How can early years practitioners continue to support the mathematical learning of all children within the framework of the revised EYFS? Di Chilvers explains

The mathematics area of learning and the Early Learning Goals at the end of the Foundation Stage have undergone significant change in the EYFS reforms, which come into practice in September.

A good starting point to get your head around these changes is to compare the current statutory requirements for mathematics (Numbers and Shape, Space and Measures) with the reformed area of mathematics (Number and Numerical Patterns) and, importantly, ask yourself:

  • How do these reformed mathematical requirements meet young children’s actual developmental needs, understanding and mastery of complex skills and dispositions?
  • How does young children’s mathematical development and learning unfold from birth – what is the process?

While the EYFS reforms have moved the goal posts for children – for example, the emphasis is now firmly placed on number and counting and reaching outcomes (ELGs) that were previously required in the National Curriculum at KS1 – we need to remember that young children’s development in their first 60-plus months remains constant, following a relatively typical pathway, which children experience in unique ways.

This is why the principle of the Unique Child becomes even more important, particularly for those children who are summer-born and will still be up to 11-plus months younger than their friends in the same group. Expectations, along with what is offered to them through the curriculum, need to reflect this.

FROM GENERAL TO DETAILED

This overview of mathematics has moved from a general description, which was a little too brief, to one which is overly detailed, prescriptive and formal. It forgets that an area of learning – now firmly called the ‘educational programme’ – begins from birth and needs to acknowledge that mathematical learning will look quite different for babies and toddlers. Maths, for them, does not begin with numbers and counting, although they do have a ‘natural interest in quantities and spatial relations – they are problem-solvers, pattern-spotters and sense-makers from birth’ (Birth to 5 Matters 2021).

Mathematical development for younger children grows through their play and exploration, active engagement, creative and critical thinking, serve and return interactions with adults, their embodied experiences and, essentially, their schematic patterns of thinking, such as interest in trajectories (horizontal and vertical straight lines) and transporting (moving things from one place to another), where they gradually come to understand concepts of length, distance, spatial awareness, speed, motion, direction, time, pattern, order, angles, sequencing and weight (Chilvers 2021).

These are all critical mathematical concepts which are the ‘necessary building blocks to excel mathematically’, which is why it is concerning that Shape, Space and Measures has become side-lined to a brief mention in the overview: ‘In addition, 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’ (EYFS 2021).

It is crucial that Shape, space and Measures remains a central part of children’s entitlement and experience in the curriculum, particularly in Reception classes, otherwise children will find it harder to make sense of these concepts in later key stages.

IMPORTANCE OF SPATIAL REASONING

Children’s spatial reasoning starts early as babies become aware of the people and things around them, exploring through sensory experiences using their mouth, lips, tongue, eyes and smell to discover objects, gradually becoming familiar with their ‘spatial and shape properties’.

They then reach out for objects and start to crawl, walk and negotiate the spaces around them, working out the best way to approach a problem and solve it to get what/where they want. Gradually these key skills become internalised and co-ordinated, or embodied. For example, as a toddler sings pat-a-cake, clapping in time to the tune.

Dr Jennifer S. Thom explains, ‘(In)formal mathematics and thinking involves the entire body of the child, not just from their neck up. Consider the potential ways that a child’s walking along the perimeter of a playground engages their senses and develops their awareness and knowledge of its “squareness” – for example, its four straight sides of equal length and four right-angles corners’ (Thom 2017 in Chilvers 2021).

Spatial reasoning becomes more complex and embedded if encouraged and supported through children’s play and interests. For example, Harry (5.6 years) shows exceptional spatial reasoning as he constructs his maps in geographically correct drawings, where buildings and roads interconnect at specific points in relation to one another and he explains how you can negotiate your way around. He has made a significant leap in his mathematical thinking from actual embodied experiences to more abstract thinking (Chilvers 2021).

BUILDING BLOCKS FOR THE FUTURE

Continue including Shape, Space and Measures as an area of learning and part of the children’s curriculum entitlement so that it does not become ‘second fiddle’ to numbers and numeracy. This will ensure that mathematics, in its fullest sense, starts where the children are from birth, and builds on their developmental momentum in appropriate and meaningful ways right to the end of the Foundation Stage and beyond. In addition:

  • Make sure that you have a good understanding of children’s mathematical development from birth to six-plus. For example, do you know how children’s learning and understanding of number develops from their early experiences into comparison, counting, cardinality and composition? (See Mathematics in Birth to 5 Matters). There is no need to create any kind of curriculum progression document or sequenced content for children to cover, as long as you know the general pattern of mathematical development, how children learn best through playing and exploring, active learning and creating and thinking critically. Also, how you can support and extend their learning appropriately. Child development is already a progression model (see Further information).
  • Observe children in their child-led play and be aware that children are frequently engaging in mathematical learning about Shape, Space and Measures through their physical play (think embodied learning and spatial reasoning), in construction activities and particularly though their interests. Create some learning stories from these observations and you will capture the richness and depth of children’s involvement, creative and critical thinking and mastery (see Further information).

Be aware of how young children’s schematic patterns of thinking and interests relate to their mathematical development. Schema, when supported, graduate into deeper mathematical concepts of comparison, measurement, spatial awareness and complex number patterns (see Chilvers 2021, p.51).



