Mathematics is an essential life skill and at Joseph Cash School children know the importance of mathematics in the classroom and in their everyday life.
What does a Math's lesson look like?
Mathematics lessons begin with a Math's MOT,' which is a daily focus on basic skills. The main part of each lesson is designed to be interactive with a significant emphasis on children's talk “ collaborative talk and talk partners. Through discussing their ideas, children construct new understanding, engage in a supportive community of practice, take responsibility for their learning and allow the teacher a window into their thinking which enables appropriate action to help them progress. Fluency, reasoning and problem solving are the three main themes of the Mathematics National Curriculum (DfE, 2014), and inform all mathematics teaching at Joseph Cash Primary School.
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'Maths No Problem' programme (Years 1 to 5)
Children in Year 1 and 5 learn Math's through the 'Maths No Problem' programme which focuses on teaching for mastery.
Teaching maths for mastery is a transformational approach to maths teaching which stems from high performing Asian nations such as Singapore. When taught to master maths, children develop their mathematical fluency without resorting to rote learning and are able to solve non-routine maths problems without having to memorise procedures.
Teaching for maths mastery is the basis for the 2014 National Curriculum for maths. Each class moves through the content at the same pace, each topic is studied in depth until the children demonstrate that they have a secure understanding of mathematical concepts. This allows children time to think deeply about the maths and really understand concepts at a relational level rather than a set of rules or procedures.
This inclusive approach allows all children to build self-confidence in maths, and its emphasis on promoting multiple methods of solving a problem builds resilience in pupils. Though the whole class goes through the same content at the same pace, there is still plenty of opportunity for differentiation. For example, advanced learners are accelerated through new content, those pupils who grasp concepts quickly are challenged with rich and sophisticated problems within the topic. Those children who are not sufficiently fluent are provided additional support to consolidate their understanding before moving on.
The 'Math's No Problem' approach focusses on developing children's understanding of concept's through the
Concrete, Pictorial, Abstract approach.
Concrete, Pictorial, Abstract
Concrete, pictorial, abstract (CPA) is a highly effective approach to teaching that develops a deep and sustainable understanding of maths in pupils. It is an essential technique within the Singapore method of teaching maths for mastery.
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. For example, if a problem involves adding pieces of fruit, children can first handle actual fruit. From there, they can progress to handling abstract counters or cubes which represent the fruit.
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. Bar modelling is an essential maths mastery pictorial strategy. A Singapore-style of maths model, bar modelling allows pupils to draw and visualize mathematical concepts to solve problems.
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, +, â€“, x, /) to indicate addition, multiplication or division.