At Calstock School we believe the importance of Mathematics in everyday life. It equips pupils with a uniquely powerful set of tools to understand and change the world. These tools include logical reasoning, problem solving and the ability to think in abstract ways. Mathematics is integral to all aspects of life and for this reason we endeavour to ensure that pupils develop a healthy and enthusiastic attitude towards mathematics that will stay with them. The National Curriculum for Mathematics describes what must be taught in each key stage. Calstock School follows the National Curriculum through Hamilton planning to ensure continuity and progression in the teaching of mathematics. Foundation Stage planning is supplemented with NCETM Mastering Number. This offers planning and visual resources to support the teaching process.
We believe it is important that a positive attitude towards mathematics is encouraged amongst all pupils and staff in order to foster self-belief and a sense of achievement. We give all children the opportunity to be creative, independent, inquisitive and confident. We also aim to provide a stimulating environment and adequate resources so that pupils can develop their mathematical knowledge, skills and understanding to their full potential. The National Curriculum says:‘Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content’.We believe all children should get the opportunity to be challenged in greater depth where they can apply their skills and articulate their thinking. We believe the use of language in Mathematics is highly important and we use a carefully sequenced, structured approach to introduce and reinforce mathematical vocabulary throughout maths lessons, so pupils have the opportunity to work with word problems from the beginning of their learning.
Problem solving and application of their learning is crucial to embed the concepts. We believe that deep learning of mathematics is important so that children can see and use the connections between different areas of the subject. Our Calculation Policy reflects the Concrete, Pictorial, Abstract (CPA) approach that is implemented across the school. The CPA approach provides pupils with visual aids, develops their fluency, enables them to reason and become confident problem solvers. We believe the CPA approach is able to meet the needs of all learners in Maths. CPA is needed for all abilities and it is important that all children are able to access it. CPA supports children by deepening their understanding and thinking. This is done through challenges set, using concrete, pictorial and abstract methods. CPA can also support children below the age expectancy by supporting their thinking and allowing them to work visually and physically. We believe CPA helps to close gaps in learning at all stages of a child’s journey. Calstock School believe it is very important to create an agreed whole school approach of which staff, children, parents, carers and governors have a clear understanding. We believe it is important to review and evaluate our mathematical policy and provision regularly, to integrate cross curricular links and to ensure mathematic planning enables continuity and progression across all year groups and key stages.
Implementation
The mathematics curriculum at Calstock School is cumulative – each school year begins with a focus on the concepts and skills that have the most connections, and this concept is then applied and connected throughout the school year to consolidate learning. This gives pupils the opportunity to ‘master maths’; by using previous learning throughout the school year, they are able to develop mathematical fluency and conceptual understanding. The curriculum is designed to make sure that the requirements of the 2014 National Curriculum for Mathematics are fully met. Each year’s curriculum includes all of the National Curriculum objectives for that year.
Our mathematics curriculum is derived through a series of carefully planned detailed small steps, designed to develop children’s understanding and learning in the subject. Pupils are provided with a variety of opportunities to develop and extend their mathematical skills in and across each phase of education. Before new learning is introduced, the children revisit and review prior learning.
Lessons follow the agreed format with a mental/oral start to strengthen their fluency, a ‘True or False’ question to get the children stimulated or revisit previous learning and a main teaching activity. Pupils are also given the opportunity to consolidate their understanding of previously taught maths in daily ‘Morning Maths’ sessions. The Mathematics teaching sequence at Calstock School provides opportunities for group learning, adult guided groups, paired learning, whole class teaching and individual learning.
All areas of Mathematics at our school follow the Concrete, Pictorial and Abstract approach. Concrete – the doing: A pupil is first introduced to an idea or a skill by acting it out with real objects. This is a ‘hands on’ component using real objects and it is the foundation for conceptual understanding.
Concrete - refers to objects such as base ten, ten frames, bead strings, Numicon, counters or other objects that can be physically manipulated.
Pictorial – the seeing: When a pupil has sufficiently understood the hand-on experiences performed, they can now relate them to pictorial representations.
Abstract – the symbolic: A pupil is now able to represent problems by using mathematical notation, for example: 12 ÷ 2 = 6.
Through the CPA approach, pupils are initially introduced to the idea through physical resources. This provides children with visual aid to support them in their learning. Once concrete resources have been used these are gradually changed to pictorial representations such as drawings or images. Finally, children progress to an abstract approach in their learning by representing calculations using number sentences and beginning to use more formal written methods. We believe children should always move between concrete, pictorial and abstract and apply all three to their mathematical thinking. We believe this will secure their understanding and enable them to make mathematical connections more easily.
We develop mathematical language within lessons that include sharing essential vocabulary at the beginning of every lesson and insisting on its use throughout, modelling clear sentence structures using mathematical language and open questioning.
Pupils engage in the development of mental strategies, compact written methods, practical tasks, investigational learning, problem solving, mathematical discussion and consolidation of basic skills and number facts. The learning environment is designed to stimulate, support and celebrate learning.
Impact
We aim that all pupils enjoy their maths lessons and develop a positive attitude to the subject. Through our CPA approach, we hope that pupils build up their mathematical resilience and apply their fluency understanding to reasoning and problem solving activities. Ongoing formative assessment is integral to every lesson ensuring that misconceptions are identified straight away and addressed within the lesson or in intervention sessions. Summative assessment includes: Low-stakes quizzing – to show improved retention of key facts, for example, multiplication facts. End of unit checks – these are administered at the end of a unit of work to assess understanding and application of small steps taught. Distance tasks – these are administered twice a half term to assess pupils’ retention of previously taught maths units. Termly summative assessments – PUMA Rising Stars – tests are administered at the end of every term to check progress against age-related expectations. End of Key Stage assessments EYFS – Pupils are assessed at the end of Reception against Early Learning Goals to assess their understanding of Number and Numerical Patterns. Year 2 (End of Key Stage 1) – pupils complete National Curriculum assessments which are used to inform teacher assessment in mathematics. Year 6 (End of Key Stage 2) - pupils complete National Curriculum assessments which are used to inform teacher assessment in mathematics.
Mental Maths Progression Document
‘The ability to calculate in your head is an important part of mathematics. It is also an essential part of coping with society’s demands and managing everyday events.’ The National Numeracy Strategy
By the end of Key Stage 2, children should be able to use an efficient method for each operation confidently and with understanding. It is encouraged that children recognise how and when to use mental methods to work out a calculation. For calculations that they cannot do in their heads they choose an appropriate written method which they can use accurately and with confidence (refer to written calculation policy).
6 Key points when planning and teaching mathematics:
Every day is a mental mathematics day
Hands-on learning is important
Seeing mathematics through models and images supports learning
Talking mathematics clarifies and refines thinking
Make mathematics interesting
Learning from mistakes should build children’s confidence
We as teachers have to;
- Commit regular time to teaching mental calculation strategies
- Provide practice time
- Introduce practical approaches and jottings with models and images children can use to carry out calculations as they secure mental strategies
- Engage children in discussion and develop oracy skills when they explain their methods and strategies to teacher/peers.
