Most textbooks teach one method, then give you twenty problems that all use it. You get faster with each one and finish feeling great. Then the exam mixes everything together, and the hardest part turns out to be something you never practised: working out which method a question needs.
Blocked vs interleaved#
Blocked practice
- AAAA BBBB CCCC
- Each set uses one method
- Feels smooth and fast
- You never choose the method
Interleaved practice
- ABCB CACB ACBA
- Problem types are shuffled
- Feels slower and harder
- Every problem starts with “what kind is this?”
In a well-known classroom study, students practised finding the volumes of different solids, either blocked by shape or shuffled together. During practice the blocked group did better. On a test a week later, the interleaved group did much better, by a wide margin.1
Why mixing works#
Two things happen when problems are mixed:
- You practise choosing. Recognising that a question needs the chain rule, not the product rule, is a skill. Blocked practice skips it entirely, because the chapter heading already told you.
- You notice differences. Seeing two similar-looking problems side by side highlights the detail that tells them apart.
There’s a spacing bonus too: when topics are mixed, each one comes back after a gap, which on its own improves long-term memory.
Where it helps most#
A large review of interleaving research found clear benefits overall, strongest when the things being mixed are similar and easy to confuse, such as related maths problems or paintings by different artists. It helped less, or not at all, for lists of unrelated words.2
So interleave within a subject, among topics that could be mistaken for one another: types of integrals, similar historical periods, related organic reactions, verb tenses. Mixing biology with French doesn’t buy you much.
How to interleave this week#
- Learn each new method on its own first. Interleaving is for practice, not for the first encounter.
- Once you’ve seen two or three methods, mix their practice problems. Cover the headings if your textbook groups them.
- Before solving, write which method you’ll use and why. That one line is where the learning happens.
- Keep old topics in the mix. Last month’s chapter belongs in this week’s problem set.
The short version
- Blocked practice feels better; interleaved practice scores better later.
- Mixing makes you practise choosing the method, which exams require.
- It works best for similar, easily confused problem types within one subject.
- Learn each method alone first, then mix, and keep old topics in rotation.
Sources
