I'd be interested to see some data on how children learning math in Hindi do, because the numbers are even less regular, enough so that even though there's a pattern, you still have to learn all the numbers from 1-100 individually. There are also more specific words for different fractions, such as a word for 3/4 that sounds nothing like the word for 1/4.
most schools in urban india and a large number of the rest are 'english-medium'.. which means i learnt math in math class (in english) and learnt to count in hindi in hindi class.. but never had to solve a math problem in hindi
i am currently learning japanese and can agree about the numbers being syllablically small.. but this language has it own complexities - http://en.wikipedia.org/wiki/Japanese_counters
which require a speaker to think a lot as well
Interesting article overall, but I found the following a little spurious:
>For fractions, we say three fifths. The Chinese is literally, 'out of five parts, take three.' That's telling you conceptually what a fraction is. It's differentiating the denominator and the numerator.
It's not obvious to me that one is better than the other, and he's not providing data to support such a claim. Is it just me, or is he just playing with semantics here?
Miller, K. F., Smith, C. M., Zhu, J. & Zhang, H. Preschool origins of cross-national differences in mathematical competence: The role of number-naming systems. Psychological Science, 6, 56-60.
I just read this paper (it took me a while to get it) and it does not make any reference to fractions at all. It only supports the first claim:
>That difference means that Asian children learn to count much faster. Four year old Chinese children can count, on average, up to forty. American children...
It does not support the second claim:
>The regularity of their number systems also means that Asian children can perform basic functions—like addition—far more easily...
I don't have a copy of the book to hand (in India and haven't managed to find it yet) - I can only see the online excerpt. Does he cite other papers in support of the fractions claim and/or the second claim quoted above?
He only cites secondary sources in the book. I just linked to that paper because I happened to know about it offhand. (Wrote a couple papers about it in college.)
If you want to find the paper supporting the second claim, Gladwell explicitly uses the keyword number-naming systems so that is a pretty big clue. There can only be so many cognitive development papers with that as the independent variable, so it should be pretty easy to find. It wouldn't surprise me if the research supporting the second claim was done by the same researchers who did the other paper I linked to.
i've lost count of the number of times i've tutored my whanau and had to use some variant of 'slice a pizza into x bits and then hand out a slice to y friends - fractions are just a quick way to write it down...' simple conceptual anchor points are crucial - everything after that leverages the basics.
I agree - Gladwell has the facts right, but his theories on the reason for the facts are quite off from reality, imo.
Even if it is hard to count numbers in english, it is still easy to see the pattern in numerical symbols. Either way it is certainly not a momentous task for a 4 year old to form relations words to numerical symbols, with their abundance of ability in memory. This is why Gladwell's theory falls apart - a much more likely theory is that math ability is more readily determined by HARD work or innate genius.
And concerning his rice farming theory, I wouldn't know whether to laugh or take it as an insult, because to me it is that ridiculous. His claiming effectively, that farmers in China work the hardest, because they farmed rice. On how many levels does this seem inconsistent?
Sounds fishy to me. In german, numbers are logical but excruciatingly long to say in words. There's no huge lag in german math skills because it takes a little longer to say the numbers than in english.
Looks right. IIRC (studied German in college), numbers are read similarly to English, with the exception that the tens place is read last. Transliterated, you would get something like "three thousand, four hundred, seven and ninety" for 3,497.
According to this logic, shouldn't kids from Kansas or Iowa do way better in math?
I'm Chinese myself, and I think there might be a simpler reason. Our schools public schools are way tougher. I'm talking 7 am to 5 pm, non stop learning hard. We're talking about doing trig in the sixth grade and calculus in middle school.
Those are the kinds of schools our parents went to and those are the kinds of schools they send their kids to. Instead of soccer practice or baseball games we take more math classes.
Also explains why we tend to suck at sports.
From my experience the difference in ability stems more from culture than from genetics.
> From my experience the difference in ability stems more from culture than from genetics.
This is actually his point: the chapter from which this excerpt is taken is from the second half of the book, which is all about how our behavior (and thus our performance) is profoundly influenced by our cultural heritage. There's a great chapter, for instance, on how cultural differences regarding deference to authority resulted in Korean Air's high crash rate in the 90's.
There's no mention of the rice paddies in this excerpt, but Gladwell argues that rice paddy cultivation was considerably more complex and required considerably more labor than typical farming practices in the West, a long history of which resulted in a culture of persistence. (Which might explain just why Asian public schools are way tougher.)
