How to fix the primary maths curriculum

Everyone knows that the goal of English teaching in primary is to get children reading for pleasure. It is the second aim of the primary national curriculum for English. It is in the Initial Teacher Training and Early Career Framework content frameworks. It is the revealed priority of school corridors, classroom displays and laminated signs on classroom doors of “What I’m reading today...”.

And we, broadly speaking, know how we’re trying to achieve this aim. We teach children to decode a set of graphemes. We get them to practise until they become fluent at decoding them. And, at every incremental level of fluency on this journey, we encourage them to read appropriate books for pleasure.

Maths should be no different. But currently, English is for pleasure and maths is for utility. And where English has a prescribed, well-evidenced and bought-into progression through the curriculum that is working extremely well, the outlook for maths is foggier, more variable across schools and too many children are not hitting the milestones they should be hitting.

Fixing this will inevitably be part of the government’s curriculum and assessment review, which aims to “refresh” the national curriculum. Education secretary Bridget Phillipson has long stressed her focus on maths. Last year, she promised “phonics for maths” at the Labour Party conference.

But what should this look like?

Why isn’t this already happening?

There is much to commend in primary maths education today. English performance in the Trends in International Mathematics and Science Study, an international survey of maths and science attainment, has found steady improvement in the maths of our Year 5 pupils for the past 30 years.

Huge work across the profession, especially by maths hubs and others, has led to a widespread understanding of powerful principles (such as variation theory) that are improving the classroom experience.

Sustained improvement of this kind is rare. It should be a matter of national celebration. But we can still do better.

Too many children do not have a grasp of the basics, at whatever stage you choose to measure this. And too many children lack experience of pleasurable maths. They have not enjoyed the buzz of solving meaningful problems.

We believe that these two shortcomings are connected. In England, we muddle fluency and problem-solving. We lack a clear conception of how they relate, and how every child achieves an entitlement to both knowledge and pleasure.

Too often, we do not spend nearly long enough on ensuring every child both learns and masters the absolute basics - number bonds to and within 10 and 20, bridging 10. Sometimes this is because we try to generate these through reasoning, rather than seeing reasoning as the thing we do with them. Sometimes it’s simply because we’re rushed.

This holds pupils back from being able to do maths for pleasure. They don’t have the cognitive capacity to reason through a problem or apply maths to a meaningful context. They’re still counting up to add four to seven.

Or they don’t get the opportunity to enjoy maths for pleasure, because of the volume of content and the absence of this goal in our curriculum means that the teacher simply moves on.

All of this leaves too many children not doing well at maths, and not enjoying it.

When the expected standard is 54 marks out of 110 (as it was in 2024 KS2 Sats), it’s clear that we do not really have a mastery system. Children who score half marks on the test feel unmotivated. They have too many gaps to be confident in secondary school, and don’t know maths well enough to enjoy it.

The result is a country where only a minority of children ever get to enjoy maths. Maths for pleasure is something for elites, not for the masses.

This is wrong. Everybody should experience the joy of grappling with a problem, finding a breakthrough, and bringing it to a solution. This should be as much a part of the educational entitlement as reading great stories.

A better model of maths curriculum

So, what should primary maths look like?

Maths is a hierarchical subject. You need to know one layer of the hierarchy to be able to know the one above. Just as knowledge grows exponentially, so do gaps.

In that way, it is very similar to early reading, and we think the curriculum should look much more like that. It should be more specific, be built on much higher expectations of fluency at every level, and be designed around opening up maths for pleasure.

Each layer in the maths curriculum should give you access to two things: pleasure in that layer, and learning the next layer.

The curriculum should define these “layers” more clearly. It should give precise definitions of what pupils are learning.

For example, “add two single-digit numbers that bridge 10” instead of “add and subtract one-digit and two-digit numbers to 20”. It should feel as specific as saying which graphemes are to be learned to be decoded.

The expectation of that layer isn’t to be able to do the things in it once, or in controlled conditions, but to practise them to fluency. Pupils need to be able to use them, not to do them.

Fluency in maths is more like blending a phoneme into a new word than saying it when the teacher holds up the corresponding card.

And then, at each layer, we should be clear about how it unlocks maths for pleasure. What is the problem-solving and application that can happen? It should be like offering a library of great graded readers.

The sequence here is important. Just as you cannot appreciate a story if your decoding speed is too slow, you cannot enjoy a maths problem if your recall of number facts is too slow. This is an approach built on creating the cognitive space, and the curriculum space, to enjoy maths.

Reduction not ‘dumbing down’

This approach will reduce the amount of content in the primary curriculum. But it is categorically not a dumbing down.

The level of difficulty of a curriculum is a function of a few things: volume of content; its intrinsic difficulty; the level of challenge of the questions that apply it; how many of those questions you need to get right to “pass”. We would dial down the volume of content in order to dial up the challenge and the expected level of mastery.

In a hierarchical subject like maths, we must expect most pupils to fluently apply everything at a given level of the curriculum before moving on. This is clearly not happening at present.

Too many children in KS2 struggle to enjoy maths because they don’t have their number bonds on the tip of their tongue.

We see the problem of under-learning a large volume of content most clearly in the transition to secondary school.

As mentioned above, the pass mark for KS2 Sats was 54/110 this year. Children arrive at secondary having finished the tough primary curriculum. But, many can only use half of it reliably. Others haven’t studied good chunks of the Year 6 curriculum at all. Their schools took the decision to focus on maximising performance in the Year 3-5 content that has always made up the majority of the Sats test.

The result of this is secondary schools re-teaching KS2 content, often for at least all of Year 7 and sometimes longer. Research by Axiom Maths, where David is CEO, shows how this experience turns pupils - especially those who did well at primary - off from enjoying maths.

