How We Teach Mathematics

Harefield Primary School
Maths Statement

At Harefield Primary School, our aim is for our children to grow into confident and successful mathematicians. We want pupils to enjoy mathematics, to see themselves as mathematicians, and to be equipped with the knowledge and skills they need to apply their learning in school and in life. Using the Ark Mathematics Mastery programme, we provide pupils with the opportunity to develop a deep, secure and adaptable understanding of mathematical concepts.

The Dimensions of Depth

At the heart of our approach are the Dimensions of Depth:

Conceptual understanding – pupils grasp the meaning behind mathematical ideas and build strong connections between them.
Language and communication – precise mathematical vocabulary and talk help children explain, justify and refine their thinking.
Mathematical thinking – pupils look for patterns, test ideas, and reason logically.
Problem-solving – at the centre, children are challenged to apply their knowledge in new situations, drawing on all three dimensions to succeed.

How We Teach

Lessons follow a clear and consistent structure, shaped by these principles:

Concrete–Pictorial–Abstract (CPA) approach – Pupils first use practical resources (such as counters, cubes, bead strings or dienes) to explore mathematical ideas. They then move to pictorial methods such as number lines, bar models and place value charts before working with abstract symbols and equations. For example, children might group counters to show multiplication, represent this as an array or bar model, and then write it as an equation (e.g. 6 × 4 = 24). In upper Key Stage 2, this could mean representing fractions with a bar model before recording and simplifying as an equation (e.g. 3/6 = 1/2). This carefully structured journey helps every learner to secure and connect their understanding.
Mathematical talk and vocabulary – Talk is at the heart of our lessons. Teachers model precise vocabulary and complete sentences, and pupils are expected to do the same. Through paired talk, class discussion and explaining to others, children learn to reason, justify and refine their ideas.
Fluency practice – Each lesson builds in practice to make number work confident and reliable. For younger children this might include number bonds or times tables; higher up the school it includes efficient written methods, manipulating fractions, and working confidently with decimals and percentages. This regular practice helps pupils develop accuracy and efficiency, so that core skills become automatic and free up thinking for problem-solving.
Carefully designed tasks – Teachers use tasks that are structured to reveal patterns, highlight key ideas and draw connections, encouraging pupils to think deeply and mathematically.
Reasoning and problem-solving every day – Pupils are regularly challenged to apply what they know in new contexts. They learn to test ideas and build resilience when faced with challenge.
Review and retrieval – Learning is revisited often so that ideas are remembered and built on over time. This ensures children keep hold of key knowledge and can draw on it as they progress through school.

Our Intent

Our intent is for every child to:

Achieve fluency – develop secure knowledge of number-facts, methods and strategies.
Reason with clarity – explain, justify and prove their thinking using precise mathematical language.
Solve problems creatively – apply knowledge flexibly, make connections, and persevere with challenge.

We also aim to nurture a positive mathematical mindset. Children are encouraged to see mistakes as valuable, to embrace challenge, and to remain curious about how mathematics connects to the wider world.

In Year R, our mathematics curriculum prioritises secure number sense through the use of the Mastering Number programme, which forms the core of our teaching for the number aspects of the Early Learning Goals. This ensures that children develop a deep understanding of number, counting, and numerical relationships from the outset. Alongside this, Ark Mathematics Mastery is used to deliver all other areas of mathematics and is embedded within continuous provision, enabling children to apply and consolidate their mathematical learning through purposeful play, exploration, and adult-guided interactions.

Our mathematics curriculum strives to build and nurture the knowledge, skills and confidence pupils need to grow as mathematicians — during their time in primary school and beyond.

Available further down the page is an attachment showing the structure of our mathematics lessons at Harefield. During each session, the ‘New Learning’ section is divided into two parts to ensure a focused introduction and rehearsal of key mathematical vocabulary (‘star words’) before application. This supports pupils to articulate their thinking and is consistent with the school’s pedagogical approach.

Please see below, research based on the Ark Mathematics Mastery programme.:

https://educationendowmentfoundation.org.uk/projects-and-evaluation/projects/mathematics-mastery

As parents/ carers, you can access the following websites to support your child/children: -

https://www.bbc.co.uk/bitesize/subjects/zjxhfg8 (BBC Bitesize KS1)

https://www.bbc.co.uk/bitesize/subjects/z826n39 (BBC Bitesize KS2)

https://www.topmarks.co.uk/Search.aspx?Subject=16

Time Tables:

https://ttrockstars.com/

https://www.timestables.co.uk/

https://www.topmarks.co.uk/maths-games/7-11-years/times-tables

https://www.bbc.co.uk/bitesize/articles/z97rdnb#zw6k7v4

https://mathsframe.co.uk/en/search#/all/1/times%20tables