Preparing for exams

Below are notes circulated to all teachers and adapted from the Times Educational Supplement about revision. They’re good for most subjects, but not for maths.

With maths, the best way to prepare for an exam is not so much revision as practice. To prepare for a football match, or a piano recital, you don’t “revise” football or “revise” piano. You practise. Same with maths.

Do past papers. And more past papers. Mark your own work, and learn from your mistakes. And then do even more past papers.

Sitting and reading the rules of football, or some book about how to play the piano, is not a good way to prepare. Nor is sitting and reading the maths textbook. In fact, since some of the methods expounded in the Edexcel textbooks are cumbersome or badly explained or even wrong, it is harmful.

Click here for some notes about how to do past papers.

If you need to refresh your memory about some formula which isn’t in the formula book, you can look at:

• the summary notes printed with the booklets of FP1 past papers

these notes for M2

• the FP3 vectors booklets I’ve handed out, or these notes on this website

• the FP2 Möbius transformation booklets I’ve handed out. (I’ll do a revised version of that booklet to make it handier for reference). Or these flowcharts: for the algebraic method and for the geometric method.

• the end-of-chapter summaries in the textbook

Revision notes from TES

Making revision notes: Making good notes is perhaps the foundation stone of good revision – all other strategies can build on high-quality notes. But much like all good revision, it ain’t what you do, it is the way that you do it.
Simply copying out chunks of a text is likely to prove ineffective. The research indicates that elaboration is the key – students need to interpret the information and connect it, drawing out questions and patterns.
Verdict: Thorough guidance, modelling and structuring are required

Reciting: By reciting crucial knowledge and learning it by rote, we help students to make recall almost automatic, enabling them to tackle the challenges of tough questions and apply their exam skill more confidently. But reciting alone is not an effective method of revision. In The Read-Recite-Review Study Strategy: Effective and Portable, Mark A McDaniel et al present us with their own twist on the tried and tested method, asking students read, then recite, before testing their knowledge of what they have recited.
Verdict: If it’s good enough for great actors…

Graphic organisers: Robert Marzano and John Hattie, both famed for their large-scale synthesis of research evidence, have corralled lots of studies that support the notion that graphic organisers work very effectively. More specifically, concept maps have been shown to be an excellent device for testing students’ knowledge.
Verdict: It isn’t just pretty pictures – restructuring topics using graphic organisers makes them stick in the memory

Flashcards: The evidence says the most effective revision method is retrieval practice. Put simply, retrieval practice is any type of revision that gets students to remember information without checking their study aids. In short, it is a quick, painless test. Flashcards are perfect for this – parents can test their children in the car on the way to the supermarket; friends can sit in the library and fend off Facebook procrastination with some flashcard fun. In many ways, the flashcard is the most effective revision tool, as it combines all of the high-impact strategies in one handy rectangle. We need only support and scaffold our students to devise them successfully.
Verdict: Small cards, big impact. A highly recommended strategy

Another method to prepare for exams

According to Steven Krantz’s book Mathematical Apocrypha, one exam on algebraic geometry set at Harvard University by the famous mathematician David Mumford consisted of just two questions:

1. Write an exam for this course.
2. Take it.

Max Zorn set an exam at Indiana University which had only one question:

sin z

(meaning, explain the theory of the function sin z when z is a complex number).

Zorn was a German mathematician who fled to the USA when the Nazis came to power in 1933, not because he was Jewish (he wasn’t), but because he was actively anti-Nazi. All his later life he spoke with a raspy, croaky voice because of throat injuries he had received in a street-fight with Nazis. He is famous for Zorn’s lemma.

When I was at university, I prepared for exams effectively by “practising” papers of that sort. I would put aside all my notes and textbooks, take a pen and some blank paper, and work at reconstructing the ideas of each course I’d studied from scratch, with all the important proofs.

It’s good practice, but hard, and I think for A level doing past papers is better preparation.