I thought I would take this opportunity to pass on some advice for GCSE and A-Level Mathematics students and, to a certain extent, any mathematics students.

I suppose the big question that everyone wants to ask when they’re preparing for exams is something along the lines of, “How can I do well in my Maths exams?” So here’s some things that I think are important in order for you to do well in your Maths exams. These are written in no particular order but just as they come to me.

  1. Give yourself time to find a solution to a problem. Sometimes this might be 20 minutes, half an hour or even an hour. I know you don’t have this time to spare in an exam but you’re NOT in the exam now! You have to learn to solve problems and you have to start slowly like anything else. Sometimes problems take time to solve – the solutions don’t just leap out of the page at you. Be prepared to work hard for a solution.
  2. Don’t be overly reliant on a calculator. Yes I realise that you can use a calculator in your exam but, I’ve already said it once and I’ll say it again, you’re NOT in the exam now. If you jump on the calculator at each and every opportunity then you will not develop the understanding that you need in the same way that you can’t learn to play a musical instrument by getting someone else to play it for you.
  3. Don’t be overly reliant on mark-schemes and ‘the answers in the back of the book’. You need to learn to determine for yourself whether your solutions are correct. This will develop your understanding and build your confidence. If you can see for yourself that something is correct then you know you have the marks in the bag. Try solving the same problem in different ways to see if you arrive at the same answer – if so, then you probably have the right answer. If not, try to figure out what’s gone wrong yourself.
  4. Challenge yourself. You may be fantastic at using the cosine rule and you might be able to solve quadratic equation like nobody’s business but are you prepared to combine these, or indeed any combination of ‘topics’ in the same problem? If not then you may not be challenging yourself. It is better to spend an hour working hard to solve a single problem than to spend that hour factorising oodles of quadratics or doing some other repetitive ‘type of problem’.
  5. Be interested in the subject. Unfortunately this is something that you can’t really fake – either you are interested in maths or you’re not. If you’re not then you will have to either try to get interested or accept that things are just going to be more difficult for you. Sometimes you get interested in something by accident (like I did with mathematics) – just be open-minded. Enjoy the subject!
  6. Don’t be afraid to go beyond the specification. Sometimes people will happily scour a specification and spend a couple of hours coming up with a reason why they don’t need to learn something. And yet, it would only have taken them 15 minutes to learn it! The thing is, learning something beyond the specification might help you understand things more clearly – so even though it’s not expected knowledge, sometimes it still comes in very useful.
  7. Concentrate on solutions. Mathematics is NOT about just writing the correct number or expression somewhere on the page – an answer without a valid solution is absolutely worthless. You need to concentrate on your solutions and make sure you understand how the parts fit together. If you understand this then the correct answers will naturally follow. If you’re ONLY interested in the answers then I suggest that you simply copy out the answers from the mark scheme or textbook that you’re using.
  8. Don’t just learn to copy someone else’s solutions. Your teacher will give you worked examples. Your textbook will contain worked examples. DO NOT try to learn these solutions as simply a series of bullet-point steps. Learn to understand the solutions and why they work – you will find that your workload drops significantly!
  9. Take your mind off the exam. Yes you will have exams – but if everything you learn is motivated purely by the fact that you have an exam then your learning will end up being laborious and very inefficient. Be more concerned with just ‘problem solving’ – solving challenging problems on a regular basis. If you do this then you will automatically learn the skills that you need for your exam and you may just need a bit of fine-tuning nearer the exam period.
  10. Work hard. If you want to do well then YOU will have to work hard. How hard depends on all sorts of things but don’t try to dodge the hard work. Working hard doesn’t necessarily mean working looooong into the night (although it might) but using your time wisely. It is both quality AND quantity to a certain degree, but quality ALWAYS trumps quantity. There are no guarantees that you will ace your exams – but you can give yourself much more certainty by working hard!

So that’s it for now – I hope that you find something useful here. There are loads of other things that I could add to the list but I’ll leave thode for now; I think these are the main points that I want to make right now. I would love to hear from other people what their advice is on doing well. Good luck with your learning over the coming year!

I’m going to make a somewhat counter-intuitive claim about how to go about preparing for exams (or tests) which is – in order to be really well prepared for exams you need to almost completely forget about preparing for exams (or tests).

This sounds ridiculous doesn’t it? But I’ll try to explain why I think this.

Exams and tests are a completely unnatural thing when it comes to learning. The anticipation of an upcoming test or exam can cause unnecessary stress and, in some cases, outright panic neither of which are any good for learning. The anticipation of exams and tests causes people to learn at a rate that is a fraction of the rate at which they are capable of learning because they will only ‘learn’ what they expect to be examined on – repetitively going over the same few, scanty bits of information trying to cram some poorly-understood and seemingly non-sensical facts into their heads – rather than challenging themselves and delving deeper into a subject to get a much greater understanding.

And of course, why bother to learn things if you won’t be examined on them? Who in their right mind would ‘waste time’ learning things that they won’t be examined on? Well that’s exactly the kind of viewpoint you will probably take if you see education and learning as nothing more than a series of exams and tests. And no wonder people with this attitude hate learning! So would I if that’s all learning meant to me.

But isn’t learning about more than just exams? Yes, I know that exams are an important part of your life if you want to go to university or become a chartered accountant etc. so I’m not saying that exams can be completely ignored – what I AM saying is that preparation for exams should not be the main focus of your learning. If you really want to learn more, learn faster and learn better then you need to be learning because you love learning about what you’re learning about and have a genuine desire to want to go further and acquire more knowledge simply because you can.

Does it sound weird to take such an approach to learning? Of course it does because no-one really encourages people to learn in this way in school. There’s constant testing week-in and week-out and so people only learn the bits of information that they need to know for the test, and as long as they can vomit up these bits of information in the test, regardless of whether they understand (which in many cases people know but don’t understand), then they get a good mark; a couple of days later and they’ve forgotten everything that they learned, rinse and repeat! And this approach is considered to be a good learning approach!!!!

If you are genuinely interested in what you’re learning and you’re learning because you love learning, then learning is easy and effortless. A depth of understanding will come to you that will never come if you see your learning as just learning to pass a constant stream of tests and exams. If you learn because you love to learn then you will pass the tests and exams with flying colours because you will be streets ahead of the rest of the crowd – you will learn at a rate that is unimaginable if you’re learning to just pass an exam and, moreover, what you learn will be much more permanent.

When I was learning GCSE maths I was learning to pass an exam – and it was hard, hard, hard! I hated it. When I was learning A-Level maths I was learning because I was excited about what I was learning – I learned way more than I needed to pass the A-Level exams and I didn’t even think about the exams until a couple of weeks before I sat them, at which point I realised, I didn’t need to do any revision specifically for my exams because I’d been doing it all along without even realising it! The outcome was that the exams were a piece of cake!