Teaching for mastery is based on a belief that all children can achieve in maths.
Concepts are built in small, logical steps and are explored through clear mathematical models and images. The focus is on depth – not acceleration – so that all children have a chance to embed learning. Teaching is supported by high-quality resources which present the flow of lessons coherently and provide opportunities for plenty of practice. Children use concrete resources and pictures to physically represent mathematical concepts alongside numbers and symbols – this helps them to visualise ideas.
A key feature of the maths mastery method is the concrete-pictorial-abstract approach where children are initially introduced to new concepts through the use of concrete resources.
What are concrete resources?
You’ll probably know them as place value counters, Numicon, Dienes (base 10), multilink cubes, lolly sticks, etc. – these are all examples of concrete resources.
Concrete resources (also referred to as manipulatives) are objects or physical resources that children can handle and manipulate to aid their understanding of different maths concepts. A mastery teaching approach encourages children of all ages to keep using these concrete resources, in Key Stage 2 as well as with younger children. While the abstract nature of maths can be confusing for children, through the use of these concrete, practical resources, they are able to ‘see’ the maths and make sense of what is actually happening.
Once children are confident with a concept using concrete resources, they progress to drawing pictorial representations or quick sketches of the objects. By doing this, they are no longer manipulating the physical resources, but are still benefiting from the visual support the resources provide.
Once children have a secure understanding of the concept through the use of concrete resources and visual images, they are then able to move on to the abstract.
Calculation Strategies and Approaches
Our approaches to helping children develop skill in calculation are summarised in our 'calculation policy'. This shows the step-by-step sequence and also gives examples of the concrete, pictorial and abstract phases.