Nomological Net

Stray thoughts from here and there. The occasional concern for construct validity. No more logic. Fish.

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faults in the clouds of delusion

Wednesday, April 25, 2007

The quest for world domination

I know it's early in the morning, maybe that's why I had to reload this page and read it three times, reminding myself that it was the BBC News website and not a hoax or joke published on some random blog.

Here's the deal -- the Royal Society of Chemistry is concerned about the differences in math standards between undergraduate English students and high-school Chinese students. With just cause for concern, as the following examples demonstrate.

First, the Chinese one.


And then the English one.


Excuse my hooting, please. I can't seem to stop :-D

Barmy-Army! *clappity-clap* Barmy-Army! *clappity-clap*

Here's the original link in case anyone would like five hundred pounds.

36 Comments:

Blogger Rahul said...

Well... I don't know much about Chinese universities, but

1. Some Indian entrance tests (eg the much criticised IIT JEE) are much more challenging than the Chinese example here

2. The Chinese example is quite straightforward; it requires no brilliant insights and very little knowledge of geometry beyond what the British example tests. It would only be a challenge under time-constraint pressure, which I believe is a bad idea for tests (this equally applies to the JEE).

3. Not all Indian universities are of the same standard as the IITs, or even Delhi University -- that's putting it mildly. And not all UK universities are Oxford or Cambridge. I'd be surprised if all Chinese universities are of a uniformly high standard.

4. The English "diagnostic test" may not be for students who had a good math education in school. The article says it is "to diagnose remedial requirements" for chemistry majors. I'm sure many Indian chemistry majors have equally poor math skills; the difference is no effort is made to diagnose remedial requirements.

Basically, comparing one question from an entrance exam with another question from a diagnostic test allows no conclusions to be drawn about the talents of average students or average universities in the countries.

4/25/2007 11:46 AM  
Anonymous bandafbab said...

TR, posts on math and cricket will always attract my attention. I´ve got some things to say, and they might not have anything to do with your post.

1) Someone should tell the Royal Chemistry Society, that nobody should shove maths down anybody~s throat. While it´s a fundamental discipline, if British students don´t like it, so be it. If they´re better of writing books or playing football, there are enough math geeks around the world who´ll do math related work.

2) The SAT maths section is possibly the simplest of any school leaving exam, and people always joke about Americans being bad at maths. I taught lots of different undergrad math courses in the US, and the average Asian undergrad got better grades, but somehow they never did well on questions which required slow thinking. At the research level, American mathematicians still end up doing as well, if not better than their Asian counterparts.

3) I spent 2 weeks in Zhejiang University and was surprised at how students and professors approached maths the same way as places like Delhi University. Rote learning, tough exams and very little lateral thinking. In fact, they have more entrance exams at each level than in India and filter out the best performing students at a young age, who are destined to do research. Sadly, like the IITs are not known for worldclass research, the same is true for Chinese universities. There are some exceptions like IISc or TIFR in India, but they´re not really universities.

4) I don´t know if I made too much sense :-)

4/25/2007 10:29 PM  
Blogger Revealed said...

I agree that lateral thinking is not encouraged in India. Fact often and often when a student *does* think laterally out of pure serendipity, the teach is as likely to tell him/her to stop being arrogant/oversmart (whatever *that* word means) or else label him/her as someone with an attitude problem. At least that was my experience. But I do think high school fundamentals in India and possibly China (I wouldn't know) are much stronger than the ones in the US/UK. I don't know how helpful it is, though as bandafbab said.

4/25/2007 10:52 PM  
Blogger Rahul said...

I agree with bandafbab and revealed about the lack of lateral thinking in Indian (and very likely Chinese) exams. This Chinese question did not require it: you just need to divide the figure into right-angled triangles.

Additionally, lateral thinking and 3-hour time limits don't go together. That's probably why the SAT and GRE are only minimal criteria, not sole criteria, for admissions in the good places in the US; and having a 99 percentile score doesn't count much more than having a 90 percentile score in those tests.

4/25/2007 11:21 PM  
Blogger km said...

@Revealed: ""oversmart" :D

I'm waiting for the day when kindergartens in India require a solution to Fermat's theorem before admitting your child.

4/26/2007 12:43 AM  
Anonymous bandafbab said...

I think a simple solution is to make sure that Indian universities don´t give permanent positions till the candidates establish their research credentials.

If they keep doing research for most of their career, they´ll continue thinking, and as a result encourage students to think laterally - even if it means taking credit for a student´s ideas. If they don´t do research, they stop thinking and judge students only on the basis of their performance on exams which require no thinking.

