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Mathematics

Intent:

At Netherthorpe Primary School we acknowledge and understand that Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. We try to ensure that our curriculum enables the children to make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence when solving problems. We believe that mathematical language is crucial to children’s development of thinking therefore mathematical vocabulary is explicitly taught and applied.

EYFS

In EYFS our educational programmes involve activities and experiences for our children, as set out under the mathematical area of learning in the statutory framework for EYFS:

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. 

KS1 and KS2

At Ks1 and Ks2 the national curriculum for mathematics aims to ensure 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.

The principal focus of mathematics teaching in key stage 1 ensures children develop confidence and mental fluency with whole numbers, counting and place value. They work with numerals, words and the four operations, alongside practical resources.  The children develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching involves using a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money. Work centres around number bonds to 20 and precision in using and understanding place value. An emphasis on practice at this early stage will aid fluency. Children use and apply mathematical vocabulary.

In year 3 and 4 the children become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. They develop written and mental methods and perform calculations accurately with increasingly large whole numbers. Children develop their ability to solve a range of problems, including with simple fractions and decimal place value, they draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. They use measuring instruments with accuracy and make connections between measure and number. Children memorise their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work. Children use and apply mathematical vocabulary.

In year 5 and 6 the children extend their understanding of the number system and place value to include larger integers. They develop the connections between multiplication and division with fractions, decimals, percentages and ratio.  They develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, the children are introduced to the language of algebra as a means for solving a variety of problems. Geometry and measures are consolidated and knowledge extended and developed in number. Children classify shapes with increasingly complex geometric properties and that they learn the vocabulary they need to describe them. By the end of year 6, children are fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages.

Implementation

EYFS

Early Years Foundation Stage (EYFS): Teachers and practitioners support children in developing their understanding of mathematics in a broad range of contexts in which they can explore, enjoy, learn, practise and talk about their developing understanding. This area of development includes seeking patterns, making connections, recognising relationships, working with numbers, shapes and measures, and counting, sorting and matching. Children use their knowledge and skills in these areas to solve problems, generate new questions and make connections across other areas of learning and development.

Children in the EYFS learn by playing and exploring, being active, and through creative and critical thinking which takes place both indoors and outside. We recognise that children learn through routine, continuous provision and incidental learning opportunities, as well as planned sessions and activities. Mathematical understanding can be developed through stories, songs, games, routine, questioning, imaginative play, child initiated learning and structured teaching.

In Foundation Stage 1, group activities are timetabled and planned and they complete a short focused maths activity once a week using the Number Blocks Programme.

In Foundation Stage 2, daily time is dedicated to mathematics and include a good balance between short whole-class work, focused group time and individual application time through continuous provision. Children in EYFS follow the mastering number programme which secures firm foundations in the development of good number sense for all children. The Word Aware Concept Programme supports the learning of mathematical concepts.

KS1 and KS2

The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace therefore most children follow the programmes of study for their year group and those who grasp concepts rapidly are challenged through being offered rich and sophisticated problems.  In each class there is a small number of children (SEND) who are not sufficiently fluent with the material of their year group and need to further consolidate their understanding of previous programmes of study. 

We use the 5 big Ideas in maths to develop and underpin our teaching for mastery and all daily classroom practice incorporates the following principles into each lesson; coherence, representation and structure, mathematical thinking, fluency and variation:

Coherence connects new ideas to concepts that have already been understood, and ensuring that, once understood and mastered, new ideas are used again in next steps of learning, all steps being small.

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 children: thought about, reasoned with and discussed with others.

Fluency:  Quick and effective recall of facts and procedures and the flexibility to move between contexts and representations of mathematics.

Variation:  Varying the way a concept is initially presented to children, by giving examples that display a concept as well as those that don’t display it. 

We believe that children who use concrete materials, develop more precise and comprehensive mental representations and are more able to apply.  Staff therefore use a range of resources in the classroom to help the children to make connections between concrete, representational and abstract levels of thinking and understanding.

We are using the NCTEM "Teaching and Curriculum Guidance for Primary Teachers" to plan our pupils’ Covid-recovery learning in maths.  The "Curriculum Prioritisation" material is a term by term framework which we are using to support planing and teaching in 2021-2022. 

Class teachers develop sequences of lessons for the week using the NCTEM Spines materials, the order in which has been prioritised using the ready to progress non statutory guidance (see mapping documents for each year group).  Activities may also be selected from a range of other resources including: Whiterose questions, Nrich activities, Ican reasoning & problem solving tasks and Times Tables Rockstars. 

