Why mixing up math problems helps you learn
Open almost any math textbook and you'll see the same pattern: a lesson on one method, followed by twenty problems that all use that method. It makes sense – practise what you just learned. But research suggests that shuffling problem types together works better.
The experiment
Psychologists Doug Rohrer and Kelli Taylor taught college students how to find the volume of four kinds of solid shape. Then the students practised. One group did their practice blocked: all the problems for one shape, then all the problems for the next. The other group did the same problems mixed together in random order.
During practice, the blocked group did better – unsurprisingly, since they always knew which formula to use. But a week later, on a test, the mixed group did far better.
Why mixing works
When every problem on a page uses the same method, you never have to decide which method to use. You just repeat the steps. On a real test, problems come in any order, and choosing the right approach is half the work.
Mixed practice (researchers call it interleaving) makes you practise that choice every time. It also tends to space out practice of each problem type, which helps memory on its own.
Mixed practice feels harder and slower. That's not a sign it isn't working – it's the reason it works.
How to use it
- Shuffle your homework practice. After you've learned a few methods, do a few problems from each, in random order.
- Go back to older chapters. Add two or three problems from last month to every practice session.
- Cover the headings. If a worksheet says "Pythagoras" at the top, cover it up and work out for yourself which method each problem needs.
- Ask "how do I know?" Before solving, say why this problem needs this method. That's the skill a test checks.
It works beyond math, too: mixing vocabulary from different units, history from different periods, or science topics from across the year all make you think harder about each question.
In TONEC STUDY
Every answer in TONEC STUDY comes with an explanation, so a wrong choice becomes a lesson. And when you want more than your daily tasks, extra practice lets you pick any subject – switch between them to mix things up.
The study
- Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics problems improves learning. Instructional Science, 35(6).