St Michael's Academy

In order to support our approach to teaching for Mastery of Mathematics, we use 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 St Michael’s we believe it is important that children develop understanding of mathematical concepts they are learning.  Therefore, for the last two years in school we have changed our teaching of maths, taking on the Concrete, Pictorial, Abstract approach (CPA) 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 maths teaching, where a teacher demonstrates how to solve a problem, the CPA approach brings the concepts to life by allowing the 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 the actual fruit before progressing to handling counters or cubes which are used to represent 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 a 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 to all.

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, subtraction, multiplication, division, greater than or less than.

In order to further embed problem solving and reasoning all year groups hold weekly guided sessions (small group). 

During these sessions, the teacher works with focus groups on developing their problem solving and reasoning skills through communication, variation and discussion of different mathematical approaches. Other children can revisit prior learning, work on developing fluency skills and automaticity.

We feel it is important that we listen to the feedback of children at St Michael’s and they are very positive about their maths lessons.

“I love working with the resources because I used to find maths hard, but now I can do it.  I actually understand!”

“I like it when my teacher gives me tricky sums because I can show off and use expanded form.”

“I didn’t really like Maths when I started SMA but now I love it because I can jot my ideas on the table and if I get it wrong, I just rub it off and start again using dienes.”