Maths

“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.”

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

Cardinality and Counting 

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.

Comparison 

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.

Composition 

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.

Pattern 

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.

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 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.

Measures 

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.)

Curriculum Intent and Implementation

In line with the National Curriculum objectives for Mathematics, our intent is that all pupils:

• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

• reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language

• can solve problems by applying their mathematics to a variety of routine and non- routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.

The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

Central to our approach are the 5 Big Ideas which underpin Mastery in Mathematics (NCETM)  - the diagram below is used to help bind these ideas together:-

Here’s a flavour of what lies behind them:

Coherence

Lessons are broken down into small connected steps that gradually unfold the concept, providing access for all children and leading to a generalisation of the concept and the ability to apply the concept to a range of contexts.

Representation and Structure

Representations used in lessons expose the mathematical structure being taught, the aim being that students can do the maths without recourse to the representation

Mathematical Thinking

If taught ideas are to be understood deeply, they must not merely be passively received but must be worked on by the student: thought about, reasoned with and discussed with others

Fluency

Quick and efficient recall of facts and procedures and the flexibility to move between different contexts and representations of mathematics

Variation

Variation is twofold. It is firstly about how the teacher represents the concept being taught, often in more than one way, to draw attention to critical aspects, and to develop deep and holistic understanding. It is also about the sequencing of the episodes, activities and exercises used within a lesson and follow up practice, paying attention to what is kept the same and what changes, to connect the mathematics and draw attention to mathematical relationships and structure.

The national curriculum for mathematics reflects the importance of spoken language in pupils’ development across the whole curriculum – cognitively, socially and linguistically. The quality and variety of language that pupils hear and speak are key factors in developing their mathematical vocabulary and presenting a mathematical justification, argument or proof. They must be assisted in making their thinking clear to themselves as well as others and teachers should ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions.

We expect and encourage children to use mathematical language to describe, discuss, examine, justify and synthesise. Children discuss mathematical concepts and approaches and share their ideas and approaches while using the correct terminology.

Teachers reinforce an expectation that all children are capable of achieving high standards in Mathematics. The large majority of children progress through the curriculum content at the same pace. Differentiation is achieved by emphasising deep knowledge and through individual support and same day (whenever possible) intervention. To ensure whole school consistency and progression, the school implements lessons based on the'Mathematics guidance: key stages 1 and 2 - Non-statutory guidance for the national curriculum in England - June 2020'  Ready to Progress and NCETM Curriculum Prioritisation documents. This publication aims to: bring greater coherence to the national curriculum by exposing core concepts in the national curriculum and demonstrating progression from year 1 to year 6 and to summarise the most important knowledge and understanding within each year group and important connections between these mathematical topics. This publication identifies the most important conceptual knowledge and understanding that pupils need as they progress from year 1 to year 6. These important concepts are preferred to as ready-to-progress criteria and provide a coherent, linked framework to support pupils' mastery of the primary mathematics curriculum. Please note that the publication does not address the whole of the primary curriculum, but only areas that have been identified as a priority. It is still a statutory requirement that the whole of the curriculum is taught (please see the programmes of study and our scheme of work documents for details). However, by meeting the ready-to-progress criteria, pupils will be able to more easily access many of the elements of the curriculum that are not covered by this guidance.

We are also part of the DfE funded Maths Hub programme and are part of the sustaining stage. The school is committed to providing staff with access to high quality continuing professional development opportunities. Every fourth staff meeting is also dedicated to Mathematics.

Year 1

Ready to Progress - Year 1

Maths Guidance Year 1

To further support teachers, we use the NCETM Curriculum Prioritisation documents.

This resource provides coherent sequencing for the primary maths curriculum. It draws together the DfE guidance on curriculum prioritisation, with the high quality professional development and classroom resources provided by the NCETM Primary Mastery PD materials

The graphic below shows the year mapped into different areas of the curriculum, to give an idea of the time that should be spent on each unit. Spare weeks are included in each term to allow for variation across schools and classes. 

Curriculum Prioritisation - Year 1

CP Map Year 1

Year 2

Ready to Progress - Year 2

Maths guidance year 2

To further support teachers, we use the NCETM Curriculum Prioritisation documents.

This resource provides coherent sequencing for the primary maths curriculum. It draws together the DfE guidance on curriculum prioritisation, with the high quality professional development and classroom resources provided by the NCETM Primary Mastery PD materials

The graphic below shows the year mapped into different areas of the curriculum, to give an idea of the time that should be spent on each unit. Spare weeks are included in each term to allow for variation across schools and classes. 

Curriculum Prioritisation - Year 2

cp Map year 2
 

To further enhance our Mathematics curriculum, 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. Children in Reception, Year 1 and Year 2 have a daily teacher-led session of 10 to 15 minutes, designed to ensure that pupils develop fluency with, and understanding of, number that is crucial to future success in maths and academic progress more generally. In Year 1 and Year 2 these daily 15 minute sessions are known as 'Whizzy Maths' on the timetable for the children and are in addition to their daily mathematics lesson that is from the NCETM Ready to progress & Curriculum Prioritisation documents.

Mastering Number: Overview of content - Reception

Mastering Number: Overview of content - Year 1

Mastering Number: Overview of content - Year 2

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.'

Improving Mathematics in the Early Years and Key Stage 1 summary recommendations from the Education Endowment Foundation

Impact

Pupils’ skill, knowledge and understanding is assessed against the National Curriculum attainment targets. The impact of the curriculum on learners will be monitored primarily by the class teacher who is responsible for all teacher assessment. Teacher assessment is recorded each term. The Maths Leads, KS1 Lead, Deputy and Headteacher monitor progress on a regular basis in the form of observations, data analysis, pupil progress meetings and work sampling.

Formative Assessment will be a key part of every lesson. The teacher will share the objectives for the lesson with the children and make sure they are clear what is being expected of them to successfully achieve the objective. The short-term assessment will also involve the teacher checking the children’s understanding at the end of the session to inform future planning and lessons.

Summative assessment is undertaken using standardised tests at intervals determined by the Headteacher.

Ultimately, the impact of Little Bowden's KS1 Maths curriculum will be measured in the children's attitudes to Mathematics alongside outcomes for learners across the Key Stage and in the nationally released data from KS1 SATS.

Key Stage 2 Mathematics: Intent, Implementation and Impact

maths scheme of work

Maths Curriculum Prioritisation overview years-1-6

Maths guidance KS1 and 2

the-essence-of-maths-teaching-for-mastery-june-2016

wrm-addition-subtraction-calculation-policy-july-2022

Multiplication and Division calculation policy July 2022