Staff develop learning sessions driven by explicit learning objectives and success criteria and thought is given to specific vocabulary, potential mistakes or misconceptions that may arise, prior knowledge and stem sentences.

‘Ping Pong’:

Ping Pong’ style input consistently interspersed with frequent pupil activity, supported by well-planned slides  to build up to the year group objective (based around success criteria).

Slides:

Review of previous learning (No more than 5 minutes)

Sometimes start with problem/concept cartoon to introduce the learning

Provide small, coherent steps to support children through the learning so that they are ready for independent work.

Allow all children the opportunity for depth of knowledge e.g concepts represented in lots of different ways; true or false?; sometimes, always, never?; prove it/convince me.

CPA approach – resources should aid understanding and not become a tool to calculate.

Example pupil activities:

Explain it to your partner

Discuss with your partner and decide on an answer

True or False

Always, Sometimes, Never

Written activity on structured maths frame

Whiteboard activity – show me, prove it with a picture.

‘Prove It/Push it’:

Independent work ON THE YEAR GROUP OBJECTIVE – usually self-marked with the children and misconceptions addressed within session. 

Same-day ‘intervention’ may happen here with children that have struggled to grasp learning of main input and need T support. Role of any additional adults is to keep main group on task or work with SEND children on their specific maths targets.

All children to complete ‘Prove It’ task which is the year group objective.

Children may move onto the ‘Push It’ task which is a greater depth task.

We use a range of assessment procedures to help children to embed and apply knowledge and assist teachers in producing clear steps for learning.

‘Marking’ is taken to mean the process whereby a teacher looks at pupils’ written work, examine it for errors, misconceptions and/or conceptual and procedural fluency, and then respond in some way, either in writing, speech or action. ‘Evidence-recording’ is taken to mean the keeping of written or other records to show evidence of pupils’ progress in their learning of mathematics.

We have adopted guidance from the NCTEM document ‘Marking and Evidence Guidance for Primary Mathematics’

Formative Assessments to Inform Teaching and learning:

We use a range of ongoing formative diagnostic strategies:

Clear and concise lesson objectives and success criteria are explicitly shared in lessons so the learning focus is clear for teachers, teaching assistants and children to make learning and assessment precise.

In the ping pong part of the lesson, teaching and learning should focus around these clear objectives, and staff circulate to identify who has understood, misunderstood and showing misconceptions.

Questioning is used to identify children having difficulty in grasping any particular aspect of learning/curriculum content very rapidly.  They are then provided with extra support to help them master that content before moving on to new material

In the independent part of the lesson, the three staff will have a clear understanding of the outcomes for the lessons and they will work with the distinct groups to achieve them:

Marking is used to inform daily pre teach and daily post learning intervention groups.

Summative Assessments to Identify Achievement

End of block assessments for each block.

 

Impact:

Children articulate a high level of positivity, engagement, enjoyment and enthusiasm for mathematics and most children display a growth mindset which enables them to use their effort to succeed.

Attainment is showing improvement at both Key Stage 1 and Key Stage 2, with a more marked improvement in arithmetic compared to reasoning. There is evidence of progress in the children's books and a considerable improvement in the children's ability to articulate their conceptual understanding, indicating a greater depth of learning.

Children are now able to demonstrate their growing understanding of mathematics through their reasoning and willingness to attempt to explain their mathematical strategies. They are growing in confidence and are encouraged to see that Mathematics is no longer solely about finding answers.

The development of mathematical vocabulary and language is having an impact on children’s progress. Children are explicitly introduced to 3 key words each session and this enables them to have the means to represent their mathematical reasoning verbally and articulate mathematical statements. This has widened access to, and enjoyment of, the maths curriculum.

Children recognise that physical and verbal representations of mathematical ideas are as valuable as written ones. Speaking, listening and responding in mathematics is now a consistently high expectation.  Children discuss what helps them learn maths best by relating to specific strategies, such as using physical resources and engaging in discussions with peers.

 

Contact the School

Netherthorpe Primary school

Netherthorpe Street
Netherthorpe,
Sheffield, S3 7JA

Main Contact: Elizabeth Gray - Head Teacher

Tel: 0114 272 6834
enquiries@netherthorpe.sheffield.sch.uk

SEN Contact: Laura hammond

SEN Email: hammondl@netherthorpe.sheffield.sch.uk