Mixing problem types before the test
Blocked practice scored 89% while students were doing it and 20% a week later. Mixed practice felt worse and held. Toggle is not required — both bars are on one chart.
Most maths sets are blocked. The lesson was cylinders, so the next twelve questions are cylinders. You can spot the formula from the heading. On a paper, the heading is gone. Rohrer and Taylor’s second experiment is the clean demonstration: the schedule that felt better in practice collapsed on the test, and the schedule that felt worse held.
Same problems, different order
Students learned volume formulas for several solids. Mixers saw the types shuffled. Blockers saw one type, then the next. Both groups practised across two sessions and sat a test a week after the second session. During practice, blockers averaged 89% and mixers 60%. The gap was largest in the first session (87% versus 43%). By the second practice session it had narrowed (91% versus 78%) and was no longer a clear statistical win for blocking.
The test reversed the story. Mixers scored 63%. Blockers scored 20%.
[[chart:ld-interleave]]| Order | During practice | Test, one week later |
|---|---|---|
| Blocked by type | 89% | 20% |
| Mixed together | 60% | 63% |
What mixed practice is actually training
Blocked sets train execution: you already know which formula, so you practise plugging in. Mixed sets train choice: each question starts with “which solid is this?” That choice is most of a novel exam stem. If your homework never asks it, the first time you pay for the missing skill is under the clock.
The practice dip is the feature people try to optimise away. A session that feels slow is not evidence the method failed. In this study it was evidence the student was doing the part the test would score. Hide the “during practice” series in the legend if you want the test bars alone — the 20 versus 63 is the decision.
The sample was small and the task was volume formulas. Do not treat 63% as a target for your own exam. Treat the direction as the lesson: if every set is one topic, you are rehearsing a situation the paper will not give you.
How to mix without a new textbook
- After you can solve a type once, stop the block.
- Build a short set of four to six questions from different types you already “know.”
- Do not label them. If you need the heading, you have not practised selection.
- When you miss, name whether you picked the wrong method or executed the right one badly. Those are different repairs.
Study Lab cards can hold the decision (“which method, and why”) on the back, not only the final number. A full practice test still belongs in Practice Hub, where the mix is the paper’s mix, not a chat’s guess. For the spacing result that sits beside this one, read spacing the same problems.
A mixed set you can build from homework
Take four questions you have already solved this fortnight, each from a different lesson: one ratio, one equation, one area, one graph read — or whatever four types you actually have. Copy the stems onto a page with no titles. Set a short clock, shorter than a full paper. Solve them in the order they appear, and when you stall, write “wrong type” or “right type, bad step” before you look anything up. That label is the repair. A wrong type goes on a card whose back is the first decision, not the final number. A bad step goes on a card whose back is the step.
Do not “help yourself” by sorting the page back into topics halfway through. That is how you rebuild the blocked set the moment it gets uncomfortable. The first-session gap in the study — 87% blocked versus 43% mixed — is exactly that discomfort. It shrank by the second session. The test, a week later, is why you tolerate it.
Keep the mixed page to types you have already learned once. Shuffling a brand-new method in with three old ones teaches panic, not choice. Learn the new method in a short block — two clean solutions — then, on another day, drop one question from it into the mixed page. Spacing and mixing are a sequence, not a single trick. The spacing result is the previous article; this one starts only after the method exists.
One mixed page a week is enough beside ordinary homework. The homework still teaches the new method. The mixed page checks whether you can choose it. If you only ever do the homework, you are rehearsing the blocked bar.