“Children are born ready, able and eager to learn. They actively reach out to interact with other people, and in the world around them. Development is not an automatic process, however. It depends on each unique child having opportunities to interact in positive relationships and enabling environments.”(i)
The first few years of a child’s life are especially important for mathematics development. Research shows that early mathematical knowledge predicts later reading ability and general education and social progress(ii). Conversely, children who start behind in mathematics tend to stay behind throughout their whole educational journey(iii).
Our intent in EYFS then, is to ensure that all children develop firm mathematical foundations in a way that is engaging, and appropriate for their age. We use materials from the NCETM that are based on international research.
The materials are organised into key concepts (not individual objectives), which underpin many early mathematics curricula. The typical progression highlights the range of experiences (some of which may be appropriate for younger children) but the activities and opportunities are developed across the Reception provision.
There are six key areas of early mathematics learning, which collectively provide a platform for everything children will encounter as they progress through their maths learning at primary school, and beyond.
SIX KEY AREAS OF EARLY MATHEMATICS LEARNING
The cardinal value of a number refers to the quantity of things its represents, e.g. the numerosity, 'howmanyness', or 'threeness' of three. When children understand the cardinality of numbers, they know what the numbers mean in terms of knowing how many things they refer to. Counting is one way of establishing how many things are in a group, because the last number you say tells you how many there are. Children enjoy learning the sequence of counting numbers long before they understand the cardinal values of the numbers. Subitising is another way of recognising how many there are, without counting.
Comparing numbers involves knowing which numbers are worth more or less than each other. This depends both on understanding cardinal values of numbers and also knowing that the later counting numbers are worth more (because the next number is always one more). This understanding underpins the mental number line which children will develop later, which represents the relative value of numbers. i.e. how much bigger or smaller they are than each other.
Knowing numbers are made up of two or more other smaller numbers involves 'part-whole' understanding. Learning to 'see' a whole number and its parts at the same time is a key development in children's number understanding. Partitioning numbers into other numbers and putting them back together again underpins understanding of addition and subtraction as inverse operations.
Seeking and exploring patterns is at the heart of mathematics (Schoenfeld, 1992). Developing an awareness of pattern helps young children to notice and understand mathematical relationships. Clements and Sarama (2007) identify that patterns may provide the foundations of algebraic thinking, since they provide the opportunity for young children to observe and verbalise generalisations.
The focus in this section is on repeating patterns, progressing from children copying simple alternating AB patterns to identifying different structures in the ‘unit of repeat’, such as ABB or ABBC. Patterns can be made with objects like coloured cubes, small toys, buttons and keys, and with outdoor materials like pine cones, leaves or large blocks, as well as with movements and sounds, linking with music, dance, phonics and rhymes. Children can also spot and create patterns in a range of other contexts, such as printed patterns, timetables, numbers and stories.
Mathematically, the areas of shape and space are about developing visualising skills and understanding relationships, such as the effects of movement and combining shapes together, rather than just knowing vocabulary. Spatial skills are important for understanding other areas of maths and children need structured experiences to ensure they develop these. Here, the focus is on actively exploring spatial relations and the properties of shapes, in order to develop mathematical thinking (rather than on shape classification, which requires prior knowledge of properties). This section is concerned with developing the two aspects of spatial awareness and shape awareness, with some progression identified within each.
Mathematically, measuring is based on the idea of using numbers of units in order to compare attributes, such as length or capacity. Although young children engage with using rulers and experience being measured in centimetres, kilos – and years! – the measuring units themselves are hard to understand.
Children need to realise which attribute is being measured, e.g. weight as opposed to size, and the idea of conservation: that the amount stays the same, even if the appearance alters, e.g. if dough is stretched out or in bits. In order to understand units, they need to realise that two items can be compared using a third item, or ‘go between’, such as a stick.
Finally, children need to understand how equal size units are used repeatedly to express an amount as a number. While young children can engage actively in making comparisons and exploring equivalence of length, volume, capacity and weight in different ways, some of these ideas are challenging and will develop later in primary school.
For instance, weight (mass or density) is difficult to distinguish from size since it is invisible, and the concept of conservation is harder to understand for weight and capacity. Measuring with non-standard units of different sizes in order to appreciate the need for equal units is less effective with younger children, so centimetre cubes are recommended as accessible units. While time is also elusive to measure, young children can sequence events and, for example, count ‘sleeps’. (Money as a measure of value is too advanced to consider here.)
