Interleaving and variation: mix it up, within limits

Think about the last time you practised anything with problem sets: a maths chapter, a grammar unit, a coding tutorial. Almost certainly the practice was arranged the way textbooks arrange it. Ten problems on one method, then ten on the next, then ten on the next. By the tenth problem you were fast and accurate, which felt like mastery. Then the exam mixed everything together and you stared at a question, knowing you could do it, unable to remember which of the three methods it wanted.

That gap isn't a memory failure. It's a skill you never practised, because the arrangement of the problems did it for you. This lesson is about that arrangement: why mixing beats grouping, what mixing trains, and where the finding stops.

The core idea

Blocked practice groups problems by type: AAAA BBBB CCCC. Interleaved practice mixes them: ABCBACCAB. Same problems, same total time, different order.

The finding is that blocked practice looks better during the session and interleaved practice wins on a delayed test. It's old. Shea and Morgan showed it in 1979 with a movement task: people learned three arm-movement patterns either in blocks or in a random mix, and the blocked group looked better during practice while the random group did better on retention and transfer tests afterwards.⁸ Motor-learning researchers call this the contextual interference effect, and for four decades it has held up in labs, gyms and clinics. The maths version arrived with Rohrer and Taylor in 2007, in a lab study on the volume formulae for four solids. I'll hold those numbers back for the worked example below, because I want you to predict them first.

What made people take interleaving seriously for classrooms came later. Rohrer, Dedrick and Stershic (2015) took it into a real school: 126 seventh-graders, over three months, in their ordinary maths classes. On a test one day after the review the interleaved group scored 80% against 64% (d = 0.42). Thirty days later the gap had widened: 74% against 42%, d = 0.79.² Notice the direction. The advantage grew with time.

Then Rohrer, Dedrick, Hartwig and Cheung (2020) ran a preregistered, cluster-randomised controlled trial across 54 seventh-grade classes, 15 teachers and five schools, over four months. On a test one month after the practice ended, interleaved classes scored 61% and blocked classes 38%, d = 0.83, and the effect was positive for every one of the 15 teachers. The teachers implemented it from the worksheets alone, without any training.³

How strong is this evidence, honestly

Strong for maths in school, with limits you should know before you generalise. Nearly all of the classroom evidence comes from one lab (Rohrer's, in Florida), with seventh-graders, on tests the researchers wrote themselves with the same problem formats as the practice. The 2015 study was one school with three teachers. Rohrer's team says all this in their own limitations sections; the 2020 paper adds that interleaved assignments took students longer, that every study so far gave students corrective feedback, and that the technique may need "at least a small amount of blocked practice" first.²³

There's also a confound to be honest about. When you interleave, you automatically space: an A problem is now followed by a B and a C before the next A. Rohrer's team says plainly that their classroom effects "probably reflect the spacing effect" in part, and that their review assignment equalised the delay between last practice and test, not the spacing of practice itself.² The study that separated the two is Taylor and Rohrer (2010): they fixed the amount of spacing in both conditions and found interleaving still roughly doubled scores on a test a day later.⁹ So mixing does something over and above spacing, but in the classroom numbers the two are working together.

The Education Endowment Foundation's 2021 review of cognitive-science approaches in classrooms rates the evidence for interleaving below that for retrieval and spacing for exactly these reasons: fewer studies, mostly maths, mostly one team.¹¹ And as with the rest of this course, nearly all of it comes from Western, mostly American, schools and universities.

The mechanism: interleaving makes you choose

Why would the same problems in a different order matter so much? The best-supported explanation is that solving a problem has two steps, and blocked practice quietly does the first one for you.

Step one is deciding which method the problem needs. Step two is executing that method. In a blocked set, the heading tells you the method. When every problem on the page is about the volume of a wedge, you never ask "is this a wedge problem?" You just apply the wedge formula ten times. You get very fluent at step two and get no practice at all at step one.

Every real test, and every real use of knowledge outside a classroom, starts with step one. A patient doesn't arrive with the diagnosis written on their forehead. Interleaving puts step one back into practice. On every problem you have to look at the surface features, work out what kind of thing it is, and pick the right tool, which is exactly what the delayed test will ask.¹² Taylor and Rohrer looked at what kind of errors blocked-practice students made on the test, and most were discrimination errors: the right procedure, applied to the wrong kind of problem.⁹ They could execute. They couldn't choose.

