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Mathematics equips pupils with the uniquely 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 endeavour to ensure that children develop a healthy and enthusiastic attitude towards mathematics that will stay with them.
The national curriculum for mathematics aims to ensure that all pupils:
At West Twyford we have adopted the Singapore Maths approach to teaching and embedding the above knowledge and skills.
The Singapore method of teaching mathematics develops pupils' 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 is based on research from a variety of sources. The work of educational psychologist Jerome Bruner and Richard Skemp's work on relational and instrumental understanding are some of the sources.
The CPA Approach
One of the key learning principles behind the Singapore maths textbooks is the concrete- pictorial- abstract approach, often referred to as the CPA approach. The concrete-pictorial-abstract approach, based on research by psychologist Jerome Bruner, suggests that there are three steps (or representations) necessary for pupils to develop understanding of a concept. Reinforcement is achieved by going back and forth between these representations.
The enactive stage - a pupil is 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.
The iconic stage - a pupil has 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.
The symbolic stage – a pupil is now capable of representing problems by using mathematical notation, for example: 12 ÷ 2 = 6
Every new concept is introduced using this approach, from the foundation stage through to Year 6.