Interleaving: why mixing problem types beats doing them in a row

You finish the practice set for chapter 4 and get almost every question right. Then the exam mixes chapters 3, 4 and 5 on one page, and you freeze. You know how to do each method. You just can't tell which one this question wants.

The short version: interleaving means mixing different types of problems in one practice session instead of doing all of one type, then all of the next. It feels slower and you make more mistakes while practicing. But in several studies, students who mixed their practice did far better on a later test, mostly because they learned to pick the right method, not just apply it.

What interleaving is

Most textbooks and worksheets use blocked practice. You learn one method, then solve ten problems that all use it. Then the next method, then ten more. Written as letters, that looks like AAAA BBBB CCCC.

Interleaved practice uses the same problems in a mixed order: A C B B A C B A C. Nothing is added or removed. Only the order changes.

That small change matters because in a block you already know which method to use before you read the question. The heading told you. On a real exam, nobody tells you. Choosing the method is part of the task, and blocked practice skips that part completely.

The key studies

Doug Rohrer and Kelli Taylor at the University of South Florida ran a small experiment with 18 college students (Rohrer & Taylor, 2007). Everyone learned to find the volume of four unusual solid shapes. Half did their practice problems grouped by shape. The other half got the same problems shuffled. During practice, the blocked group looked much better: they averaged 89% correct, the mixed group 60%. One week later came the test. The mixed group scored 63%. The blocked group scored 20%. The group that struggled more during practice did three times better on the test.

Eighteen students is a small sample, so on its own this would be a curiosity. It was not on its own. Rohrer and colleagues later moved the idea into real classrooms (Rohrer, Dedrick & Stershic, 2015). They worked with 126 seventh graders in nine math classes. Across ten homework assignments, each student did some topics as blocked homework and others as mixed homework, so every student was compared with themselves. Then came a surprise test. When the test was one day later, students scored 80% on topics they had practiced mixed and 64% on topics practiced in blocks. When the test was 30 days later, the gap grew: 74% versus 42%.

Interleaving is not only for math. Nate Kornell and Robert Bjork asked students to learn the painting styles of 12 artists, studying six paintings by each (Kornell & Bjork, 2008). Some artists were shown in blocks, all six paintings in a row. Others were mixed in among the other artists. Then students had to name the artist of paintings they had never seen. In the first experiment they got 61% right for mixed artists and 35% for blocked ones. The strangest part came after. Asked which way had helped them learn, 78% said blocking had worked as well or better. Most people picked the method that had just done worse for them.

Why it works

Two things seem to be going on.

First, mixing forces you to choose. Each new problem makes you ask, "what kind of problem is this?" That is exactly the skill an exam tests. In a block, you can solve ten problems in a row without ever asking it.

Second, mixing puts different things side by side, so you notice how they differ. Seeing a Monet right after a Renoir makes the difference between them easier to spot than seeing six Monets in a row. Same with two formulas that look alike but fit different situations.

This is one example of what Robert Bjork calls a desirable difficulty: a way of practicing that makes learning feel harder in the moment but leads to better memory later. The catch is in the name. It feels worse. Your practice score drops, you feel less sure, and it is easy to decide the method is not working. The Kornell and Bjork result shows how strong that feeling is. Judge interleaving by your test scores, not by how smooth practice felt.

Where it falls short

Interleaving is not magic, and the full research picture is more mixed than the headline studies.

Martin Brunmair and Tobias Richter pooled 59 published papers with more than 8,000 participants (Brunmair & Richter, 2019). Overall, interleaving helped, with a moderate effect. But the effect depended a lot on what was being learned:

• It helped most with paintings and similar visual categories, where the job is to tell look-alike things apart.
• For math problems, the benefit was smaller and varied a lot between studies.
• For learning lists of words, blocking actually did better.
• For reading expository texts, like textbook passages, they found no clear benefit.

They also found that similarity matters. Interleaving helped more when the different categories looked alike, because that is when telling them apart is hard and practice at it pays off. When the things you mix are already very different from each other, there is less to gain.

A few common mistakes follow from this:

• Mixing before you understand anything. Interleaving is for practice, not for a first explanation. Learn each method first, even in a block, then mix.
• Mixing unrelated subjects. Switching between biology and French in one hour is just switching. The benefit comes from mixing things you could confuse, like types of integrals or similar diseases.
• Quitting because it feels bad. Lower practice scores are expected. That is the effect, not a sign it failed.

How to use it yourself

You can do this with a textbook and a pencil.

1. 1Learn the new method first. Do a few problems in a block until you can follow the steps.
2. 2Then build mixed sets. Take problems from the current chapter and the last two or three chapters and shuffle them. Cover the chapter headings so you cannot see which method each one needs.
3. 3Before solving, name the method. Say or write "this is a chain rule problem" first. That step is where most of the learning happens.
4. 4Mix things that look alike. Put similar formulas, similar diagrams, or similar case types next to each other on purpose.
5. 5Keep old topics in rotation. Each week, add a few problems from older chapters. This also spaces your practice out over time, which helps memory on its own.
6. 6Check your results on a mixed test, not on the practice set. That is the honest score.

Tip: if your exam mixes topics on one paper, your last week of practice should mix them too.

How lezrn uses it

lezrn does not have a separate interleaving mode. Two parts of how review already works mix topics for you. Daily review pulls every due idea from all your lessons, oldest due first, not just the last lesson you read, so different topics show up side by side. And a quiz can be written from a whole chapter, not only one lesson, so you have to work out which idea each question is about.

• How daily review builds your list
• Quizzes and flashcards, including chapter quizzes

Sources

1. 1Brunmair, M., & Richter, T. (2019). Similarity matters: A meta-analysis of interleaved learning and its moderators. Psychological Bulletin, 145, 1029-1052. https://doi.org/10.1037/bul0000209
2. 2Kornell, N., & Bjork, R. A. (2008). Learning concepts and categories: Is spacing the "enemy of induction"? Psychological Science, 19(6), 585-592. https://doi.org/10.1111/j.1467-9280.2008.02127.x
3. 3Rohrer, D., Dedrick, R. F., & Stershic, S. (2015). Interleaved practice improves mathematics learning. Journal of Educational Psychology, 107, 900-908. https://doi.org/10.1037/edu0000001
4. 4Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics problems improves learning. Instructional Science, 35(6), 481-498. https://doi.org/10.1007/s11251-007-9015-8