Mathematical understanding helps children to make sense of the world around them, interpret situations and to solve problems in everyday life. It is a specific area of learning tin the Early Years Foundation stage.
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. Conversely, children who start behind in mathematics tend to stay behind throughout their whole educational journey
We recognise that there are maths possibilities in all work with young children. In the home and school environment children develop mathematical concepts as part of their everyday life of play and real experiences. Their exploration of space and the environment develops their spatial concepts and the understanding of relationships. We provide a carefully structured learning environment in which effective communication and stimulating challenging experiences are a priority. Thus children work towards making meaningful choices, concentrate for sustained periods, engage in dialogue with adults and work in co-operation with peers.
It is our aim to ensure children develop a strong grounding in mathematical concept, as we recognise that this will enable them to be successful educational and social progress. We recognise that having a carefully sequenced and planned curriculum for developing mathematical concepts is key and can be provided through a high quality vocabulary rich play based environment with explicit teaching around key identified concepts.
Within our awareness of the individual needs of the children we recognise that children are actively attempting to make sense of their environment and that an important factor influencing whether or not they solve a task is whether it makes "human sense" (Donaldson 1978)
Our curriculum aims for our children are:
- To make mathematics relevant to real-life situations.
- To develop mathematical skills based on previous experience and to provide new experience appropriate to the child’s conceptual level.
- To help children develop an appreciation and enjoyment of mathematics.
- To understand the importance of mathematics as an effective and efficient means of communicating information and ideas.
- To emphasise the cross-curricular nature of mathematics.
- To develop positive attitudes enabling confidence and motivation.
- To appreciate the forms, structures and shapes of the natural and man-made environment.
- To help children explore mathematical ideas through the process of discovery.
- To provide many different activities covering a variety of concepts.
- To provide activities which are imaginative and enjoyable
- To provide children with a good grounding in number to five and beyond through practical experience.
- To provide opportunities for children to subitise (Piaget) – develop the ability to instantaneously recognise the number of objects in a small group without the need to count them. We use the Birth to five guidance which is developed from the Early Years Foundation Stage Guidance as framework for planning our mathematical provision.
The DfE published revised guidance in March 2021 to take effect in September 2021.The mathematics component now incorporates many elements of the mastery approach.
Specifically, the revised framework says:
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
We have a carefully sequenced curriculum outlining our maths curriculum. We have identified key learning objectives which are organised into key concepts which underpin many early mathematics curricula. There are seven 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.
We have organised our teaching of concepts under the following areas:
When children understand the cardinality of numbers, they know what the numbers mean in terms of knowing how many things they refer to.
Learning to count in the early years is a fundamental skill and key to mastering mathematical concepts in the future. According to researchers Rochel Gelman and C.R. Gallistel, these are the steps needed to successfully count:
- The one-to-one principle: children must name each object they count and understand there are two groups: the one that has been counted and the one that hasn’t yet been counted
- The stable order principle: children must know how to count in the right order
- The cardinal principle: children need to understand the last number in the set is the total amount
- Counting anything: children need to realise that anything can be counted, not just objects that can be touched, but also things like claps and jumps
- Order of counting doesn’t matter: children need to understand that the order of counting in the set is irrelevant and will still lead to the same amount
- Assessing children to find out which step they are struggling with is key to helping them overcome difficulties and become confident counters.
Comparing numbers involves knowing which numbers are worth more or less than each other.
Learning to ‘see’ a whole number and its parts at the same time is a key development in children’s number understanding.
Developing an awareness of pattern helps young children to notice and understand mathematical relationships.
Shape and space
Mathematically, the areas of shape and space are about developing visualising skills and understanding relationships, such as the effects of movement and combining shapes
Measuring in mathematics is based on the idea of using numbers of units in order to compare attributes, such as length or capacity.
Our long term curriculum plan ensures that we have a systematic approach to teaching Maths. We implement our curriculum through the following:
- Ensuring we have a carefully planned environment. Our environment provides a variety of opportunities for children to experience Mathematical concepts in a multi-sensory way, promoting problem solving and child led enquiry.
- Highly trained staff. We have adults support children’s learning and consolidation of Mathematical concepts whilst they are engaged in meaningful Maths opportunities in their play.
- We plan for maths in our continuous provision using the long term plan.
- We teach mathematical concepts through adult led focused activities which take place during our Group Time sessions, where children are taught and encouraged to explore concepts of number, shape, space, pattern and measure.
