Maths: Concrete, Pictorial and Abstract...?

Our recent Maths INSET was a focus on the use of 'manipulatives' which means practical resources in lessons. Ofsted’s 2012 report ‘Made to Measure’ suggests that although manipulatives are used in some primary schools to support teaching and learning they are not used as effectively or as widely as they might be. Research suggests the use of manipulatives give children a deep understanding of maths. We discussed the use of concrete, pictorial and abstract ways of learning which need to be considered with equal importance when learning new concepts. Concrete resources give time for pupils to investigate a concept first - and then make connections when formal methods are introduced.  The pictorial stage allows pupils to demonstrate and sustain their understanding of mathematical concepts and processes. Most importantly, the abstract stage should run alongside the concrete - pictorial stage to enable pupils to read mathematical statements and show their understanding using concrete resources or pictorial representations.