White Rose Maths

Our Intent

Maths is a journey from which many start at different places. At Howden Juniors, our intention is that children foster a love of mathematical learning, whatever their ability or starting place and that they are able to confidently use and apply mathematical concepts across a variety of situations. We expect children to clearly articulate their ideas and thoughts and reasoning processes, enabling deeper learning. We expect children to make mistakes, analyse them and learn from them, justifying and explaining as they do this. At each stage of learning, children should be able to demonstrate a deep, conceptual understanding of the topic and be able to build on this over time.

We aim to provide all pupils with some direct teaching every day, which is oral, interactive and stimulating. Teaching styles and lesson structure provide opportunities for pupils to consolidate their previous learning, use and apply their knowledge, understanding and skills, pose and ask questions, investigate mathematical ideas, reflect on their own learning and make links with other work.  A typical lesson will comprise of a ‘Get Ready’ and Let’s Learn activity followed by independent work using the ‘White Rose’ workbook where appropriate.

Implementation – What does Maths look like at HJS?

 Mastery Curriculum

At Howden Junior School, we follow a Mastery for Maths curriculum using White Rose Maths Hub resources and work books.  This means that children are not streamed by ability because we expect all children to be given the opportunity to achieve age related expectations.  Mastery teaching provides our children with the time to acquire a deep and transferable understanding of mathematical concepts. We appreciate how important it is for our children to become fluent in all aspects of calculation, therefore, one session per week must be dedicated to practicing arithmetic/times tables through a given test.

Introducing the concept

New concepts should always be introduced with a link back to objectives covered previously.  Children should be given many opportunities to make links between embedded and new learning.  Scaffolds (such as new vocabulary and representations should be included on the Maths Working Wall)

Sequence of learning

Concrete, pictorial, abstract (CPA) is a highly effective approach to teaching that develops a deep and sustainable understanding of maths in pupils.

The Concrete Step of CPA

Concrete is the “doing” stage. During this stage, children 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. 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.  

The Pictorial Step of CPA

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.

The Abstract step of CPA

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 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, subtraction, multiplication or division.

Although CPA is understood as three distinct stages, a skilled teacher will go back and forth between each stage to reinforce concepts.

Impact

•  Learners who can clearly explain their reasoning and justify their thought processes
•  Quick recall of facts and procedures
•  The flexibility and fluidity to move between different contexts and representations of     mathematics.
•  The ability to recognise relationships and make connections in mathematics.
•  Happy, confident, articulate and autonomous learners with a life-long passion for learning

A mathematical concept or skill has been mastered when a child can show it in multiple ways, using the mathematical language to explain their ideas, and can independently apply the concept to new problems in unfamiliar situations.