- The teaching and learning of Maths takes place indoors and outdoors, through a wide range of practical ‘hands on’ activities.
- Adults in our setting make the most of opportunities throughout the day to use maths in daily routines, play and cross curricular activities, seizing the chance to reinforce Mathematical language and concepts.
- Using CPA method to teach children a mastery maths mind-set. A maths mastery classroom is the ‘CPA’ (Concrete, Pictorial, and Abstract) approach. It was first proposed by Jerome Bruner in 1966 as a means of scaffolding learning. The psychologist believes that the abstract nature of learning (and this is especially true in mathematics) is a “mystery” to many children. It, therefore, needs to be scaffolded by the use of effective representations. He saw that, when pupils used the CPA approach, they were able to build on each stage towards a fuller understanding of the concepts being learnt and, as such, the information and knowledge were internalised to a greater degree. This allowed the teacher to build upon this secure learning. Bruner, and others, demonstrated that each stage of the approach acts as a scaffold for subsequent and connected learning.
What you will typically see in classroom
- Zoned maths area with a variety of resources which provide children to learn mathematical concepts.
- A range of maths resources in other areas such as the malleable , sand, water and role play area as well as in the outdoor area.
- A number line with corresponding items so children are able to see the representation of the number.
- We teach concepts around cardinality using the CPA method. C is for concrete. Concrete is the “doing” stage. During this stage, children use concrete objects in play or groups to model problems. Unlike traditional maths teaching methods where teachers demonstrate how to solve a problem, the CPA approach brings concepts to life by allowing children to experience and handle physical (concrete) objects.
- Supporting a mastery mind-set. This is when children can confidently solve problems and count using concrete objects, they can then progress to pictorial representations, and finally to more abstract numbers. It may be as simple as sharing pasta between a groups of dolls in the home corner. Is there enough for every doll to have an equal amount? How do you know? Is there any pasta left over? We support this by explicit teaching in grouptimes and supporting play.
- We use number frames to enable children to have resources to organise their learning. Number frames are a key teaching and learning resources by giving children time to understand numbers is key. Introducing five frames in nursery and playing key songs such as five currant buns (with children physically standing in a large five frame) can progress to introducing ten frames in Reception and building on their prior knowledge of number
- Children engage in developing mathematical vocabulary through being skilfully supported by adults in play in the indoor and outdoor area. When children play and interact with other children, there are always opportunities for maths talk. Putting maths top of mind and providing children with careful questioning can help children develop a deep understanding of it.
- A daily maths meet where children learn the days of the week, counting and other concepts
- Children engaged in mathematical learning in the indoor and outdoor area
By the end of the time at McMillan, we feel children have achieved a maths mastery mind-set where children have developed a more in-depth understanding and grounding of mathematical concepts and therefore have better outcomes.
We aim to ensure that all pupils know the following knowledge and skills by the end of their time in the following classrooms:
2 year olds:
Enjoys filling and emptying containers and talks about full and empty
Beginning to select a shape for a specific shape
Beginning to arrange items in their own patterns
Shows an interest in size and weight Comparison
Is able to compare items using more or lots
Says some counting words and can accurately count up to 3
Uses number words, like one or two and sometimes responds accurately when asked to give one or two things
Beginning to use knowledge of number to solve problems
3 year olds
Compares 2 small groups up to 10 objects and saying the number of objects in each group
Points or touches each item saying the number for each item using the stable order of 1-10
Counts up to five objects recognising that the last number said represent the total number counted so far
Beginning to use understanding of number to solve practical problems in play
Responds to and use languages of position and direction
Shows awareness of shape similarities and differences between objects
Explores and adds to simple linear patterns of two or three repeating patters (AB) or (ABC)
In meaningful contexts, finds the longer or shorter, heavier or lighter and more or less between two items
4 year olds
Uses number names and symbols when comparing numbers, showing an interest in large numbers
Increasingly confident in putting numbers in order up to 20
Counts up to 10 objects from a larger from
Matches the numeral with a group of items to show how many there are
Investigates turning and flipping objects in order to make shapes fit and create models: predicating and visualising how they will look like
Uses mathematical terms to describe 2D shapes as well as beginning to describe 3D shapes
Chooses familiar objects to create and recreate repeated patterns beyond AB patterns such AAB
Enjoys tackling problems, involving predication and comparisons of length, weight or capacity paying attention to fairness or accuracy