The second thing interleaving trains is discrimination. When problem types sit next to each other, you notice how they differ. Two solids can look similar in a diagram; seeing them back to back teaches you what to attend to. Blocked practice hides the contrast, because the contrasting case is always three pages away. Brunmair and Richter (2019) put this at the centre of their meta-analysis: interleaving works when the categories are confusable, because its job is to teach you to tell them apart.⁵

This is why Bjork and Bjork (2011) list interleaving alongside spacing and testing as a desirable difficulty.⁶ It makes practice slower and less accurate now, and that slowness is the work of learning being done rather than skipped.

Worked example: the volume formulae

This is the Rohrer and Taylor setup. It was their second experiment, and it was small: 18 college students.¹ They learned to compute the volume of four uncommon solids: a wedge, a spheroid (a stretched or squashed sphere), a spherical cone (a cone with a rounded cap), and a half cone. Each solid has its own formula. Everyone got a tutorial on each formula, then practised on the same set of problems in one of two orders.

The blocked group did all the wedge problems, then all the spheroid problems, then the spherical cones, then the half cones. The interleaved group did the identical problems shuffled.

Now watch what the interleaved student actually had to do, problem by problem. Suppose the shuffled sheet runs spheroid, half cone, wedge, spherical cone, half cone.

Problem 1 describes a solid with two rounded ends and no flat faces. Step one: is this a spheroid or a spherical cone? No point, no flat base, so a spheroid. Step two: retrieve the spheroid formula from the four you were taught and apply it.

Problem 2 has a flat semicircular base and comes to a point. Step one: a point rules out the spheroid; a flat base with a straight edge rules out the spherical cone; it's a half cone. Step two: retrieve the half-cone formula and apply it. Notice that the formula you used a minute ago is the wrong one, and you have to reject it.

Problem 3 has straight edges and flat faces only. Step one: the only solid with no curves is the wedge. Step two: wedge formula.

Compare the blocked student. For the first quarter of the sheet every problem was a wedge, so step one never happened; the heading did it. Read the numbers with lesson 1's vocabulary. The 89% was retrieval strength: the formula was sitting at the front of the mind because the last nine problems had used it. The test a week later measured the two things blocked practice had never trained, identifying the solid and pulling the matching formula out of a full set. The interleaved student had done that on every single problem, which is why their practice score was lower and their test score three times higher. Here are the four numbers side by side; the reversal between the two panels is the whole finding:

A harder example: the painters

The volume study is about choosing a procedure. Kornell and Bjork (2008) asked whether the same thing happens when there is no procedure at all, only a style to recognise.⁴

In their first experiment, 120 people studied paintings by twelve artists, six paintings each. For half the artists (the massed condition), the six paintings appeared one after another. For the other half (the spaced condition), an artist's paintings were mixed in among the others. The test wasn't "which of these paintings have you seen?" It was recognition of new paintings: here's a picture you've never seen, which of the twelve artists painted it?

The natural prediction is that seeing six of an artist's works together gives you a better feel for the style, and that mixing would blur the styles into each other.

Now the wrinkle. After the test, participants were told what massed and spaced meant and asked which had helped them learn more. In that first experiment, 78% said massing was as good as or better than spacing, the same 78% figure as the share who had done better with spacing. In a second experiment with 80 people and no feedback during the test, 72 expressed a preference, and 64 of them said massing had been more effective.⁴ They were never shown their scores by condition, but they'd just sat a test in which the mixed artists went better, and the feeling of the blocked study still won. Kornell and Bjork's phrase for it is that people rated massing more effective even after their own performance had demonstrated the opposite. This is the same illusion you met in lesson 1, and it's the reason interleaving is so rarely chosen by learners left to themselves: it feels worse while it works better, and the feeling wins unless you have a reason to distrust it.

