write a story given a certain theme, and they’ll be able to make an attempt worthy of some reasonable grading, but when they can’t start a maths problem, they can’t start! It’s also stubbornly demanding. A method taking you down the wrong route simply doesn’t lead to a solution. This makes it very hard to revise mathematics without outside help. I learned my maths in the days before such great help existed on the internet, and when it wasn’t so easy to “phone a friend”, and under those circumstances, when you’re alone with a problem you can’t solve, you really are alone. When you can’t do it, mathematics is not pleasant or friendly. Nowadays there’s no excuse.
So what’s the best way to tackle such a daunting subject?
1) Learn the key facts
When you meet a new topic, ask yourself what are the key points, the formulae to learn, the techniques that allow you to solve problems, then learn them! Formula sheets and fantastic calculators are no substitute for straightforward learning. For example, it may be possible to look up the formula for sin2x when you need it, but in some problems, you need to recognise 2sinxcosx as the same thing, and you aren’t likely to look that up on a formula sheet. That’s an example of how it’s important in maths to know things backwards – factorisation is more important than multiplication tables, integration is arguably more important than differentiation - it scores more marks at A-level, anyway! Those who refuse to learn key things seldom do very well in exams.
2) Don’t shy away from thinking
Sometimes you have to battle with new ideas. Don’t be afraid to spend time on them. Homework is often set to make you think. If you just treat it as something to be done and out of the way as quickly as possible, you’re doing it without thinking and missing the point. Thinking is more important.
3) Ask for help if you need it.
People are more willing to help you than you think. A quick phone call to a friend can solve a problem, or you could take the question to your teacher or tutor. Don’t let problems fester.
4) Watch out for the mistakes to avoid
When you have mastered a topic, think what mistakes you might have made – using the diameter of a circle instead of the radius, forgetting the effect of a minus sign outside a bracket, and be on the watch for them.
5) Practise
This is really important. Practise. Get a decent textbook with lots of exercises, or look for questions on the net, and do the questions for yourself. It’s best if these resources also give you access to answers, so you can check, and to full solutions, in case you really can’t solve them for yourself. Then look at what’s been done and copy it next time.
6) Enjoy the success.
Becoming proficient in a new mathematical topic is an achievement. Enjoy it. If you can get higher marks within your class, that’s great, but just enjoy being able to solve the problems. You will probably find that the skills you’ve gained are needed for later work, so by doing well here, you’re making life easier for yourself later. Enjoy the success.