Maths

Intent

At Brunel Field Primary, we are all mathematicians. Our desire is to journey through the BF Maths Curriculum together, instilling the confidence, skills and knowledge to not only succeed as mathematicians but develop a love of maths. We aim to develop a deep, secure understanding of new mathematical concepts; a strong and flexible sense of number; and a curiosity and value of proving and disproving our theorems. We want to shift our attention to wrestling with the process of maths and finding solutions rather than simply 'knowing the answer'. We strive to engage our Core Learning Skills in maths by persevering in learning how to accept and relish the times when we become STUCK! and make connections to draw on previously developed tenacity, skills and knowledge.

Implementation

At Brunel Field, we follow a teaching for mastery approach, involving all children in a year group working on the same learning objectives together. Learning is broken down into very small and carefully sequenced steps, which mean that all children (except those on individualised curricula) can access the learning appropriate for their year group. As a result of adopting this approach, we follow the BF Maths Curriculum, arranged mindfully; well-researched; and trialed extensively to support deep foundations and enable quicker grasping of new concepts in later year groups.

In every year, once a new concept has been learnt, the attention focuses on ‘Going Deeper’, for children to apply learning in a range of new contexts with a high level of flexibility, efficiency and problem solving to ensure they become ‘masters’ of the BF Maths Curriculum. We place high priority and time on mastering a strong sense of numbers, starting in the early years with a focus on, for example, “What makes eight ‘8’? Whatisits‘8ness’? How can we make and break a number?” through to Year 6, where we may ask, “What makes ten million ’10,000,000?” This investigation is an integral part of building the skills to ‘see numbers’ (subitising) and eventually moving beyond counting in ones, especially on fingers, to building up a mathematical toolkit of mental and written strategies for counting and calculating. In addition, we focus on using and explicitly teaching mathematical language from an early age to support confident and accurate reasoning (for example, the commutative law, inverse, subitising). We create a learning culture where we speak in ‘full sentences’ to explain our thinking and enable children to achieve this by providing scaffolds such as word banks, sentence stems and generalisations to practice hearing themselves say out loud and use increasingly independently.

Central to the learning of maths at Brunel Field is a focus on planning for and pre-empting misconceptions. We have experienced practitioners in every year group, who know a wide variety of misconceptions and mistakes children may make and therefore design lessons to expose and discuss misconceptions head-on, helping to avoid them occurring as much as possible, particularly through the use of appropriate, carefully chosen physical manipulatives (e.g. Numicon, Dienes) and helpful pictorial structures (e.g. Part-PartWhole). When a new concept is taught, teaching is particularly focused on, for example, what a triangle is and what it is not, again to pre-empt some misconceptions occurring in the first place: for example, a triangle must have a ‘point at the ‘top’. Physical or pictorial resources are used as a visualsupport to enable all children to access a task, especially as all children in a classroom are working on the same learning objectives together. Not only this but physical manipulatives are used at the start of each new concept taught to expose and ‘see’ the structure of, for example, decimals, especially in relation to previous learning, before moving onto purely abstract numbers and ideas.

Teachers apply various ‘exit strategies’ to gradually use physical and pictorial resources less, when each individual has secured an abstract understanding of the mathematical concept. To allow teachers to have time to focus their efforts on quality, well-informed planning, we have chosen to use a ‘tick and flick’ approach to marking maths tasks rather than writing in detail in books. This approach allows teachers to then support children 1:1 or in small groups in ‘maths catch up sessions’, which can be more tailored to individual needs and also creates space for pre-teaching sessions to boost self-esteem, allowing children to ‘hit the ground running’, who might otherwise have found a mathslesson overwhelming to even start. Once children have developed a secure understanding of key structures and mathematical rules, particularly associated with addition, subtraction, multiplication and division, they are given opportunities in school and at home to become fluent with key number facts.

In Key Stage 1, we have a step by step programme of securing one digit addition and subtraction facts, explicitly teaching children a range of strategies to ensure understanding and success with applying these number facts to more complicated problems. By the end of Year 2, we aim for all children to be able to add and subtract from 0+0 up to 10+10. Similarly, in Key Stage 2, we have developed an extensively-researched system of securing times table fluency. The essential foundational understanding of multiplication begins in Year 2 and results in discrete ‘times table workshops’ and daily practice of times tables in Year 3 and 4 and beyond if appropriate. Each times table is taught in a particular order, emphasising the commutative law at work and the intrinsic connection between multiplication and division, and relies on embedding specific sentence stems as part of collective oral rehearsal to enable these facts to reach children’s long-term memory. All members of a class secure a times table set at the same time until the vast majority of the class are able to show they know those facts, again ensuring that the vast majority of pupils will move at broadly the same pace. We place high importance and support on factual fluency because we know that these facts are not ‘the maths’; they are ‘tools’, much like a ruler for measuring, that help children to explore the world of mathematical thinking. If a child finds learning these facts hard, this will not define them as a mathematician at Brunel Field but they will be supported individually because we know that the more facts that can be secured the lesser the cognitive load will be, enabling children to focus on being creative, problem solvers rather than children who ‘know their times tables’.