What if the way Scottish schools teach numeracy is entirely wrong?

A couple of years ago, I took a trip to a primary school in Glasgow to observe an experiment.

I stood in a classroom of primary 4 and 5 pupils at St Marnock’s, watching as they worked their way through a series of tasks built around understanding the ways in which different shapes relate to one another, and how they can be combined to create new objects.

The pupils started by creating six-pointed stars with smaller shapes, and moved on to forming different types of triangles using items like rhombuses.

I watched some go through a process of physical trial and error, placing and shifting the base shapes in pursuit of their goal, while others seemed to be able to do a lot of that in their minds before completing the task in what otherwise might have looked like a simple, single step.

In amongst all this activity, the pupils were being encouraged to talk to each other, explain their ideas, and try to work out solutions. Their teacher asked questions designed to make them really think not just about what they were doing, but also the broader implications for their learning.

The lessons weren’t designed to pour knowledge into their little heads, or train them to produce the correct answer to a set of questions. The goal was to support a much deeper kind of understanding.

Why? Because the people behind this programme hoped that in shifting the approach to maths teaching, and introducing an explicit focus on something called ‘spatial reasoning’, they could improve pupils’ overall confidence and abilities when dealing with numbers.

That’s a goal worth pursuing, given what official statistics say about numeracy levels in Scottish schools: the most recent figures (which are horrendously flawed, but that’s another story) suggest that three in ten primary school pupils do not reach the expected levels in numeracy before going on to high school.

The lesson I got to observe represented a very early stage in a trial that was being run by the University of Glasgow and supported by the Turner Kirk Trust, a philanthropic organisation founded by Dr Patricia Turner and Dr Ewan Kirk.

Dr Jack Parkinson and Professor Quintin Cutts, who had been heavily involved in the project, told me that although the early data they were gathering looked promising, this was still very experimental.

In short, they really didn’t know if it was going to work.

This, as it happens, is why Turner and Kirk were involved in the first place. Their organisation seeks to support promising but potentially high-risk projects that governments and many other organisations aren’t (yet) willing to get behind.

These sorts of programmes, Kirk told me at the time, offer “the greatest potential to transform access to, and quality of, education.” They are, he added, exactly the sort of thing that philanthropists should be funding.

That visit took place towards the end of 2023. The article I wrote was well received, and from there the project continued quietly, away from the glare of the media. Would it work out in the end, or would the researchers ultimately find that the impact was minimal – or even non-existent?

Well, now we know a lot more, and the results are impressive.

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Over the last two years, dozens of schools and thousands of pupils took part in the scheme, and academic analysis has confirmed a significant improvement in overall maths skills for those involved. The data also suggests that progress is particularly notable amongst girls and pupils from the most deprived backgrounds.

As a result, the work is going to continue.

The University of Glasgow has now opened a Centre for Spatial Reasoning, with the Turner Kirk Trust once again providing financial support. This time, the Scottish Government has also chipped in some cash.

The centre was launched with the announcement of an even larger research project, taking the spatial approach to maths instruction to hundreds of schools, and with the goal of reaching 40 percent of primary school classrooms by 2028.

And there was also another school visit, so I got to see even more of how these ideas work in practice. This time we went to Kelvindale Primary School and watched as a primary four class was guided through a series of tasks involving the visualisation and construction of complex, three-dimensional shapes. Once again I saw lots of discussion and collaboration, which was encouraged by the teacher, as the pupils worked through the problems.

Even more impressively, they were able to really think about what they were learning – for example, at one point they were asked about the sorts of mistakes that they thought people might make when completing the tasks, and the ways in which the shapes in question could be misinterpreted.

There is sometimes a tendency to assume that problems in education are rooted in the movement away from what many regard as traditional, tried-and-tested teaching methods (Nicola Sturgeon’s book admits that her own lack of understanding in this area drove the introduction of standardised testing) and that probably applies to maths more than any other subject.

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Some think that dealing with numbers is, or should be, about sitting in rows, working silently, learning things off by heart, memorising patterns and formulae, showing your working, and getting the right answer.

But the reality is much more complicated, and if we genuinely want to improve the maths skills of a generation of children, we’re going to have to be willing to think much more deeply about the problem.

Just like those primary 4 children were doing.