![]() At this stage, the teacher introduces the abstract concept (for example, arithmetic symbols). ![]() Students do not move forward to this step until demonstrate a solid conceptual understanding of the concrete and pictorial phases of the problem. The abstract steps make the symbolic level of CPA stages, where students model problems using abstract symbols. What is the Abstract Stage of the CPA approach? An example of the pictorial step is using the bar model where bars represent the unknown and known quantities in more complex multi-step problem-solving. In absence of pictorial representation, children may find it difficult to visualise a problem.ĭrawing or developing a model makes it easier for the students to understand complex mathematical and conceptual concepts (for instance, adding mixed numbers). Some mathematics teachers tend to leave this step out, but visual recording is crucial to ensuring that students can make the connection between a physical resource and abstract notation. While benefiting from pictorial representation, students would no longer manipulate the physical objects, but still take advantage of the pictorial support the resources may provide. Once students understood a maths concept using real objects, students may proceed with drawing quick sketches or visual representations of the objects. This step of CPA method motivates children to make a direct connection between the concrete object they just dealt with and the visual representation, models or diagrams that represent the problem. In this stage, problems are modelled using the visual representation of a physical object. What is the Pictorial Stage of the CPA approach? It involves shifting from concrete materials, to pictorial representations, and then towards abstract concepts and symbols. The distinct stages of the CPA approach to teaching builds on children’s current understanding by instructing abstract concepts using tangible and concrete methods. Many children find mathematics hard because it is abstract.
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