“Mathematics is not about numbers, equations, computations or algorithms: it is about understanding.”
William Paul Thurston
Intent: What are our aims when teaching Mathematics?
Our vision is for all pupils to begin a lifelong journey with maths by become independent learners with lively enquiring minds who seek pleasure in developing mastery in Mathematics. Put simply, we want our pupils to be able to ‘think mathematically’ – we want to provide them with a range of skills and techniques they can use to tackle any problem rather than fixed methods for particular calculations. This, we believe, best prepares children for the mathematics they will experience in the wider world after school.
The process of "Mathematical Mastery" is one where students achieve a level of mastery in prerequisite knowledge before moving forward to apply these in a variety of situations and while utilising a range of skills. This approach is supported by the National Curriculum (DfE, 2013) which clearly specifies its three aims of developing fluency, reasoning and problem solving.
Our aims will be achieved by providing stimulating, practical lessons which include the opportunity to question and explain and to develop a deep mathematical vocabulary. During lessons, rather than simply focusing on questions and answers, we want an environment where children are encouraged and supported to clearly articulate their ideas, thoughts and reasoning processes – all of which promote a deeper understanding. We expect children to make mistakes, analyse and learn from them, justifying and explaining this process as they do it.
At Pluckley Church of England Primary School, we believe it is important for pupils to be fluent in Maths and have a rapid recall of mathematical core knowledge, including: number bonds and times tables. We believe it is important for pupils to practice and revise this core knowledge regularly and, as such, we provide engaging opportunities for pupils to develop their counting and times tables. Additionally, we believe it is important for pupils to understand and be fluent in the four operations conceptually and fluently using daily arithmetic practice to support this. This combination of fundamental core knowledge and skills underpins all of mathematics and without secure fluency of these children are unable to progress further.
Implementation: How is Mathematics taught across the school?
At Pluckley, Mathematics is taught daily. To help structure and plan our lessons, we use the White Rose Maths scheme of learning which ensures firm foundations and sequences our learning. Alongside the White Rose Maths scheme, we use a range of rich resources to enhance our lessons and deepen understanding from websites such as NCETM and Nrich.
We recognise the importance of early mathematics and its role in underpinning all mathematical understanding that follows. This is why, alongside our normal maths lessons we also teach ‘Mastering Number’ sessions to all children in EYFS and KS1. These sessions are designed to strengthen our children’s understanding of early number. Our aim is to provide our children with the automaticity, rapid recollection and confidence with basic number facts e.g. subitising, number bonds within 20, odd and even, addition and subtraction, enabling our children to enter KS2 with these key fundamental strategies solidified within their long term memory.
Mathematical concepts are taught in blocks so that skills can be embedded, developed and mastered. Throughout the teaching of these blocks, our ‘connect’ phase of lessons allows us to show pupils where their current learning is situated between core knowledge and skills that they have previously learnt and those that they will be learning in the future. The ‘spaced learning’ phase of our lessons ensure that previously taught concepts are revisited regularly to ensure secure knowledge that is retained in the long-term memory. This is supported by our daily arithmetic practice – ‘Fluent Five’ – which focuses on the practice and retention of key arithmetic skills and concepts.
Within lessons, we use a structured approach to learning; specifically chosen questions are provided which build on and develop pupils learning as well as challenging their thinking. Pupils are able to practice their skills; firstly becoming fluent in calculations before moving on to reasoning and problem solving questions in order to apply (and secure) their skills further.
Throughout lessons, pupils will work in groups, with learning partners and independently – at all times giving learners the thinking time they need to develop their own ideas and discuss them openly (Williams, 2021); ensuring they develop the skills to clarify their understanding for others and themselves. The understanding of the 'how's' and 'why's' is extremely important; we utilise a 'deepening understanding' approach to encourage children to develop the skills of metacognition which in turn enables them to clearly communicate their thoughts and ideas. Rather than simply focusing on questions and answers, we aim to develop an environment where children are able to have wider conversations about maths. For example, by asking learners to explain how they arrived at an answer and discussing this with them (Sylva et. Al 2020).
Understanding the four rules of number, and the core knowledge and skills that go with this, is the foundation of our implementation. Teachers follow a clear progression of core knowledge and skills throughout the curriculum which ensure that children are both fluent and confident by the end of Year 6.
We believe in using many different ways of teaching concepts and these all begin with a ‘concrete’ visual or practical approach. (eg EYFS children look for the number 3 in the classroom and outside, and explore in their home environment. They make 3 using many different concrete apparatus, then see 3 in many visual representations.) The children in Key Stage 1 build upon these initial concepts and begin to look at formal methods alongside practical/visual work and modelling. Throughout Key Stage 2, children use different concrete materials such as ten frames, place value counters, dice and playing cards to embed and secure their knowledge and understanding of a range of mathematical concepts.
Throughout their time at Pluckley, children learn specific mathematical vocabulary – this is highlighted on their knowledge organisers, taught specifically during lessons and is also embedded through cross curricular application.
Impact: How do we know what the children have learnt and understood?
Teachers use formative assessment to evaluate the learning during a lesson. They may ask questions to check understanding, or scrutinise independent work in order to identify common misconceptions or share thinking. Such assessment allows teachers the flexibility to intervene in a lesson to remind, redirect or reteach pupils as required.
At Pluckley we understand that the majority of pupils will be able to move through our programmes of study at broadly the same pace. However, decisions about when to progress are always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Where pupils have grasped concepts rapidly, they are challenged through a range of rich and sophisticated problems – designed to develop their understanding, reasoning and explanation skills - before there is any acceleration through new content. If there are pupils who are not sufficiently fluent with earlier material, they are given opportunities to consolidate their understanding, often through additional practice, before moving on.
A mathematical concept or skill has been mastered when a child can show it in multiple ways, using the mathematical language to explain their ideas, and can independently apply the concept to new problems in unfamiliar situations.
Formal termly summative assessments, supported by written NTS tests or past SATs tests, allow teachers to evaluate how individuals, groups and the class as a whole are progressing compared to national expectations. They also give an excellent opportunity to see what concepts may need to be given additional time, and to adjust planning accordingly. Additionally, they give the Maths Leader the opportunity to see where strengths and weaknesses lie, where additional support needs to be focused and what training requirements there are.
Alongside this, the teaching of maths throughout the school is also monitored through the deep dive process of book and planning scrutinies, learning walks and through the use of pupil and staff voice.