Mixed maths practice: why it beats ten in a row
Most maths homework is ten of the same kind of question. It feels productive, and by question three you are flying. But the exam will not hand you ten of the same, and a classroom experiment suggests that how you practise matters more than how long.
What the experiment found
Researchers gave 140 seventh-grade students maths practice over nine weeks, either in blocks (all the problems of one kind together) or interleaved (different kinds mixed in one set). Two weeks later, without warning, everyone sat a test. Mixed practice scored 72%, blocked practice 38% (Rohrer, Dedrick & Burgess, Psychonomic Bulletin & Review, 2014). The problem types in the mixed sets were quite different from each other, so the effect was not just about telling lookalike questions apart.
Why blocks feel good and work less well
In a block, you know the method before you read the question, because the last nine questions used it. In an exam, working out which method to use is half the job. The researchers' explanation is that mixing makes you choose the method from the problem itself, which strengthens the link between each kind of problem and its strategy.
There is a second trap: it feels worse and works better. In a different study, people learning to recognise paintings by different artists did better when the artists were mixed, yet they rated the blocked order as more effective, even after their own test results showed the opposite (Kornell & Bjork, Psychological Science, 2008). Fluent practice feels like learning. It is not always the same thing.
How to do it tonight
- Collect the questions you already have. This week's worksheet, last month's, a past paper. You do not need new material.
- Take two or three questions from each topic. Fractions, equations, ratio, area, whatever you have covered. Mix the order.
- Name the method before you start. Write three words on the page, such as "set up an equation", before you do any working. If you cannot name it, that is the thing to revise.
- Check, then log mistakes by type. Was it the wrong method, or the right method with a slip? Wrong-method mistakes are the ones mixing exposes.
- Keep older topics in every session. Add a few from last month so they do not fade (see how spaced repetition works).
Free tools that help
- Formulas and units: every maths, physics and chemistry formula on one searchable page, to check a method after you have chosen it.
- Step-by-step maths: type a problem and see each step in plain words, to compare with your working.
- Scientific calculator: check that it says DEG, not RAD, before the paper starts.
Where this shows up in real exams
Exam papers do not come sorted by topic. A school maths paper, a GCSE or O-Level paper, and the SAT all mix topics in the order the examiner chose, so a practice set that mixes them is closer to the real thing than a tidy worksheet. Doing a mixed set in a quiet room, or alongside other people in a study room with a shared 25-minute timer, makes it easier to start and to keep the habit.
What this does not say
The experiment was one year group and one school subject. It is a strong reason to try mixing, not a promise of 72% for everyone, and it works alongside understanding the method in the first place, not instead of it. If your child gets the wrong answer every time, the problem may be a misunderstood step; our parent-facing post on why a child is not careless in maths covers that.
Versed is free to use in a browser: flashcards in your browser (guest mode, no account needed to try it) or get it on the App Store. Free. Start as a guest, no account needed.