Going back to school for maths
I was prompted to write another math post after all the strong reactions to my math challenge. First let me state, there are many areas of our education system that I'm critical about but one thing I've never doubted is the quality of Singapore's maths education. What I love about it is it really teaches understanding of concepts.
I never used to understand this - when I was back in school, my mother would ask me, "Do you understand the concepts?" and I would say impatiently, "yes, yes, of course." But I didn't, not really. You see, I knew all the formulae, like Area of Rectangle = Length x Breadth, Distance = Speed x Time, etc but they were just formulae to be executed, I never got the real meaning behind those formulae.
A case in point: Adeline was recounting how when she saw the sum ½ ÷ 1/4, she tried to teach her son the "inversion" method, ie flip the 1/4 and change the sign to "x", so you get ½ x 4/1 = 2. That's the way we were taught in school some 20 (ok, ok, closer to 30!!) years ago. But she couldn't explain it to her son and we didn't really GET the meaning behind the answer, until Lilian's son Brian explained, "well, 2 quarters go into half, that's why the answer is 2." Doh!
I'm confident that the Singapore education system is laying a very strong foundation in maths because having undergone the primary math curriculum for six years with Lesley-Anne, I can see how it systematically reinforces the understanding of math concepts, first in solid, tangible methods before moving into abstract forms. Maths in Singapore doesn't teach blind application of formulae to narrowly defined, topical questions. Eg. it used to be that if you came across a question with a circle, you just need to apply one of the formulae for circles and you should be able to find the answer.
These days, a question may feature a pie chart but involves your application of knowledge not just of pie charts but maybe also of circles, percentages, fractions and algebra. Which is very reflective of maths in real life - afterall nothing ever falls neatly in pre-determined categories! And that is the reason why many Singaporean parents find their kids' maths so difficult even at the lower primary levels. It's not that we're dumb or bad at maths, we were just never taught that way!
Many parents, being unable to solve their kids' maths problems (let alone teach it), immediately dismiss the subject as too difficult and call for a tutor. I would like to suggest an alternative solution that is quite straightforward. The catch is that it may not be too palatable for parents - we need to re-learn our maths. Before you groan, let me tell you why: I find that when parents embark on the learning process together with their kids, their kids often are more motivated to work. Never say you're too old - it's doable!
Let me share my experience with Lesley-Anne thus far and hopefully this will encourage you. I never attended a single math workshop and my kids never had math tuition. I was one of those stubborn and tidak apah types who only bothered to find out more about a topic if my kids didn't understand something. I naively thought, "This is primary school maths! How hard can it be??" Until Lesley-Anne hit p3 and was stumped by a question that required models in an exam paper. I knew nothing about models then. When I saw the sum, I was indignant. "Siao! Expect 9-year-olds to solve this kind of question!" I still remember complaining to Lilian when she happened to come back to Singapore for a visit. I showed her the paper expecting sympathetic horror but she said calmly, "oh, this one needs models." (Lilian, I don't know if you remember this!) I was like whaaa..tt?
From there, I looked up model drawing in assessment books and I fell in love with the ingenuity of it. It introduced me to a whole new way of visualising maths problems that I never knew existed. So that was the start. From then on, I would always keep one topic ahead of whatever Lesley-Anne was learning in school by referring to her My Pals Are Here math textbooks and understanding how it's taught (usually very simply yet brilliantly). Consistently, I found that it emphasised understanding of concepts, using meaningful drawings. New topics start from the basics and more complex ones build on topics previously taught in a logical manner. Qualifier: I'm referring only to mainstream maths. I never bothered with topics under the GEP maths syllabus.
However, the textbooks cover only the straightforward and foundational stuff. Often, in assessment books or exam papers of top schools, you will find the questions are much tougher. These are the ones that usually cause much angst in parents. To be able to solve these problems, you need PRACTICE. No two ways about it, sorry. Once the net is cast open for maths questions to involve applications of multiple concepts, there are just too many computations and permutations, you cannot possibly learn ALL the possible ways of solving them by rote. The only way is to ground yourself so firmly in the principles that you are able to manipulate them in different ways to solve the problem. That's what our kids are taught. And they're made to practise. A LOT.
I haven't got it down pat. As you can tell from my less than stellar score in the Nanyang prelim paper, I still have lots to learn. But you know, I'm enjoying it. Once you realise that maths is about applying concepts to solve problems, it becomes fun. For me, it's like doing puzzles (of course I realise that's not everyone's cup of tea!) But it certainly is more interesting and effective than simply doing math by rote.
If you still need more convincing, here are some numbers for you: The Trends in International Mathematics and Science Study (TIMSS) measures the performance of math and science achievements of students around the world. In 2007, the TIMMS ranked Singapore students second in the world (just after Hong Kong) for Grade 4 (equivalent to p4) and third in the world for Grade 8 (equivalent to sec2), after Chinese Taipei and Korea. In 2003 when the TIMSS was last conducted, Singapore ranked first in both categories.
The consistently high results achieved by Singapore students in math have attracted attention in the US and several states have already adopted our math curriculum and are beginning to see results. You can read this article in the Philadelphia Inquirer and another in the LA Times.
So as I stated in the beginning of this post, the Singapore maths curriculum is rock solid. (Now if they can only do that for English!) I encourage you to take the time to "go back to school" and re-learn your maths. If not for your kids, then for yourself. Approach it with an open mind, I think you might surprise yourself.