 Harmony Neighbourhood Nursery PHOTO by Alex Deverill

CREATING AND THINKING CRITICALLY

There is no direct reference to the Characteristics of Effective Learning (CoEL), especially the creating and thinking critically strand. This is inherently mathematical, including critical dispositions such as problem-setting and solving, testing out hypotheses/ideas, making predictions and noticing patterns, groups, sequences, cause and effect. These, along with playing and exploring and active learning, support children’s flexible thinking and the ability to move from the concrete (of the here and now) to the abstract (internalised and embedded learning), deeper levels of understanding and mastery. It is an important shift in thinking, especially in mathematical development.

However, welcome references to deep understanding, applying understanding, positive attitudes, interests, ‘having a go’ and not being afraid to make mistakes all have their roots in the CoEL.

MATHEMATICAL MASTERY

Mathematics and mastery have become the ‘double act’ in primary schooling through the implementation of the Shanghai and Singapore maths programmes. We now see this creeping further into the EYFS without any discussion about what mastery means and looks like for younger children. The educational programme says ‘children will develop a secure base of knowledge and vocabulary from which mastery of mathematics is built’. This leaves the door open for formal maths mastery programmes to find their way into early education with little (or no) understanding of early child development.

We can support children’s mastery orientation as they play and explore, through their active learning and creating and thinking critically. Through observation, six key aspects have been identified that contribute to this:

  • Children’s talk…serve and return
  • Self-regulation and meta-cognition
  • Children’s agency and self-belief
  • Characteristics of Effective Learning
  • Sustained shared thinking
  • Child-led play and activities (Chilvers 2021).

Our main aim should be to maintain children’s early mathematical momentum and build on that.

ABOUT THIS SERIES

This series on the seven areas of learning aims to help you prepare for the introduction of the revised EYFS in September this year by:

  • comparing the 2017 and 2021 educational programmes and Early Learning Goals
  • highlighting the significant changes
  • exploring key aspects of practice.

REFERENCES AND FURTHER INFORMATION

Di Chilvers’ latest book is How to Recognise and Support Mathematical Mastery in Young Children’s Play: Learning from the Talk for Maths Mastery Project (David Fulton).

Mathematics before and after: the changes in close-up

Educational programmes

EYFS 2017

Mathematics involves providing children with opportunities to develop and improve their skills in counting, understanding and using numbers, calculating simple addition and subtraction problems; and to describe shapes, spaces, and measure.

EYFS 2021

Developing a strong grounding in number is essential so that all children develop the necessary building blocks to excel mathematically. Children should be able to count confidently, develop a deep understanding of the numbers to 10, the relationships between them and the patterns within those numbers. By providing frequent and varied opportunities to build and apply this understanding – such as using manipulatives, including small pebbles and tens frames for organising counting – children will develop a secure base of knowledge and vocabulary from which mastery of mathematics is built. In addition, 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. It is important that children develop positive attitudes and interests in mathematics, look for patterns and relationships, spot connections, ‘have a go’, talk to adults and peers about what they notice and not be afraid to make mistakes.

The changes in close-up

Positives

  • This is a more detailed description of the mathematics area of learning with some helpful points around children having a deep understanding of numbers. The use of the term ‘understanding’ is welcome as it is frequently missing across the EYFS due to the emphasis on ‘knowledge’. Knowledge is not helpful if there is no understanding!
  • While it is not mentioned directly, there is a hint that children need to play with all sorts of materials to build and apply their mathematical understanding. Importantly this is where the adults will see if children have mastered a range of mathematical concepts, not just numeracy.
  • Building children’s confidence, attitudes (mindsets) and interests in mathematics and not being afraid to make mistakes is a welcome focus, though much depends on how maths is taught to fulfil this aim. If children’s own mathematical momentum is recognised, they frequently feel like confident mathematicians.

Negatives

  • Unfortunately, there is no recognition that it begins at birth with early experiences in the first 36 months forming ‘strong foundations’ on which to build. The progression of mathematical development begins from birth where young children are very competent and capable spatial explorers.
  • Shape, Space and Measures is not given the status it should have. Bearing in mind that children have a natural disposition towards construction play, taking things apart and connecting them together, filling and emptying, it does not recognise or value their mathematical momentum. Mathematics is not just about numeracy, so this is a skewed view and narrowing of the curriculum along with the loss of Technology as an area of learning.

EARLY LEARNING GOALS:EYFS 2017

Numbers

Children count reliably with numbers from 1 to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing.

Shape, Space and Measures

Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them.

EYFS 2021

ELG: Number

Children at the expected level of development will:

  • Have a deep understanding of number to 10, including the composition of each number;
  • Subitise (recognise quantities without counting) up to 5;
  • Automatically recall (without reference to rhymes, counting or other aids) number bonds up to 5 (including subtraction facts) and some number bonds to 10, including double facts.

ELG: Numerical patterns

  • Children at the expected level of development will:
  • Verbally count beyond 20, recognising the pattern of the counting system;
  • Compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity;
  • Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally.

The changes in close-up

Positives

  • The emphasis on children having a deep understanding of numbers to 10 is welcome, rather than rushing them on.
  • Including subitising is interesting as this links to children’s conservation of number where they can recognise that a group of objects is still four however they are arranged. This depends on a deep understanding of numbers up to five. Some children will be nearly a year older than others in the group so there is a wide variable of development.
  • Practitioners can now use their own ‘expert professional judgement’ to decide where children are at the end of the Foundation Stage.

Negatives

  • No ELG for Shape, Space and Measures.
  • There is a danger that some of these ELGs are setting up children to fail. For example, automatic recall without using ‘reference to rhymes, counting or other aids’ is developmentally challenging for some young children.
  • There is a danger that teaching in the Reception year will be focused on Number and Numerical patterns and not on Space, Shape and Measures because there is no ELG.