![]() ![]() This is no surprise, with ‘mastery’ being the Government’s flagship policy for improving mathematics and with millions of pounds being injected into the Teaching for Mastery programme a programme involving thousands of schools across the country. Origins of Concrete Pictorial Abstract ApproachĪnyone working in primary mathematics education can’t fail to have noticed that the word ‘maths’ is rarely heard these days without a mention of the term ‘mastery’ alongside it. 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. Then they are asked to solve problems where they only have the abstract i.e. ![]() When they are comfortable solving problems with physical aids, they are given problems with pictures – usually pictorial representations of the concrete objects they were using. Pupils are introduced to a new mathematical concept through the use of concrete resources (e.g. The Concrete Pictorial Abstract (CPA) approach is a system of learning that uses physical and visual aids to build a child’s understanding of abstract topics. The CPA approach illustrated by one of our Third Space Learning resources What is the Concrete Pictorial Abstract in Maths? The maths curriculum is far too broad to cover in one blog, so the focus here will be on specifically how the CPA approach can be used to support the teaching and learning of the four written calculation methods. Please see the document below (CPA in Action – Data) that demonstrates how the CPA model in action.The Concrete Pictorial Abstract approach is now an essential tool in teaching maths at KS1 and KS2, so here we explain what it is, why its use is so widespread, what misconceptions there may be around using concrete resources throughout a child’s primary maths education, and how best to use the CPA approach yourself in your KS1 and KS2 maths lessons. Once we believe our pupils have mastered maths concepts through using concrete and pictorial resources we move into the abstract.Įven when working abstractly in maths our pupils always have access to concrete and pictorial resources to support them. It includes pictures and diagrams of resources that our pupils are familiar with and are sometimes included in the Fact Files that we provide as part of Additional Learning. The pictorial aspect of this model is a vital step for enabling all our pupils to move from concrete maths to abstract maths. Please see the document below (Concrete Resources) that details some of the resources we use as part of our everyday teaching of mathematics at Stony Dean.Īs our pupils gain understanding of a concept through using concrete materials they move into using pictorial resources to support them moving away from using concrete resources. We use a range of concrete resources in teaching all areas of mathematics but specifically with reference to number work. This is to make the concepts being taught real to our pupils so they can make sense of the maths rather than dealing with ideas that are abstract. When starting a new concept whatever the year group or ability of our pupils we use concrete apparatus. For example, even when a pupil has worked out the answer using an abstract method, we may ask them to use concrete manipulatives to convince others that they are correct. This model is not linear, we use a cyclical approach. We believe if our pupils fully understand the concept they are learning and keep revisiting it, then they will be able to apply the maths independently in the future. ![]() It is about giving our pupils the tools to understand the maths that they are focusing on. This approach is not about getting the answer quickly or teaching quick fix ‘tricks’. ![]() We use this approach to enable our pupils to fully understand and master the maths concepts that we are teaching. The Concrete, Pictorial and Abstract (CPA) Model of learning is one that fully encompasses the way we teach mathematics at Stony Dean. ![]()
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