Secondary schools are re-teaching KS2 content from scratch anyway. So, there is time in the curriculum to move some of this content from primary to secondary. This would create a better experience for pupils, and create space for the curriculum approach we propose.

What might this look like in practice?

It is all well and good to say these things in broad terms. But how might this look? We make some suggestions below.

Early years

Too many gaps emerge between children before they even meet the Early Years Framework, let alone the national curriculum. The government should double down on their commitment to give every child the best start in life. They should launch a national mission to engage parents in readying their children to love maths.

This could start with a simple bank of age-appropriate activities: from pouring liquid between containers of different sizes to making patterns and subitising games with dice. It could include toy recommendations for different ages, ensuring that children play with toys that develop their fine motor skills and their sense of shape.

There is scope to improve the early years foundation stage, too. The early learning goals in the current framework are appropriate, but too narrow. We should go beyond numbers and numerical patterns to include other types of patterning and spatial awareness, preparing the way for deeper exploration in KS1 and KS2. There is now a raft of evidence pointing to these being critical for later success in mathematics.

And this is where we set the foundations of mathematics for pleasure. Children in the early years can solve problems with shapes and numbers, too.

Key stage 1

The explicit goal of KS1 maths should be developing full fact fluency with number bonds to and within 20. This unlocks everything else, just as not reaching this point holds back children throughout the rest of their journey in maths.

If the government is serious about “phonics for maths”, this is the place to do it. The curriculum should be structured with greater specificity to show the “layers” children should work through to build fluency, just as the reading curriculum shows the groups of graphemes children work through before moving on to the next.

This would carefully structure when and how concepts like bridging 10 are introduced. New ideas would only be taught when children have the cognitive space to explore them - because they already have other related facts on the tips of their tongues.

But “phonics for maths” here isn’t enough - this is also the place to introduce “maths for pleasure”. Just as fluency in decoding starts to open up great story books for pupils to read, fluency in number facts starts to open up great maths problems.

The curriculum should include examples of problems that pupils can enjoy at each level. Teachers and resource writers can take these as starting points and develop their own, but having some examples will help reduce the workload of adapting to the new curriculum.

And if the goal of KS1 is fluency in these number facts then we need to check it has been achieved. The government should make available an optional screening check that schools can choose to opt into. It would help them understand how well their pupils are doing and compare this to the rest of the country.

Lower key stage 2

If Years 1 and 2 were about additive number facts, Years 3 and 4 should be about multiplicative ones - plus greater agility in mental maths. This is where children develop their early multiplicative reasoning.

A solid foundation in number bonds to and within 20 allows children to spot the patterns that become times tables. They can then learn these, again with the goal being fluent recall to open up a greater range of interesting problems.

Lower KS2 should also dial up its focus on mental maths and, in turn, dial down its focus on written algorithms. Pupils must learn written algorithms for calculating, but these are less important than becoming an agile mental mathematician. Too often, we get this the other way around.

Too many pupils finish Year 4 with poor mental maths and a reliance on written algorithms to do all their calculations. The curriculum should state, clearly, the mental maths methods and tactics to learn.

These include scaling up known number facts and using them to derive others. This facility in mental maths builds the number sense that is critical for pupils as they progress on to more advanced maths and real-world applications.

Upper key stage 2

The goal of Years 5 and 6 then is to extend this deep fluency and number sense beyond integers, into fractions and decimals. As in prior phases, a more specific curriculum would show exactly what pupils should become fluent in, and examples of the enjoyable problems that this opens up.

But upper KS2 is also the home of Sats, and there is scope to make these better. The changes proposed above should all lead to Sats tests with less content but a much higher pass mark.

This would also remove incentives to game Sats by altering the curriculum. There are too many perverse incentives at present - from skipping Year 6 content to skipping reasoning to focus on arithmetic scores.

There is also an opportunity to deal with the post-Sats gap. Children too often lose the rigour in their maths after their Sats, and so are more than a bit rusty when they arrive at secondary school.

This knocks their confidence and contributes to their frustration as secondary schools re-teach familiar (but unpractised) content. The government should explore whether it is possible to move Sats later in the summer term to avoid this. If not, it should have a clear, statutory curriculum expectation for what maths pupils should do following the tests.

Is this really practical?

Changing a curriculum is a big deal, and isn’t without costs. We think that this proposal, though, is manageable.

Rather than adding things to the primary curriculum, this removes. It spreads content out, reducing the volume of things to be learned in each year. The intention of this is to reduce the amount of planning needed, while making space for more practice.

The specificity of this curriculum should help with what new planning is needed. This includes having example problems for “maths for pleasure” written into the curriculum.

Of course, these are just examples, jumping off points, rather than constraints on what mathematics pupils get to explore and enjoy.

The biggest implementation challenge will be teacher training.

There has been much good work done on principles around maths teaching in primary over recent years, not least by the NCETM and their Big Five principles of mastery.

But implementing this curriculum well will take more. Teachers will need to learn more about mental maths and the structure of number than perhaps they learned at school. They will need to learn the tactics, heuristics and relationships to navigate number fluently. They’ll need to become familiar with things like divisibility tests that they may not have routinely taught before.

Fortunately, we have a great infrastructure for professional development in this country, which we are sure is up to the challenge.

Peter Foulds is a maths school improvement adviser for a large and growing MAT in the North East. He has over 20 years of experience working in the primary sector and has taught in all primary year groups. 

David Thomas is CEO of Axiom Maths, a former Department for Education special adviser and he has worked as a maths teacher as well as in school leadership roles.

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