Interleaved or Blocked? The Order You Practise Problems In

Blocked practice runs problems of one type in a row; interleaved practice mixes types so that consecutive problems need different methods. The order matters because blocking removes a step — once the previous question has told you the method, you never have to choose it — and choosing is the part that a test, or real life, actually asks for.

The counter-intuitive part is the direction of the effect. Interleaving usually makes the session itself go worse and the later test go better. That is not a paradox; it is the difference between performance and learning.

The two orders, defined

Take a practice set of twenty problems. In a blocked set, the first ten might all be "multiply by 25" and the second ten all "divide by 4". In an interleaved set, those same twenty problems are rearranged so that no two neighbours share a method.

The description given by the researchers who have studied this most closely in mathematics is precise: "Practice problems are interleaved if the problems are arranged so that consecutive problems cannot be solved by the same strategy." Note what that does and does not say. Interleaving is a property of ordering, not of spacing. You can interleave inside a single sitting, and you can block across a whole term. Distribution over time is a separate variable, covered for another domain in spaced repetition for language learning.

The reason the distinction bites in arithmetic is that solving a problem has two steps, and a blocked set only ever exercises one of them. Given "256 + 99", you must first decide that rounding up and correcting is the efficient route, and only then execute it: 256 + 100 = 356, then subtract the 1 you added, giving 355. In a block of twenty "add 99" problems, the decision is made once and executed nineteen more times. In a mixed set, the decision comes back every time.

What the classroom experiment found

The clearest evidence comes from a study run in real classrooms rather than a laboratory. Interleaved Practice Improves Mathematics Learning, by Rohrer, Dedrick and Stershic in the Journal of Educational Psychology, gave 126 seventh-grade students the same practice problems across a three-month period. The only thing that varied was the arrangement: some skills were learned through interleaved practice and others through "the usual blocked approach". The practice phase ended with a review session, followed one or thirty days later by an unannounced test.

The result, in the authors' own summary: "Compared with blocked practice, interleaved practice produced higher scores on both the immediate and delayed tests (Cohen's ds = 0.42 and 0.79, respectively)."

Two features of that design are worth holding onto. The students did the same problems in both conditions, so the effect cannot be explained by one group getting better material or more of it. And the advantage was roughly twice as large after a month as after a day, which is the signature of a manipulation that improves retention rather than momentary fluency.

The federal IES practice guide on organising instruction and study points in the same direction from a different angle: its second recommendation is to "interleave worked example solutions with problem-solving exercises", alternating between studying a worked solution and attempting a problem rather than doing all of one and then all of the other.

Why mixing feels like it is not working

During a mixed set you will be slower, you will make more errors, and the session will feel less satisfying than a block. That experience is real, and it is also the reason interleaving is underused: the feedback you get while practising points the wrong way.

Soderstrom and Bjork's review Learning Versus Performance states the general form of the problem. During training, "what we can observe and measure is performance, which is often an unreliable index of whether the relatively long-term changes that constitute learning have taken place" — and, more pointedly, "improvements in performance can fail to yield significant learning", with certain manipulations having "opposite effects on learning and performance". Interleaving is the textbook case of a manipulation with opposite effects on the two.

The practical instruction that follows is uncomfortable but simple: when you choose a mixed set, you are choosing to be worse at practice on purpose. Judging the choice by the session score will always tell you to stop.