How to study maths: methods that actually work in technical courses
Plenty of students who are effective in theoretical subjects hit a wall in maths, statistics, mechanics and programming. Usually it is not because they are worse at maths, but because they are using a study technique built for text on a subject that is not made of text. Maths is a skill, and skills are trained.
Why reading is not enough
Reading a worked solution feels productive. Every step makes sense, and a feeling of understanding sets in. The problem is that the feeling is unreliable: being able to follow an argument is not the same as being able to produce it on a blank page. Bjork and colleagues (2013) call this the illusion of competence, and it hits technical subjects hardest precisely because the solutions are so easy to follow after the fact.
The test is simple. Cover the solution and solve the problem from scratch. If you cannot, you have not learned it yet, no matter how obvious it felt ten minutes ago.
Six principles for problem solving subjects
1. Solve more than you read
A rule of thumb: at least two thirds of your time in a maths course should be your own problem solving with a pen in hand. You read the theory in order to solve problems, not the other way round.
2. Struggle before you check the answer
Give each problem a genuine attempt before opening the solution, ideally 10 to 15 minutes on a standard problem type. That fumbling phase feels inefficient but is exactly where the learning happens, something often called productive struggle. If you get stuck, look at the next step only, not the whole solution, and then continue on your own.
3. Use solutions as a check, not as teaching
Once you have read a solution, close it and redo the problem from a blank page the same day. Only then does it move into knowledge you own. Ticking off "I understood the solution" is the single most common reason an exam goes worse than the practice suggested.
4. Interleave problem types instead of doing blocks
Doing 20 problems of the same type in a row feels good, because after three it runs on autopilot. But the exam does not tell you which method applies, and choosing the method is the hard part. Research on interleaving, above all Rohrer and Taylor's study on maths problems specifically (2007), shows that mixed practice feels worse during training and produces clearly better exam results. Mix chapters, mix weeks, mix methods.
5. Build a library of problem types
Most exams are variations on a limited set of problem types. Create your own register: for each type, note the giveaway ("how do I recognise it?"), the method in three or four steps, and one trap to avoid. That is the version of active recall suited to technical subjects, and it works very well as spaced repetition before the exam.
6. Explain it out loud to someone
If you cannot explain why a step is allowed, you have memorised a procedure rather than understood it. The Feynman technique is built for exactly that check, and it exposes gaps faster than anything else we know of.
Structuring a course week
| Activity | Share of time | What you do |
|---|---|---|
| Theory | approx. 20 % | Read the section, write definitions and theorems in your own words |
| Basic problems | approx. 30 % | Drill the technique until the mechanics are automatic |
| Mixed problems | approx. 35 % | Problems from different chapters, without knowing the method in advance |
| Review | approx. 15 % | Old problem types from previous weeks |
Before the exam
Do past papers under time pressure, in one sitting and with no solutions within reach. That trains three things at once: method selection, pace and nerves. Mark them afterwards and build an error log: write down each mistake and whether it was carelessness, a method you did not know, or a problem you did not recognise. Those three categories need completely different responses. More on practising with past papers in our guide to old exams, and on nerves in exam anxiety.
When you are completely stuck
Go to tutorials and ask. Sitting alone for three hours with the same problem is rarely worth it, whereas ten minutes with a teaching assistant can untie a knot that is blocking a whole chapter. Study groups also work particularly well in technical subjects, provided everyone solves problems on their own first and the group is used to compare solutions, see group study or studying alone.
With Memmo you can upload lecture notes and compendiums and get questions generated on the material, which is a convenient way to keep definitions, theorems and standard cases active between problem sessions.
Frequently asked questions
How many problems do I need to solve?
Fewer than you think if they are mixed and solved without the answer key, more than you think if you drill blocks of the same type. Quality lies in how much you had to think, not in the count.
Should I write my formula sheet by hand?
Yes, if the exam allows your own formula sheet. The act of writing forces you to prioritise and structure, and that work is revision in itself. This holds even if you end up never looking at it.
I understand it in class but forget it by next week. Why?
Because understanding with guidance is not the same as independent production. Redo the day's problems that evening without help, and revisit them a week later. Spaced practice is precisely what is missing.