For maths teachers, one of the most interesting books published in recent years has been Craig Barton’s How I Wish I’d Taught Maths, packed full of insights from cognitive science and how it applies to the classroom. So to help primary teachers understand and make use of these findings, we’ve got a new a series of blog posts by primary headteacher Clare Sealy. 

This first post is on cognitive load and how it applies to primary maths teaching. 

All of Clare’s blog posts in this ‘How I Wish I’d Taught (Primary) Maths’ series are available from our website (follow the links at the end of this blog). They’re long reads. But they’re worth it.

And if you’re short on time, just download the How I Wish I’d Taught Maths Crib Sheet which takes all the key points from all 6 blogs in a condensed form.

Craig Barton – The book behind the blog

As a primary school teacher, you might not have heard of Craig Barton. But if you’ve ever used any of the White Rose Diagnostic Questions, then you have Craig Barton (among others) to thank. Craig Barton is a legend among secondary school maths teachers.

As well as being behind Diagnostic Questions, he also created the incredibly useful website, Mr Barton Maths, has a very well-regarded podcast, the Mr Barton Maths Podcast and is a maths advisor for the TES.  And now he has written an amazing book – How I Wish I’d Taught Maths.

The intended audience for his book is secondary maths teachers, but almost all of it is directly applicable to primary maths classrooms.

The Third Space Learning context

One of the reasons we asked Clare to write this series of blog posts was because the book How I Wish I’d taught Maths reflects much of the approach we aim to take in our 1-to-1 maths lessons each week.

Tutors are trained on the importance of breaking down learning into small steps, building pupils’ metacognitive skills, and presenting questions and activities in a clear order, building one onto the next. If you’re interested  in finding out more about the effectiveness of the 1-to-1 we give 7,000 UK primary pupils every week, just give us a ring on 0203 771 0095 or book a demo here. 

While some of the examples Craig uses are more obviously from the secondary curriculum, many involve fractions or percentages or geometry examples that might well be used in any year 6 classroom.

Short on time? Download the crib sheet from Clare's blogs here.

Teacher Crib Sheet free

Crib Sheet for How I wish I'd Taught Primary Maths

Download the key findings from research; share with your staff, your SLT, and at your next job interview!

Systematic reflection on education research and cognitive science

However, the examples he uses are not what’s important about this book. What makes it essential reading is the systematic way Craig reflects on how learning about educational research, and in particular cognitive science, revolutionised how he taught maths.

Like many of us, Craig never really thought much about how children think and learn. It rarely features in initial teacher training or later CPD.  He now realises that lots of his most cherished assumptions about what made good maths teaching were wrong. In How I wish I’d taught maths, Craig explains what cognitive science teaches us about how people learn and what the implications of that are for teaching maths effectively.

All of this is completely transferable to a primary school context.

In this series of blogs, I will be outlining what Craig learnt from cognitive science and how it challenged his assumptions. I will also then share the strategies he now uses instead, all of which you will find you can use teaching your primary pupils maths.

In this first introduction blog I look particularly at cognitive load as this is essential to all his findings about teaching maths.

Craig’s findings from research: How students think and learn

Cognitive scientist Daniel Willingham explains in Why Students Don’t Like School that knowing about the interplay between working memory and long-term memory is extremely useful when trying to teach anybody anything.

Cognitive Load in Primary schools

Working memory is where thinking actually happens

Working memory only has a very finite capacity; it can hold and process roughly only four different items at a time. In our ignorance of the limits of working memory, our teaching often overwhelms its capacity, expecting learners to think about far too many things all at once. As a result of this overload, learning fails as the working memory simply cannot process so much information all at once, so ‘forgets’ some of it.

Use the long-term memory to store facts

However, there is a way to work around the limitations of working memory. This is where knowing about long term memory comes in. Unlike our working memories, our long-term memory has huge – almost infinite – capacity. It is here that we store our knowledge of facts and procedures. This vast repository of information resides outside our conscious awareness, but can be summoned into our working memory when needed.

Long term memory therefore enables us to bypass the problems presented by our small working memories. By stocking our long-term memories with knowledge in a well organised, easily retrievable way and making recall of key aspects automatic, we drastically cut down on the processing our poor, beleaguered working memories have to do.

