At Oulton First School it is our intent that we provide every child with a rich and meaningful mathematics education. We aim to develop a love of maths learning and create confident and accomplished mathematicians. We have a number of key objectives for our children:
- To become fluent in the fundamentals of number
- To have strong conceptual understanding
- To become confident in reasoning and solving problems
- To build their knowledge as they progress through school and with new learning
- To be confident retrieving prior learning which is essential in securing deep conceptual understanding
Our curriculum map is based on the White Rose mastery scheme of work. However, teachers have the flexibility to decide how long they focus on different concepts depending on their own formative assessment. The long term plans show that number is at the heart of learning to ensure competency. Teachers are also encouraged to give pupils the opportunity to practice gaining confidence and fluency with topics adding additional lessons where required or moving on to application or problem solving and reasoning.
At Oulton, maths progression is cumulative where children build their understanding from previous year groups. Using progression maps, teachers become aware of previous stages of learning and the next steps meaning that assessing the prerequisite understanding for each topic is used regularly. In addition, differentiation through scaffolding is used where required using these progression maps taken from White Rose and the NCETM.
At Oulton, we use the CPA approach (Concrete-pictorial-abstract). This approach ensures children’s conceptual understanding and fluency is strengthened if they experience concrete, visual and abstract representations of a concept during a lesson. Moving between the concrete and the abstract helps children to connect abstract symbols with familiar contexts. Bar models, PPW (part, part, whole) and other pictorial representations are used at the same time. We deliver a mastery approach which ensures that depth before breadth is delivered to ensure children do not move on until they have mastered a concept. Pupils move through each lesson as a whole group.
Each maths lesson at Oulton beings with daily retrieval practice. KS1 and KS2 use the White Rose FB4 (flashback 4) which is a series of quick questions covering something from the previous lesson, previous week and topics from earlier in the year. The start of the lesson may also incorporate some true or false questions and fluency practice such as times tables and number bonds.
The lesson is then based on the following structure:
- Clear modelling of new learning
- Shared practice
- Independent work including fluency, reasoning and problem solving practice.
Teachers use the White Rose teaching slides and resources and in KS1 and KS2 the workbooks. In addition to this, the NCETM mastery and greater depth questions are used to promote additional challenge. Throughout the lesson, teachers are able to assess pupils’ knowledge and understanding, address any misconceptions and ensure the correct mathematical vocabulary is being used.
Confidence and fluency in key instant recall facts (KIRFS) are developed in all keystages, both at school and for home learning, using online learning programmes such as TTRockstars, Numbots, White Rose 1 minute maths and timestables.co.uk. Once a week, pupils in KS2 are given a times tables test.
Interventions are provided for those pupils that require additional support.
The teaching of mathematics at Oulton First School ensures that skills, knowledge and understanding are built up year upon year and gives pupils the opportunity to apply their skills and knowledge in different real life situations. Skills are applied cross-curricular, such as creating a pictogram in science when observing mini-beasts. Through our maths curriculum the children develop as confident mathematicians who have a positive approach to learning maths and who gain a sense of achievement as they progress through each year. Ultimately pupils are provided with mathematical skills they can build on in their next stage of education.
What is mastery in maths?
Maths mastery is a teaching and learning approach that aims for pupils to develop deep understanding of maths rather than being able to memorise key procedures or resort to rote learning.
The end goal and expectation is for all pupils (with very limited exceptions) to have acquired the fundamental facts and concepts of maths for their year or key stage such that by the end of it they have achieved mastery in the maths they have been taught. At this point they are ready to move confidently on to their next stage of maths.
What is the CPA approach?
Children and adults can find maths difficult because it is abstract. The CPA approach helps children learn new ideas and build on their existing knowledge by introducing abstract concepts in a more familiar and tangible way.
C - Concrete
Concrete is the “doing” stage, using concrete objects to model problems. Instead of the traditional method of maths 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.
P - Pictoral
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.
A - Abstract
Abstract is the “symbolic” stage, where children are able to use abstract symbols to model problems.
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 we’ve presented CPA as three distinct stages, a skilled teacher will go back and forth between each representation to reinforce concepts.
Our approach encourages teachers to vary the apparatus the children use in class, for example, one day they might use counters, another day they might use a ten frame. Likewise, children are encouraged to represent the day’s maths problem in a variety of ways, for example, drawing an array, a number bond diagram or a bar model. By systematically varying the apparatus and methods they use to solve a problem, we help children to make quicker mental connections between the concrete, pictorial and abstract phases.
When teaching young children, exposing to abstract concepts too early may mean that children are missing out on the opportunity to build the conceptual mathematical understanding which they need to take them through their education. However, it should never be a case of concrete ‘good’, abstract ‘bad’. It is important to recognise that the CPA model is a progression. By the end of KS1, children need to be able to go beyond the use of concrete equipment to access learning using either pictorial representations or abstract understanding. What is important, therefore, is that all learners, however young, can see the connections between each representation.
Our calculation policy is currently being reviewed.
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