Research School Network: Maths in the early years: what the research does (and doesn’t) tell us – Part One Julian Grenier and Debbie Morgan explore the evidence behind new changes to the Early Years Foundation Stage

In this two-part blog, Julian Grenier (Director of the East London Research School) and Debbie Morgan (Director for Primary Mathematics, National Centre for Excellence in the Teaching of Mathematics) look at some of the changes to maths in the EYFS.

Improving Mathematics in the Early Years and Key Stage 1 from the Education Endowment Foundation is an important summary of the best research into early maths. It also guided the content of the Mathematics section in the DfE’s revised Development Matters which we were both involved in drafting.

In this blog, we’re going to explore the term ​‘evidence-informed practice’ in relation to early years maths. In our second blog, we’re going to be exploring some of the strengths, and also some of the limitations, of this approach.

Evidence-informed practice

The practice which the EEF recommends in its guidance report is based on a robust evidence base. That means studies will have been carried out with an appropriate methodology, results will have been interpreted with rigour, and findings will have been peer-reviewed before publication. All the same, the report does not present us with surefire solutions to the sort of complex challenges which will always arise in education. Just because an approach to teaching maths to young children worked in, say, suburban Los Angeles doesn’t mean it will transfer easily to another context. Even if this transferability looks easy, there are other tricky factors which intrude. Contexts in the UK are often very different from other countries, particularly when it comes to Reception classes, where all four-year-olds attend school and have access to trained teachers. This might afford some positive opportunities that are unique to the UK context. Practitioners in different settings and schools have different levels of training and qualification, for example. Some leaders are really good at implementing change, others less so. That’s before you bring in a completely unpredictable event like the Covid-19 pandemic.

‘Best bets’ not ​‘surefire winners’


So it makes sense to see the approaches recommended in the EEF guidance report as ​‘best bets’ rather than ​‘surefire winners’. Leadership, staff culture, training, qualifications and local context are all going to be influential. Sometimes perfectly sound approaches might not work for a perfectly good reason. For example, if children are struggling with the transition from their Early Years setting into Reception, the quality of the maths curriculum and teaching might be pretty irrelevant. It will be important to focus on improving transition, in order to create the context for children to feel confident, to flourish, and to learn well. Other times, staff teams are worn out by constant change. I know there have been many times as a leader when I have tried my best to support a new approach to early education, but I have been derailed by day-to-day problems with staffing, budgets and premises, and I haven’t been able to provide enough ongoing support to the team.

Finally, the Early Years cover the whole phase from birth to the end of the Reception year, but the EEF guidance report is for children from three to seven years old. That’s largely because we don’t yet have enough robust knowledge about effective practice for children before they reach their third birthday.

It’s also noteworthy that there is practice which is supported by many years of practical development in Early Years settings which has not yet been thoroughly evaluated. Block play is a good example of this. In my experience as a nursery school headteacher, this is an enormously powerful way for children to learn maths – both using the small unit blocks from Community Playthings, and larger hollow or Outlast Blocks outdoors.

Block Play

Block play probably has a positive impact on mathematics. But, as the EEF guidance report points out on page 11, there is only a ​‘small body of research’ into the development of geometry and spatial thinking with respect to young children. Further, as Schmitt (2020) comments, ​‘although a growing body of work has linked block play to mathematical development, there remains little causal evidence to support these relationships’ (Schmitt 2020). Schmitt has been awarded a research grant to explore this and we await with interest the outcomes as understanding the relationship will provide insight into how we enhance practice to maximise impact. So we would argue that it is important for schools and settings to be cautious about the research and evidence, before committing large amounts of time and resources to new approaches.

Myths of early maths

Whilst some aspects of early maths are under-researched, there are other aspects of practice which have been challenged by new evidence. Despite the evidence, the myths remain, and the practice continues. Clements and Sarama (2008) provide research evidence on several of these myths. One example is the claim that all maths learning in the early years has to be concrete, using contexts and manipulatives. In one study, kindergartners performed just as well without as they did with manipulatives, in both accuracy and in their discovery of arithmetic strategies.

In recent talk (June 2020), Clements provides the example of Abby, a 4‑year-old who is able to calculate 9 minus 4. She does this mentally using gestures and explains that the answer is five, because she knows that 4 and 4 is eight, so 8 minus 4 is 4 and because 9 is one more than 8, the answer is 5. There is a lot going on here in the child’s abstract reasoning, which may not have happened had she been given concrete bricks. It would seem that knowing double 4 is eight played a role in Abby’s reasoning and allowed her to strategise. We cannot ignore the role that knowledge of facts plays in conceptual learning, avoiding overload and freeing up the working memory to ​‘think and reason’.

