![]() 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. And, the mathematical symbols at the abstract stage.ĬPA is widely used to teach mathematics to primary school students in Singapore (hence it's association with this area).īut, as a general teaching principle, it is also used to teach mathematics in secondary schools (especially in lower secondary classrooms).the visual representations of the mathematical concepts or techniques.the essential learning experiences using the concrete materials.Under the CPA approach, the learners will be taught by providing: Why use the Concrete Pictorial Abstract approach to teach Maths?ĬPA is developed to help learners understand mathematics meaningfully. In this article we will unpick CPA and also link you to other research areas related to this strategy. The block models are effectively a projection of the students thinking, they are manipulating and viewing their cognition, a powerful form of assessment for learning in any learning situation. The visual stimulus enables learners to build a visual representation of the content they are studying. The block building method that we regularly use to help children understand new classroom ideas can be applied across subjects and year groups. Our research has also shown us that this teaching approach shouldn't be limited to just Maths. ![]() Learners need to be able to explore the problem using multi sensory approaches. Many of the concepts children encounter within the curriculum are too abstract to fully understand during their early exposure. Through our work with schools, we have seen first hand how physical experiences can shape thinking. CPA approach is a crucial strategy to teach maths for mastery in Singapore. Often marked as the concrete, representational, abstract framework, CPA was first proposed by the American psychologist Jerome Bruner. What is a Concrete Pictorial Abstract approach?Ĭoncrete, Pictorial, Abstract (CPA) is an effective method for teaching that offers a sustainable and deep understanding of maths to the students. ![]()
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