“What is mathematics? It is only a systematic effort of solving puzzles posed by nature.”
To support our pupils in truly understanding and discovering mathematical patterns, we use a combination of White Rose, Nrich and Target Maths to build a mastery maths scheme which supports the needs of all our children. We begin each year with a strong focus on place value as this underpins all areas of maths.
To further support children, we use the concrete, pictorial and abstract approach (CPA) to teaching to ensure the maths is embedded. The CPA approach is a system of learning that uses physical and visual aids to builds a child’s understanding of abstract topics.
Concrete representation— a pupil is first introduced to an idea or skill by acting it out with real objects. This is a ‘hands on’ component using real objects and is a foundation for conceptual understanding.
Pictorial representation – 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.
Abstract representation—a pupil is now capable of representing problems by using mathematical notation, for example 12 x 2 = 24. It is important that conceptual understanding, supported by the use of representation, is secure for all procedures.
Reinforcement is achieved by going back and forth between these representations. Building these steps across a lesson can help pupils better understand the relationship between numbers and the real world, and therefore helps secure their understanding of the mathematical concept they are learning.