Study
Interleaving
Interleaving is a way of studying: you mix different kinds of problems in one sitting, instead of doing all of one kind and then all of the next. Say your math homework has three kinds of fraction problems: adding, multiplying and dividing. With interleaving, you do one of each in turn. (The word has other meanings in computing and in printing. This page is about studying.)
Last updated
Reviewed by Mohammed Raqeeb
The idea
What is interleaving?
Interleaving means mixing up what you practice. The opposite is called blocking: you finish one kind of problem before you start the next kind. Most homework is blocked. A chapter teaches one thing, and then gives you a page of problems on that one thing.
Here are the same twelve fraction problems in two orders.
Blocked
You know what kind the next problem is before you read it.
Interleaved
You have to work out what kind each problem is.
The order matters because of what happens on a test. On a test the problems are mixed, and nobody tells you which kind each one is. You have to look at each problem and decide what to do with it.
A blocked page never makes you decide. After the first adding problem, you know that the next one is adding too. A mixed page makes you decide every time. So you practice two things at once: picking the right method, and using it.
An example
What does an interleaved week look like?
An interleaved week has the same work as a blocked week, in a different order. Here is an example that we made up. Maya has a math test on Thursday. It covers three kinds of fraction problems, and she has 12 practice problems of each kind. She has three evenings to do them.
| Evening | Blocked week | Interleaved week |
|---|---|---|
| Monday | 12 adding | 4 adding, 4 multiplying, 4 dividing, in a mixed order |
| Tuesday | 12 multiplying | 4 adding, 4 multiplying, 4 dividing, in a mixed order |
| Wednesday | 12 dividing | 4 adding, 4 multiplying, 4 dividing, in a mixed order |
| In all | 36 problems | 36 problems |
Both weeks have the same 36 problems. In the blocked week, Maya does her last adding problem on Monday, three days before the test. In the interleaved week, she does all three kinds every evening. So each kind comes back on Tuesday, and again on Wednesday.
Try it
Make your own interleaved plan
The planner below makes an interleaved plan from your own topics. Type three or four topics. Then choose how many days you have, and how many problems or questions you do in a day.
From 2 to 14 days, and 4 to 30 problems a day.
Your mixed plan
- Adding fractions: 12 in all
- Multiplying fractions: 12 in all
- Dividing fractions: 12 in all
Day 1
Day 2
Day 3
Each letter is one problem. Do them from left to right: 4 of each topic a day.
The plan is not saved. Copy it before you close this page. Nothing you enter leaves this page.
What studies found
Does interleaving work?
Interleaving led to higher test scores in math, in a study that tested it in real school classes.
In that study, seventh-grade math classes in five schools got worksheets for four months. In some classes, the problems on the worksheets were mostly mixed. In the other classes, they were mostly grouped by kind. A month later, all the students took a surprise test. The mixed classes scored 61%, and the other classes scored 38% (Rohrer and colleagues, 2020).
The limits
Where does interleaving not help?
Interleaving does not help with everything. A review of 59 studies found that it depends on what you are learning (Brunmair and Richter, 2019).
| What people were learning | What the review found |
|---|---|
| Telling pictures apart, such as the styles of painters | Mixing helped the most. |
| Math problems | Mixing helped, by a smaller amount. |
| Texts that explain a subject | No clear result either way. |
| Learning words | Grouping worked better than mixing. |
The review also found that mixing helps more when the things you mix are easy to confuse, like adding and dividing fractions. And the school study mixed kinds of problems inside one subject, math. It did not test jumping between two different subjects.
Why does interleaving feel harder?
Interleaving feels harder, most likely because you have to stop and think at every problem. In the school study, every teacher said the mixed worksheets took the students more time, and most said the students found them a little harder (Rohrer and colleagues, 2020). So expect a mixed set to take longer. That does not mean it is going badly.
How to do it
How to do interleaving this week
To do interleaving this week, use the practice problems you already have, and change the order you do them in.
- List what the test covers. Pick three or four kinds of problems, or topics, that are easy to mix up.
