Mathematics: Is Understanding Underemphasized in Our Schools?

[lookingaround]

There are some information you can google around.

This is one of the mathematics question of Singapore's PLSE 2009 (which is standard 6 UPSR in Malaysia, though the quality is not comparable.)

Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim's sweets to chocolates became 1 : 7 and the ratio of Ken's sweets to chocolates became 1:4. How many sweets did Ken buy?. Ans: 68 sweets

Algebra? I remembered that algebra is only taught in middle school in Malaysia, and it has been about 10 years ago for me. And can you answer the question above? If you cant, then you failed the Singaporean's standard 6 exam.

Do some readings:

http://www.springerlink.com/content/...w/fulltext.pdf
http://sitemaker.umich.edu/cohenbc.3...lum_comparison
http://www.nctm.org/resources/content.aspx?id=1618
http://www.merga.net.au/documents/MERJ_19_1_Lim.pdf

And also go to google books and search the title:
How Chinese learn mathematics: perspectives from insiders
Mathematics curriculum in Pacific rim countries--China, Japan, Korea, and Singapore

To really success in mathematics:
1. hardworking - no need explanation for this word
2. good teacher - teachers in malaysia? how many of them can answer your question directly and instantly?
3. syllabus - syllabus in malaysia really [muted]

I have my friends, also top students, studying higher education at singapore. They say those chinese (who really come from China) in their schools always score full marks, if not then highest marks in the exams, and those chinese seldom study mathematics in school (in singapore). Can you see the differences?

[luke]

Originally Posted by lookingaround

Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim's sweets to chocolates became 1 : 7 and the ratio of Ken's sweets to chocolates became 1:4. How many sweets did Ken buy?. Ans: 68 sweets

(S/2) - 12 : (C/2) = 1 : 7
(S/2) : (C/2) - 18 = 1 : 4

Use one of the equations to get C in term of S and use it in the second equation to get the value of S.

But damn, if this was in my UPSR, I wonder if I would be able to answer it

[chongkeat]

Actually, for the Form 6 math (and physics) syllabus, a lot of the teaching includes, if I'm not mistaken, the understanding or the derivations of many different formulae.

Though, I'd have hoped they started maintaining such standards of difficulty back when we started school. I remember spending an entire month or so learning the 24 hour clock...

Man, if I ever decide to run for political office I'd have to remove my posts here.

But then again, I'd vote for any politician with the l33t haxxor skillz (yes, to the z) to get hold of such information, considering the aliases and all that...

[youngyew]

Originally Posted by chongkeat

Actually, for the Form 6 math (and physics) syllabus, a lot of the teaching includes, if I'm not mistaken, the understanding or the derivations of many different formulae.

Though, I'd have hoped they started maintaining such standards of difficulty back when we started school. I remember spending an entire month or so learning the 24 hour clock...


But then again, I'd vote for any politician with the l33t haxxor skillz (yes, to the z) to get hold of such information, considering the aliases and all that...

I guess the case in our country is that we try to go for the lowest-common-denominator amongst all students, but the LCD in our case is way lower than the standard in other countries.

[youngyew]

BUMP:

Timothy Gowers, one of the prominent mathematicians actively involved in improving maths education has pointed out the deficiency of modern mathematical education which echoes my sentiment of this thread. He wrote about his conversation with a 17 year old a-level candidate regarding differentiation:

http://gowers.wordpress.com/2012/11/...rily-give-you/

[Sillyboy]

Originally Posted by youngyew

BUMP:

Timothy Gowers, one of the prominent mathematicians actively involved in improving maths education has pointed out the deficiency of modern mathematical education which echoes my sentiment of this thread. He wrote about his conversation with a 17 year old a-level candidate regarding differentiation:

http://gowers.wordpress.com/2012/11/...rily-give-you/

Mathematics is all about formulas and I suspect this to be more widespread in Malaysia nowadays. Heck, I was one of those students who didn't give two hoots about 'understanding' Mathematics, not until university anyway.

In all seriousness, Mathematics is a difficult subject and more often than not, concepts like these are either not well explained or just not well grasped by students. The latter could very well be the consequence of poor teaching but there is nothing from stopping a student from admitting that 'they just don't get' because frankly, maybe they simply just don't.

[youngyew]

Originally Posted by Sillyboy

Mathematics is all about formulas and I suspect this to be more widespread in Malaysia nowadays. Heck, I was one of those students who didn't give two hoots about 'understanding' Mathematics, not until university anyway.

In all seriousness, Mathematics is a difficult subject and more often than not, concepts like these are either not well explained or just not well grasped by students. The latter could very well be the consequence of poor teaching but there is nothing from stopping a student from admitting that 'they just don't get' because frankly, maybe they simply just don't.

I agree with you to a huge extent. Copy and pasting what I have wrote on this topic in another discussion:

I am not sure how much better we could have done.

I am pretty sure the derivation from the first principle is taught in A-Level and would in fact be test-able (at least that's the case in Malaysia's SPM syllabus). The fact that this student couldn't do it from prompting either mean that he has not learned it very well, or did not have the capacity to fully take it to heart and reproduce it without prompting.

The thing with mathematical education is that we ought to recognise that a lot of people, while perfectly capable to understand first principles given enough time and effort, will soon forget them as soon as life's other woes overwhelm their memory. I believe that everyone in this group [current and past members of Malaysia IMO team] would be able to remember the first principle even if you aren't doing maths-related things, and in fact even though I haven't done any advanced maths for the last 8 years, when I read about the derivation by first principle in the blog post, I was able to recall [f(x+h)-f(h)]/h because my understanding remained solid even without day-to-day use. I think we are a group of privileged people with brain wiring more capable of deep and indelible understanding of logical truths, but the same is not necessarily true for many high school kids. Yes spend enough time explaining fundamental principles and they will understand it eventually, but invariably they will forget them.

My two cents.

[acgerlok7]

Originally Posted by Sillyboy

Mathematics is all about formulas and I suspect this to be more widespread in Malaysia nowadays. Heck, I was one of those students who didn't give two hoots about 'understanding' Mathematics, not until university anyway.

In all seriousness, Mathematics is a difficult subject and more often than not, concepts like these are either not well explained or just not well grasped by students. The latter could very well be the consequence of poor teaching but there is nothing from stopping a student from admitting that 'they just don't get' because frankly, maybe they simply just don't.

Yes, bro i agree with you...Mind you, i even had a Physics lecturer who was so dumbstrucked with a question and its' answer, and he couldn't even explain why that was the answer. In the end, he asked us to memorized the answers. Btw, most of the time, when he couldnt explain the concepts properly, or at the least make physics sounds a tad bit interesting rather than making it SO mundane for him and his students, he will just tell us to memorize the concepts, formulas and even the derivations. What kind of Physics learning is this?? I was utterly disappointed that this happen during My A Level, whatmore at a so called Tier 6 college in Malaysia.

For Mathematics, all i could remember in primary, was if we got one damn question wrong, i was caned until i had bruises. And later i was forced to do corrections and memorized the methods of deriving the answers. In Form Four mathematics, i had a stand-in teacher, so called an "intern" from UITM to teach us for 3 months as part of her course, she could not even speak proper English, and the medium for mathematics is in English. She could only answers my classmates' questions vaguely and sometimes even totally unsure of her answer.

[youngyew]

It's evident that the quality of teacher in our country is part of the problem too.