In the sixth and final blog in this series, Primary School Headteacher Clare Sealy looks at why retrieval practice is important in the classroom, and how this can help them to remember maths in the long-term.

In the introduction to this series, I outlined how Craig Barton in his book How I wish I’d taught maths described how he had changed his teaching as the result of reading research around cognitive science. In the latter part of his book, the focus turns to helping pupils remember what they already know, and how they can use their memory of previous learning to free up cognitive capacity for new learning.

At the end of a sequence of lessons on a particular topic, teachers may feel reasonably confident that most of the class have learnt how to do whatever it was they have been learning – the grid method, for example. Children may perform reasonably well in an end of unit assessment. However, revisit the topic a few weeks later and not only can children not remember how to do the grid method, several deny all knowledge of having even heard of it before!

This bemusing situation can leave teachers feeling rather dispirited and wondering where they have gone wrong. Don’t worry if this sounds like you though as you are not alone. 

Results From The Research: Forgetfulness Is A Worldwide Problem

You will be perhaps reassured to discover that this phenomenon of mass amnesia is almost universal. It is a relief therefore to find out that cognitive science has thoroughly researched this area and has some sound strategies for overcoming it.

Performance and learning are two key elements in this area of research, and Soderstrom and Bjork (2015) explain the difference between the two:

Retrieval Practice Helps Long-Term Maths Skills

Frustratingly, current performance is a terrible guide to knowing whether or not learning has actually happened. Teachers and leaders are at risk at being fooled by current performance and thinking that change in the long-term memory (a.k.a learning) has taken place.

In lessons, teachers provide all sorts of clues and prompts that help children give the right answers. This is fine as a first step, but unless teachers also have strategies that enable learners to move beyond performance, little might actually be retained longer-term. Fortunately, there is lots of research from cognitive science that provides strategies teachers can use to ensure long-term learning actually happens.

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Retrieval Practice Is Key In The Classroom

Strange as it may seem, there is very robust evidence from cognitive science that when we try to remember something, that specific memory gets stronger. Conversely, if we don’t have opportunities where we have to try to remember something, that memory will become weaker.

Retrieval practice is a strategy teachers can use to give pupils opportunities to have to try and remember things they have learnt previously; things they have begun to forget. Retrieval practice is quite simply giving children tasks where they have to try and retrieve an answer from their long-term memory. Each time pupils try and do this, that memory will become a bit stronger and a bit easier to find next time.

As Bjork (1975) puts it:

Retrieval Practice Helps Long-Term Maths Skills for KS2

What is important for teachers to understand is that for the memory strengthening to happen, pupils must try to remember without any priming or reteaching from us. For retrieval practice to work, there has to be an element of struggle; it has to be at the very least, a bit hard to remember. There is no point in doing retrieval practice in the same lesson in which you have just taught something. That’s too easy; it’s the struggle that strengthens the memory. It works best when memories have been forgotten!

Remembering Maths In The Long-Term: Translating This To A Primary School Context

If KS2 children are to remember what we teach them long-term, we will need to go back to material throughout the year and revisit it. But re-teaching it will not be effective. Instead, we need to give children low stakes quizzes where they have to try to answer questions from topics learnt a few weeks ago that the teacher has not revised with them first.

This can feel mean.

Usually, as teachers we would go over something we had not done for a while before retesting it. This why the way in which you do retrieval practice is really important and why it should be low stakes.

This is not a test.

It is not about assessing what children can and can’t do.

It is about strengthening memory. Retrieval practice is a learning technique, not an assessment technique. This needs to be explained to children.

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.

There Are Multiple Ways To Use Retrieval Practice In the Classroom

One unique way to to  help with retrieval practice is to tell your pupils they are going to play hide and seek with the knowledge in their brains. Their knowledge might be quite good at hiding but they are going to try to find it.

Quizzes are another good idea, but they don’t always have to be on paper. Writing answers on whiteboards is fine too. One important thing to note though is that after the quiz, whatever you do, do not get children to swap with a partner to mark them. If you do this, first of all it heightens the anxiety around the quiz (children will perceive it as a higher stakes test, not a quiz), and secondly when you go over the questions, they might be concentrating more on checking that their partner is marking their ‘test’ correctly than they are concentrating on you explaining the answers.

It doesn’t matter if children change their wrong answers when you explain because this is not an assessment. In fact, that’s useful. Nor should you ask them to calculate how many out of ten they got correct. Adding elements of assessment into the process is simply not beneficial at this point in time.

Don’t Over Complicate Things – Save Assessments For Another Time

If you want to glean assessment information from this, do this in a subsequent lesson when you repeat the very same quiz (possibly tweaking the actual numbers but being sure to keep the necessary maths exactly the same), only this time, make it clear that it is not a quiz, it’s a test. If you use maths homework, as a way to give children further practice between the quiz and the second attempt, make it clear that the second time around it is a test.

