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Summary and extended reading

Here we provide some extended reading for the second week.
Student reading a book in a library
© University of Southampton

In Week 2 of the course you should have learned the following main points:

  1. Two key principles in Singaporean mathematics education are the Concrete-Pictorial-Abstract (CPA) approach and the Bar Model method.

  2. Both approaches are firmly rooted and evidenced in research.

  3. You will have seen examples of both CPA and the Bar Model method.


Some useful reading for this week is:

Week 2

Leong, Y. H., Ho, W. K., & Cheng, L. P. (2015). Concrete-Pictorial-Abstract: Surveying its origins and charting its future. The Mathematics Educator, 16(1), 1-19.

Kho, T. H., Yeo, S. M., & Fan, L. (2014). Model Method in Singapore primary mathematics textbooks. Paper presented at 2014 International Conference on Mathematics Textbook Research and Development. In Jones, K., Bokhove, C., Howson, G., & Fan, L. (Eds.), Proceedings of the International Conference on Mathematics Textbook Research and Development (ICMT-2014) (pp. 275-282). Southampton: University of Southampton, United Kingdom. The full proceedings are (page 275).


Kho, T. H. (1987). Mathematical models for solving arithmetic problems. In Proceedings of the 4th Southeast Asian Conference on Mathematics Education (pp. 345-351). Singapore.

Ng, S. F., & Lee, K. (2009). The model method: Singapore children’s tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education, 40(3), 282-313. Can read online for free by registering via JSTOR:

Next week

Next week, we will focus on other Asian mathematics teaching methods. We will particularly focus on the Two Basics from mainland China, and Variation theory, which is used a lot in Hong Kong.

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World Class Maths: Asian Teaching Methods

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