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## Macmillan Education

Skip to 0 minutes and 0 seconds CPA stands for Concrete, Pictorial and Abstract. It is the most prominent approach in the teaching of Mathematics in Singapore classrooms. It is used not only as a general principle guiding the curriculum design in textbook development, but also as a general principle guiding the teachers classroom teaching. CPA is designed to help students learn mathematics meaningfully and a CPA approach the students will be first provided with the necessary learning experiences, with the concrete materials and then with a pictorial presentation of the mathematics concepts or methods and finally it is followed by the mathematics symbols, notations at the abstract stages. That’s why it’s called CPA.

Skip to 1 minute and 7 seconds The CPA approach is particularly widely used in primary mathematics classrooms in Singapore, but as a general pedagogical principle it’s also applicable for teaching mathematics at a higher level. Particularly lower secondary level. Dr. Bokhove will explain some research and theoretical background about the CPA later; here I just show you one concrete example. To introduce how to add two 1 digit numbers 6 + 9 to lower primary school students.

Skip to 1 minute and 52 seconds So at the concrete stage we will use Lego to let us do hands-on activity that is putting six pieces and nine pieces of Legos together and then students will count them one by one and they will find the answer 15 pieces; So under the pictorial stage we will use a pictorial representation to represent numbers 6 and 9 so the students can still count how many ones are there all together And they will get the answer 15. The final stage is the abstract stage. In this stage we ask students to use numeral symbols to write the number sentences. That is here; it’s 6 plus 9 equals 15

# 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.
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