![]() ![]() Other people might say it as Concrete Pictorial to Abstract, so you might also hear it as CPA. The first vignette will illustrate the use of concrete manipulatives for teaching the concept of equivalent fractions while the second vignette will exemplify the use of concrete experiences, in the form of children’s literature, to empower students to discover the concept of odd and even numbers. I always call it C-R-A, it’s just easier to say. This sequence is evident in both the National Syllabus and varied textbooks adopted in schools. It is an essential technique within the Singapore method of teaching maths for mastery. The Concrete-Pictorial-Abstract (C-P-A) sequence is the key instructional strategy for the development of primary mathematics concepts in Singapore (MOE, 2007, 2012). Often referred to as the concrete, representational, abstract framework, CPA was developed by American psychologist Jerome Bruner. This will be expounded through two classroom vignettes. Concrete, Pictorial, Abstract (CPA) is a highly effective approach to teaching that develops a deep and sustainable understanding of maths in pupils. We will discuss the enactive, iconic and symbolic modes of representations (Bruner, 1966) and multiple embodiment principle (Dienes, 1971) as our theoretical underpinnings for the C-P-A approach. Concrete manipulatives are fundamental to the powerful Concrete-Pictorial-Abstract (CPA) approach and are a key resource in developing a deep understanding. In this approach, teachers provide students with opportunity to interact with concrete manipulatives or concrete experiences to construct meanings and connect this learning experience with the pictorial and abstract representations of the mathematics concepts. Concrete Pictorial Abstract approach Concrete representation The children are first introduced to an idea or a skill by acting it out with real objects. The Concrete Pictorial Abstract (CPA) approach is a system of learning that uses physical and visual aids to build a childs understanding of abstract topics. To facilitate students to build their understanding of abstract mathematical concepts from meaningful contexts and relevant everyday experiences, the Concrete-Pictorial-Abstract (C-P-A) approach is widely used in Singapore, especially at the primary level. She discusses the benefits of this approach to achie. Multiple representations of knowledge and their connections are fundamental pedagogical considerations to enable students to develop conceptual understanding of mathematics. Professor Berinderjeet Kaur introduces the concrete-pictorial-abstract (CPA) approach to teaching Maths.
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