The Concrete-Pictorial-Abstract approach

This video explains what the Concerete-Pictorial-Abstract (CPA) approach is. We will demonstrate it with some concrete examples.

CPA is the most prominent approach in the teaching of mathematics. It is not only a general principle guiding curriculum design and textbook development, but it also guides teachers’ classroom teaching.

CPA is designed to help students learn mathematics meaningfully. Under CPA approach, the students will be provided with:

1. firstly, the necessary learning experiences with the concrete materials
2. then pictorial representation of the mathematics concepts or methods
3. finally, the mathematical symbols/notations at the abstract stage.

CPA is widely used in primary mathematics classrooms in Singapore. But as a general pedagogical principle, it is also applicable for teaching mathematics at a higher level (particularly lower secondary level). As the next video will demonstrate, the CPA approach has strong roots in research, for example, from the psychologist Jerome Bruner. There is also more recent work in cognitive science on so-called ‘concreteness fading’, in which sequences of tasks are ‘faded’ from more concrete to abstract, via pictorial representations.