Interleave It
Mix problem types within practice so students choose the method as well as use it
What is it?
Interleave It means mixing different problem types within a practice set, so that consecutive questions call for different methods. In a block of ten similar questions, students soon stop choosing a method, because the page has already chosen it for them; in a mixed set they must work out what kind of question they are facing before they can begin. Exam papers mix their questions, so the choosing itself needs practice too.
The steps
- Start once each type is accurate on its own. Teach a new problem type and let students practise it in a block first. Move to mixed sets once most of the class can solve each type unaided. A short blocked warm-up will show you whether they are ready.
- Build the set from types students confuse. Choose three or four problem types for a single set of eight to ten questions. Pick types that look alike at first glance, such as area and perimeter, or mean and median. To save time, reuse an old worksheet and swap half of its questions for earlier types.
- Order the questions so neighbours need different methods. Shuffle the questions until no two consecutive ones use the same method. Then check the finished set: if a student could guess the method without reading the question, reshuffle.
- Tell the class why the set is mixed. Give the reason before the first mixed set, and repeat it whenever students protest.These questions are mixed on purpose. In the exam, nobody tells you which method to use, so today you practise choosing it. It will feel harder than a normal page. Stick with it. Choosing the method is a skill, and this is how you train it.
- Ask for the method before the working. Ask students to write the method name in the margin before they solve each question. One word is enough, such as "perimeter" or "factorise". The margin note shows both you and them where the choosing goes wrong.
- Mark the choice as well as the answer. When you go over the set, ask which method each question needed and how students could tell. Name the clue in the wording, such as "around the edge" pointing to perimeter. Spend longest on the questions where several students chose the wrong method.
What it looks like
Mr Sandhu's maths class of 13-year-olds spent Tuesday on circle area, and the blocked page went well. Today's ten questions mix area, perimeter and volume. By question three, hands are going up. Jess, who scored ten out of ten on Tuesday, calls him over: "Sir, is this an area one?" "What is it asking you to find?" "The distance round the edge." "So which method?" "Perimeter."
They mark the set together and the class averages six out of ten. He can feel the dip in the room, and for a moment he wonders whether he has undone Tuesday's lesson. Then he reads the margins: most students picked the wrong method but carried it out correctly. "Circle every question where your margin word was wrong. Those are Friday's starter questions." They circle, and he notes the three worst questions in his planner.
How you’ll know it’s working
- Method words start appearing in the margins before the working begins, without a reminder from you.
- The gap between blocked and mixed scores narrows. A class scoring nine out of ten on blocked pages and five on mixed pages in October may reach seven or eight on mixed pages by December.
- Questions like "is this an area one?" fade during mixed practice, and students begin to point to the wording that gives the type away.
- Marking a mock reveals fewer wrong-method answers and fewer blanks, especially on questions drawn from earlier units.
Pitfalls & fixes
- Interleaving on day one. A mix that includes a type students cannot yet solve unaided tends to produce guessing. Give new material its blocked practice first, and bring it into the mix from the following lesson or week.
- Mixing types nobody confuses. If the method is obvious for every question, the set is harder to build and teaches little. Rebuild it around near neighbours, the pairs that your marking shows students mix up.
- Retreating when scores dip. Mixed sets tend to score below blocked pages for weeks, and the blocked page flatters everyone. Judge the technique on delayed results, such as how the same mix fares when it returns a fortnight later.
- Drifting back to the textbook. Published exercises arrive blocked, so mixed sets can quietly vanish in a busy fortnight. Keep a file of mixed sets organised by topic cluster and reuse it; the second year costs far less than the first.
Weigh it up
Why it’s worth it
- It rehearses the choice that exams demand. Papers mix their questions, so a student who has only practised in blocks meets method-choosing for the first time in the mock.
- The measured gains are large. In Rohrer and colleagues' randomised trial, classes that mixed their practice for four months scored 61% on a test a month later, while blocked classes scored 38%.
- Every mixed set doubles as spaced review. Earlier types keep returning within ordinary practice, so the previous topic stays live while the new one is taught.
- It shows you who cannot tell the types apart. Blocked pages hide this entirely, while a margin word for each question tells you which pairs to reteach, and to whom.
- It needs no new resources. The questions already exist in your textbook and worksheets; the work lies in reordering them, and a set built once serves every year that follows.
The costs
- Lessons feel less successful while the technique beds in. Scores drop, more hands go up, and the class gets through fewer questions, because each one now begins with a decision.
- The reordering falls to you. Published exercises arrive blocked, so building mixed sets takes planning time until your file of them has grown.
- The early dip lands on students too. Confidence takes a knock for a few weeks, and in a room where mistakes feel risky, a mixed set can read as a trap.
Adaptations
- Early years / lower primary: keep the mix small and concrete. A shuffled pile of addition and subtraction cards makes 6-year-olds read the sign before reaching for the cubes, and two types is plenty.
- Primary: mix word problems above all. A page where addition, subtraction and multiplication problems are shuffled together makes 9-year-olds read for the operation rather than assuming it is today's topic.
- Secondary / exam classes: end each homework with a mixed section drawn from the whole course so far. Past papers arrive ready-mixed; move on to them once each topic's accuracy is in place.
- Beyond maths: the approach works wherever methods get confused. Mix tenses within a single translation task in languages, or mix science questions so that students choose the formula as well as substitute into it. The research base is strongest in maths, so check your own results elsewhere.
Where this comes from
Psychologists first documented the effect in motor-skill research in the 1970s, under the name contextual interference. Doug Rohrer and colleagues at the University of South Florida carried it into school mathematics through a series of shuffled-practice studies, culminating in a randomised trial across 54 classes whose analysis plan was published in advance; Rohrer's free practice guide for teachers remains the best-known codification. The classroom evidence is strongest in mathematics, where problem types are easily confused; Dunlosky and colleagues' 2013 review rated interleaving as moderate utility, though it was written before the largest school trials were run.
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