## Thursday, June 23, 2011

### Singapore Method

Estimado Dr. Yeap Ban Har: Desde la Región de La Araucanía en el sur de Chile, reciba un cordial saludo. Soy profesora de matemática y me gustaría saber los orígenes del Método Singapur para la enseñanza de las matemáticas, cuál es su filosofía, que está a la base del método, aquí en Chile sólo nos han capacitado en la forma y no más allá, necesito mayor sustento teórico para poder empoderarme y transmitirlo de la misma forma a mis estudiantes. Agradeceria me informara acerca de lo que me inquieta.

Mirhna, a mathematics teacher in Chile

The Singapore mathematics curriculum was introduced in 1992. One of its features is the CPA Approach which is based on Jerome Bruner's idea of representations. Bar model is used extensively in Singapore textbooks. The curriculum was developed in the late 1980s based on research and writings from around the world especially the US and UK. Our teachers are taught learning theories by Bruner, Skemp, and Dienes as well as ideas by Polya.

## Wednesday, June 8, 2011

### Durian Puffs

Here is a Primary problem which is from Primary 1 SA1 Paper 2 2011 from an unknown school. (Note: The mother who asked the question has since written back to say that it was not from an SA but from one of the continual assessment tools the school uses as part of its holistic assessment - it is called semestral review in this school. Also that she has mistakenly mention it is Paper 2.)

Question:
Mother has baked some cream puffs and durian puffs. She wants to put 8 puffs into a box. In how many ways can she put the puffs in order to have at least one of each kind of puffs in the box?

Is this a problem that can be solved by the bar 'model' method or some other way? What is its test objective?

How to solve by the 'model' method, or whatever method? Sorry, but I find this problem at Primary 1 really very tough, leh!

A Mother in Singapore

I am really not sure if you have got it right but this may not be a Primary 1 problem for these reasons:
(1) Schools generally no longer conducts SA1 at Primary 1 - that is the MOE guideline. Fornon-Singapore readers, SA1 is a semestral assessment after half a school year. It tends to be a written examination. MOE Singapore has suggested that children entering the first year of formal schooling should not be subjected to such assessment. Alternative assessment modes which may includes 'small' test at the end of units may be used.
(2) I have never heard of any school that has Paper 1 and Paper 2 in Primary 1. Paper 1 and paper 2 format tends to be for upper primary (P5 and P6) with Paper 2 allowing the use of calculators.

Note: It has since been established that it is a task used as part of a continual assessment that the school used. The person who asked the question has also clarified that she has mistakenly mentioned that it was from Paper 2.)

But it can be a Primary 1 problem because the content is from Chapter 2 (Number Bonds).

One way to solve the problem is to make a list - 1 cream puff + 7 durian puffs, 2 + 6, 3 + 5, 4 + 4, 5 + 3, 6 + 2, 7 + 1 (0 + 8 and 8 + 0 are out. You know why.). Thus there are 7 ways.

Bar model is not suitable. Rememmber that there are many ways to solve problems and model is only one such method. The objective of this item is to assess ability to solve an unusual problem.