Where interleaving stops working

"Mix everything up" is not the lesson. Brunmair and Richter (2019) pooled 59 studies and found an overall advantage for interleaving of g = 0.42, but the average hides very different results in different materials.⁵ The subgroups are smaller than the whole, so treat the figures as a pattern, not as precise values.

• Paintings and similar artistic styles: g = 0.67. Large. This is Kornell and Bjork territory: many categories that look alike and must be told apart.
• Naturalistic photographs (birds, butterflies, and the like): g = 0.35. Still helpful, smaller.
• Mathematics problem types: g = 0.34. Moderate, and the classroom studies above show it holding up over months.²³
• Expository text: mixed results, nonsignificant overall. Reading passages on different topics in a mixed order has not reliably helped.
• Word learning: g = −0.39, favouring blocking. This category covers things like names sorted into conceptual categories, pronunciation rules and translations, not flashcard vocabulary lists as such. The closest study to a vocabulary list, Hausman and Kornell (2014), mixed anatomy terms with Indonesian words and found no reliable effect either way.⁵¹²

So the decision rule for any subject has one primary question and one further trigger. The primary question: could I confuse these things with each other? If yes, interleave, whether or not any method is involved. The painters had no method to choose, and mixing still helped. The second trigger: does using them require choosing which one applies? If yes, interleave, because a test will make you choose even if the categories don't look alike. If both answers are no, block, and use spacing and retrieval instead, which work regardless.

Variation is a different lever

"Variation" is in this lesson's title, and it isn't the same thing as interleaving. Interleaving mixes different skills: A, then B, then C. Varied practice keeps one skill and changes the conditions it's practised under: throwing to different distances instead of one; solving the same kind of equation with different-looking numbers and contexts; practising a piano passage at several tempos rather than one. Bjork and Bjork (2011) list "varying the conditions of practice" as a desirable difficulty in its own right, beside interleaving.⁶

The two often travel together, because a shuffled set varies the surface of each problem as well as the type. But you can vary without interleaving (one skill, many contexts) and interleave without much variation (three skills, each on one standard kind of problem). The reason to vary is transfer: a method practised under one set of conditions tends to stay tied to those conditions. When you build the practice set at the end of this lesson, vary the surface of the problems within each type as well as mixing the types.

Why textbooks block, in the textbooks' own terms

It's easy to read all this and conclude that textbook authors are lazy. They aren't, and their reasons deserve a hearing.

You can't mix in what hasn't been taught yet, so early in a course there is little to interleave with. A block of problems on the day's skill lets a teacher see straight away which students can't do it, which a mixed set hides. Novices need some blocked practice to get a procedure's steps down; Rohrer's own 2015 paper says a small block at the outset "might be optimal", his 2020 trial almost certainly gave students some blocked practice before the interleaved worksheets, and the interleaved condition in the 2015 study began each new skill with a block of four problems before spreading the remaining eight across later assignments.²³ Interleaved assignments also take longer to finish and depend on students getting corrective feedback, which is more work for the teacher. And some textbooks already interleave: the Saxon maths series has built its assignments that way for decades, and Rohrer's complaint about the rest is mostly that their mixed-review sections are too short and too rare.²

So the practical target isn't "never block". It's "block briefly, then mix", with the mixed portion much larger than the mixed-review section at the end of a chapter.

What people get wrong

"Practise one thing until it's perfect, then move on." This is the standard advice and it describes blocked practice exactly. It feels right because perfection arrives quickly, and the collapse a week later is invisible until the exam. The fix isn't to abandon focused practice entirely; when you're first learning a method you may need a few problems in a row to get the steps down. But move to mixing much sooner than feels comfortable, and treat the drop in accuracy as the signal that discrimination is being trained, not that something went wrong.¹⁶

"Interleaving is always better." It isn't. A learner who mixes vocabulary lists or reading passages on this principle will get nothing for the effort and may lose some. Interleaving is a tool for confusable categories and method selection. For everything else, spacing (lesson 4) and retrieval (lesson 3) are the tools, and they're stronger and more general.⁵

"I shuffled it, so it's interleaved." Only if the problems don't announce their own type. A set of items that read "Past perfect: translate..." in random order is blocked practice with the blocks scrambled: the label makes the choice for you on every item. Interleaving needs the choosing step to be yours. Strip the labels.

