Interleaving in maths

What is interleaving?

Interleaving is a teaching method where topics are mixed together rather than being practised or taught in blocks of topics. 

Interleaving can be a really powerful way of teaching maths and is particularly useful as a way of practising and revising mathematical topics that a student has already been taught.

Teaching through interleaving involves introducing several new topics or skills in the same lesson rather than just focusing on one. 

Practising with interleaving involves attempting questions from multiple topics that have already been taught to the student. 

Teaching through interleaving is quite different to how maths is traditionally taught in schools and one of the best ways to understand why interleaving is so powerful is to contrast it with how maths is normally taught.

I have created many interleaving maths resources which I have uploaded to my maths resource website called mathslinks.co.uk

How maths is taught in schools

Most schools follow a linear scheme of work, introducing each maths topic separately and in a pre planned order.

For instance they might spend two weeks working on solving equations before moving on to three weeks of number work. Some schools will spend an entire term looking at one distinct branch of maths. 

With a lot of schools now following a three year GCSE course it can lead to students studying a topic in year 9 and potentially not doing it again until they are revising in year 11.

For me this linear pathway (although an understandable way of teaching a course in a school) is flawed for several reasons:

• Connections between topics (and therefore a deep understanding of maths) are hard for the students to make. 

• Topics get forgotten as our brains will naturally begin to forget something if we’re not coming back to it regularly (more on this).

• The chance to learn something happens only once - what if you’re absent that week

• It bears no resemblance to how the students are assessed in exams - a maths paper will be a mixture of topics and involve questions that bring various topics together.    

What interleaving is and how it is different

Interleaving is when you mix up the topics and teach them in a non-linear way - which is quite different to how subjects are generally taught in school. 

Three or four topics can be taught alongside each other and the lesson may involve jumping between these topics.

The benefits include:

• Connections between topics are clearer and easier to find.

• This repeated practice leads to better retention in the long term.

• This way of learning is exactly the way we are eventually assessed (generally an exam paper).

• Students are given multiple opportunities to understand a topic 

• If a student dislikes a topic it won’t be too long until we have moved on

How I use interleaving in my maths tuition

Over the years I have gradually adapted my teaching style to teach almost entirely in an interleaving style. It was a method I stumbled upon long before I became aware of what it was called and that it was an actual teaching style. 

I have always enjoyed giving students a large worksheet which has a variety of questions and asking the students to attempt what they can, particularly if this was a first lesson with a child. 

Watching a student tackle a variety of questions from different topics would always give me a great insight into what they know; how they tackle problems and their general academic level. 

I would, within a very brief amount of time, have a really good understanding of what we needed to work on in that lesson and upcoming lessons.

When the student had finished we would then go over the sheet with me praising their correct answers, pointing out places where they went wrong and we would slowly go through all of the questions they didn’t attempt. 

What rapidly became clear was that I wasn’t always teaching them things they had never learnt before I was often simply reteaching them things they had already learnt but had forgotten. 

This then led me to look at why students would over time begin to forget areas of maths and I began to introduce spaced repetition into my teaching as a way to help students retain their maths skills. 

By teaching through interleaving I was able to find the time for spaced repetition in every lesson.

You can view and download some of my interleaving worksheets here.

You can also see how I explain how to solve the questions from these worksheets here.

Some links to some interesting articles on interleaving in maths:

How interleaving can help students retain maths knowledge

Interleaving in maths

Read about how I use spaced repetition in my teaching.