At Binley Woods we use a Concrete-Pictorial-Abstract (CPA) approach to teaching mathematical concepts. Reinforcement of learning is achieved by going back and forth between these representations, building pupils' conceptu.al understanding instead of an understanding based on completing mathematical procedures.
- Concrete - the doing: A pupil is 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 Dienes apparatus, fraction tiles, counters, or other objects that can be physically manipulated.
- Pictorial - the seeing: A pupil may also begin to relate their understanding to pictorial representations, such as a diagram or picture of the problem.
- Abstract - the symbolic: A pupil is now capable of representing problems by using mathematical notation, for example: 12 ÷ 2 = 6. This is the most formal and efficient stage of mathematical understanding. Abstract representations can simply be an efficient way of recording the maths, without being the actual maths