- Learn each new kind first. Do a few problems of a new kind in a row, until you know the steps. The researchers who ran the school study suggest this too.
- Mix the rest. Take one problem of each kind in turn. Cover the chapter title, so that you have to work out what kind of problem it is.
- Check every answer. In the school study, students saw the right solutions after each worksheet and fixed their mistakes. Do the same.
- Come back on another day. Do a mixed set again later in the week. The page on how to study effectively shows how to spread study over days, and the study planner turns an exam date into hours a day.
Some subjects have facts and no problems to solve. There, you can mix the topics you quiz yourself on. The page on active recall shows how.
The test
How do you know interleaving is working?
The test
On a mixed set of problems you have not seen before, you get more right than you did the week before
for two weeks in a row.
Mixed practice feels slow, so it is easy to skip. A week later, it is hard to remember how many evenings you really did it.
A good way to check that you really did the practice is to count your study hours from what you write or say about your day. Most journaling apps ask how the day felt. They do not show how many hours of the week went to practice.
One app built for this is Think in Numbers, a smart journaling app with time tracking built in.
You write or say your day in your own words, as it happens or all at once. The app reads what you wrote and counts the hours that went to each part of it: your study, homework, sleep, your phone, and the time you never mentioned (shown as unaccounted). Then it shows those hours over days and weeks. So you can see how many hours of practice you really did each week. Add tonight’s mixed set as a to-do; when what you write about your day says you did it, the app ticks it off.
1. You write your day
2. It counts the hours
- Math0m
- Work0m
- Sleep0m
- Unaccounted24h
3. It shows your week
Math this week: 0m
On 6 of 7 days. The gap is the day without it.
An example day and week.
For iPhone and Android. Try it on your own day before you pay.
Sources
Where the findings come from.
The findings on this page come from the two sources below. We read the school study in full, and the authors’ summary of the review.
- Rohrer, D., Dedrick, R. F., Hartwig, M. K. and Cheung, C.-N. (2020). A Randomized Controlled Trial of Interleaved Mathematics Practice. Journal of Educational Psychology, 112(1), 40 to 52.
- Brunmair, M. and Richter, T. (2019). Similarity matters: A meta-analysis of interleaved learning and its moderators. Psychological Bulletin, 145(11), 1029 to 1052.
Keep reading.
- LearnAnswers about sleep, habits, study, people and work, in hours.
- Blurting methodRead, close the book, write down everything you remember, then check. The five steps, one full example, and a timer with a box to write in.
- How to study effectivelyThe methods with the strongest evidence, and a study planner.
- Active recallRecalling instead of rereading: the evidence, and a schedule.
- Where did my week go? calculatorEnter a typical day and see your week accounted and unaccounted.
- Time journalingThe method: write or say your day in your own words, then see it as hours.
Questions
Questions people ask.
What is interleaving?
Interleaving is a way of studying: you mix different kinds of problems in one sitting, instead of doing all of one kind and then all of the next. The word also has other meanings in computing and in printing.
What is an example of interleaving?
An example of interleaving is a math homework with adding, multiplying and dividing fractions, done in a mixed order. You do one adding problem, then one multiplying problem, then one dividing problem, and go round again.
Is interleaving the same as spaced practice?
No. Spaced practice means you come back to a topic on a later day. Interleaving means you mix topics inside one sitting. A mixed plan does both, because every topic comes back on several days.
Does interleaving work for every subject?
No. A review of 59 studies found that mixing helped most with telling pictures apart, and helped with math. It found no clear result for texts. For learning words, grouping worked better.
How do I keep track of my interleaved practice?
A calendar works: tick each day you did a mixed set, and write how long it took. Look for a way that adds up your study hours for the week. One app built for this is Think in Numbers, a smart journaling app with time tracking built in. Think in Numbers counts your study hours from what you write or say about your day, and shows them week by week. In the app, a daily mixed set can be a habit, ticked off on each day your words show you did it.
Try it on my day.
Write today down in your own words, and see where the hours went.
For iPhone and Android. Try it on your own day before you pay.