The latest results from the Trends in International Mathematics and Science Study (Timss 2023) are in, and there’s plenty for England’s teachers to be proud of.

Our already-high Year 5 maths scores remained in line with their previous historic highs, despite the challenges of the pandemic. We ranked ninth in the world - with Lithuania and Turkey the only countries outside East Asia to score more highly.

Meanwhile, although our Year 9 science scores have stagnated in recent decades, they climbed in 2023 to their highest ever. We now rank sixth in the world, and are the top country outside of East Asia. These are huge achievements that show the great work of school staff, parents and pupils across the country.

But the job is far from done. We remain significantly behind the best countries in the world. Our children are no less intelligent than those in Singapore or South Korea, so we should not be content with this gap. To accept it would be to do them a terrible disservice.

Fortunately, Timss points at how we might close the gap.

1. Geometry

In both Year 5 and Year 9, English pupils performed excellently at questions around data but relatively poorly at questions around geometry. This is the opposite pattern to the best-performing countries in the world, and a huge missed opportunity.

Geometry is a fundamental part of maths. There’s no reason our pupils should be doing worse at it than others around the world, and doing so puts them back in many cutting-edge fields.

But it’s problematic for a deeper reason, too - geometry is the place in school mathematics where we learn to reason. The closest most pupils will get to a mathematical proof in school is constructing an argument in geometry, arguing from a set of known rules that some other fact must be the case.

We cannot get to more advanced and exciting maths without practising the reasoning that we do through geometry. Yet, shape and space are absent from the early learning goals that pupils in the early years foundation stage work towards. We should, at a minimum, begin by correcting this.

2. Reasoning at KS3

Timss assesses three “cognitive domains”: knowing, applying and reasoning. In Year 9, our scores at reasoning were noticeably lower than the other two. This was not the case in Year 5.

Some of this will be to do with the point above about geometry - an essential practice ground for reasoning. But, in key stage 3, it’s more than this.

We know from our research at Axiom Maths that the challenge of filling varied knowledge gaps across a Year 7 cohort means secondary schools often have to teach a “revision curriculum” for much of KS3.

This crowds out reasoning and bores many pupils. The curriculum review needs to take this challenge seriously and look hard at improving the experience of transition.

3. The lowest attainers

The reason our Year 5 scores didn’t improve was that there was a decrease in pupils scoring as “Intermediate” and an increase in pupils scoring as “Low” or “Very low”.

These are pupils who, in 2019, would have shown an understanding of core maths concepts but who now do not. It’s hard not to see this as a negative impact of the pandemic, where pupils on the margins have faced greater challenges than their peers and fallen behind.

These are more likely to be pupils facing delays waiting for special educational needs and disabilities (SEND) support or not regularly attending school. If we don’t get on top of the crises in these areas then we don’t have a chance of raising performance even higher.

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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