There has been a great deal of controversy recently about the new Early Learning Goal for Number in the 2021 EYFS Statutory Framework, which includes:

This has raised the concern that there is an inappropriate focus on rote learning in the new ELGs. However, automatic recall comes from knowing and understanding something so well, that we no longer need to think about it (Twomey Fosnot, C and Dolk, M, 2000). But just because you have automatic recall, doesn’t mean you are unable to think about a mathematical operation. In Clements’s example, Abby could draw on her automatic recall to think about something new. Her automatic recall was supporting new learning – it wasn’t empty ​‘rote learning’. Learning some facts to automaticity may be a way of reducing cognitive overload and improve learning, for all children. By making these sorts of systematic improvements in teaching and learning, we can begin to work towards closing the attainment gap between disadvantaged children and their peers – something which we urgently need to do, especially if fears that the gap has widened during the Covid-19 pandemic prove to be correct.

It is reasonable to argue that the third section of ELG in number, quoted above, is not evidence-based. It is simply the case that no one has researched it yet. But there is significant research in the area of cognitive science to suggest that automaticity in number facts has the potential to relieve cognitive load and free up working memory space. Since younger children have the smallest capacity for working memory, this is important.

It is important to remember that the ELGs are assessments, and should not drive the early maths curriculum. We welcome the fact that deep understanding of numbers to 10 is included, rather than numbers to 20, as in the previous ELGS. A focus on numbers to 10 will give children a much smaller set of numbers to focus on and the time for all children to attain this. The great thing about the concepts underpinning smaller numbers, is that they are the same for larger numbers, but easier to handle and see with a smaller set. Working with smaller mumbers, children can securely develop key concepts such as composition of number, that inside numbers there are other numbers. Once children understand this, they can partition and combine numbers, transforming them into other numbers. And it’s this type of activity which supports the development of automaticity in number bonds. Similarly, the ability to subitise (e.g. seeing a three and one more and realising it is 4) also supports automaticty. In this way, all of the goals feed into each other. Comparative research regarding a focus on just numbers to 10, rather than 20 with a focus on composition of number hasn’t been undertaken. But we see the focus on numbers up to 10 as a ​‘good bet’.

Sticking to smaller numbers will encourage teachers and practitioners to ensure that children’s learning is secure, rather than feeling pressured to move them onto larger numbers too quickly. As the EEF guidance states (page 9):

The EEF’s independent evaluation of the pilot Early Learning Goals found, in a similar vein, that ​‘teachers liked the clarity and specificity of this ELG and felt the focus on numbers one to ten was appropriate and would help to cement children’s understanding.’

Secure understanding

A well-designed maths curriculum will focus on checking that children securely understand the early stages of counting and operating with numbers, not rush them onto the content of the ELGs before they are ready for this learning. It’s only when children’s understanding is secure that it will be appropriate for them to keep practising what they know so that they become more fluent and can operate with numbers automatically. Without such fluency and automaticity, children remain dependent on actual objects. The manipulation of those objects can use up a great deal of their working memory and has the potential to drive a mechanical process. Abby’s 9 minus 5 may have become the process of counting out 9 (in ones), take 5 and then count (in ones) what remains. It is highly likely that manipulatives did play a significant role in her development, but we need to think carefully about when and when not to use them. We need to encourage the use of other skills, such as mental reasoning, children’s own recording and the use of visualisation.

Focusing on curriculum design is important. Children need plenty of opportunities for play in high-quality ​‘enabling environments’ which support their mathematical learning. But having the right equipment available is not, in itself, enough. Direct teaching and carefully sequenced planning will also play a key role if the goals are to be achieved. Another myth that Clements and Sarama exposed was that just leaving equipment out for children to explore is insufficient. They state that ​‘only intentional activities focused on mathematics appear to make significant contributions to children’s learning (p3).

Similarly, early years guidance from the New Zealand Education Review Office recommends that ​‘a balance of child-initiated learning experiences and deliberately planned activities provide a platform for teachers to extend children’s developing mathematical understanding’.

Shape, space and measures

There have also been concerns about the dropping of the Shape, Space and Measures ELG. However, the 2021 EYFS Statutory Framework clearly states that shapes, measures and spatial reasoning should remain in the curriculum. The new educational programme says that ​‘it is important that the curriculum includes rich opportunities for children to develop their spatial reasoning skills across all areas of mathematics including shape, space and measures.’ (DfE, 2020: page 10). The Maths Hubs Work group on Building Firm Mathematical Foundations in Reception will be exploring this in the coming year.

It is important to note that in their independent evaluation of the updated Early Learning Goals, the EEF noted that ​‘while no school had stopped teaching this area, schools had reduced the emphasis on shape, space and measures in their teaching practice. One reason for this was because they believed that its removal from the ELGs meant that it was no longer part of the Reception curriculum’. This is a cause for concern. It is important for schools to design their curriculum in line with the educational programmes, drawing on the best evidence like the EEF guidance report. The curriculum should be broad, and not designed with a narrow focus on the ELGs.

In this blog, we’ve explored some of the evidence in early years maths.

In our next blog, we will be considering some of the potential benefits of taking an ​‘evidence-informed’ approach – and also discussing some of the potential limitations.