◆ Study method · Method

Study Strategies That Actually Raise a Math Score

5 min read · Free to read · No sign-up required

Some study methods feel productive and do very little. Others feel harder and work. The difference is well understood, and knowing it is worth more than extra hours.

The comfortable methods that do not work

Three habits dominate most students' preparation, and all three are weak:

• Re-reading worked solutions. Following a solution you are shown produces a strong feeling of understanding, because the reasoning is right there and nothing is difficult. That feeling is not learning — it is recognition, and it disappears when the scaffolding is removed.
• Highlighting and note-copying. Almost entirely passive. It occupies time and attention while requiring nothing to be retrieved from memory.
• Practising what you are good at. Comfortable, satisfying, and close to useless. Marks are lost where you are weak.

These persist because they feel productive. Effective study usually feels worse in the moment — a well-documented and deeply unhelpful property of how learning works.

Retrieve, do not review

The single most valuable change most students can make: test yourself instead of reviewing.

The act of pulling something out of memory is what strengthens it. Putting it back in — by reading it again — does very little. So when you sit down with a topic, do not re-read the method. Attempt a question cold, from memory, and only then check.

Applied to worked solutions, the discipline is: read the question, close the solution, attempt it yourself, and only then compare. If you cannot attempt it, read one line of the solution, close it, and try again from there. That is retrieval. Reading the whole solution and nodding is not.

This is uncomfortable — being unable to recall something feels like failure. It is the mechanism working.

Space it out

The same total study time produces substantially more durable recall when it is distributed rather than concentrated. Four sessions of thirty minutes across a week beat one two-hour session, for the same two hours.

The reason is the same as above: each time you return after a gap, the material has partially faded, so retrieving it requires effort — and that effort is what consolidates it. Practising something twice in a row is easy the second time and therefore does little.

This is the honest argument against cramming. Cramming does work for a day or two, which is why students keep doing it; it simply does not survive to test day, and it builds nothing you can reason from under pressure.

Mix your practice

Most practice is blocked: twenty quadratics questions, then twenty geometry questions. It feels efficient and produces good session performance.

Interleaved practice — mixing topics within a session — feels worse and transfers better. The reason is directly relevant to exams: in blocked practice you already know which method applies before you read the question, so you never practise the hardest step. On the exam, nothing tells you which tool to reach for. That selection is a skill, and only mixed practice trains it.

A practical compromise: block when first learning something genuinely new, then move to mixed practice as soon as the method is understood.

Keep an error log

For every question you get wrong, record four things:

1. The question, or enough of it to recognise.
2. The skill it actually tested.
3. Why you got it wrong — content, process, or careless (see the common mistakes guide).
4. What you should have done instead.

Then review the log weekly. Its value is not in any single entry — it is in the pattern. Nobody notices that eleven of their last fourteen errors were sign handling while making them one at a time, weeks apart. Written down, it is obvious in a minute, and it turns a vague sense of "I'm bad at algebra" into a specific, fixable behaviour.

Practise at the edge of what you can do

Useful practice is difficult but achievable. Questions you can already do reliably build nothing. Questions far beyond you build frustration.

The productive zone is questions you can attempt but do not reliably get right — where you have to think, and where you fail sometimes. If you are getting nearly everything right, the practice is too easy to be improving you.

Two habits keep you in that zone: work from a current diagnosis rather than a fixed syllabus, and re-test previously weak skills rather than assuming a fix held.

Frequently asked

How many hours a day should I study for a math exam?

Consistency matters more than volume. Regular, focused daily sessions outperform occasional long ones for the same total hours, because spacing and retrieval do the work rather than time spent. A shorter session done every day is a better plan than a longer one done sometimes.

Is it better to do many questions or study a few deeply?

Depth, especially when material is limited. A question studied properly — attempted cold, classified when wrong, revisited later — is worth several answered casually. Volume without diagnosis mostly reinforces what you already do.

Why do I understand the solution but still get it wrong next time?

Because understanding a solution you are shown is recognition, not recall. The fix is retrieval: close the solution and reproduce it yourself, then attempt a similar question cold a few days later. If you cannot, you had not learned it — you had followed it.

Does cramming work?

For a day or two, which is why it persists. It does not survive to test day and it builds nothing you can reason from under pressure. The same hours spread across weeks produce substantially more durable recall.