The national curriculum for mathematics aims to ensure that all pupils:

• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
• reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
• can solve problems by applying their mathematics to a variety of routine and non-routine problems, including breaking down problems into a series of simpler steps and persevering in seeking solutions

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects, as well as the real world.

Teaching and Learning 

Modelling

High quality modelling underpins all aspects of mathematics teaching. Teachers provide clear, structured models of mathematical processes, which combine demonstration, explanation, and active student engagement, ensuring that mathematical thinking is both visible and transferable. This modelling is delivered both live via the visualiser and through worked examples, allowing students to observe the full process from start to finish. Modelling sets the standard for what the quality of students’ work should look like.

Teachers deliberately use variation in their examples to help students to recognise patterns and make generalisations. Teachers think out loud during the modelling process, making the reasoning behind each step explicit, as well as modelling metacognitive skills such as planning, monitoring, and evaluating.

Modelling is interactive and responsive, with teachers pausing to ask questions to check for listening and for understanding. This ensures students actively engage with the modelling process rather than passively observing. Through repeated, high quality modelling, students develop independence, confidence, flexibility and understanding. 

Modelling is not limited to correct solutions; teachers also demonstrate common errors and misconceptions, explaining why they occur and how to identify and avoid them. This approach helps students develop critical thinking, and a deeper understanding of mathematical ideas.

Explanations

Clear and concise explanations are central to ensuring that students develop a secure understanding of a concept. All modelling is accompanied by an explanation that breaks complex concepts into manageable, sequential steps, ensuring accessibility for all learners. Explanations are carefully sequenced to reduce cognitive load. New ideas are introduced gradually with prior knowledge being checked, then explicitly linked to new concepts. Best practice is discussed during department development time to allow for consistency in explanations. 

The scheme of learning is carefully and logically sequenced so that topics interlink and can be interwoven, but also allows the opportunity to scaffold, stretch and challenge. This allows for regular recapping of key concepts. Explanations do not simply focus on procedural steps but also on helping students understand why particular methods work. This approach encourages students to recognise patterns, make generalisations, and see connections across topics.

Teachers use questioning, mini-whiteboards, and live checks for understanding, deciding whether to extend, revisit, or adjust the pace. Explanations are also adapted in response to students’ needs, ensuring misconceptions are addressed swiftly. Teachers promote resilience, reminding students that making mistakes is an essential part of the learning process.

Explanations are always teacher-led in the first instance, then students are given the opportunity to articulate their understanding.  Students are encouraged to construct and verbalise their own explanations using precise mathematical vocabulary. This helps in reinforcing their knowledge, improving mathematical communication, and building confidence to tackle unfamiliar problems. They listen carefully to each other's explanations, evaluating accuracy and clarity, which develops their reasoning skills.

Questioning

In mathematics, questioning serves as a powerful tool for both assessment and learning. Teachers employ a wide range of questioning strategies to check understanding, challenge students’ thinking, and promote meaningful mathematical discussion. Questions are carefully planned and sequenced to guide students from surface level recall to deeper conceptual understanding. Lessons always begin with a prerequisite knowledge check on mini whiteboards, to ensure solid foundations. For example, if a class is going to be learning about the quadratic formula, the teacher will check that they have a secure grasp on substitution. If they do not, this barrier is tackled before any new learning begins to take place. 

During the modelling and explaining process of teaching, teachers pause to ask ‘check for listening’ questions, as well as quick checks for understanding, building up to deeper prompts that encourage reasoning and problem-solving. Students are given thinking time to provide the opportunity for them to respond with clarity and mathematical precision. Students are encouraged not only to respond to questions but also to ask their own, demonstrating ownership of their learning. Questioning is also used to encourage precision in reasoning, and promote the use of accurate mathematical language. Students are expected to respond in full sentences, articulating their thought processes clearly and correctly. Teachers frequently ask learners to build on their own, or other students’, responses by asking “why?”, “how do you know?”, and “what if?” questions. By engaging in mathematical dialogue, students learn to listen actively, respond thoughtfully, and refine their reasoning through discussion. This ensures that students are not passive recipients of information but active participants in their learning. It nurtures intellectual curiosity and confidence, empowering students to think mathematically and to view mistakes as opportunities for growth.

