How to study maths, because it is not like your other subjects

You have been taught how to study, roughly once, and it was probably advice built for History. Read the chapter. Make notes. Underline the important bits. Read the notes again before the test.

That works reasonably well for a subject where the exam asks you to reproduce information. Maths does not ask you to reproduce information. It asks you to do something you have never seen before, using tools you have. Studying it the same way is why you can feel prepared and still get 62.

The trap: it feels like it is working

Re-reading a solved example is genuinely pleasant. Every line makes sense. You follow it easily. Your brain reports back that you understand this chapter now.

That feeling is the problem. It is measuring whether you recognise the material, which is easy, and telling you something about whether you can produce it, which is hard. Those two things are not the same, and only the second one is examined.

What to do instead

Four changes. The first is worth more than the other three combined.

1. Cover the solution. When you work through a solved example, cover it with a sheet of paper and attempt it yourself first. Only uncover when you are properly stuck, and only uncover one line. This single habit converts passive reading into real practice.
2. Redo the ones you got wrong, later. Not immediately, when the method is still sitting in your short-term memory and it feels easy. Two or three days later, from scratch. If you can still do it then, you have actually learned it.
3. Mix chapters together. Once you have learned a chapter, practise it jumbled with others. Doing twenty questions from one chapter trains solving. It never trains recognising, because the heading already told you the method. The exam does not have headings.
4. Explain it out loud. To a friend, a sibling, or an empty room. The moment you have to say why a step is allowed, you find out immediately whether you know or whether you were copying a pattern.

How long, and how often

Short and frequent beats long and rare, by a lot. Forty minutes on five days will beat three and a half hours on Sunday, for the same total time.

The reason is that forgetting a little and then retrieving it is what makes memory stick. If you study everything in one block, you never forget anything in between, so you never practise the retrieval. Gaps are not wasted time. They are part of the method.

Within a session, aim for something like: ten minutes reviewing what went wrong last time, thirty minutes on new questions with the solutions covered, five minutes writing down what tripped you up.

Keep one page

One sheet, kept all year, with every mistake you make written in your own words. Not the questions, just the mistakes.

• What went wrong, specifically.
• Why it went wrong, if you know.
• What you will do differently.

Read it before every session. By February that sheet is the single most valuable piece of paper you own, and it takes about thirty seconds a day to maintain.

If none of this seems to help

If you are studying properly, in the way described above, and a chapter still will not go in, the problem is usually not the chapter. It is something earlier that never quite settled, and it is quietly making the new work harder than it should be.

That is extremely common and it is not a statement about your ability. It is worth finding out rather than grinding at the same chapter and concluding something unkind about yourself.