Maths at Westwood Farm
Maths Leads: Miss Hunter and Miss Lewis
At Westwood Farm Schools, we follow the National Curriculum for Mathematics. We believe it is an essential life skill and our wish is that all children enjoy maths and become confident mathematicians who thrive on challenge.
The main strands in the programme of study for mathematics are number, measure, geometry and statistics. We follow the White Rose Maths small steps to plan the teaching and learning journey, focusing on three key principles: becoming fluent in the fundamentals of mathematics (quick recall of number facts and application of knowledge), reasoning mathematically (justify, generalise and explain why) and problem solving.
In doing this, we deepen children’s knowledge and understanding of mathematics. Our teaching and learning strategies are underpinned by the concrete pictorial and abstract teaching approach.
We teach mathematics using a mastery approach. This involves providing learning opportunities that help pupils develop a deep and secure knowledge and understanding of mathematics at each stage so that by the end of every school year or Key Stage, pupils will have acquired mastery of the mathematical facts and concepts they’ve been exposed to. In this way, they become equipped to move on confidently and securely to more advanced concepts. When taught to master mathematics, children develop their mathematical fluency without resorting to rote learning and are able to solve non-routine maths problems without having to memorise procedures. (A good example of developing mathematical fluency is ‘Table Mountain’, our schools-wide method for the teaching and learning of times tables (see parent section for more detail).
Each class moves through the content at the same pace and 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 challenge. Unlike the old model, where 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 White Rose programme allows children to make small steps to move through the following aspects of mathematical thinking:
Fluency - having number sense, understanding how numbers relate to each other, seeing how numbers can be split and put together in different ways and having knowledge of number facts and efficient methods to calculate.
Problem Solving - drawing on problem solving skills such as working systematically, trial and improvement, logical reasoning and spotting and exploring patterns. Problems often have multiple solutions.
Reasoning - thinking through mathematical problems logically and systematically and involves using and applying their mathematical knowledge to explain or justify a solution.
Alongside the White Rose sequence, the CPA approach is a highly effective in supporting children to develop a deep and sustainable understanding of maths. Developed by American psychologist Jerome Bruner, it is an essential technique within the Singapore method of teaching maths for mastery;
- Concrete – students should have the opportunity to use concrete objects and manipulatives to help them understand what they are doing.
- Pictorial – students should then build on this concrete approach by using pictorial representations. These representations can then be used to reason and solve problems.
- Abstract – with the foundations firmly laid, students should be able to move to an abstract approach using numbers and key concepts with confidence.
Concrete is the ‘doing’ stage. During this stage, students use concrete objects to model problems. This 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 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. 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. A Singapore-style of maths modelling, bar modelling is an essential maths mastery pictorial strategy as it allows pupils to draw and visualise mathematical concepts to solve problems.
Abstract is the ‘symbolic’ stage, where children use abstract symbols to model problems. Children will not progress to this stage until they have demonstrated that they have a solid understanding of the concrete and pictorial stages first. 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.