Using GeoGebra to act as the pictorial phase of the approach, this book is a. They will move backwards and forwards between the three throughout their teaching.įor a more detailed guide on the CPA model, use this link to an explanation for parents. Author: The GeoGebra Resource Work Group, part of the Central Maths Hub, are a small group of teachers, both primary and secondary, who have come together to design, create and trial resources to support using 'Concrete-Pictorial-Abstract' approaches in their teaching. Teachers make links between the concrete, pictorial and abstract to strengthen the children's understanding. This progression enables students to master concepts by stages. Jerome Bruner proposed that we should use three modes of representations when teaching mathematical concepts: 1.) Action Based (Concrete) 2.) Image-Based (Pictorial) 3. Using the Singapore math method, Saint Teresa Catholic Schoo l employs a Concrete, Pictorial, and Abstract (CPA) progression in mathematics instruction emphasizing number bonds, bar modeling, and mental math. We encourage all of the teachers in our Mathematics Initiative to teach all mathematical concepts through Concrete, Pictorial, and Abstract means. The final part of this process is moving to an abstract model, using numbers to show a calculation. Saint Theresa Catholic School, (Sugar Land, Texas). This may be children drawing 3 figures in a group and 2 figures in another group, showing that there are 5 altogether. This can be as simple as a young child learning about adding by taking 3 animal figures and a group of 2 animal figure and putting them together to show that there are 5.įrom this stage we move to pictorial models that support the understanding of this concept. The CPA approach is fundamental as it builds on children’s existing knowledge by introducing abstract concepts in a concrete and achievable way. Why is this important in childrens learning Children (and adults) can find maths difficult because it is abstract. It is known as the doing stage and involves physically manipulating objects to solve a math problem. C PA (concrete, pictorial, abstract) Approach. The first step is called the concrete stage. Concrete components including manipulative objects such as cake, measurement tools, or the other object can be used during learning and teaching process. CONCRETE PICTORIAL ABSTRACT (CPA) Concrete Pictorial Abstract (CPA) is a three step instructional approach that has been found to be highly effective in teaching math concepts. This system is rooted in allowing children to use apparatus to help them understand a concept. of concrete objects, 2) learning by representation of pictorial of concrete manipulation, and 3) solve the problem by mean an abstract notation (Witzell, 2005). Parents' Guide to Concrete, Pictorial, Abstract modelĪt LEH, we use the concrete, pictorial, abstract (CPA) model in our teaching of mathematical concepts.
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