When we teach maths (and anything else for that matter), we need to think about how we can ensure that what we teach makes the precarious journey from working memory and long-term memory successfully. To do this we have to be mindful of cognitive load.

What is cognitive load?

Cognitive load is the term used in cognitive science to describe how much capacity something takes up in the working memory. Cognitive overload is what happens if too many demands are placed on working memory at once. For a further explanation of how memory works, read here and you can also check out my blog on beating summer brain drain in maths.

Cognitive load in a primary school maths context

Look at children learning to use the vertical addition algorithm with the following example:

+35

27

A child who has their number bonds stored in their long-term memory and knows that 5 + 7 = 12 can import that fact into their working memory without conscious effort.

None of that precious, finite capacity of working memory has to be wasted working out 5+7.

Whereas a child who does not know the answer automatically has to divert processing resources away from thinking about columns, value and regrouping, thinking instead about what 5+7 adds up to.

Their overloaded working memory can’t cope with this additional demand on top of everything else it is already thinking about, so it ‘forgets’ one of the important steps in the procedure. The child therefore gets the answer wrong.

Or even if the child doesn’t get the answer wrong, they do not learn how to use the vertical algorithm as a useful method they can generalise and transfer to other similar problems.

The right amount of cognitive load for learning in primary maths

The main focus of How I Wish I’d Taught Maths is how to create just the right amount of cognitive load so that teaching can be as effective as possible, about making sure knowledge makes it from the working memory to the long-term memory by cutting out anything that might cause cognitive overload and replacing them with better alternatives.

A good example of this can be found here in this blog post on how to teach telling the time at KS1 and KS2, breaking it down to the simplest core elements.

Next in this series of How I Wish I’d Taught Primary Maths

I will be considering several of these alternatives in turn.

1. Cognitive Load

2. Explicit instruction and worked examples

3. Focusing thinking and goal free questions

4. The 5 stages of deliberate practice

In the latter part of the book Craig considers how teaching can facilitate effective remembering. Having explained strategies for making sure learning makes it from the working memory to the long-term memory, the focus now turns to helping students use what they know. This will be covered in the last two blogs in this series.

5. ‘Same surface different deep’ problems

6. Remembering maths in the long term

In each of these blogs, I am going to ‘translate’ what Craig is saying into more primary maths relevant terms and use more primary maths curriculum focused examples than he has used.

Each blog has a section highlighting primary school maths context. Here I give practical examples of how Craig’s insights might be deployed in a primary classroom, rather than directly explaining what he says himself in his book.

Where I need to use the first person in sections these ‘translated’ sections, I have used ‘she’ rather than ‘he’ as a way of emphasizing that this is my interpretation of Craig’s work, rather than a summary of his own words or examples. It is not intended as a slight on male primary teachers! The references for the research Craig has used that I have mentioned are listed at the end of each blog under the title Sources of Inspiration.

Sources of Inspiration

Barton C. (2018), How I Wish I’d Taught Maths


This is the first blog in a series of 6 adapting the book How I Wish I’d Taught Maths for a primary audience. If you wish to read the remaining blogs in the series, check them out below:

How I Wish I’d Taught (Primary) Maths Blog 2: Explicit Instruction And Worked Examples

How I Wish I’d Taught (Primary) Maths Blog 3: Focused Thinking And Goal Free Questions

How I Wish I’d Taught (Primary) Maths Blog 4: The 5 Stages Of Deliberate Practice In Education

How I Wish I’d Taught (Primary) Maths Blog 5: Critical Thinking Skills And Problem Solving Activities in KS2

How I Wish I’d Taught (Primary) Maths Blog 6: How Retrieval Practice Helps Long-Term Maths Skills

For more of Clare Sealy’s thought provoking pieces on primary learning and leadership, take a look at the Confessions of a Headteacher series on how she changed marking, feedback and observation.

Further reading: 20 maths strategies that we use in our teaching to guarantee success for any pupil. 

Clare Sealy , Primary Headteacher , St Matthias School

As Headteacher of a school in Bethnal Green, Clare "loves learning more about doing her job better". She writes on Ofsted, grading, school budgets and more on our blog.