I never used to understand this - when I was back in school, my mother would ask me, "Do you understand the concepts?" and I would say impatiently, "yes, yes, of course." But I didn't, not really. You see, I knew all the formulae, like Area of Rectangle = Length x Breadth, Distance = Speed x Time, etc but they were just formulae to be executed, I never got the real meaning behind those formulae.
A case in point: Adeline was recounting how when she saw the sum ½ ÷ 1/4, she tried to teach her son the "inversion" method, ie flip the 1/4 and change the sign to "x", so you get ½ x 4/1 = 2. That's the way we were taught in school some 20 (ok, ok, closer to 30!!) years ago. But she couldn't explain it to her son and we didn't really GET the meaning behind the answer, until Lilian's son Brian explained, "well, 2 quarters go into half, that's why the answer is 2." Doh!
I'm confident that the Singapore education system is laying a very strong foundation in maths because having undergone the primary math curriculum for six years with Lesley-Anne, I can see how it systematically reinforces the understanding of math concepts, first in solid, tangible methods before moving into abstract forms. Maths in Singapore doesn't teach blind application of formulae to narrowly defined, topical questions. Eg. it used to be that if you came across a question with a circle, you just need to apply one of the formulae for circles and you should be able to find the answer.
These days, a question may feature a pie chart but involves your application of knowledge not just of pie charts but maybe also of circles, percentages, fractions and algebra. Which is very reflective of maths in real life - afterall nothing ever falls neatly in pre-determined categories! And that is the reason why many Singaporean parents find their kids' maths so difficult even at the lower primary levels. It's not that we're dumb or bad at maths, we were just never taught that way!
Many parents, being unable to solve their kids' maths problems (let alone teach it), immediately dismiss the subject as too difficult and call for a tutor. I would like to suggest an alternative solution that is quite straightforward. The catch is that it may not be too palatable for parents - we need to re-learn our maths. Before you groan, let me tell you why: I find that when parents embark on the learning process together with their kids, their kids often are more motivated to work. Never say you're too old - it's doable!
Let me share my experience with Lesley-Anne thus far and hopefully this will encourage you. I never attended a single math workshop and my kids never had math tuition. I was one of those stubborn and tidak apah types who only bothered to find out more about a topic if my kids didn't understand something. I naively thought, "This is primary school maths! How hard can it be??" Until Lesley-Anne hit p3 and was stumped by a question that required models in an exam paper. I knew nothing about models then. When I saw the sum, I was indignant. "Siao! Expect 9-year-olds to solve this kind of question!" I still remember complaining to Lilian when she happened to come back to Singapore for a visit. I showed her the paper expecting sympathetic horror but she said calmly, "oh, this one needs models." (Lilian, I don't know if you remember this!) I was like whaaa..tt?
From there, I looked up model drawing in assessment books and I fell in love with the ingenuity of it. It introduced me to a whole new way of visualising maths problems that I never knew existed. So that was the start. From then on, I would always keep one topic ahead of whatever Lesley-Anne was learning in school by referring to her My Pals Are Here math textbooks and understanding how it's taught (usually very simply yet brilliantly). Consistently, I found that it emphasised understanding of concepts, using meaningful drawings. New topics start from the basics and more complex ones build on topics previously taught in a logical manner. Qualifier: I'm referring only to mainstream maths. I never bothered with topics under the GEP maths syllabus. However, the textbooks cover only the straightforward and foundational stuff. Often, in assessment books or exam papers of top schools, you will find the questions are much tougher. These are the ones that usually cause much angst in parents. To be able to solve these problems, you need PRACTICE. No two ways about it, sorry. Once the net is cast open for maths questions to involve applications of multiple concepts, there are just too many computations and permutations, you cannot possibly learn ALL the possible ways of solving them by rote. The only way is to ground yourself so firmly in the principles that you are able to manipulate them in different ways to solve the problem. That's what our kids are taught. And they're made to practise. A LOT.
I haven't got it down pat. As you can tell from my less than stellar score in the Nanyang prelim paper, I still have lots to learn. But you know, I'm enjoying it. Once you realise that maths is about applying concepts to solve problems, it becomes fun. For me, it's like doing puzzles (of course I realise that's not everyone's cup of tea!) But it certainly is more interesting and effective than simply doing math by rote.
If you still need more convincing, here are some numbers for you: The Trends in International Mathematics and Science Study (TIMSS) measures the performance of math and science achievements of students around the world. In 2007, the TIMMS ranked Singapore students second in the world (just after Hong Kong) for Grade 4 (equivalent to p4) and third in the world for Grade 8 (equivalent to sec2), after Chinese Taipei and Korea. In 2003 when the TIMSS was last conducted, Singapore ranked first in both categories.
The consistently high results achieved by Singapore students in math have attracted attention in the US and several states have already adopted our math curriculum and are beginning to see results. You can read this article in the Philadelphia Inquirer and another in the LA Times.
So as I stated in the beginning of this post, the Singapore maths curriculum is rock solid. (Now if they can only do that for English!) I encourage you to take the time to "go back to school" and re-learn your maths. If not for your kids, then for yourself. Approach it with an open mind, I think you might surprise yourself.
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