Mathematics -- Singapore Approach using Modeling Method

"Mary has one pen. Her mother gives her two more. How many pens does Mary have?"

When I looked at the question above, I always wondered why the teacher never asked like this? 1 + 2 = ? Now... consider these primary one questions.

1) There are 10 chickens and cows in a farm. John counted 32 legs in total. How many chicken are there in the farm?

2) Mary gives 120 apples to Tom and Tim such that Tom has 10 apples more than Tim. How many apples does Tom get?

3) Complete the number sequence : 1, 1, 3,4,5,7,?,?,9,13. What are the two missing numbers?

These questions were our secondary school questions (during our time 20-30yrs ago), weren't they? I was taught to use algebra, to form mathematical equations to solve these problems. At that time, it did not matter to me whether I understood or not, as long as I got the equation right, I could produce an answer to score marks.

Mathematics in Singapore today is very different. The question is no longer routine and needs a lot of analysis. I think you will agree by looking at those questions I posted above. More importantly, I like the modeling approach adopted in Singapore Mathematics teaching. The purpose of this posting is to introduce the modeling approach. If you want to know more about Singapore's method using modeling approach, the following book is relevant. The price is SGD28.80. This is a little bit expensive to me as I am interested in only a few portions of the book. I found this book from a nearby library.



The modeling method starts with simple questions, however, pictures are drawn to model the question so that children can visualize the problem. Look at my note below...

You can see that the pictures are later replaced with the two "bars" to represent the numbers. Please do not under estimate the effect of drawing those "bars"... Please take a look at the following question that I selected and observe how those bars are used to visualize the problem.... (oh)... as well as the answers.

Can you see that the bars are drawn to deduce that 3 units equal to 24? If you are not convinced? Ok, how about this question (a lower secondary school question). The book has shown how the modeling method can be applied to solve this question.

My son is interested in Mathematics. He tried to read the book and persuaded me to teach him. After learning the tricks, he even brought the questions to discuss with one of his good friends in school. Why? I think he loves "seeing" the answer.

This is the type of mathematic education I want for my kids. The contents is interesting and useful. Most importantly, it is none routine and focus on understanding. This is a piece of good work by Singapore's educator. Wonderful work, isn't it? I really salute them and thank them for the efforts to improve teaching of mathematics.