Maths at Cardinham
At Cardinham School, we use a mastery approach to mathematics to ensure that all pupils develop a deep, secure and connected understanding of mathematical concepts. We follow the White Rose Maths schemes of learning as a basis for sequencing our curriculum, using carefully structured small steps that build progressively on prior learning. Progression across year groups and mathematical domains is supported by NCETM progression documents, ensuring that knowledge and skills are developed systematically throughout the school. Our mastery approach ensures that pupils learn together as a whole class, with support and challenge provided through responsive teaching rather than through different curriculum content.
In EYFS, we follow the NCETM Mastering Number programme. Mathematics is taught through daily whole-class teaching, small-group adult-led activities and carefully planned opportunities within continuous provision. Children are encouraged to explore, apply and embed their mathematical understanding through practical experiences and purposeful play.
Central to our mathematics curriculum is the belief that all children can succeed in mathematics. We ensure that every lesson addresses the three key aims of the National Curriculum: fluency, reasoning and problem solving. Pupils are given regular opportunities to explain their thinking, justify their reasoning and apply their knowledge in a range of contexts. Mathematical language is explicitly taught and consistently modelled, enabling children to communicate their understanding with increasing precision and confidence.
Lesson Design
Lessons are carefully designed around the principles of mastery and small-step learning. Assessment is an integral part of the learning process and begins before the lesson takes place. Teachers continually assess pupils' understanding of previous learning to determine whether they are ready for the next small step. Where assessment identifies gaps in prerequisite knowledge, pre-teaching is provided to ensure pupils have the understanding they need to fully access the lesson.
At the end of each small step, teachers assess learning and respond to identified misconceptions through immediate intervention or reteaching. This responsive approach ensures that pupils keep up rather than catch up and are able to move forward with confidence.
Within each lesson, new learning follows a carefully structured sequence. Teachers first model the new concept, making thinking explicit and using appropriate representations and mathematical language. This is followed by guided practice, where pupils and teachers work together to develop understanding and build confidence. Before pupils move to independent practice, teachers use carefully chosen assessment questions designed to reveal common misconceptions and check understanding. This allows misconceptions to be addressed immediately through further explanation, modelling or reteaching where necessary.
Pupils then move to independent practice, applying their understanding of the small step independently. Where pupils require further support, they continue practising alongside the teacher until they are ready; however, it is vital that all pupils are ultimately given opportunities to demonstrate their understanding independently.
The same process is then applied to reasoning and problem-solving activities. All pupils are given the opportunity to engage with mathematical problems and challenges. Teachers explicitly teach both the mathematical skills required and the processes needed to tackle unfamiliar problems, helping pupils develop resilience, confidence and strategic thinking.
Teachers use the White Rose termly overviews to support progression and sequencing but draw upon a range of high-quality resources, including NCETM and NRICH, to enrich and deepen learning. Staff also refer to the school's Calculation Policy when teaching formal written methods, while recognising and valuing efficient strategies developed by pupils.
Lessons begin with a Fluent in 5 task, enabling pupils to revisit and strengthen previously taught concepts and procedures. From Year 2 onwards, pupils participate in regular times tables sessions designed to develop rapid recall of multiplication and division facts up to 12 × 12. Pupils also have access to Times Tables Rock Stars, providing additional opportunities for practice, engagement and competition.
Across the school, we employ a range of teaching approaches that develop mathematical knowledge, understanding and skills both collaboratively and independently. Particular emphasis is placed on developing efficient mental calculation strategies alongside written methods.
Pupils are encouraged to represent mathematical concepts physically and visually before moving to abstract representations through the Concrete-Pictorial-Abstract (CPA) approach:
Concrete – pupils use practical resources and manipulatives to explore, represent and explain mathematical concepts.
Pictorial – pupils build on concrete experiences by using diagrams, pictures and representations to deepen understanding and support reasoning.
Abstract – pupils apply their understanding using numbers, symbols and mathematical notation with increasing confidence and fluency.
Assessment
Assessment is a continuous process that takes place before, during and after learning. Prior assessment identifies whether pupils are ready for the next small step and informs pre-teaching where required. During lessons, teachers use questioning, discussion, observation and assessment checkpoints to identify understanding and misconceptions in real time. Following learning, assessment is used to determine next steps, plan interventions, inform future teaching and ensure pupils secure the intended learning before moving on.
Formative assessment takes place daily and is used to adapt teaching responsively. Teachers may question pupils, review independent work, identify misconceptions or use pupil discussions to evaluate understanding. This enables teachers to remind, redirect, reteach or deepen learning as necessary.
Summative assessments take place at the end of each term using NFER assessments or previous SATs papers where appropriate. Outcomes are analysed and discussed through pupil progress meetings to identify strengths, areas for development and the next priorities for teaching.