Build in time to do retrieval practice at gradually increasing intervals; three days, three weeks and three months after having learnt it. And do the same for material learned one year, two years and three years ago. By struggling to remember something half-forgotten, that memory will be strengthened. Once they have struggled, by all means reteach it, if necessary.

Automaticity Is Key To Improving Working Memory In The Classroom

Making sure that pupils remember what we have taught them is important because maths is a hierarchical subject that needs firmly remembered foundations. However, it is also important for another reason.

Pupils’ finite, precious working memory capacity needs to be reserved for the new stuff we are teaching. It shouldn’t be cluttered up processing things that should be remembered so well that recall of them is automatic.

Retrieval Practice Helps Long-Term Maths Skills for Primary Pupils

One of the biggest things that holds some children back in maths is an over-reliance on counting because foundation number facts have not been learnt to automaticity. Because some children do not know basic number bonds automatically, then even at secondary school they are reduced to counting rather than calculating.

The cognitive load this places on the working memory means that there is less cognitive capacity available to think about the maths, let alone solve problems. Whatever else primary schools do, they must ensure that children know all their number bonds within 20 and their times tables. If we do not give children the time they need to learn these to automaticity, we are potentially setting them up for a lifetime of finding maths hard.

However, there is often an aversion within the profession to what is seen as meaningless ‘rote’ learning. If all we did was drill children in recall without ever applying what was learnt, then that would be pretty meaningless.

Don’t Let Your Pupils Become Prisoners Of Counting

Alongside ensuring that children really understand what addition and multiplication mean, alongside their relationships to subtraction and division, we also need to devote curriculum time to ensuring that children are not prisoners of counting. Even in the early years, we need to help children become automatic with simple number bonds within 5 and to 10.

By doing so, we do them such a favour. Instead of fumbling on their fingers, children have mental capacity freed up to think. Once liberated from the shackles of counting everything, they can discover patterns and relationships within numbers; they can reason mathematically. It is having to laboriously count everything that is meaningless, not knowing things automatically. Sometimes, knowing stuff by heart and reasoning mathematically are seen as opposites. But they are not mutually exclusive, they are mutually codependent.

However, ‘drill’ has got such a bad press over the years that even where children are given time to practise basic skills, this might not be enough time for all children to become really fluent in their recall. Teachers worry that they will not have time to cover the curriculum if they spend time practising basic number facts until they are automatic. However, this is a false economy. Without automatic recall of number facts, less of the maths curriculum teachers do cover will be understood anyway, and will end up taking longer to teach. This is why retrieval practice is so important.

There’s More To Automaticity Than Recalling Number Bonds And Times Tables

As important as secure and automatic recall of number bonds and times tables are, they are not the only things that we should make sure are remembered to automaticity.

Procedures such as vertical addition and subtraction, long multiplication and division also need to be practised so thoroughly that the steps in each procedure are automatic and do not need to be actively remembered. Of course it is really important that children actually understand how and why these algorithms work. But one casualty in the important drive for ensuring conceptual understanding has been making sure procedural fluency gets enough focus.

Again, these are not either/ors. Children need both. So if you have been told in the past that once children can do five of a calculation correctly they should move on to something else otherwise they are not making progress, please ignore that advice. Progress can entail learning something more securely, it does not always involve learning something new. Children need to practice not until they don’t get it wrong, but until they can’t get it wrong, so embedded is the procedure in the long-term memory.

Practice does not make perfect, practice makes permanent

We need to ensure that our children leave us ready for the challenges of secondary school maths with really secure recall of number bonds, times tables, algorithms for the 4 operations, and knowing prime numbers and square numbers off by heart. Children should be able to tell the time, know the days of the week and months of the year and how to convert measures effortlessly.

Secondary schools have the right to expect the overwhelming majority of children to be able to do those things easily. Of course we also want them to be able to reason mathematically, but automatic recall of facts and procedures is not the enemy of comprehension; rather it is its partner. Entwined together, procedural fluency and mathematical automaticity give birth to mathematical reasoning! Unless we ensure children have both, then Craig and his secondary colleagues will be left muttering about us primary teachers, ‘How I wish they’d taught maths!’

Sources of Inspiration

Soderstrom, N. C. and Bjork , R. A. (2015) ‘Learning versus performance: an integrative review’,  Perspectives on Psychological Science 10 (2) pp. 176-199

Bjork, E. L. and Bjork, R. A. (2014), ‘Making things hard on yourself. But in a good way: creating desirable difficulties to enhance learning’ in Gernbachet, M. A. and Pomerantz, J. (eds) Psychology and the real world: essays illustrating fundamental contributions to society. 2nd edition. New York, NY: pp.59-68

This is the sixth 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 other blogs in the series, check them out below:

How I Wish I’d Taught (Primary) Maths Blog 1: An Introduction To Cognitive Load

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

Clare Sealy has also written several thought provoking pieces on primary learning and leadership. If you are interested in this, take a look at the Confessions of a Headteacher series on how she changed marking, feedback and observation.

Additional 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.