At Greenside, our goal is for pupils to develop a deep and lasting mastery of mathematics through a Concrete, Pictorial and Abstract (CPA) approach. We want children to develop fluency, mathematical reasoning and precise use of mathematical language, alongside a passion for the subject and the resilience to persevere when mathematics is challenging. Our curriculum is carefully sequenced so that pupils build secure knowledge over time, make connections between mathematical ideas and are able to apply their understanding in increasingly varied and unfamiliar contexts.

We want children to do more than learn mathematical facts and procedures. We want them to become confident mathematicians who understand what they are doing, why it works and when they can use it. For us, mathematical mastery means that pupils develop sufficiently secure understanding to use, connect and apply their mathematical knowledge flexibly, rather than simply being able to recall a procedure.

Our approach to mathematics is built around four key stages:

Practise → Apply → Reason → Deepening Understanding

Children first practise and develop fluency with important mathematical knowledge and skills. Through carefully structured practice, retrieval and repetition, pupils secure foundational knowledge and develop accuracy and efficiency.

They then apply what they have learned to different questions, representations and contexts, making connections between mathematical ideas and developing flexibility in their thinking.

We encourage children to reason mathematically by explaining their thinking, justifying their answers, spotting patterns, making comparisons and asking, “How do you know?” Precise mathematical vocabulary and purposeful mathematical dialogue help pupils articulate their ideas, identify misconceptions and develop conceptual understanding.

Once children have developed secure understanding, we provide opportunities for Deepening Understanding. This may involve solving a more complex problem, making connections between different areas of mathematics, finding more than one solution, identifying and correcting an error, or applying knowledge in an unfamiliar context. This allows pupils to develop the depth and flexibility of understanding that is central to mathematical mastery.

Our mastery approach does not mean that every pupil progresses at exactly the same pace or in exactly the same way. Teachers respond to pupils' individual starting points and needs, using concrete resources, pictorial representations, modelling, questioning, targeted practice and appropriate scaffolding to secure understanding. Pupils who demonstrate secure understanding are encouraged to deepen their thinking, make connections and apply their knowledge in increasingly sophisticated ways, rather than simply moving on to new content.

For pupils with SEND, the curriculum is carefully adapted to remove barriers while maintaining high expectations. Appropriate representations, resources, vocabulary, repetition and scaffolds are used to help pupils secure foundational knowledge and develop increasing independence. This ensures that all pupils have meaningful opportunities to develop mathematical understanding and achieve their potential.

Mathematical knowledge is continually revisited and built upon throughout the curriculum. Retrieval and purposeful revision help pupils retain important knowledge, while opportunities to apply and connect learning enable them to broaden and deepen their understanding as they progress through school. Mathematical communication is central to this process, allowing pupils to explain, justify, question and refine their thinking.

Ultimately, we want pupils to leave Greenside as fluent, confident and resilient mathematicians who have mastered key mathematical concepts and can think mathematically, explain their ideas, solve problems, make connections and apply their knowledge independently in new and unfamiliar situations.