Maths

How do we teach Mathematics?

Intent

At Bromham CofE Primary School we aim to teach children how to make sense of the mathematics in the world around them by developing their; ability to calculate, reason and problem solve, whilst developing the linguistic skills to articulate their mathematical thinking accurately and precisely. We aim to ensure maths is accessible to pupils of all backgrounds, with all areas of the mathematics curriculum consolidating on previously acquired knowledge, leading to extension and challenge, to deepen children’s mathematical thinking. We promote this at every stage of their academic life. We ensure this through the use of a mastery curriculum, which is underpinned by the five big ideas: structures of mathematics, mathematical thinking, variation, fluency and coherence through small steps.

Our aims in the teaching of mathematics are:

To promote enjoyment of learning through practical activity, exploration and discussion;
To develop confidence and competence with numbers and the number system;
To become fluent in the fundamentals of mathematics, through varied and frequent practice, including retrieval practice;
To develop a curiosity about the nature of number alongside the ability to solve problems through decision-making and reasoning in a range of contexts;
To reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.
To stretch and challenge children’s thinking through a growing complexity of concepts over time, so that pupils develop conceptual understanding, the resilience and confidence to apply learning in new contexts;
To develop a practical understanding of the ways in which mathematics supports other areas of the curriculum in a range of contexts;
To help children understand the importance of mathematics in everyday life and how their skills can support them in developing economic stability and success in adult life.

Implementation

Teachers are provided with the foundations for effective mathematics teaching through the delivery of ESSENTIALS:Maths developed by Herts for Learning Education (HFL for Education). This scheme of learning has been developed by consultants, with expertise in the effective teaching of Primary Mathematics, who undertake current research to ensure classroom pedagogy reflects current good practice in the subject.

At our school we encourage children to identify that Mathematics is a symbolic, abstract language. To decode this language, the symbolism of numerals needs to have tangible meaning that has context in a child’s world. We believe that all students, when introduced to a key new concept, should have the opportunity to build competency in this topic by taking the concrete-pictorial-abstract approach:

Concrete – students should have the opportunity to use concrete objects and manipulatives to help them understand what they are doing.
Pictorial – students should then build on this concrete approach by using pictorial representations. These representations can then be used to reason and solve problems.
Abstract – with the foundations firmly laid, students should be able to move to an abstract approach using numbers and key concepts with confidence.

All classrooms have a varied range of concrete resources that can be used in the teaching of mathematics. It is the expectation that these resources are accessible to children every lesson. At times, resources will be modelled directly by the teacher and their use explicit in teaching. However, once children are competent and confident in a concept, they may use a manipulative of their own choice and should have the ability to communicate why this was their preference. The use of these resources is not restricted to ability and the expectation is that all children use these resources, whether as a scaffold to meet the expected standard or to challenge and deepen more complex thinking.

At our school, we teach mathematics to all children, personalising learning to their ability or individual need, with the expectation that ‘children will keep up-not catch up.’ Through quality first mathematics teaching and the cyclical nature of concrete, pictorial and abstract, applied in lesson design, we provide learning opportunities that enable all pupils to make good progress, narrowing the gap between the most and least able learners. 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 will always be based on the security of pupils’ understanding and their readiness to progress to the next stage, in order to avoid cumulative dysfluency. Pupils who grasp concepts rapidly will be challenged to deepen their understanding by being offered rich and sophisticated problems and not accelerate through to new content.

Wherever possible, we provide meaningful contexts and encourage the children to apply their learning to everyday situations. Although mathematics is best taught discretely, it has many cross-curricular links. Teachers need to use opportunities in other subjects to rehearse skills in a context, particularly in Science and Design Technology.

Early Years
Our EYFS team use and follow the associated Essentials: Maths Reception scheme of learning. This builds on the core mathematical foundations, which all children need to continue to thrive and become successful mathematicians. Children receive short inputs and modelling from their teacher and consolidate this through adult-led interactions and/or small group work. As children continue through the foundation stage, children are prepared for the KS1 curriculum through the deepening of number and the introduction of more formal ‘lessons’ in the summer term. Pupils are given plenty of opportunities within continuous provision to use and apply the mathematical skills and concepts they have learned with their teachers and adult interactions are vocabulary rich and challenging to develop children’s thinking.

All classrooms will have a display area specifically for mathematics. This is called a working wall and will display items that children need to support and develop the unit's learning. For example, key vocabulary, models, key questions. In the Early Years’ Foundation Stage there are also specific mathematical areas for children to access in their everyday learning.

Special Educational Needs Disability (SEND) / Pupil Premium / Higher Attainers
All children will have Quality First Teaching. Any children with identified SEND or in receipt of pupil premium funding may have work additional to and different from their peers in order to access the curriculum dependent upon their needs. As well as this, our school offers a demanding and varied curriculum, providing children with a range of opportunities in order for them to reach their full potential and consistently achieve highly from their starting points.

Topics taught across the year groups:
See Subject Breakdown Document and Essentials: Maths long term plans

Rationale for organisation:
The sequence is planned to ensure that the foundation for strong mathematical knowledge is embedded in the foundation stages. Children leave secure in the 6 areas of mathematics: counting and cardinality, comparison, composition, pattern, shape and space and measures. Upon this our curriculum acts as a spiral, with each year group building upon the previous years’ learning. Each sequence in the Essentials: Maths curriculum maps previous taught content and has direct links to the natural curriculum study for mathematics.

What have you done to ensure every skill is covered?
Every Essentials: Maths sequences is matched to the national curriculum to ensure every skill and domain of maths is covered throughout the academic year. Within the teacher information, it also includes which sequences teachers are building from earlier sequences/ year groups and will also signpost where this learning will be needed further into the current academic year group, ensuring teachers do not miss anything crucial to stretch learning.
Every sequence has destination questions, which are a means to assess whether children have achieved the skills they need from this sequence. At the end of every half term, students complete diagnostic assessments which highlight any gaps in understanding and teachers can plan post-teaching to ensure this is met.

Impact:
Assessment for Learning is fundamental to the essence of Mathematics at Bromham CofE Primary, as well as quality Maths teaching, in order to have impact, raise standards and enable children to reach their full potential. Formative assessment in mathematics takes place daily using a range of strategies such as:

• Retrieval practice in verbal or written form
• Daily fluency sessions to build on prior learning and promote over-learning
• Verbal questioning
• Discussion and students’ explanations of their use of concrete or pictorial representations
• Assessing children’s understanding of mathematical vocabulary throughout their learning
• Marking and feedback of work. Teachers should be ready to respond to the needs of all, either through providing scaffolding or further challenge to ensure progress, with the emphasis on intervention at the point of understanding

Throughout the academic year, summative assessments will be completed, which act as diagnostics to inform planning and to identify gaps in children’s knowledge. These take the following form

• Years 1-5 complete Headstart assessments termly
• Year 2 and Year 6 complete ‘mock’ SATS papers, which are used to inform progress, but also plan for pre-teaching, post-teaching and consolidation.
• Teacher assessment is completed after formal assessments in order to ensure judgements on attainment are accurate.
• Essentials: Maths diagnostics are completed once learning sequences have been completed. These diagnostics assess children on the content of the curriculum taught and help identify where consolidation or over-teaching may be required to secure learning. The outcomes of these diagnostics influence intervention content, fluency content and revision of the curriculum.
• Annual reporting of standards across the curriculum.

Maths

Maths

How do we teach Mathematics?

Programme of Study EYFS - Year 6

Vocabulary Progression EYFS - Year 6

Mental Arithmetic Progression EYFS - Year 6

Calculation Policies

Times Table Rock Star Guidance