This article was originally published on 6 December 2023

When Bridget Phillipson, as shadow education secretary, announced Labour’s ambition to introduce a new “phonics for maths” programme in primary schools, it wasn’t the first time that this phrase had been used.

Daniel Ansari has been talking about the benefits of taking a phonics-inspired approach to early maths for years. He is a professor in the department of psychology and the faculty of education at Western University in Canada, where he heads the Numerical Cognition Laboratory.

In Ansari’s view, the idea of a “phonics of maths” isn’t about trying to make numeracy more like literacy, but rather “taking a developmental perspective on the learning of maths”.

This involves “identifying key foundational competencies in the early years and developing programmes to strengthen those, just like we do with reading”, he says.

But how might such an approach work in practice? And how does it align with what we know about how young children acquire mathematical understanding? Here, Ansari answers these questions and updates Tes on his latest research.

Tes: What do you mean when you talk about the “phonics of maths”?

Ansari: Over the past 30 years or so, the research community, in conjunction with educators and policymakers, have done a great job in identifying the key foundational building blocks of reading. These are the basic competencies that children need to have in place to be able to read well, and are strong predictors of later skills.

When I talk about the “phonics of maths”, I mean something equivalent, but not exactly the same. What I would emphasise is that we can also identify key foundational competencies underlying maths, and develop educational approaches to strengthening them in the early years, so that children are set off on a trajectory of success in maths.

That doesn’t mean that is the only thing we need to do, but it is important that we think about maths developmentally. You need these building blocks in place and then, on top of those building blocks, you build increasingly higher-order structures of thinking and reasoning about mathematics.

With reading, most of the world has now moved away from a “whole language” approach that emphasises comprehension from the beginning and towards an approach that emphasises decoding and learning the code and then, of course, using that to begin comprehension.

It’s much the same in maths. I believe that we need to first help children understand numerical symbols; link symbols to quantities; understand ordinality; understand the structure of the Indo-Arabic numeral system - and that builds them a toolkit that they can use to do higher-level mathematics.

Is there anything we need to be cautious about when thinking about how to apply this idea in practice?

I think what we need to be very cautious about is focusing only on one thing. By that, I mean saying, “OK, there is a phonics of maths, so let’s find that one component”. No - reading and mathematics are not the same. There are many different components to mathematics, perhaps more so than there are to reading.

We need to take a broad approach and understand that, while early maths consists of a lot of different things, we now have evidence to tell us which of the components are particularly important.

For example, we know that spatial reasoning in the early years is a predictor of later maths. We know that children’s understanding of symbols is critically important.

But while these things are necessary, they’re not sufficient. We mustn’t lose sight of the fact that we also need to continue developing children’s mathematical learning and skills over the early years, and then into later stages of education.

So, it’s not a panacea to focus on what we might call the “phonics of maths”. And we must be cautious not to create a complete equivalence between the learning trajectories that underpin reading and maths.

Are there any common misconceptions about how mathematical ability develops?

I think there are a couple. One is the idea that some people are innately better at maths than others. We don’t see evidence for that. We see evidence for individual differences, but there is no test that would discriminate, with great accuracy, between somebody who’s going to be really good at maths and somebody who’s going to be terrible at maths.

I think another misconception is that there are strong gender differences in maths between boys and girls. All the evidence that we have points more to gender similarities than gender differences.

In fact, the gender stereotype - that “girls can’t do maths”, which is still prevalent despite decades of research showing data to the contrary - is having adverse effects, especially on female pupils, who feel this stereotype and might therefore experience high levels of mathematics anxiety.

Finally, I’m not sure if this is a misconception, but we know that children cannot construct their own mathematical knowledge by themselves.

There’s a very strong constructivist school in education, and it has some components that are valid. But when it comes to mathematics, we need to appreciate that although young children may have intuitions about quantities and sets and how sets can be transformed, the symbolic system is something like the alphabet that needs to be explicitly taught.

Maths learning is a process of inculturation that has not been around for millions of years, but rather thousands of years. It requires interaction between human beings and requires explicit instruction as well.

What do we know from the research about the best ways to teach early maths?

I don’t think we have a consensus. I am an advocate for playful learning in the early years, but playful learning that is designed very intentionally by the instructors.

To return to the constructivist point, we need to find a middle ground between an extreme constructivist position and one that only wants to put children in rows and have them be explicitly instructed right from the beginning.

So, in the early years, we can offer children opportunities for play but the teacher needs to be involved, in that place of guided play.

‘Isn’t all mathematics “real world”, really?’

And then, thinking developmentally, one thing that is universal in maths is the so-called “concrete, representational, abstract” continuum. That involves children, early on, playing with three-dimensional objects, then going to pictorial representations and then going to the abstract form.

I think that if teachers know about that, and about having to take a developmental perspective, then that can translate into very effective instruction.

In the UK, it’s recently been proposed that it might also be helpful to incorporate more “real world” elements into numeracy teaching. What are your thoughts on that idea?

It depends on what’s meant by “real world”. My question would be: isn’t all mathematics “real world”, really?

We can maybe get a little bit more concrete and say that we want pupils to gain financial literacy so that they can manage their finances when they grow up. They can learn about the economic system, about financial transactions - that’s “real world”.

But I fear that a buzzword like “real world” could be interpreted in many different ways. We have to be careful here, because if teachers use materials that are too colourful and varied in a bid to make learning feel more “real world”, then young children may be distracted from focusing on the maths itself.

