It is a three-stage learning process where students learn through physical manipulation of concrete objects, followed by learning through pictorial. As the childs experience and confidence grows, they may no longer need physical objects to actually move around. The idea was developed by Jerome Bruner in 1960. Once we believe our pupils have mastered maths concepts through using concrete and pictorial resources we move into the abstract.Įven when working abstractly in maths our pupils always have access to concrete and pictorial resources to support them. The Concrete-Pictorial-Abstract (CPA) is also referred to as Concrete-Representational-Abstract (CRA) or Concrete-Semi Concrete-Abstract (CSA). It includes pictures and diagrams of resources that our pupils are familiar with and are sometimes included in the Fact Files that we provide as part of Additional Learning. The pictorial aspect of this model is a vital step for enabling all our pupils to move from concrete maths to abstract maths. Please see the document below (Concrete Resources) that details some of the resources we use as part of our everyday teaching of mathematics at Stony Dean.Īs our pupils gain understanding of a concept through using concrete materials they move into using pictorial resources to support them moving away from using concrete resources. The purpose of teaching through a concrete-to-representational-to-abstract sequence of instruction is to ensure students develop a tangible understanding of. Fundamental to the powerful Concrete-Pictorial-Abstract (CPA) approach, concrete manipulatives are a key. We use a range of concrete resources in teaching all areas of mathematics but specifically with reference to number work. Select View more for an accompanying video. This is to make the concepts being taught real to our pupils so they can make sense of the maths rather than dealing with ideas that are abstract. The psychologist believes that the abstract nature of learning (and this is especially true in mathematics. It was first proposed by Jerome Bruner in 1966 as a means of scaffolding learning. When starting a new concept whatever the year group or ability of our pupils we use concrete apparatus. One of the most fundamental learning theories to be implemented within any mastery classroom is the ‘CPA’ (Concrete, Pictorial, and Abstract) approach. For example, even when a pupil has worked out the answer using an abstract method, we may ask them to use concrete manipulatives to convince others that they are correct. This model is not linear, we use a cyclical approach. We believe if our pupils fully understand the concept they are learning and keep revisiting it, then they will be able to apply the maths independently in the future. It is about giving our pupils the tools to understand the maths that they are focusing on. This approach is not about getting the answer quickly or teaching quick fix ‘tricks’. We use this approach to enable our pupils to fully understand and master the maths concepts that we are teaching. The Concrete, Pictorial and Abstract (CPA) Model of learning is one that fully encompasses the way we teach mathematics at Stony Dean.

Concrete pictorial abstract