Mathematics – Intent, Implementation and Impact

Elham Church of England Primary School

Intent

At Elham Church of England Primary School, our intent in Mathematics is to develop confident, fluent and resilient mathematicians who can reason, problem-solve and make meaningful connections within and beyond mathematics. Rooted in our school values of faith, achievement, community and empathy we aim is to equip all students with the skills and confidence to solve a range of problems through fluency with numbers and mathematical reasoning. Students are encouraged to see the mathematics that surrounds them every day and enjoy developing vital life skills in this subject

We believe that all children can achieve in mathematics. Through a mastery approach, pupils build deep and secure understanding of mathematical concepts, enabling them to apply their learning flexibly across a range of contexts. Mathematics is taught as an interconnected subject, where new learning builds coherently on prior knowledge and misconceptions are addressed proactively.

Our curriculum is fully aligned with the National Curriculum, supported by the White Rose Scheme of Learning, and informed by the NCETM 5 Big Ideas of Teaching for Mastery. We work closely with the Kent and Medway Maths Hub to ensure high-quality, research-informed practice and continuous professional development.

EYFS

The principle focus in EYFS is that children leave this stage with a strong sense of number. They have developed fluidity and flexibility with numbers and have an understanding of what numbers mean, and can begin to perform simple mental mathematics. They can count reliably with numbers from 1 to 20, as well as (when using quantities and objects) add and subtract and solve problems that involve doubling, halving and sharing.

Key Stage 1

The principle focus of mathematics teaching in Key Stage 1 is to ensure that students develop confidence and mental fluency with whole numbers, counting and place value. This involves working with numerals, words and the four operations.

Lower Key Stage 2 – Years 3-4

The principle focus of mathematics teaching in lower Key Stage 2 is to ensure that students become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. This should ensure that students develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers.

At this stage, students develop their ability to solve a range of problems, including with simple fractions and decimal place value.

Upper Key Stage 2 – Years 5-6

The principle focus of mathematics teaching in upper Key Stage 2 is to ensure that students extend their understanding of the number system and place value to include larger integers. This should develop the connections that students make between multiplication and division with fractions, decimals, percentages and ratio.

At this stage, students 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, students are introduced to the language of algebra as a means for solving a variety of problems.

By the end of Year 6, the aim is for all students to be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages.

Implementation

Mathematics is taught daily using small steps of progression, ensuring carefully sequenced learning that builds conceptual understanding over time. Lessons are designed around the principles of Teaching for Mastery, with a focus on depth rather than acceleration.

Teaching is underpinned by the NCETM 5 Big Ideas:

• Coherence: Lessons are structured into small, connected steps that build logically on prior learning.
• Representation and Structure: Concrete, pictorial and abstract representations are used consistently to expose mathematical structures.
• Mathematical Thinking: Pupils are encouraged to explain, justify and generalise their thinking using precise mathematical language.
• Fluency: Regular practice enables pupils to recall and apply facts efficiently while maintaining conceptual understanding.
• Variation: Carefully designed examples and questions deepen understanding and highlight connections.

High-quality questioning, talk-partner work and collaborative learning promote a strong sense of community and empathy, allowing pupils to learn from one another and value different approaches. Adaptive teaching ensures that all pupils, including those with SEND and those working at greater depth, are supported and challenged appropriately within the lesson.

Assessment is integral to teaching and learning and will enable the impact the mathematics curriculum to be measured. Ongoing formative assessment informs planning and responsive teaching, while summative assessments are used to monitor progress and inform next steps.

Mathematics is taught to the whole class over five lessons per week in KS1 and 2, and with five 20-30-minute lessons per week in EYFS. Lessons are planned based on formative assessment of what students already know and all students are included in learning mathematical concepts. At the planning stage, teachers consider what scaffolding may be required for students who may struggle to grasp concepts in the lesson and suitable challenge questions for those who may grasp the concepts rapidly.

Misconceptions

Potential misconceptions are identified during the planning process and key questions are constructed to allow students the opportunity to address these misconceptions. These possible misconceptions are always planned for and students will be supported when addressing these.

Questions

Questions are used to challenge thinking as well as to probe student understanding. Responses from students are expected in full sentences, using precise mathematical vocabulary.

Key questions are planned for and often repeated in order to provide many reasoning opportunities for the students: How do you know? Can you prove it? What would happen if…? What’s the same/different …? Can you explain…?

Questions are also used to challenge students who have grasped the concept. Students are expected to listen to each other’s responses and may be asked to explain someone else’s ideas in their own words, or if they agree/disagree etc.

Achieving depth of understanding

Each lesson focuses on one key conceptual idea and connections are made across mathematical topics. It may appear that the pace of the lesson is slower, but progress and understanding is enhanced. Assessment procedures recognise that the aims of the curriculum cannot be assessed through coverage but through depth within a topic.

As we aim to embed a deep understanding of maths, we employ the concrete, pictorial, abstract approach (CPA) across all phases– using concrete materials (e.g. objects) and pictorial representations (e.g. pictures, diagrams) alongside the use of numbers and symbols. This supports students to develop a deeper conceptual understanding of the underlying mathematical structure as opposed to solely learning routines, procedures and algorithms without developing a deep understanding of mathematics.

Fluency

We recognise that ‘fluency’ is not just about remembering facts and develop all aspects of fluency through lessons. Fluency encompasses skill and dexterity when using number, being able to use number creatively and with skill. This is based on a fluency with basic facts - there is a whole school focus on developing an instant recall of key facts, such as number bonds, times tables and root addition facts.

Intervention 

In mathematics new learning is built upon previous understanding, so in order for learning to progress and to keep the class together, students need to be supported to keep up and areas of difficulty must be dealt with as and when they occur. We do this through same day feedback, targeted to students in lessons as teachers ‘helicopter mark’ around the classroom. In addition, we still run intervention sessions outside of the maths lesson for some targeted students, based on the marking and feedback from formal assessments.

Feedback 

The most valuable feedback is given during the lesson, and is a result of pupil-teacher interaction, based around targeted conversation and questioning. The feedback policy for mathematics follows the NCETM guidelines published April 2016. The policy requires that learning is ticked, and a comment is only made if/when a teacher feels this is necessary to move learning forward. Students are encouraged to use self/peer assessment during lessons.

Impact

As a result of this approach, pupils at Elham Church of England Primary School:

Demonstrate secure conceptual understanding and increasing fluency in mathematics.

Can reason mathematically, explain their thinking clearly and use accurate mathematical vocabulary.

Apply their knowledge confidently to problem-solving and real-life contexts.

Show resilience and independence, viewing mistakes as opportunities for learning.

Achieve well in line with, or above, national expectations.

Pupils leave our school with a positive attitude towards mathematics, equipped with the skills and understanding they need for the next stage of their education and for life beyond the classroom. Our mathematics curriculum supports our vision of enabling every child to flourish academically and personally, guided by faith and shaped by strong values