MATHS

Mathematics equips pupils with a powerful set of tools to understand and change the world. These tools include logical reasoning, problem solving skills and the ability to think in abstract ways.

Mathematics is important in everyday life. It is integral to all aspects of life and with this in mind we aim to ensure that children develop a healthy and enthusiastic attitude towards mathematics that will stay with them.

The national curriculum for mathematics aims that all children:

• Become fluent in the fundamentals of mathematics, including the varied and regular practice of increasingly complex problems over time.
• Reason mathematically by following a line of enquiry, understanding relationships and generalisations, and developing an argument, justification or proof using mathematical language.
• Solve problems by applying their mathematics to a variety of problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

At West Twyford we have adopted the Singapore Maths approach to teaching and embedding the above knowledge and skills.

Singapore Maths

The Singapore method of teaching mathematics develops children's mathematical skills and confidence without having to resort to memorising procedures to pass tests - making mathematics more engaging and interesting.

The Singapore method of teaching mathematics was developed in the 1980s and is now recognised as one of the world's leading approaches to maths teaching. It is based on research from a variety of research sources. West Twyford uses this approach through the Maths No Problem scheme, which is a complete curriculum covering all the National Curriculum requirements using the key approaches developed in Singapore Maths. We use this scheme across the school from reception to year 6. This ensures that children develop the key skills and have a consistency of approach.

The CPA Approach

One of the key learning principles behind the Singapore maths approach is the concrete/pictorial/abstract approach, often referred to as the CPA. The CPA approach, based on research by psychologist Jerome Bruner, suggests that there are three steps (or representations) necessary for children to develop understanding of a concept. Reinforcement is achieved by going back and forth between these representations.

It very important that all three approaches are used at each stage and in each year group. In the younger years maths teaching is likely to be more concrete in approach and as children become older it will become more abstract but all three approaches are used across all the year groups as this helps to develop and deepen understanding and support retention of key concepts.

Concrete representation

Children are first introduced to an idea or a skill by acting it out with real objects. In division, for example, this might be done by separating apples into groups of red ones and green ones or by sharing 12 biscuits amongst 6 children. This is a 'hands on' component using real objects and it is the foundation for conceptual understanding.

Pictorial representation

Children have sufficiently understood the hands-on experiences performed and can now relate them to representations, such as a diagram or picture of the problem. In the case of a division exercise this could be the action of circling objects.

Abstract representation

Children are now capable of representing problems by using formal mathematical notation, for example:

12 ÷ 6 = 2

Every new concept is introduced using this approach, from the foundation stage through to Year 6.

Investigation and working together

A key feature of our approach is to give children the opportunity to investigate aspects of maths. This is motivating and gives pupils a mathematical experience that is more memorable and helps them understand the more deeply. This is often accompanied by working with others. This has a number of benefits: explaining and sharing ideas is a key way to develop one's own thinking and to clarify ideas and working together helps all children to develop key concepts.   

Maths Intent

At West Twyford Primary, we want to create life-long Mathematicians. To achieve this, we have designed our curriculum to spark and kindle an interest and enthusiasm for the subject. Our aim is to cultivate a deep understanding, confidence and competence in maths that produces strong, secure learning.  

Children are given opportunities to grapple, tussle, explore, question, challenge and be challenged so as to logically arrive at thoughtful conclusions. We facilitate this through a classroom conversation ensuring all children achieve. As a school, we recognise that the key to unlocking the potential in our children is through the development of basic mathematical skills and the understanding of mathematical concepts. We therefore place great emphasis on the use of concrete resources and pictorial representations at all ages, to enable children to fully understand the concepts and principles, when presented with abstract calculations and questions.  

By investing in highly skilled teachers, we aim to build mathematical fluency, develop reasoning skills and provide children with the opportunity to articulate their understanding, thus nurturing mathematicians of the future. Most of all, we aim to build a love of Maths.  

Maths Implementation 

The Maths – No Problem! approach is at the heart of how we teach at West Twyford Primary and the key features of the Maths No Problem approach are as follows: 

• The teacher facilitates discussion through effective questioning.  

• The discussion is pupil-led with an emphasis on collaboration. 

• Children use concrete, pictorial and abstract representations in all lesson 

• Children approach the same task employing a range of methods 

• Maths is placed in real life context to ensure a deeper understanding. 

• Mathematical vocabulary is central to learning and used regularly  

• Children work in mixed attainment groupings allowing all children to access meaningful dialogue 

• Teachers reinforce an expectation that all pupils are capable of achieving high standards in mathematics.  

• Pupils are taught through whole-class teaching, where the focus is on all pupils working together on the same lesson content at the same time.  

• Differentiation is achieved by emphasising deep knowledge and/or through individual support and intervention.  

• If a pupil fails to grasp a concept or procedure, this is identified within the lesson structure and timely intervention ensures the pupil is best placed to move forward.  

• Key facts such as multiplication tables and addition facts within 10 are retained through retrieval practice to develop automaticity; this avoids cognitive overload in the working memory and enables pupils to focus on new concepts. 

• Pupil record their mathematical thoughts and processes in a Maths Journal, providing an excellent assessment into the knowledge and understanding of every child.  

Maths Impact

In Maths lessons daily, on-going assessment is a crucial method of assessment which provides instant feedback to the teacher and ensures progress within every lesson. AFL strategies provide a clear picture of a child’s level of understanding and, ensure that teachers can quickly assess when a child does not understand and needs greater support. Teachers are supported through team teaching by resident Maths experts. Our teachers are effectively trained to nurture an environment that allows children to approach maths in a deep and meaningful way.  

The impact of Maths teaching is monitored through pupil voice, test/data outcomes, planning, book looks and displays, learning walks, discussions with teaching staff, pupils and parents. The outcomes are joined-up, analysed and evaluated to assess impact and drive teacher development.  

By the end of Year 6, we aspire that a West Twyford Primary mathematician will have developed a bank of efficient and accurate skills that can be used to calculate effectively. These will have been underpinned by the CPA approach so children understand rather than just do, which ultimately will allow children to identify when solutions do not make mathematical sense. Children will be able to apply these calculation skills and understanding of other areas to become confident and resilient problem-solvers with the ability to reason and articulate their ideas mathematically. Children will have acquired the language to be able to justify, reason and explain their lines of enquiry and subsequent answers. 

“Teachers’ feedback includes setting a degree of challenge for pupils to extend their learning. This is proving successful, and an increasing number of pupils are starting to achieve the higher standard in the end of key stage tests, particularly in mathematics and writing.” Ofsted Inspection Report, 2018 

Useful Websites for Parents and Children

We are a Maths - No Problem! Accredited School. If you would like to know more about our Maths - No Problem! approach please click the link below. We are always happy to explain this and you can also contact the school office and we will be happy to help.

You can find out more about our maths curriculum using the links below:

 Maths No Problem Website                Additional information for parents       Enrichment activities for students

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