Interleaved practice

Why does mixing problem types during practice feel worse yet leave you better prepared?

Almost every textbook in the world is blocked: twenty problems on the quadratic formula, then twenty on completing the square. The advice underneath it — master one thing before moving to the next — is not foolish, and within the session it demonstrably works. Accuracy during a blocked run is higher, the pace is smoother, and the learner feels competent.

Shuffle the same problems so that consecutive items come from different topics, and everything gets worse: slower, more errors, more irritation. Yet on an unannounced test weeks later, the shuffled group does better. Nothing was added — same problems, same total time, only the order changed. So what could make practice performance and later test performance come apart like that?

Start by asking what a blocked page quietly does for you. Solving a problem is really two acts: work out which method this situation calls for, then execute it. Under a heading that says "Exercises 1-20: quadratic formula", the first act has already been performed — by the heading. You do the second act twenty times.

So what has the practice actually trained? Execution. Now look at the test, where nothing announces the type. The very step the learner never rehearsed is the first step they need. Does that suggest the blocked student has been practising a slightly different task from the one they will be examined on?

That is the first candidate mechanism, usually called discriminative contrast. Setting unlike items side by side makes the differences between them salient; running one kind in a block makes the commonalities within a kind salient instead. Interleaving is the only schedule in which the "which kind is this?" step exists at all, so it is the only schedule that can train it.

There is a second candidate, and it is worth taking seriously because it is simpler: interleaving is spacing wearing a disguise. Mixing types necessarily spreads out the repetitions of any one type, and spaced repetitions are known to be worth more than massed ones. On this reading nothing about discrimination is required. The honest position is that both are operating and their relative weight is still argued over; the two are genuinely hard to separate, because you cannot interleave without also spacing.

What would distinguish them? If spacing were the whole story, interleaving should help fairly uniformly. It does not. In category-learning work it helps most when the categories are confusable and can actually reverse when they are dissimilar, where blocking seems to help learners find what the members of a category have in common. That pattern is what a discrimination account predicts and a pure spacing account does not.

The size is not trivial. In a study by Rohrer, Dedrick and Stershic, 126 seventh-graders worked the same practice problems over three months with only the arrangement differing; on an unannounced test the interleaved group led with an effect size of about 0.42 one day later and 0.79 thirty days later. Notice the direction of that change — the gap grows as the delay grows, which is the signature of these difficulties generally.

Then there is the feeling, which is where the practical damage happens. Judge your learning by how the last ten minutes went, and blocking wins every time: fluent, error-free, fast. Interleaving supplies visible failure. Asked afterwards which schedule taught them more, most learners name the one that produced the worse result — having just experienced the better one.

Three refinements keep this from becoming a slogan.

Interleaving is not "variety is good". It works by contrast, so it needs items that could plausibly be confused with each other. Mixing French vocabulary with press-ups mixes nothing that competes.

It is a schedule for consolidation, not for first contact. You cannot discriminate between two methods before you have been taught either one, and early instruction that jumbles unfamiliar material tends simply to overload. The usual finding is that some initial blocked exposure followed by interleaved practice beats either alone.

And the cost is real, not illusory. Interleaved practice genuinely produces worse performance now in exchange for better performance later. That is why it belongs in the family of desirable difficulties: the awkward word is "desirable", because to the person doing it the method feels exactly like the method failing.

• How much of the effect survives when spacing is deliberately equated between the two schedules.
• Why blocking wins for categories that are easy to tell apart, and what that says about what "difficulty" is doing.
• Whether learners can be taught to distrust fluency as a signal, or only to override it.

Every term the collection defines is gathered in the glossary.