It´ll also go a long way in breaking down the perception in India that a professor is a ¨teacher¨, unlike in the west, where a professor is someone who concentrates more on research.

Things could start off with financial incentives for papers published in international journals. At least, it´ll allow the ones who do good research to live more comfortably.

4/26/2007 12:59 AM  
Blogger km said...

a professor is also someone who listens to a lot of Grateful Dead and cracks awful puns.

4/26/2007 4:27 AM  
Blogger Tabula Rasa said...

all:
in general i'm all for lateral thinking (especially if done lying down). however, the point of this post was my astonishment that college science students need to be tested on pythagoras' theorem. iirc we learnt that in the eighth grade (and basic trigonometry in the tenth).

rahul (first comment):
your first three points are OT, the fourth goes straight to my point that it's astonishing that the system feels the need to detect "average" students who don't know pythagoras' theorem or tan theta.

bandafbab:
i'm glad this is rapidly becoming your favorite blog :-D

your first point about shoving maths down throats -- i'm of the opinion that all scientists need to know the *basics*. (actually, i'm of the opinion that the world wouldn't be a worse place if *everyone* knew the basics of *every* subject.)

your second and third points about research universities versus places where people get taught the basics -- i don't think anyone would argue, just as you said, that indian and chinese universities are better at ensuring that students learn the fundamentals, no matter how. after that, the fact that they
are far inferior at generating research is a *different* problem (and one that rahul will probably contest). ultimately, people who are grounded in the basics and have the motivation to learn more can choose to move to a research university to do their research (just as you did), but no research university will accept a student who doesn't know the basics.

revealed, rahul:
points well taken about lateral thinking and three hour exams, but the purpose of most exams is not to foster lateral thinking, it's to test understanding of material. and no one who had not understood the material would know that you needed to divide the figure into right angle triangles. pattern recognition is a major component of expertise in any field -- it's a natural corollary of a well-developed schema since it allows you to make sense of what might look like a random or impenetrable mass of data.

km:
i like the way you said "your" :-D
oh, and bandafbab said "in the west".

bandafbab:
such a pecuniary system exists in korea, and from what i hear, it gives rise to corruption in many interesting forms (of the sort where "international" gets defined).

4/26/2007 10:57 AM  
Blogger MockTurtle said...

I'm trying to think of one bit of post 8th grade math that I still find useful at work or practical for daily life. Trignometry, Laplace transforms, Calculus.. all ring distant bells, but more to do with night sweats before exams than with any particular learning.
In fact I don't think any of my mathematical education aside from some basic algebra and statistics have ever come in handy over the years.

4/26/2007 12:42 PM  
Blogger Rahul said...

bandafbab, mt -- while I agree some professions don't require a knowledge of trigonometry, chemistry certainly does. And not just because molecules are 3D objects with angles between bonds. The trigonometric functions are solutions of differential equations that occur all over the place in the real world. Right angled triangles are just a convenient way to introduce them in high school: they can be introduced algebraically with no reference to geometry (as bandafbab, at least, knows).

tr - we may like to think that the "drill" we go through in school means students' "basics" are in place, but in reality it is far from the case, even in countries where "rote learning" is normal. I actually think rote learning Indian-style doesn't teach you anything and it is only using mathematical tools that teaches you anything about them. It is quite likely that a student "mugged up" the definition of tan theta and then forgot it because it wasn't in the "portions" later.

As for your comment about research standards, many researchers in India were trained abroad and many researchers in the US were trained in India or other Asian countries. So it's hard to draw any conclusions about the educational systems.

As to points 1-3 being OT, the BBC article, as well as your post, had the tone "look at these smart chinese and look at these dumb Brits" (after all they're offering 500 pounds to solve that question). So I was saying that the Chinese question is not particularly hard and the Brit question, when one realises that it's a diagnostic question and not an examination question, is not particularly surprising. I don't see why that's OT.

4/26/2007 1:10 PM  
Blogger Big Wave said...

i'm just kicked that i'm not the only anal one here who felt the need to instantly solve both. err i'm not, no?:)

4/26/2007 6:04 PM  
Anonymous bandafbab said...

I realise I´d missed the reference earlier, that it was part of the chemistry students´ curriculum. Anyway, I think I just branched off into my disdain for exams.

I´m not sure if Indian and Chinese students know the fundamentals better. It´s more of a question of having a lot of things shoved down their throat. The way they learn the fundamentals doesn´t allow the average student to ask questions or disagree, something which most Americans do without fear. It´s also a cultural thing.