Another common approach to check understanding when a new concept is taught is the use of diagnostic questioning, which anticipates misconceptions in advance and highlights where mistakes have occurred. Through the use of carefully designed multiple choice questions, the teacher is swiftly able to diagnose, with precision, during which part of the mathematical process an error has been made, and the reason behind it. The teacher then uses their professional judgement to rectify this either through teacher explanation, modelling or through student discussion.

As students are independently practising fluency, the teacher will circulate the room and live mark their work, checking for understanding, praising good practice, and identifying and addressing misconceptions. This provides the opportunity to evaluate learning and partake in questioning where required.

Planning

Our curriculum is carefully sequenced to ensure knowledge is built systematically and revisited regularly. Any new knowledge builds on what has been taught before and prepares students for what comes next. From Key Stage 2 to Key Stage 5, the long term plan ensures a coherent journey through number, algebra, geometry, ratio and proportion, statistics, and probability. This progression allows students to revisit and deepen key concepts over time while making clear connections across different areas of mathematics.

Each unit of work is broken into carefully planned small steps. Lessons introduce new ideas gradually to avoid cognitive overload and to secure understanding. In line with the National Curriculum, learning begins with fluency, then problem-solving and reasoning.

• Fluency: guided and independent practice, incorporating variation to deepen understanding rather than promote rote learning.
• Reasoning: opportunities to explain, justify, and prove, to support mathematical communication.
• Problem-solving: carefully chosen tasks that encourage students to make connections, try different strategies, and reflect on their approach.

Retrieval practice is built into lessons through daily starters and interleaving. This ensures that previously taught material is revisited in different contexts, helping students transfer knowledge to new problems.

Planning is responsive. Teachers use questioning, mini whiteboard checks, and live marking to assess understanding during lessons and adapt accordingly. 

Finally, planning ensures that students develop positive mathematical habits such as resilience, precision, logical thinking, and curiosity. By balancing fluency, reasoning, and problem-solving, lessons support mastery while nurturing independent, confident learners.

Marking and Feedback

Marking and feedback are purposeful and designed to improve learning. Teachers provide timely, specific, and actionable feedback so students understand what they have achieved and what they need to improve.

Verbal feedback is prioritised during lessons to address misconceptions immediately.

Written feedback highlights individual strengths and areas for development, while whole-class feedback allows teachers to address common errors efficiently.  Students are given dedicated time to respond to feedback, ensuring it leads to improvement.

Assessment for learning is embedded in every lesson through targeted questioning, retrieval and independent practice. Teachers use this information to adapt teaching, ensuring misconceptions are corrected quickly. Students are also required to self-assess their work, and make any amendments where necessary.

Long Term Memory

Our mathematics curriculum is designed to strengthen students’ long-term memory. We recognise that mathematical knowledge builds cumulatively; core facts, methods and concepts must be committed to memory and recalled with fluency in order to free cognitive capacity for reasoning and problem-solving. Our intent is to ensure that all students retain key knowledge over time, enabling them to make connections across topics and apply their understanding in increasingly sophisticated contexts.

We aim for students to develop automatic recall of number facts, such as times tables and metric conversions. Their retention is strengthened through regular retrieval practice, spaced repetition, and interleaving of topics. By revisiting and retrieving knowledge in different contexts, fluency and flexibility are built.  Lessons are planned carefully to give all students the opportunity to apply prior knowledge to new learning. This enables students to draw links between mathematical concepts and real life situations. 

It is essential that the content of the course is consolidated. Skills from KS2 and KS3 are the foundations of the KS4 curriculum, hence it is vital for students to engage with regular retrieval for maximum attainment. For example, understanding place value is an important skill which was covered in KS2, and this skill will be applied to all aspects of the curriculum throughout KS3, KS4 and KS5.

Teachers at times, use the Do Nows to do a recall check on previous learning to ensure students can transfer skills to long-term memory.