Actually, we tend to suck at sports because we're shorter in stature and we're slower at building certain muscles. I would know. We have like what, 50 guys on my school's cross country team. 40 are Asian, but 5/10 of the caucasian guys to the best out of the 50. They get injured less, even if they aren't as good early on for some strange reason. They also improve faster.
Though you have to admit, with all that video game playing, it's no small wonder that asians are pretty decent at baseball.
Ah yes, another hack who believes math is all about memorization and fast arithmetic. Who cares if our 7 year olds can add slower? We all add the same speed once we lift the calculator ban. And once you start doing real (abstract) math, this memorization advantage becomes completely useless. I'll believe the "Chinese Math Dominance" story when I see it.
Asian children, by contrast, don't face nearly that same sense of bafflement... maybe that makes them a little more likely to enjoy math, and maybe because they enjoy math a little more they try a little harder and take more math classes and are more willing to do their homework, and on and on, in a kind of virtuous circle.
The argument is not that the clarity of the Chinese-language numbers is, in itself, that big of an advantage once kids grow beyond four, five, or seven years of age. The argument is that kids who are comfortable with math at age four are more likely to remain happy with math throughout the rest of their schooling, whereas loss of confidence at an early age results in loss of future confidence.
Obviously, while you can test the difference in math skills among seven-year-olds, this stronger hypothesis is hard to test rigorously, because you can't easily control for all the other cultural differences. But it's a very interesting idea, nonetheless. One of the most amusing things about this hypothesis is that it mirrors the difference between the English and Chinese written languages: Chinese writing is badly designed compared to alphabetic systems, to the point where there are serious effects on the literacy rate. See Moser at http://www.pinyin.info/readings/texts/moser.html and DeFrancis' The Chinese Language: Fact and Fantasy, linked from http://www.pinyin.info/readings/chinese_language.html
Pinyin.info is largely devoted to an anti-character crusade that doesn't represent mainstream academic thought. Mark, if you're reading this, I don't mean any disrespect to the work you've put into making the resource it is. I've sent many people there for the rules on pinyin punctuation and spacing.
DeFrancis was the undisputed pre-eminent sinologist of his time, however many of the literacy claims are unfounded. The truth of it is, China is a huge country, full of people speaking dozens of different languages and the Chinese writing system has helped its cohesion.
As a 6-year resident of Taiwan, I feel I have some capacity to comment on this. Here we use traditional characters, which are more complex than those currently in use in China, and despite not being as economically developed as the US, Taiwan has a higher literacy rate. Japan does, too. For that matter, China's literacy rate is higher than other countries with similar levels of economic development, such as Brazil.
Using characters entails some disadvantages, but also allows for some benefits, such as increased reading speed and clearer differentiation of homonyms.
FYI Moser has long since conquered his difficulties and become a literate Chinese reader.
This is why we need to teach numbers and concepts, not names.
I admit that the English number system is flawed, but that's what digits are for, right? 37 = 3(10s)7. Its just a shortcut, we can express 37 to be 3*10 + 7, but its just not worth saying every time
I think his point, however, was that even an exclusive English speaker can communicate (in writing) arithmetic calculations without involving English. You don't have to 'mentally say' anything in English, so the inefficiency is mitigated.
I thought he had a good point, but then I realized his intro test was rigged: twice he said "say them out loud", so I tried to memorize the sound of the numbers.
But then I thought about how I remember passwords, PINs, and phone numbers, and I don't memorize any of these by the sound of their digits (perhaps because it would be so inefficient in English!).
I remember sequences of digits (or chars) by visualizing how I use them, i.e., spatially. In this case, I pretended the 7 digits made up a phone number and mentally placed them on a phone. Now I can't seem to forget 485-3976.
I disagree with the proof here. He implies that the two statements:
Asian children have a simpler number system vocabulary.
- and -
Asian children learn to count at a younger age.
prove the third:
A simpler number system vocabulary allows children to count at a younger age.
This may be true, but he implies it as fact, without even granting that they may be other factors at work. Like a better education system perhaps.
http://www.sf.airnet.ne.jp/~ts/language/number/hindi.html
http://faculty.maxwell.syr.edu/jishnu/101/numbersfractions/d...
(My apologies if any of this is wrong. I'm not a native speaker, just took a few years of Hindi in college.)