Interleaving: why mixing problem types helps you learn
Practicing one kind of problem at a time feels efficient. Mixing kinds together feels messy and slower. Yet in study after study, mixed practice leaves people better at the thing exams actually test: recognizing which idea a problem needs
Nila team · Updated · 3 min read
Blocked and interleaved practice
Most textbooks teach one method and then give a page of problems that all use it. That is blocked practice: AAA, BBB, CCC. Interleaved practice mixes the types: A, C, B, A, B, C. A survey of maths textbooks found that 78% of practice problems were blocked and 11% interleaved [1].
The difference matters because on an exam the problems are mixed. Knowing how to do a method is only half the skill; the other half is recognizing which method a problem calls for. Blocked practice never asks that question, because the answer is always “the one from this chapter.”
The evidence
A large classroom trial. Rohrer and colleagues ran a preregistered randomized trial with 787 seventh graders in 54 classes [1]. Some classes got mostly interleaved maths homework, others mostly blocked. On a surprise test a month later, interleaved classes scored 61% against 38% (d = 0.83). The benefit was positive for every one of the 15 teachers.
The original lab study. With college students learning to calculate the volumes of unusual solids, blocked practice looked far better during practice: 89% correct against 60% [2]. A week later the result reversed: 63% for the mixed group against 20% for the blocked group. Most of the blocked group’s errors were not mistakes in using a formula, but picking the wrong formula. The study was small (18 people).
Beyond maths. People learning to recognize painters’ styles from examples did better when paintings by different artists were mixed (.61 against .35 correct) [3]. Yet 78% of participants believed grouping by artist had helped them more, the reverse of their own results. The test came right after study, so this shows learning to tell categories apart rather than long-term memory.
Why it feels worse
Blocked practice produces quick, visible progress. Interleaved practice makes you stumble, because each problem first asks you to work out what kind it is. In a study of learning a motor skill, people who practiced in blocks predicted an error rate of 8% and actually made 20% [4]. The smoothness of blocked practice is part of what misleads.
When interleaving helps, and when it doesn’t
A meta-analysis of 59 studies found an overall benefit (g = 0.42), but it varies a lot [5]:
- Helps most when the categories look similar and are easy to confuse: types of maths problems, similar diseases, painting styles (g = 0.67 for paintings, 0.34 for maths).
- No clear benefit for learning from expository text.
- Worse than blocking for lists of words (g = −0.39).
So the advice is not “always shuffle everything.” It is: once you have learned each idea, mix it with the ideas it is most likely to be confused with.
How to use it
- Learn first, then mix. Practice a new method on its own until you understand it. Then mix it with earlier ones.
- Mix the confusable things. Two drugs with similar names, two economic models, two types of integral. Put them side by side and practice telling them apart.
- Review old material alongside new. A review session that includes earlier lectures is both spaced and interleaved. See spaced repetition.
- Expect it to feel slower. That is the point. The effort of choosing is the skill you are building.
References
- Rohrer, D., Dedrick, R. F., Hartwig, M. K., & Cheung, C.-N. (2020). A randomized controlled trial of interleaved mathematics practice. Journal of Educational Psychology, 112(1), 40–52. doi.org/10.1037/edu0000367
- Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics problems improves learning. Instructional Science, 35(6), 481–498. doi.org/10.1007/s11251-007-9015-8
- Kornell, N., & Bjork, R. A. (2008). Learning concepts and categories: Is spacing the “enemy of induction”? Psychological Science, 19(6), 585–592. doi.org/10.1111/j.1467-9280.2008.02127.x
- Simon, D. A., & Bjork, R. A. (2001). Metacognition in motor learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 27(4), 907–912. doi.org/10.1037/0278-7393.27.4.907
- Brunmair, M., & Richter, T. (2019). Similarity matters: A meta-analysis of interleaved learning and its moderators. Psychological Bulletin, 145(11), 1029–1052. doi.org/10.1037/bul0000209