Saturday, July 18, 2009

Concrete Representations in Mathematics

My co-teacher asks me to e-mail you because she attended a conference in Manila, the Philippines in May 2009. What are the different processes in teaching concrete ideas in mathematics? Thank you so much.


I assume you are asking about the use of concrete representations to help students learn abstract mathematical ideas. This is the CPA Approach, as we call it in Singapore.

It is important to match the cognitive processes required in handling the abstract idea with the cognitive processes used in handling the concrete materials. For example, in doing addition within 20 (say, 7 + 5), one abstract ideas we want students to have is 'making 10'. Students should be able to visualize that 7 + 5 is the same as 10 + 2 (making 10 from 7 by moving 3 from 5). A suitable concrete activity is to use tens frame. Use two tens frames - one with 7 counters and another with 5 counters. Then get students to move 3 counters from the second frame to the first. The cognitive processes match.

The photograph shows tens frame made by public school teachers involved in the LEAP Project in the Philippines (December 2008, Ateneo de Manila University).

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