How to Prepare for a Maths Exam
Preparing for a Maths Exam
How can you use your study time to best effect when preparing for a maths exam? Well, having sat quite a few and prepared students for quite a few more, here are my tips for using your study time wisely.
In summary, there are three principles to keep in mind, and three stages of preparation to progress through.
Let’s look at the three principles first.
Doing Is Better Than Reading
I’ve got some bad news for you: simply reading through your text book or notes is not going to significantly improve your mathematical prowess. Your notes are simply a guide to doing maths. Elite athletes may spend time reading training guides, nutritional guides, anatomy books, and so forth, but they rely on their hours of training to win them medals. The same is true of maths: doing is far more important than reading.
Practice make perfect
Believe it or not, maths is an active pastime. True, you’re generally sitting at a desk while you’re performing it, but you are carrying out a sequence of tasks. (Think of that episode in Big Bang Theory when Sheldon and Raj are doing physics, staring at their white board and thinking hard, as “Eye of the Tiger” plays on the soundtrack!) So, just like any other activity, the more you rehearse it, the better you’ll be.
That’s why the best advice I can give you is to get better at maths by doing maths: doing questions – many questions – and doing them often! And (and this is important): keep practicing the ones you can do.
Obviously, I don’t mean staying in your comfort zone and only doing problems you feel are ‘easy’: you need to tackle the hard stuff, too. But every few weeks, go back through the work covered so far, and do half a dozen of each type of question to keep your hand in. This is an excellent practice to develop during Foundation Time (see below).
Join the dots
The world of mathematics is one big beautiful entity, even though it sometimes seems to be made up of entirely separate things.
OK, even if you’re not with me on the “beautiful” part just yet, trust me that those sections of mathematics which seem worlds apart from each other are actually just different features of the one landscape of knowledge. The shapes of geometry belong to the same world as the rules of algebra, even though pictures of shapes might not look much like letters mixed with numbers on a page; matrices, with their lattices of numbers, rest on the same bedrock of learning as differentiation and integration.
Perhaps you haven’t come across some of those mathematical terms yet. That’s fine! The point is, mathematics is like a planet – each part links to each other part somewhere along the line. The skills and knowledge you learn studying one topic will help you master the next.
As you learn a new topic, you might ask: Have I done something similar to this in the past? What does this method remind me of? What does this sequence of steps remind me of? What are the key logical links here? Keep these questions in the back of your mind as you progress through your mathematical education. Finding these links will help you transfer skills from one topic to the next.
Now let’s turn to the three stages of exam preparation.
You begin preparing for your exam when the maths course begins. During the foundation phase, you are:
· receiving information about what you will learn in the course, what will be assessed, and how it will be assessed
· covering the bulk of the course material in class time
· rehearsing new skills and knowledge, and
· (depending on the course and where you’re studying) undertaking formative and summative assessment tasks.
After each lesson or lecture, you should go over the material covered as soon as possible, preferably that evening and certainly within a few days. Some students find it helpful to re-write their class notes or summarize them for later revision. Make sure you understand any new vocabulary; many text books have a glossary at the back, which can be a helpful resource. Go through the worked examples line by line, and ensure you can see how each step flows logically from its predecessors. Make notes of anything you don’t understand to ask your teacher or lecturer later.
Then – most importantly! – practice what you have learnt. While it is good to go over your class notes, the bulk of your time should be spent rehearsing skills and knowledge. What do I mean by this? Doing exercises. Do all the exercises your teacher has set, and if you find the work challenging, then do some more! If need be, borrow a different text book from a library, so you have a second source of questions and answers.
Every few weeks during Foundation Time, go back and re-visit past work. Do a few questions from each exercise. Even if you think “I can do that easily”, do a couple anyway – just to keep your hand in. Rehearsing the work you find easy will ensure you can do it quickly and accurately under exam conditions, freeing up time for the more challenging questions.
This is when you begin preparing for your exam in earnest. Generally, Surge Time begins 6 – 8 weeks prior to an exam and last until within one week before it.
At the start of Surge Time, make sure you have an up-to-date course outline and assessment guide, so you know what will be examined. Make sure you understand what you can take into the exam room: What type of calculator? What reference works (which may include so-called “cheat sheets”*)?
During Surge Time, you are consciously going back over the entire course, making sure you understand and can do each type of question. Ideally, you’ll run through the whole course three to four times during Surge Time. Remember, the aim is to do maths, not simply read about it.
You will also be preparing summaries of the work covered, which may take the form of mind maps or other visual aids.
Finally, you will be doing practice exams and rehearsing your exam technique. Begin by allowing yourself as much time as you need to do a practice exam in its entirety; you might like to allow yourself full access to your text book and notes during your first couple. Then work towards doing practice exams in the time allowed for them, using only the resources you will have in the exam itself. By the end of Surge Time you will have completed 2 – 4 practice exams under exam conditions. (Some of these may be completed during class time.) By the end of this process you will have fully prepared any materials you are allowed to take into the exam room.
If you can, leave some practice exams with solutions for use during Consolidation Time.
In the final run up to the exam, you are reassuring yourself that you are ready for the paper, and identifying any areas of lingering concern.
By now you have a good working knowledge of the curriculum. In the last few days before the exam, run through some practice exams or revision sections of your text book.
Ask yourself: “Can I do this question?”
If the answer is “yes”, then – at this late stage – if you can do it, skip it. The time for rehearsing things you can do is past.
If the answer is “maybe”, attempt it, using any resources you’re allowed to take into the exam, then check the solution. If you got it right, great! Go on to the next question. If you got it wrong, look through the solution; maybe even write it out. Can you do the question now? Excellent! Perhaps find another like it in the text book and try again.
If you really cannot do the question, even after checking the solution and reading the relevant section in the text book, put it aside to ask for help, and move on to the next question.
These steps are summarized in a flow chart here.
During Consolidation Time, the emphasis is on practising using material you’re allowed to take into the exam, reassuring yourself that you know the course work, and identifying the types of questions you may have trouble with under exam conditions. These latter you can then ask for help with.
* Which, I hasten to add for anyone not familiar with the term, has nothing to do with cheating at all, but rather notes students are sometimes allowed to take into exams.