How interleaving can help students retain maths knowledge

Practice is essential to learning new facts, but not all practice is equivalent. To help students retain knowledge in the long-term, teachers can interleave (alternate) practice of different types of content, and space practice over time, with content being reviewed over weeks or months.

Why is this important?

Maths is most often taught using blocked practice, for example when learning about fractions, pupils will often practise one type of problem repeatedly (eg addition of fractions) before moving onto a different problem (eg subtraction or multiplication of fractions). This means that pupils know the appropriate strategy for solving a problem before they read the question.

By mixing up types of problems, pupils are required to think more carefully about the problem and choose the correct strategy needed to solve it. This improves maths learning as it helps pupils to see the links, similarities and differences between ideas, and strengthens associations between each kind of problem and its corresponding strategy. In addition, problems of the same kind are spaced and are then reviewed, which can help improve retention.

What are some effective approaches?

An interleavingAn approach to learning where, rather than focusing on one p... More teaching method mixes different kinds of problems, or material, and is particularly useful for teaching something that involves problem solving – like maths. If pupils are learning four mathematical processes, it is more effective to interleave (alternate) practice of each different problem type, rather than practise just one type of problem, then another type of problem, and so on (ABCBCACBA rather than AAABBBCCC). However, this can make learning harder, and less satisfying, for learners in the short-term, while resulting in better long-term retention.

• Switch between ideas during a lesson. Don’t focus on one idea for too long. (ABCABCABC rather than AAABBBCCC)
• Go back over the ideas again later to strengthen understanding.
• Make links between different ideas as you switch between them.

What research evidence is there around this area?

Research in interleaving shows that pupils’ retention of mathematics knowledge is enhanced by simply rearranging the order they practise problems. In a study by Doug Rohrer and colleagues Year 8 pupils were taught using either interleaved or blocked practice over a nine-week period, and then received an unannounced test two weeks later. The mean test scores were greater for material learned by interleaved practice rather than by blocked practice.

Research on spacing suggests that pupils’ long-term retention of information is improved by reviewing previously-learned information at periodic time intervals of several weeks. A study by Cepeda and colleagues (2008) suggests that there may be an optimal spacing gap.

In the study adult participants experienced a different combination of spacing gap and test delay, with spacing gaps ranging between seven and 350 days. Cepeda found that the optimal spacing gap was dependent on the test delay. Shorter spacing gaps tended to produce better information retention after relatively short delays, whereas longer spacing gaps tended to produce better retention for longer delays. Retention was best when the spacing gap was around 10-20% of the test delay. The results suggest that in order to make best use of spacing, learners should be aware of how long they want to retain information for, with longer spacing gaps for long-term retention.

What are some ideas I can try in the classroom?

There are a number of practical ways that teachers and educators can implement spacing and interleaving in their lessons:

• Include a brief review of previously learned material: this could be during lessons or class activities, or implemented as homework assignments.
• Cumulative tests and quizzes: by testing pupils on recently learned material as well as in the more distant past, the tests will serve to re-expose pupils, and also provide pupils with a good incentive to review and revise what they’ve learnt in their own time.
• Mix-up the types of problems that you give to pupils, and give them in an order that is unpredictable: for example, when teaching pupils about fractions include some problems that require addition of fractions, some with multiplication and some with division, etc, rather than several addition problems, followed by several multiplication problems etc.

Things to consider

• Maths textbooks are often organised in blocks, so how will you plan to interleave practice?
• How will you evaluate the effectiveness of interleaving and spacing?

Questions for reflection/discussion

• Interleaving and spacing do not come without challenges – what obstacles and challenges do you think you will have?
• Interleaved practice is one example of ‘desirable difficulties’, which are tougher for learners in the short-term but lead to better learning. Why not also consider others, such as using tests, or varying the conditions of practice?

Case study: examples of practice

In the following blog posts, practitioners discuss how interleaving has worked in their classrooms:

• Spacing, Interleaving, the Testing Effect and Distributed Practice (the Diet Coke version), by mrbenney
• Building interleaving and spaced practice into our pedagogy, by William Emeny
• Learn to study using …  interleaving, by Yana Weinstein & Megan Smith

Further useful resources

• Six Strategies for Effective Learning Posters, presentations, bookmarks and stickers for use by you and your students. Interleaving practice is covered in these Teaching How2s – free downloadable resources.
• The effects of interleaved practice, Applied Cognitive Psychology, 24. This study looks at whether previously observed test benefits of interleaving may be due to spacing rather than interleaving by itself.
• What makes great teaching? Review of the underpinning research, Sutton Trust, 2014. Interleaving practice is one of the approaches covered in this “best practice” guide.
• Deans for Impact: the Science of Learning  A resource that provides guidance to anyone working in education who is interested in understanding the science of how learning takes place and what that means for how we teach.