![]() 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. This will be expounded through two classroom vignettes. 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. ![]() 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. It begins at the concrete level when students physically act out a math problem, or use manipulatives such as blocks, toothpicks, fraction pieces, or other three-dimensional objects to model a mathematical relationship. Teaching multiplication and division can involve different graphical or pictorial representations that emphasize different aspects of the operations. Concrete, pictorial, abstract (CPA) is a highly effective approach to teaching that develops a deep and sustainable understanding of math for pupils. The CPA Approach is considered to be a multisensory mode of teaching. However, Ding and Carlson (2013) suggested that these experiences should be faded so that students transfer understanding to abstract tasks involving numbers and symbols. the use of the Concrete-Pictorial-Abstract Approach in 1.2 teaching mathematics. 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. Many folks are familiar with the Concrete-Pictorial-Abstract model of representation (seen below), or at least the idea behind it. Research on the Concrete-Pictorial-Abstract (CPA) Sequence Conceptual understanding of quantity follows a developmental sequence. The research topic selected is entitled The Concrete-Pictorial-Abstract (CPA) Approach. ![]() Multiple representations of knowledge and their connections are fundamental pedagogical considerations to enable students to develop conceptual understanding of mathematics. Concrete, pictorial, abstract (CPA) concepts should not be confused as differentiation for lower, middle, higher attaining children. ![]()
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