"Interleaving is the same as spacing." They travel together, because shuffling A, B and C problems puts gaps between the A problems, and that's part of why interleaving works in classroom studies. But they're different levers. Spacing is about time between encounters with the same material; interleaving is about mixing types within a session. Taylor and Rohrer held spacing fixed and interleaving still helped,⁹ and you can space without interleaving (a vocabulary list reviewed at growing gaps), which is the right design for vocabulary.

Building a set: a worked example

Say you're learning three French past tenses: the passé composé, the imparfait, and the plus-que-parfait. They pass the primary test (English "I went", "I was going" and "I had gone" all look like past tense to a beginner, and choosing wrong is the commonest error) and the second (every sentence forces a choice). So this is a case for interleaving.

Step one: write items that don't name the tense. "Translate: Yesterday I went to the market." Not "Passé composé: translate...".

Step two: for each item, decide the tense before you write a word of French, and write your decision down. Item 1: a completed action at a stated time, so passé composé: Hier je suis allé au marché. Item 2, "I was reading when he came in": an ongoing background action interrupted by a completed one, so imparfait for the reading and passé composé for the coming in: Je lisais quand il est entré. That item needs two choices, which is the kind of wrinkle a good set includes.

Step three: vary the surface within each tense (different verbs, different time expressions, questions as well as statements), so the choice can't be made from one giveaway word.

Step four: when you mark it, count choosing errors and executing errors separately. A wrong tense with the right conjugation is a choosing error, and it's the one this arrangement exists to fix.

Practice

Connections

This lesson is lesson 1 seen from a new angle. Blocked practice is the fluency illusion built into a worksheet: it raises retrieval strength, produces confident performance, and leaves storage and discrimination untouched. The painters study showed the illusion surviving a test that had just gone the other way, which is why you can't rely on how a method feels.

It also sits on top of lessons 3 and 4. Interleaved problems are retrieved, not recognised, because each one makes you pull the right method from a full set. And mixing spreads the repetitions of each type out across the session, which is spacing at small scale. The three techniques stack, and in the classroom studies they were stacked.

Lesson 6 adds a complication that the ECG evidence makes vivid: very early in learning, blocked practice and worked examples reduce load in a way a novice needs, and first-year medical students with no ECG background did worse when their practice was mixed. Move to mixing as soon as you can execute each method at all. Lesson 8 shows how to arrange a week so that mixing happens by default.

Go deeper

• Brown, Roediger & McDaniel, Make It Stick (2014), chapter 3, "Mix Up Your Practice": the readable account of interleaving and variation, the studies above told as stories, and the practical advice for students and teachers.
• Rohrer, Dedrick, Hartwig & Cheung (2020), Journal of Educational Psychology 112, 40–52: the preregistered trial. Worth reading for the method as much as the result, and for the four caveats the authors list at the end.
• Brunmair & Richter (2019), "Similarity matters", Psychological Bulletin 145, 1029–1052: the meta-analysis that draws the boundary. If you want to know whether interleaving will help in your subject, this is where the answer lives.
• Dunlosky, "Strengthening the Student Toolbox", American Educator (Fall 2013): the plain-English version of the ten-technique ratings, with interleaving in context.
• RetrievalPractice.org, "How to use interleaving" and The Learning Scientists, the interleaving poster and blog posts: short, free, and built for students and teachers who want to try it this week.

