Maths at Blackgates incorporates fluency, reasoning and problem solving and is taught using a concrete, pictorial, abstract (CPA) approach. It develops a deep and sustainable understanding of maths in pupils and is an essential technique of maths mastery that builds on a child’s existing understanding. The variety within the approach means the children really learn the why behind what we do rather than just the how.
Children (and adults!) can find maths difficult 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 from concrete materials, to pictorial representations, to abstract symbols and problems
Concrete is the “doing” stage. During this stage, students use concrete objects to model problems. Unlike traditional maths teaching methods where teachers demonstrate how to solve a problem, the CPA approach brings concepts to life by allowing children to experience and handle physical (concrete) objects. With the CPA framework, every abstract concept is first introduced using physical, interactive concrete materials.
Pictorial is the “seeing” stage. Here, 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 (for example, fractions). Simply put, it helps students visualise abstract problems and make them more accessible.
Abstract is the “symbolic” stage, where children use abstract symbols to model problems. Students 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 the teacher introducing abstract concepts (for example, mathematical symbols). Children are introduced to the concept at a symbolic level, using only numbers, notation, and mathematical symbols (for example, +, –, x, /) to indicate addition, multiplication or division.
Here at Blackgates, we also understand the importance of language and the significance this has in a child being able to access the Primary Maths Curriculum. We have high expectations of the language that is used, both in written work and in class discussions. To help with language development, we use stem sentences. This technique gives students the opportunity to respond in the form of a complete sentence to effectively communicate. Sentence stems provide scaffolding to help students get started in speaking or writing without the added pressure of thinking about how to correctly formulate a response. It also allows the children to learn mathematical definitions of key concepts that can travel with them through school.
In Nursery the children access a wide range of maths activities and resources in the areas of provision. Through the use of equipment and templating the children are able to develop their ideas and concepts of number, size, shape, space and measure, and develop their mathematical language and vocabulary. The children participate in small group activities with the teacher which are always practical and focus on a particular area of learning. Their work and achievements are recorded through observations on Tapestry and in profiles.
In Reception the children also access a wide range of maths activities and resources in the areas of provision. Challenges are set up in the environment for the children and they are able to access a wide range of maths resources in the maths area. The children participate in short sessions with the class and then work in small groups with the teacher to enhance their understanding of that particular area of learning, in practical activities. Their achievements are recorded through observations on Tapestry and profiles, and the children begin to make some of their own recordings in their maths books. The Reception classes are also introducing a 'Golden box' which celebrates children's independent work that they have created in their own free play.
Throughout the academic year, children in Year 1 learn about a range of topics within mathematics. They begin by focusing on number. The children spend time representing numbers to 20 in many different ways. They then use this knowledge of number to support their work in addition, subtraction, multiplication and division. The children learn to read, interpret and write a number sentence; showing that they know each of the related mathematical signs. Year 1 children also explore 2D and 3D shapes with a focus on naming each one and their properties. They also learn about different measures involving money, length, weight and capacity. Year 1 children gain an understanding of fractions by finding a half and a quarter of shapes and numbers. The language developed around halves and quarters in this unit is useful when the children begin to think about position and direction. All the units taught within mathematics in Year 1 are completed in a practical way. Within each lesson, the children apply their practical strategies to answer questions to help develop their reasoning skills and also have extension and problem solving activities to extend their knowledge. The work completed in Year 1 is evidenced through photographs and the children’s written work in their maths books. Year 1 also has a 5 minute snappy maths lesson each day. We work on number bonds, counting in 2s, 5s and 10s, and the 2, 5 and 10 times tables.