EYFS and KS1 teachers are currently working with the NCETM Maths Hubs in their year group specific work groups to implementing the 'Mastering Number Programme 2021-22.' This programme develops solid number sense, including fluency and flexibility with number facts, which will have a lasting impact on future learning for all children. This programme also involves high quality professional development for teachers. The mastering Number programme is wholly consistent with teaching for mastery. Please click on the icon below to see what the children will be learning in each half term:-
In the EYFS we follow the ‘Statutory Framework for the Early Years Foundation Stage - Setting the standards for learning, development and care for children from birth to five - Published: 31 March 2021.’
This states that the areas of learning and development:
“1.3. There are seven areas of learning and development that must shape educational programmes in early years settings. All areas of learning and development are important and inter-connected.
1.4. Three areas are particularly important for building a foundation for igniting children’s curiosity and enthusiasm for learning, forming relationships and thriving. These are the prime areas: • communication and language • physical development • personal, social and emotional development.
1.5. Providers must also support children in four specific areas, through which the three prime areas are strengthened and applied. The specific areas are: • literacy • mathematics • understanding the world • expressive arts and design Educational Programmes
1.6. Educational programmes must involve activities and experiences for children, as set out under each of the areas of learning.”
Educational Programme for Mathematics:
“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.”
At Little Bowden Primary we understand the importance of early experiences of maths and have committed to implementing the NCETM Maths Hub ‘Mastering Number Programme 2021-22 This approach places a significant emphasis on developing a strong grounding in number, understanding that this is a necessary building block for children to excel in the subject.
Early Learning Goals
“1.7 The level of development children should be expected to have attained by the end of the EYFS is defined by the early learning goals (ELGs) as set out below.
1.8 The ELGs should not be used as a curriculum or in any way to limit the wide variety of rich experiences that are crucial to child development, from being read to frequently to playing with friends.
1.9 Instead, the ELGs should support teachers to make a holistic, best-fit judgement about a child’s development, and their readiness for year 1.
1.10 When forming a judgement about whether an individual child is at the expected level of development, teachers should draw on their knowledge of the child and their own expert professional judgement. This is sufficient evidence to assess a child’s individual level of development in relation to each of the ELGs. Sources of written or photographic evidence are not required, and teachers are not required to record evidence.”
There are two Early Learning Goals for Mathematics:-
Mathematics Early Learning Goal: 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.
Early Learning Goal: 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.
At Little Bowden practitioners provide creative and engaging opportunities for children to ignite their curiosity and enthusiasm for the subject of maths, while focusing on the three prime areas. Activities and experiences are frequent and varied and allow children to build on and apply understanding of numbers to 10. Concrete manipulatives are a key focus within sessions, as is the use of pictorial representations including ten frames, part/whole models. Children are actively encouraged to use mathematical terminology within their understanding, with a focus on developing positive attitudes and interest in the subject. Children participate in daily maths sessions and are given time to explore mathematical concepts, test ideas, develop their understanding and practise taught skills through play. Maths can be found in all areas of our provision, so children experience it in a purposeful and meaningful context within their play and daily routines.
Daily Maths sessions follow the Mastering Number Programme from the NCETM Maths Hub 2021-22 for 4 days a week and for 5 weeks each half term. The remaining sessions are devoted to securing understanding of any gaps in their knowledge and also on the Shape, Space and Measure work in the Programme of Study. The EYFS lead has completed a year long training programme on Number Patterns and Structures and another year long training programme on Pattern and Shape, Space and Measure with the local NCETM Maths Hub to ensure the rest of the time is used effectively. We are committed to high quality CPD for teachers and have applied for further members of the EYFS team to attend the year long training with the local Maths Hub. There is a lot of research documenting the forms of effective and appropriate early years mathematics pedagogy that can be used through play, guided learning or direct teaching. They include mathematizing routines, playful experiences, exploring familiar rhymes and stories and participation in games, puzzles and activities. At Little Bowden, we use different models flexibly from whole class to group work to individual interactions depending on the needs of the children. These models should not be seen as discrete, but connected opportunities to further make links between learning. What is essential at Little Bowden, is that we provide the children with daily, intentional, number focused mathematical activities to successfully build their understanding. We provide opportunities for extended mathematical discussion to further develop thinking.
We are committed to improving Mathematics in the Early Years and undermining all our work is the implementation of the 5 key recommendations from the Education Endowment Foundation report 'Improving Mathematics in the Early Years and Key Stage 1.'