Maths at Crawford
In order to support our approach to teaching for Mastery of Mathematics, we use the White Rose Maths materials to support our planning and teaching.
These materials:
- Have number at their heart. A large proportion of time is spent reinforcing number to build competency.
- Ensure planning supports the ideal of depth of learning before breadth of learning.
- Provide plenty of opportunities to build reasoning and problem solving elements into the curriculum.
At Crawford Village, we believe it is important that children develop a deep understanding of the mathematical concepts they are learning. To support this, we have changed our teaching of maths, taking on the concrete, pictorial, abstract (CPA) approach. This is a highly effective approach to teaching that develops a deep and sustainable understanding of maths.
Concrete
Concrete is the “doing” stage, using concrete objects to model problems. Instead of the traditional method of m
aths teaching, where a teacher demonstrates how to solve a problem, the CPA approach brings concepts to life by allowing children to experience and handle physical objects themselves. Every new abstract concept is learned first with a “concrete” or physical experience.
For example, if a problem is about adding up four baskets of fruit , the children might first handle actual fruit before progressing to handling counters or cubes which are used to represent the fruit.
Pictorial
Pictorial is the “seeing” stage, using representations of the objects to model problems. This stage encourages 
children to make a mental connection between the physical object and abstract levels of understanding by drawing or looking at pictures, circles, diagrams or models which represent the objects in the problem.
Building or drawing a model makes it easier for children to grasp concepts they traditionally find more difficult, such as fractions, as it helps them visualise the problem and make it more accessible.
Abstract
Abstract is the “symbolic” stage, where children are able to use abstract symbols.
Only once a child has demonstrated that they have a solid understanding of the “concrete” and “pictorial” representations of the problem, can the teacher introduce the more “abstract” concept, such as 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.
Although above, CPA is shown as three distinct stages, our teachers will go back and forth between each representation to reinforce concepts.
A high priority is placed on times tables throughout the school and we make use of a number of resources to support this, including ‘Times Table Rockstars’, which is a carefully sequenced programme of daily times tables practice to help boost our pupils' recall speed.
National Curriculum Maths Programmes of Study