The Benefits of Interleaving to the Learning of Maths

Written by Dr Flavia S Belham, Seneca Learning Thursday, 13 September 2018

Dr Flavia Belham is the Chief Scientist at Seneca Learning who are exhibiting at #MathsConf17.

Maths is a fascinating but complex subject to learn. Students need to understand the concepts but should also acquire procedural fluency when solving problems. What is the best way to do that?

Dr Doug Rohrer has conducted important research on effective learning strategies focused on Mathematical content. He has done experiments both in the lab and also in the classroom. One of his main findings taps into the idea of interleaving.

What is interleaving?

Interleaved study is the opposite of blocked study. For example, if students are trying to revise topics A, B and C for an exam, their study routine can be:

  1. AAABBBCCC, or

Routine 1 is blocked, whereas routine 2 is interleaved. Research in the field of cognitive sciences has consistently shown that routine 2 leads to deeper learning and stronger memory.

It is easy to understand this, if you use a gym analogy. Imagine you are going to take part in a fitness competition in 3 months. Would you train only your arm muscles for the first month, only the leg muscles for the second month, and do only treadmill exercises for the last month? Or would you spread out the three types of exercise so that they are frequent but mixed?

How does interleaving improves learning of Maths?

Interleaving improves learning. How does it actually work and how can Maths students benefit from it? There are two main reasons. The first one is that it helps students to differentiate between two concepts. It is easier to understand the difference between an elk and a moose if you see them side by side than one after the other. The same happens with other concepts.

The second reason why interleaving improves learning of Maths is that it helps students to figure out the right strategy or formula on the basis of the problem itself. For example, imagine that students are learning how to calculate the volume of different shapes. Usually, they would learn the formula for a cylinder and apply it to several problems involving cylinders. Then, they would lean the formula for a sphere and apply it several times to problems involving spheres. This is just like the blocked routine 1 from before.

The problem with this routine is that, even before they read the question, students already know which formula to use! That’s simply because they know that block of problems will be of the same kind and will require the same strategy.

If, however, you present them with a set of questions that can be about spheres or about cylinders in a random order (like in routine 2), students will need to understand how to figure out the right formula based on the problem and nothing else. Doing this will massively help them on cumulative examinations, as questions can be about any topic. That way, interleaved practice not only boosts learning, but also prepares students for future examinations.

For more practical examples of interleaving being used in Maths, read the practical guide written by Dr Rohrer

How does Seneca Learning do it?

Seneca is a free online homework and revision platform that helps students learn 2x faster by using strategies from cognitive science - including interleaving. Our Maths content is 80% questions and problem solving. More than that, the order of questions is pseudo-randomised so that students need to think about the problem and figure out the right strategy on their own. This leads to deeper learning, stronger memory, and better exam results.

To help with procedural fluency, a large part of our Maths courses is made up of worked examples, in which students answer bit after bit and receive immediate feedback for each. The content is written by senior educators and is exam board specific too.

Here are some of our Maths courses. Try them out and create a teacher account. You will be able to link your account to your students’ and monitor their progress on the platform. All free!

KS4 -

KS3 -

We will be at the Maths17 conference in Birmingham in October! Come and visit our stand to learn more about our free platform, the science behind it and how it can benefit the learning of Maths!

About the Author

Dr Flavia S Belham, Seneca Learning

Flavia worked as a teacher for two years before doing her PhD in Cognitive Neuroscience. She is now the Chief Scientist at Seneca Learning, an online revision and homework platform that provides KS3, KS4 and KS5 resources for free.

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