For many students, studying maths becomes a source of constant stress: every test is an unknown, every new exercise seems impossible, and performance anxiety blocks even those who have the ability. Yet you don’t need to be a genius to do well in maths: you need study habits suited to the subject.
In this article I share the four habits that I see make the biggest difference in my students.
1. Study every day, but a little
Maths cannot be caught up the night before the test. It is a “muscular” subject: it needs constant training. Thirty minutes a day for five days a week produce far more results than four hours in a row on Saturday.
The reason is that maths is based on patterns that the brain has to recognise automatically. Seeing a quadratic inequality and knowing straight away how to set it up requires having solved many. A few exercises every day build these automatic responses, isolated intensive sessions do not.
A strategy that works: devote the first 10 minutes of your maths study to redoing an exercise you did the week before. You will notice how quickly the patterns consolidate.
2. When you get stuck, rephrase first
Faced with a hard exercise the temptation is to read it, not understand it, and start writing something anyway. It is the quickest way to waste time and build up anxiety.
The right habit is to rephrase the problem in your own words before writing any equation. “They are asking me for the area of a region bounded by these curves. So first I need to understand where the curves meet.” Only after understanding what they are asking does it make sense to move on to the maths.
If after two minutes of thinking you can’t even rephrase the problem, it is a sign that you are missing a concept upstream. Go back to the theory, don’t keep banging your head against it.
3. Create your “mistakes notebook”
Keep a separate notebook where you rewrite the exercises you got wrong. Not just the right result: also write where you got stuck and why.
“I applied the discriminant formula to a cubic equation.” Or “I forgot to consider the domain of the function.” Rewriting in your own words where you went wrong activates a different memory from just correcting the result. When you pick up the notebook the week before the test, you will notice that some mistakes you made more than once: that is exactly where you need to concentrate.
Five lines per exercise are enough. The important thing is to be honest about what you didn’t understand.
4. Explain it to someone
The only way to be sure you have understood a concept is to explain it. Find a classmate, a brother or sister, a parent, and try to explain a maths topic to them as if they knew nothing about it.
While you explain it you will notice the parts you took for granted but don’t really know well. It is frustrating the first time, but it is the most reliable sign there is of your real level of understanding. My students who arrive at oral tests with this habit well established rarely do badly: by then they have already heard themselves explain the topic.
How to fit it all into half an hour a day
“Thirty minutes a day” sounds good until you sit down at your desk and don’t know where to start. The scheme I give my students is always the same:
- 10 minutes — recall. Redo an exercise from previous weeks, chosen at random from the mistakes notebook. It serves to reactivate the patterns, not to learn new things.
- 15 minutes — the new piece. Two or three exercises on the current topic, done well, written out in full. Better three complete exercises than ten sketched ones.
- 5 minutes — review. Note down what blocked you today. It is the material that will end up in tomorrow’s recall.
It seems little, and that is the point: a session you can really do every day beats an ideal session you skip three times out of five.
Theory and exercises are not two separate phases
The setup mistake I see most often is studying all the theory and then moving on to the exercises. In maths it doesn’t work, because theory is only really understood while you use it.
The right way is to alternate in small blocks: you read a theorem or a definition, and straight afterwards you do an exercise that uses it. If you can’t do the exercise, it is not “too little practice”: it is that you haven’t understood the theory, and you find out after five minutes instead of after three days.
It also works the other way round: when an exercise works out but you couldn’t say why the method works, go back to the theory. That is a fragile automatic response, the first to break under exam conditions.
When to look at the solution (and when not to)
The solution is not a trick, it is a tool — but the moment you open it changes everything.
The rule that works: before looking at the solution you must be able to say what you are missing. “I don’t know how to set up the integral” is fine, go ahead and open it. “I can’t get it” is not: stay a few more minutes, or go back to the theory.
And when you read it, don’t stop at “ah, I see”. Close the book and redo the exercise from scratch. If you can’t, you hadn’t understood it: you had only recognised it.
If the problem is not method but anxiety
The habits above act on the two causes of stress that depend on how you study: having studied too little and having studied badly. But there is a third cause that cannot be solved with method — the fear of making a bad impression, the blank in front of the page, the time running out.
If you recognise yourself more in that description than in this one, method is not enough: I have written a dedicated article with five concrete techniques on how to manage test anxiety in maths and physics.
To put these habits into a calendar there is how to build a real study plan; for the timed part, the routine for practising against the clock; for the mistakes notebook, a starting list in the five maths mistakes that look right. If you ever turn to a chatbot for help, I have written what works and what ruins you in using AI to study maths and physics, and when the teacher writes “it’s immediate” on your test, the teacher’s translations tells you what is behind it. If you have a failed subject to clear, the catch-up exam is covered in maths catch-up exam. To measure the daily half hour, the high school maths and physics tests by year and topic are the testing ground.
If instead you want to build a study method tailored to you, write to me or on WhatsApp: we look together at what isn’t working. If the block is more about content than method, you will find the full programme in maths tutoring.
