Saturday, March 6, 2010

A Singaporean's perspective on Singapore Math

I just came across an online article by a Singaporean named Justin Lee, the founder of two education businesses in Singapore.  In reaction to many articles "fussing about Singapore Math on the Internet," Lee writes: 

While many authors bemoaned or even whined about the difficulty American kids had with Math, it made me at times sympathetic or even amused. You see, Math in Singapore was highly enjoyable in my time and we dreaded other subjects like English and Science instead. Why is this so?
One reason, Lee points out, is that, for about 50% of the Singaporean population, English is not the native language.  As a result:
Math in primary school (for 7-12 year olds) was one of the easiest subjects to ace. It did not involve language application as extensively as Science. Although the word problems in Math papers still involved the English language, it required us only to write one-liners as conclusions. Many friends of my age then scored above 80 marks out of a 100 in Math on a regular basis. Being able to score so highly in Math (as opposed to barely passing English or Science) easily made Math our favourite subject in school!
This, of course, makes me think of all the language impaired math buffs who suffer under Reform Math's much more language-intensive "story problems" and verbal explanations requirements.

Lee goes on to lament a development in Singapore that is taking math standards in Singapore in the opposite direction as that which American math standards have followed.  Apparently, "there has been a rising trend of schools setting impossible-to-pass Math tests and examinations in the late 2000s." Instead of parents being upset that standards are too low, Singapore parents are upset that standards, which have long been higher than ours, have now risen too high.

Lee proceeds to describe how he and his classmates found Singapore math to be easy and enjoyable, with plenty of time left over for fun:
It is true that the Mathematical concepts are built year upon year and concepts that have been taught are not taught again, but merely revisited briefly. This is as opposed to the slightly incoherent system in the US, where kids can sometimes wonder why they are doing the same things again. While this arrangement may appear to be harder on Singapore students, I actually felt it was very easy on us. In fact, we felt that it was a gift from heaven to be able to do fractions at primary 6 again, right after we learnt something similar the year before.
It might appear as though a Singapore student would have had to spend many hours poring their beady eyes other Math textbooks and Math problems to acquire such ‘astounding’ proficiency in the subject. The truth is, the pace of learning was rather fine. I could do quite well in school without having to attend extra lessons (tuitions), and school only lasted from 730am to 1pm, Monday to Friday. There was still ample time for monkey business after 1pm.
To sum up, I am positive that Math in primary school was enjoyable for most students in the 1990s. This may not be so after internal Math examination standards were revised upwards in the late 2000s, but we shall address this issue in another article.
I look forward to more!  In our self-absorbed, American-exceptionalist country, the Singaporean perspective, which should be a key element in the debate over math reform, is all too often overlooked.


Anonymous said...

One person's perspective is not "the Singaporean" perspective. For the primary level, I didn't see much increase in standards in their new standards compared to the old ones. Now they even include calculator use which they did not earlier. Also, it would be interesting to see exactly how their tests have changed. I read on a Singapore blog: "Logically, with the use of calculators being allowed, computation is no longer the skill being assessed. The examiners is more interested in how students make use of a computation to solve a problem. In other words, in some problems, a computation is necessary but not sufficient to obtain a solution.
The examiners are also able to use authentic information which often results in tedious computation not easily done mentally in the problems. With calculators the issue of tedious computation is non-existent." So more "real world" push earlier before they have cemented the basic skills. My impression from supplementary books that they use in tuition is that they have added more questions that do not have one answer, and more that need to be answered by guess and check. More of the pattern recognition and puzzle type of "critical thinking" type problems that they have not been taught the math involved but is not being called problem solving. I have seen a lot of discrete math types of problems that could be solved with a formula but since they haven't studied the topic they need to use trial and error. I saw on another blog ideas on how to do trial and error faster to get through the test. The problem could have been easily and quickly solved without trial and error. What I really liked about the original math is that students were taught skills so they did not have to do trial and error. The bar models allowed them to solve problems that students who have not learned formal algebra would have to use trial and error. Now they are putting other topics in that come from more advanced math but not teaching them. Their students are apparently good at computation, but need to become critical thinkers in math. Like with reform math.

Anonymous said...

Here are some problems from one of their tuition books:

12. Use a calculator to find these, then predict what the next in the
pattern will be when your calculator display is not big enough.
11 × 11
111 × 111
1111 × 1111

Worked Example 2
If the key is disabled, how would you find the value of
176 ÷ 4? How would other key operations guide you to a solution?
Answers vary.
Worked Example 1
Three birds eat a total of 15 nuts.
Each bird eats an odd number of nuts.
Each bird eats more than one nut, and no two birds
eat the same number of nuts.
How many nuts does each bird eat?
How many different solutions are there?
9. There are 4 routes from town A to town B, and 3 routes from town B to
town C. Jason plans to travel from town A to town C. How many
different routes can be take between the two towns?
(From what I remember of my college classes, this is a discrete math type of problem.)
Worked Example 1
The sum of all the digits of a 4-digit number is 16.
The digit in the ones place is equal to the digit in the thousands place.
The digit in the thousands place is twice the digit in the hundreds place.
What is the digit number?
Let’s tabulate the possible combinations, then use elimination.
The 6th grade tuition book had all kinds of problems involving prime factorization, but their official syllabus does not have that as a topic. Maybe the book just had them to get students to think, but if their tests really do include topics that are not on the syllabus or in the textbooks yet, that would upset parents and require the extra tuition. Some of the problems were quite challenging. From a 6th grade tuition book:
6. There are 9 × 8 × 7 × … × 3 × 2 × 1 = 362 880 different ways of
forming a nine-digit number using the digits 1 to 9 exactly once. What
percentage of these are prime numbers, correct to the nearest 1%?
Ans: 0%.
The sum of the digits of any of the 9-digit number formed is 1 + 2 + 3 + … + 9 = 45, which is
divisible by 9. Thus the number is always divisible by 9. Hence none of the numbers are prime.
But if prime numbers are not part of the syllabus, it is even more challenging.
Worked Example 1
There are 5 children around a table. They are Ann, Beth,
Corine, Denise and Ethel. Mr Jones has 33 sweets. She
passes them around the table until they are all taken up.
Ann gets the first sweet, Beth gets the second sweet,
and so on. Who gets the 33rd sweet?

Mrs. C said...

I had to laugh. SOME of the problems in SM are worded oddly, as in, "Sean had six pots of plant" instead of "potted plants" or the like.

And here this fella is talking about kids getting up to "monkey business" after 1 p.m. :)

Well, I like SM well enough, but don't like the direction our country is taking with a standardised national curriculum. It doesn't even matter what curriculum standards are chosen; the whole idea is scary.