Children are already doing “real world” maths because when they’re in kindergarten, they’re interacting with objects and they’re changing the set size, and lots of early years educators try to integrate things from the real world into the mathematical experiences that their pupils have.

So, I don’t know whether that would require any kind of wholesale change to the curriculum, honestly.

As you mentioned earlier, we are moving towards more of a consensus, globally, around how we should teach reading. Is there currently a lot of variation in how maths is taught around the world?

Yes, I think there’s massive variation. I spent some time in Singapore, where I got to observe classrooms and see the differences for myself.

There’s also the Third International Mathematics and Science Study, which was a really intensive video study in 1995, whereby researchers took four or five countries and they videotaped thousands of maths lessons, and then they coded them meticulously.

The differences were remarkable. One of the things that stood out to me was that if you look at the number of problems that children are doing in a single lesson in, for example, Japan, I think it was a third of what they do in the US.

‘In any kind of policy approach to maths education, we must involve teachers and listen to them’

So, this is one of the differences. In some countries, we believe that maths is best taught by giving children lots of problems and lots of repetition, while in other countries and cultures, the emphasis is on developing problem-solving skills through examining one problem from multiple perspectives.

There are also differences in the amount of homework that is being assigned.

But sometimes I wonder whether the variations within countries are just as great as the variations between countries, especially in education systems like the US’, where there isn’t a national curriculum that needs to be followed.

Do those differences matter? Do we need to move towards a more universal approach?

Education is a deeply cultural activity. So, in many ways, I expect that there will always be variations.

I think the opportunity that we have is to study those variations and to evaluate what works in what context, and what could be transferable and what is not transferable.

And also to encourage education researchers and maths educators from around the world to speak to one another to expose each other to different approaches, which will hopefully lead to mutually beneficial outcomes.

But I don’t think standardising anything is realistic, nor is it necessarily required. Why not have variation and see the consequences of that variation?

If you look at very rural cultures - subsistence cultures, for example - the way that children learn about quantity in those contexts is going to be different. It wouldn’t work to harmonise it globally, I don’t think.

Approaches to maths teaching in East Asian countries are widely seen as being worth emulating. How successful do you think these approaches are?

Well, it depends. There are lots of different approaches that are marketed as Singapore maths, or a Japanese approach to maths.

I think there are some principles we can take away, for example, from the Singaporean approach. There, they use two methods in conjunction in the classroom: what you might call the symbol method, which involves having a symbolic representation of a problem, and the model method, which involves having a pictorial or graphical representation. This means that pupils learn abstract and pictorial representations at the same time, which is helpful.

So, there are some lessons we can learn from those highly successful countries. But we also have to understand that those approaches are embedded within particular cultures, where mathematics is valued very highly and considered to be a sort of gatekeeping skill, and so parents will do everything to ensure that their children become successful in maths.

I also think that in any kind of policy approach to maths education, we must involve teachers and listen to them, and not just tell them “this is how you should teach it” but say: “This is one approach - what do you think? How can we co-create our own approach to this?”

And give teachers autonomy within their classrooms, as well, to do things that they value and that they have studied and read about and practised.

Yes, we can make suggestions and have curriculum expectations, but we must never underestimate the professional experience and the wealth of knowledge that teachers have from interacting with children every day and observing them solving problems.

That’s something that we, as researchers, don’t do. We conduct studies and we make inferences. Teachers are doing that on a daily basis, in the moment and in dynamic ways, and this is something that cannot be prescribed.

Is there a particular element of maths learning in a certain culture that you are studying at the moment?

One thing that we’re working on right now is looking at how children develop multiple strategies to solve the same problem. There has been work on this in the past, but we’re taking another look at it.

We’ve been inspired by an approach used by teachers in North America, called “number talks”. This is when you put a single problem on the whiteboard, ask elementary school pupils to suggest different problem-solving strategies, and then engage them in a discussion of those strategies.

‘We need to find ways of keeping maths classrooms places that children enjoy learning in’

We decided to develop a measure based on this concept. When you measure children’s maths, you typically say, “here’s a bunch of problems, solve as many of them as you can, we’ll count them up and then you’ll get a score”.

But what we’re trying to do is to say, “OK, let’s develop a test that actually captures pupils’ thinking and their strategies”.

That’s something we’re very excited about working on because I think that strategies and strategy variability are really important.

We use multiple strategies for everything in life. We have different ways of walking to the same place; we have different ways of preparing our lunch. We always have variability in how we approach things, and that makes us experts and makes us flexible.

We’re trying to capture that development while not losing track of the approach towards gaining mathematical fluency.

In the UK, maths suffers from something of a reputation problem. How do we fix that?

I don’t know how we do that in our Western cultures, because it does seem to be quite ingrained. I get that a lot as a researcher in the maths domain. Our students won’t take my courses, because they’re fearful they might have to do maths.

I think a lot of adults have very bad memories of their maths instruction. Of course, the teaching of maths has changed over the generations and so many parents also don’t recognise the maths that their children are taught. So, engaging parents a lot more in what their children are doing in the mathematics classroom could be an effective way of helping them to understand how maths is being taught now.

But more generally, in society, I don’t know. Should we create superheroes who are maths whizzes? It doesn’t really seem to help.

I think we need to find ways of keeping maths classrooms places that children enjoy learning in. I don’t know exactly how we do that, but maybe that’s how we get older children, adolescents and adults feeling more positive towards maths.