Maths is an adventure for children (and adults) to engage with, explore and succeed.
At Hayfield Lane we use a whole-class mastery programme designed to spark curiosity and excitement and help children nurture confidence in maths. At the heart of our Maths curriculum is the belief that all children can achieve. It’s built around a child-centred lesson design that models and embeds a growth mindset approach to maths.
At Hayfield Lane each class moves through topics at broadly the same pace. Each topic is studied in depth and teachers do not move to the next stage until children demonstrate that they have a secure understanding of mathematical concepts. We allow time for children to think deeply about maths and really understand concepts and how they relate to one another rather than a set of rules or steps.
Concrete, Pictorial, Abstract (CPA)
Children (and adults!) can find maths challenging because it is abstract. The CPA approach builds on children’s existing knowledge by introducing abstract concepts in a concrete and tangible way. It involves moving between concrete materials, to pictorial representations, to abstract symbols and problems. CPA develops a deep and sustainable understanding of maths in children.
Concrete is the ‘doing’ stage. Concepts are brought to life by children using concrete objects to model and solve problems by handling physical objects.
Pictorial is the ‘seeing’ stage. Visual representations of concrete objects are used to model problems. This stage encourages children to make a mental connection between the physical object they just handled and the abstract pictures, diagrams or models that represent the objects from the problem. Building or drawing a model makes it easier for children to grasp difficult abstract concepts.
Abstract is the ‘symbolic’ stage. Children use abstract symbols to model problems. Children will not progress to this stage until they have demonstrated that they have a solid understanding of the concrete and pictorial stages of the problem. The abstract stage involves teachers introducing abstract concepts (for example, mathematical symbols). Children are introduced to mathematical symbols (for example, +, –, x) to indicate addition, multiplication or division.
In KS1 we introduce children to ‘part-part-whole’ models to show how number bonds are split or combined. In Y2 and KS2 children are introduced to ‘bar modelling’ which allows children to draw and visualise mathematical concepts.