Numeracy
Concrete, Pictorial, Abstract Approach
One of the key learning principles behind mathematics teaching at Hollywood Primary School is the concrete, pictorial, abstract approach often referred to as CPA. This is a three step instructional process to teach mathematics concepts. This model develops pupils' mathematical ability and confidence making mathematics more engaging and interesting.
Concrete
The "doing" stage. During this stage, students use concrete objects to model problems. This approach brings concepts to life by allowing students to experience and handle concrete objects.
Pictorial
Pictorial is the "seeing" stage. Visual representations of concrete objects are used to model problems. This stage encourages children to make a mental connection between the physical object they handled and the abstract pictures, diagrams or models that represent the objects from the problem.
Abstract
Abstract is the symbolic stage where children use abstract symbols to model problems. Students will not progress to this stage until they have solid understanding of the concrete and pictorial stages. Children are introduced to the concept at a symbolic level using only numbers and mathematics symbols (+ - x /).
At our school we use Maths Trek as our whole school numeracy program from Foundation to Year 6. It gives every classroom a consistent, curriculum aligned approach to building mathematical understanding, fluency, reasoning and problem solving.
Maths Trek is built around an explicit teaching model of "I do, we do, you do." Teachers first model a concept, then work through examples together with students, before students apply their learning independently. This gradual release of responsibility is well supported by research as an effective way to build understanding and confidence.
Alongside this, our teachers draw on the Concrete, Pictorial, Abstract approach when introducing new concepts. Students first work with hands on materials, then move to visual representations such as diagrams, and finally to abstract symbols and notation. Moving through these stages helps children build genuine understanding before working with numbers alone, and it gives every learner an accessible entry point.