Also, TR, your blog is the only blog I read regularly these days considering my nomadic lifestyle.

4/26/2007 8:52 PM  
Anonymous bandafbab said...

Also, what does OT mean?

4/26/2007 8:55 PM  
Blogger km said...

(@bandafbab: OT = Off-topic. And YAW.)

4/26/2007 10:28 PM  
Blogger MockTurtle said...

@rahul: I agree. There are some professions that require advanced math, but should all of us be put through it in the off chance that we select to work in one of them? In the Western model school kids are made to study just the basics, and only college students aiming for scientific careers have to undergo the rest. Seems like a good idea to me.
If we followed the same principle in India, I may have actually looked forward to going to school.

4/26/2007 10:54 PM  
Blogger GhostOfTomJoad said...

To partly echo Big Wave, am I the only anal one here who thought that this post was about ...er... grammatical mistakes? ;-)

For the record, I couldn't care less for anything other than Literature and History. Math and Chemistry? Pfft!

:-)

4/26/2007 11:19 PM  
Blogger Revealed said...

@rahul: Very good point! I'm living proof of that. I did a ton of math in school and then a bit in college and now if you asked me to solve even simple calculus I'd google to see if there was a software to do it for me. But it isn't cos I mugged with no understanding (because I'm unluckily constitutionally incapable, you have no idea how hard school in India can be for my kind) *but* I did forget most of the stuff I learnt, which would imply that I didn't really need it cos if I was using it constantly I'd have remembered no? So I think MT's right. A lot of the rote learning we do didn't help *me* (and I do quite a bit of biochemistry) but maybe it helps engg grads and so forth?

@bandafbab: I rather liked your idea of research in Indian universities. Most of my "professors" in college didn't know which end of a pipette to hold *and* they actually MOUTH pipetted! I had to crash-learn basic research skills in close to 3 months.

Also, whether Indian basics help or not, I *definitely* believe our system of education gives us the capacity to read copious amounts of written material and understand it very quickly. In my experience.

4/26/2007 11:20 PM  
Anonymous Anonymous said...

it seems to me that precisely the approach that says "math was not useful to me in my later life" is what's responsible for downplaying it in the required curriculum at high schools in the US. and believe you me, it makes for some seriously under-prepared undergrads.

at an ivy league university a *master's* student once complimented me for being able to tell her without a calculator that 20 out of 200 was 10%. there's a fear of quantitative stuff that is just reinforced by allowing people to opt out. why not just get them to shut up and deal with it? that's my approach when i teach, anyway. math can be fun, and we need to be able to show that to the students.

it's also very useful. even if not all of it will be used in your later jobs or whathaveyou, it instils a way to think logically and systematically that can be very useful, and that shouldn't be discounted. return to my ivy league master's student. she probably walks through life utterly bewildered by half the practical decisions she has to make...

note by the way, it was a master's in *education* she was getting.

4/27/2007 12:20 AM  
Blogger Tabula Rasa said...

all:
quite a hornet's nest stirred up here, eh? looks like no one wanted to do their homework. more seriously, i'm very strongly in favor of a well-rounded basic education for *everyone*, be in in maths, chemistry, literature, or sport. post hoc declarations of the type i never used "x" anyway or i didn't see the point of studying "y" because i hated it get the whole deal ass backwards, in my opinion. that type of thing undercuts the whole point of education.

mt:
like the last anonymous said, the most important part of a math education is to teach people to think logically. and i'm not sure you could have been doing what you do today if you hadn't gone through the AND OR NOT XOR routine.

rahul:
not sure what you're talking about. before the board exams sure i may have memorized the formulae and identities, but i also "used" them in a ton of problems. as did everyone else who prepared for those exams. many of us will forget what tan theta means at some point in our lives, but i guarantee you every science student in delhi university knows pythagoras' theorem.

big wave:
not sure -- we'll try and find you a buddy. (calling algebraics anonymous :-) thanks for stopping by!

bandafbab:
if pythagoras' theorem is shoved far enough down someone's throat that they remember it, to me that's indistinguishable from their having learned it any other way. we may debate about the pros and cons of the various pedagogical methods involved, but my point is at least they know the damn thing.

ghost:
i'll say it again slightly differently -- i'm glad you got to know enough to form your preferences.

revealed:
the idea of only being taught what we might "need" is later life is dangerously narrow. for one, what if your preferences change?

anon:
exactly, thanks. one of other articles i read about the royal society of chemistry said something like kids in england are opting out of taking maths at their a-levels because "it's too hard". to me that signals institutional failure bigtime.