Sources

1. Rohrer, D. & Taylor, K., "The shuffling of mathematics problems improves learning", Instructional Science 35, 481–498 (2007). Experiment 2, N = 18; four solids (wedge, spheroid, spherical cone, half cone); about 89% vs 60% during practice, 63% vs 20% at one week; d = 1.34 on the test.
2. Rohrer, D., Dedrick, R. F. & Stershic, S., "Interleaved Practice Improves Mathematics Learning", Journal of Educational Psychology 107, 900–908 (2015). 126 seventh-graders, one school, three teachers, nine classes, three months; 80% vs 64% (d = 0.42) at one day; 74% vs 42% (d = 0.79) at 30 days. Interleaved condition began each skill with a block of four problems; authors note the effect "probably reflects the spacing effect" in part, that the review equated test delay, that a small initial block "might be optimal", and that the Saxon series interleaves.
3. Rohrer, D., Dedrick, R. F., Hartwig, M. K. & Cheung, C.-N., "A Randomized Controlled Trial of Interleaved Mathematics Practice", Journal of Educational Psychology 112, 40–52 (2020). Preregistered cluster RCT, 54 seventh-grade classes, 15 teachers, five schools in one Florida district, four months; 61% vs 38% at one month, d = 0.83, positive for every teacher (ds 0.23 to 1.48); researcher-written test; teachers untrained; caveats on time on task, test delay, initial blocked practice and feedback.
4. Kornell, N. & Bjork, R. A., "Learning Concepts and Categories: Is Spacing the 'Enemy of Induction'?", Psychological Science 19, 585–592 (2008). Exp 1a: N = 120, twelve painters, six paintings each; spaced .61 vs massed .35, d = 0.99; 78% did better with spacing and 78% said massing was as good or better. Exp 2: N = 80, no feedback during the test; of 72 who expressed a preference, 64 said massing was more effective. Participants were not shown scores by condition.
5. Brunmair, M. & Richter, T., "Similarity matters: A meta-analysis of interleaved learning and its moderators", Psychological Bulletin 145, 1029–1052 (2019). 59 studies; overall g = 0.42; paintings g = 0.67; naturalistic photographs g = 0.35; mathematics g = 0.34; expository text mixed and nonsignificant; words (names in conceptual categories, pronunciation rules, translations) g = −0.39.
6. Bjork, E. L. & Bjork, R. A., "Making things hard on yourself, but in a good way", in Psychology and the Real World (Worth, 2011), 56–64. Varying the conditions of practice and interleaving named as separate desirable difficulties; a difficulty is desirable only if the learner can meet it.
7. Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J. & Willingham, D. T., "Improving Students' Learning With Effective Learning Techniques", Psychological Science in the Public Interest 14, 4–58 (2013). Interleaved practice rated moderate utility; literature "currently small, but it contains enough null effects to raise concern"; Table 4 rates learners insufficient and materials qualified; maths effects called "relatively dramatic".
8. Shea, J. B. & Morgan, R. L., "Contextual interference effects on the acquisition, retention, and transfer of a motor skill", Journal of Experimental Psychology: Human Learning and Memory 5, 179–187 (1979). Three movement patterns practised blocked or random; blocked better during acquisition, random better on retention and transfer.
9. Taylor, K. & Rohrer, D., "The effects of interleaved practice", Applied Cognitive Psychology 24, 837–848 (2010). Children practised four kinds of maths problems with the degree of spacing fixed across conditions; interleaving lowered practice performance and roughly doubled scores on a test one day later; blocked-practice test errors were mostly discrimination errors.
10. Yang, C., Luo, L., Vadillo, M. A., Yu, R. & Shanks, D. R., "Testing (quizzing) boosts classroom learning", Psychological Bulletin 147, 399–435 (2021). 222 classroom studies; g = 0.50. Used here as a scale for effect sizes.
11. Education Endowment Foundation, Cognitive Science Approaches in the Classroom: A Review of the Evidence (2021). Rates classroom evidence for interleaving below that for retrieval practice and spacing.
12. Hausman, H. & Kornell, N., "Mixing topics while studying does not enhance learning", Journal of Applied Research in Memory and Cognition 3, 153–160 (2014). Mixing anatomy terms with Indonesian vocabulary had no reliable effect.
13. Hatala, R. M., Brooks, L. R. & Norman, G. R., "Practice makes perfect: the critical role of mixed practice in the acquisition of ECG interpretation skills", Advances in Health Sciences Education 8, 17–26 (2003). Mixed practice 46% vs blocked 30% on new traces.
14. Monteiro, S., Melvin, L., Manolakos, J., Patel, A. & Norman, G., "Evaluating the effect of instruction and practice schedule on the acquisition of ECG interpretation skills", Perspectives on Medical Education 6, 237–245 (2017). 80 first-year medical students; on the delayed test blocked practice beat mixed, 34% vs 24%, attributed to insufficient initial mastery.