Maths
“Math. It’s just there … You’re either right or you’re wrong. That’s what I like about it.”
Katherine Johnson
Intent
At Puss Bank School and Nursery our curriculum is to make mathematics make sense to all learners through a teaching to depth mastery approach to mathematics. Through collaboration, problem solving and reasoning mathematically, children embed a secure sense of number that can be applied fluently across a range of contexts and situations, including in real-life. Our approach is based on research evidence from the Education Endowment Foundation (EEF) recommendations for Improving Mathematics.
Implementation
Mathematics teaching at Puss Bank follows a mastery approach. Our curriculum ensures a coherent and detailed sequence of essential content to support sustained progression over time. We teach in small steps to depth which means that learning is progressively built upon, and children develop a deep understanding of each concept. Teaching progresses to the next concept when the majority of the class have understood a mathematical idea to depth as demonstrated by the children’s independent work. Children struggling with a mathematical concept are supported through timely intervention which enables the vast majority of children to progress through the curriculum at the same pace.
To provide appropriate challenge for all, children work collaboratively, in mixed ability groupings to discuss and solve problems. This provides opportunities for children to develop explanations, reason about a problem and to have their thinking challenged. Through skilful questioning from the teacher, children can look at a problem in a different way, thus deepening their knowledge of mathematical procedures or concepts. If a child has grasped a concept quickly, they will be given the opportunity to deepen their reasoning skills to describe, explain, convince, justify or prove their thinking.
The concrete-pictorial-abstract approach is evident throughout our curriculum, particularly as concepts are first introduced. We use the smallest set of models and representations that underpin and support the understanding of the greatest number of mathematical concepts. These examples have been carefully selected to expose the structure of mathematical concepts and emphasise connections, enabling pupils to develop a deep knowledge of mathematics.
Implementation
Our EYFS children follow the Development Matters framework, and in Reception, their early mathematics curriculum is delivered through the Mastering Number at Reception and KS1 | NCETM. This programme aims to secure firm foundations in the development of good number sense for all children in Reception which gives them a confidence and flexibility with number. The NCETM Mastering Number programme prepares children for small steps of learning that will be introduced in Year 1 ensuring that there is consistency between all stages of learning. Space, shape and measure are taught discreetly outside the mastering number programme.
In Year 1-6, our mathematics curriculum is planned and sequenced using the small step progression unit sequence from Oak National Academy Curriculum Plans for KS1 and KS2. We believe this fantastic resource supports our teachers understanding of the pedagogy, key vocabulary, likely misconceptions and progression through small steps in a concept. Oak Academy has drawn on findings from research organisations such as the Education Endowment Foundation (EEF) as well as their mathematics curriculum being inspired by the NCETM Curriculum Prioritisation materials to develop mastery of core concepts at an early age.
A typical lesson would begin with a short ‘connect’ activity which activates the children’s prior knowledge in order to build new knowledge onto. It would then move to an ‘explore’ image – a low threshold, high ceiling image which provides an entry point for all learners to access the new learning and acts as an opportunity for all children to share what they see, what they notice and what they wonder about the new learning. We would then move to explicitly explaining new learning in small steps to minimise cognitive load and maximise understanding and retention. During this part of the lesson, we would focus on dialogic teaching which aims to get children reasoning, discussing and explaining in order to develop their higher order thinking and articulacy. Answers provoke further questions and become the building blocks of dialogue rather than simply providing an answer. This is a great way to deepen children’s knowledge of a mathematical procedure or concept. We would then check for understanding where teachers can assess pupils by targeting common misconceptions and mistakes. From here, teachers will have a clear understanding as to whether their class is ready to move onto the independent practice part of the lesson. Independent tasks are progressive in their complexity and provide procedural and conceptual variation allowing teachers to assess the depth of children’s understanding.
At Puss Bank, we believe that independent practice is an essential part of learning but is not a substitute for explicit and systematic instruction and guided practice. We incorporate independent work after children begin to demonstrate mastery of the new skills or concept, providing an opportunity for them to demonstrate their ability to complete a task without (direct) teacher guidance. We aim for the children to spend most of the lesson time engaging in active learning with a short independent activity. Independent work is needed to embed procedural fluency as well as being used for teacher assessment.
The NCETM Mastering Number programme is used in Year 1-6 as an additional daily teacher-led session of 10 to 15 minutes which is separate to the main mathematics lesson. In KS1, the aim is that children will leave the key stage with fluency in calculation and a confidence and flexibility with number. Whereas, in KS2, the focus is on developing pupils’ automaticity in multiplication and division facts through regular practice.
We assess our children through summative assessments at the end of each term in Year 2-6. These assessments are based on the key end points set out in the ready-to-progress statements Mathematics guidance: key stages 1 and 2 (covers years 1 to 6). These assessments help measure the attainment of pupils in relation to the standards set out in the national curriculum, and help teachers in making accurate termly judgements as well as identifying where pupils may need additional support in a certain area. They are also useful in supporting children to gain experience of being assessed this way to prepare them for the end of KS2 tests.
Impact
Our children will leave Puss Bank confident in the three aims of the national curriculum: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument using mathematical language and solve problems by applying their mathematics to a variety of routine and non-routine problems. Through our mastery approach, our children will know more and remember more. They will enjoy learning mathematics and feel confident to take risks and make mistakes.