4/27/2007 12:44 AM  
Blogger MockTurtle said...

Yes, yes.. but I have chosen to work in technology, so it made sense that I had to go through 4 levels of engineering math + post grad math + business school math. But, if instead I had wanted to get into advertising or pastry making or ballet dancing, then calculus and trig would have been total overkill.
Regarding my personal growth through math - sure, math helped me think logically in the long term, but so did 6 years of technical education. It's a question of structure, not volume of content.
I am not against a mathematical education, just for ensuring that those who have absolutely no mathematical inclination are not forced to endure what others think is good for them.
I still maintain that arithmetic, algebra and statistics are probably a good foundation for all, but an advanced math education should be reserved for those who seek it out.

(PS - Aren't you supposed to get things 'ass backwards'?)

4/27/2007 1:00 AM  
Blogger Rahul said...

tr - "guarantee you every science student in delhi university knows pythagoras' theorem."

To quote me in the first comment: Not all Indian universities are of the same standard as the IITs, or even Delhi University -- that's putting it mildly. And even in DU, I suspect what you say isn't true outside the better "campus colleges". It would be an interesting exercise though (and note that the biology students may not have studied math in class 11-12, thanks to our retarded school system).

4/27/2007 1:05 AM  
Blogger M (tread softly upon) said...

Whew...talk about a hornet's nest.
But this reminded me of this thing someone sent me on an email that I simply had to share. I apologize in advance for taking up your comment space:

Fifty (50) Years of Math in the USA 1957 - 2007

Last week I purchased a burger at Burger King for $1.58. The counter girl took my $2 and I pulled 8 cents from my pocket and gave it to her. She stood there, holding the nickel and 3 pennies, while looking at the screen on her register. I sensed her discomfort and tried to tell her to just give me two quarters, but she hailed the manager for help. While he tried to explain the transaction to her, she stood there and cried.

Why do I tell you this?

Because of the evolution in teaching math since the 1950s:

1. Teaching Math In 1950's

A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit?


2. Teaching Math In 1960s

A logger sells a truckload of lumber for $100 His cost of production is 4/5 of the price, or $80. What is his profit?


3. Teaching Math In 1970s

A logger sells a truckload of lumber for $100. His cost of production is $80. Did he make a profit?


4. Teaching Math In 1980s

A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Your assignment: Underline the number 20.


5. Teaching Math In 1990s

A logger cuts down a beautiful forest because he is selfish and inconsiderate and cares nothing for the habitat of animals or the preservation of our woodlands. He does this so he can make a profit of $20. What do you think of this way of making a living? Topic for class participation after answering the question: How did the birds and squirrels feel as the logger cut down their homes? (There are no wrong answers. )


6. Teaching Math In 2007

Un hachero vende una carretada de maderapara $100. El costo de la producciones es $80. Cuanto dinero ha hecho?

4/27/2007 1:27 AM  
Blogger Tabula Rasa said...

mt:
i think that's why calculus and trig only appear late in high school, so i think the system gets it mostly right.

and that's the whole point of "ass backwards" :-D

rahul:
i agree on the retarded bit. i have no experience of the "lesser" universities, but i'm strongly optimistic that indian science students will be able to recognize the a^2 + b^2 = c^2 setup. (note that the test in question was from a "well known and respected English university".)

m:
that's absolutely hilarious!
reminds me of the time i took four boxes of something to the counter, and gave the cashier a newspaper cutout containing two identical coupons, both of which said "50c off if you get two boxes". She and I went back and forth for a while on whether the coupons could be used or not, since a coupon was valid only for *two* boxes, and i had four. ultimately we appealed to the manager. he came, he scratched, he thought, and then he took out a pair of scissors and cut the piece of paper into two, separating the two coupons, and rang up my four boxes in two separate pairs.

4/27/2007 1:44 AM  
Blogger Rahul said...

tr - that reminds me of a library in Bangalore. (I made up the numbers below, the originals being lost in the mists of memory, but the story is the same.) I had two overdue books, each 40 days late; the library charged Rs 10 for the first 30 days and Rs 1 for each additional day. So I expected to pay a fine of Rs 20 per book. Nope -- the woman at the counter added up the total number of days, got 80, and charged me Rs 10 for the first 30 and Rs 50 for the next 50, ie Rs 60. I said no, that's not how you do it. She would not listen to reason. So finally I said "ok, I'm not returning the second book; I'm only returning the first book." She calculated and got Rs 20. I paid up, and then said "Ok, now I'm returning the second book..."

4/27/2007 2:00 AM  
Blogger Revealed said...

@tr: No, no. I agree. I think that a lot of the stuff we do in school *actually* helps later on. But a lot of it doesn't. Surely there's a happy mean between our way and theirs where students can be taught the fundamentals really well but then also taught how to think laterally/logically/innovatively. Cos I think that instead of teaching me advanced calculus if they'd taught me how to approach a problem, I'd be much better off now, no?

4/27/2007 2:26 AM  
Blogger Revealed said...

Also, *all* science students in India know the PT.

4/27/2007 2:26 AM  
Anonymous z said...

the question should not be whether one is using such and such a subject in his/her profession. the question should be how can we use such a disparate and apparently unrelated subjects into our profession. Physicist David Bohm found his solution through the art work of Cezzane. No matter whether one is in any field, be it medical field or technology or engg. or artistic or culinary field or any such diverse fields, knowledge of a subject, more than just the basics of it, helps those really bent on exploring the limits of their profession. So, though there are cons of "feeding too much", those really interested find in the later part of their life that those times and knowledge helped. Thats when the "light flashes" and inventions come through.

Peace and share that love!

4/27/2007 7:00 AM  
Blogger Tabula Rasa said...

rahul:
i can just picture it :-D

revealed:
i definitely think that "problem solving" should be taught in schools. as a "should", it's a no-brainer. the questions of how to do it, and how to convince their parents that it should be done, and how to change entrenched teacher attitudes, and how to test students on what they've been taught, are all less tractable.
having said that, i do believe there are areas in biology these days that come dangerously close to needing some knowledge of pretty advanced calculus. you might still be thanking your stars for the math you learned!

(what's the PT?)

z:
beautifully put. thank you.

4/27/2007 10:16 AM  
Anonymous Anonymous said...

i think the educational system in india (and elsewhere) could do with a lot of improvement. but there's a confusion in these comments about content vs. teaching style.

yes, mindless memorization is probably counterproductive. but content? how is the school system supposed to know what you will use in later life and what you will not? and is the rationale for education only to learn "useful" stuff? what about learning for the joy of learning? calculus is cool. so is lots of history and philosophy and biology, and the list goes on. our problem is that in forcing the students to memorize and then traumatizing them about their exams and the colleges/IITs they do or do not qualify for, we turn the whole thing into a burden. only those made with nerves of steel or those who are naturally inclined to do well or work hard, make it through with flying colors. but that's not an argument about content.

by the way, did you read this:
http://www.zeenews.com/
articles.asp?aid=367173&sid=REG

4/28/2007 11:39 PM  
Anonymous Anonymous said...

I agree with those comments about that solving the Chinese math example should be easily accomplished by whoever can solve the UK example test - with a little lateral thinking. The modern Chinese maths education emphasises lateral thinking just as much as in maths education in any good UK schools. The important difference is that the Chinese put 'lateral' thinking in practice in school maths. My niece in a Chinese school in Shanghai is often asked to solve one maths problem in 3 different ways in her homework. I have never seen a similar practice in maths for my daughter who is in one of the top UK independent schools. Perhaps the Chinese maths teachers don't mind having three times the workload in marking pupils' homework. - lateral thinking?

4/29/2007 3:16 AM  
Blogger Tabula Rasa said...

anonymous 11:39:
thanks, very well put. a lot of this exachange was exactly that -- confusion between style and content.

anonymous 3:16:
hah! that's interesting!

4/29/2007 10:44 AM  
Blogger Tabula Rasa said...

anonymous 11:39:
that zee news article isn't very good news is it? i wonder what proportion of the population (i'm sure it's very large) *needs* to say that they're "10th class pass". i don't see the point of keeping those exams in *only* for those who want to study further -- what about those who want out? hmmm.

4/29/2007 11:00 AM  
Blogger gaddeswarup said...

Check:http://news.bbc.co.uk/2/hi/uk_news/education/6589301.stm

5/03/2007 5:55 AM  
Blogger gaddeswarup said...

Sorry; the link has not come out properly and cannot find it agaian. It was some announcement of prize for sending the solution.

5/03/2007 6:02 AM  
Blogger Tabula Rasa said...

oh, too bad! right now it takes it back to the original website.

5/03/2007 9:35 AM  
Blogger gaddeswarup said...

The page is still on my computer. Unfortunately, I did not read it completely. The last bit is:
"Anyone wishing to enter the competition should go to the RSC website and send the correct answer by Friday 27 April to be included in a prize draw.


Source: Royal Society of Chemistry"

5/03/2007 12:25 PM  

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