How Language And Math Intersect: Chinese v. English
Following my 1+1= post, here’s another post about numbers. But, this post is less about numbers and more about the words used to articulate those numbers. Below, you will see a comparison of the actual words used to say the numbers represented on the left. The first set of words is the number represented in the English language, and the second set of words is the number represented in the literal English translation of the Chinese language. So the sequence is (#, English, Chinese). Here we go:
- 1: one, one
- 2: two, two
- 3: three, three
- 4: four, four
- 5: five, five
- 6: six, six
- 7: seven, seven
- 8: eight, eight
- 9: nine, nine
- 10: ten, ten
Nothing earth shattering here. When you count from 1–10 in English and Chinese, ten unique words emerge representing the most basic of numbers. But, from 11–20, the languages diverge (#, English, Chinese):
- 11: eleven, ten one
- 12: twelve, ten two
- 13: thirteen, ten three
- 14: fourteen, ten four
- 15: fifteen, ten five
- 16: sixteen, ten six
- 17: seventeen, ten seven
- 18: eighteen, ten eight
- 19: nineteen, ten nine
- 20: twenty, two ten
In the English language, to count from 11–20, you need to learn ten new words. So, to count from 1–20 in English, 20 unique words need to be learned. In the Chinese language, to count from 11–20, no new words are introduced. Chinese language reincorporates the same words used for 1–10, to cover all the numbers from 11–20. If you can count from 1–10 in Chinese, you can count to 20 by default. What if you expand it to 100 (#, English, Chinese)?
- 30: thirty, three ten
- 40: forty, four ten
- 50: fifty, five ten
- 60: sixty, six ten
- 70: seventy, seven ten
- 80: eighty, eight ten
- 90: ninety, nine ten
- 100: one hundred, one hundred
In the English language, to count from 21–100, eight new words are introduced (thirty, forty, fifty…hundred.). In the Chinese language, to count from 21–100, only one new word is introduced: hundred. No new words are introduced to count from 11–99 in Chinese. Therefore, to count from 1–100 in English, you need to learn 28 words. To count from 1–100 in Chinese, you only need to learn 11 words. It’s a profound difference and impacts learning.
Watch kids learn to count in Chinese. After a child learns to count from 1–10 in Chinese, it’s seamless to watch them count from 11–99 – it happens in a snap. Why? Because they don’t have to learn a single new word to count from 11–99. By learning to count from 1–10, they have learned everything they need to count from 1–99.
Watch a child learn to count in English. What happens after they learn 1–10? They get confused, because it’s ten new words to count from 11–20. And what happens after they count to 20? It’s a quick hop and skip to 26, 27, 28, 29…. But then they often get stuck at each ten segment for the very simple reason that it’s a new word – thirty, fourty, fifty, etc.
Some researchers hypothesize that one possible reason some Asian cultures show proficiency in math at an early age ironically has nothing to do with math – it has to do with language. It is easier to learn to count in Chinese than it is in English because it requires learning fewer words. While numbers are the building blocks of math, maybe language plays an unspoken role in making math easier.
Thinking About Thinking 
Malcolm Gladwell wrote about this issue at length in one of his three books. I’m pretty sure it was Outliers.
I think you’re right Steve. That must be where I first heard about it.
@Larry… Nice comparison. but.. I dont see such ease in language in indian numbers. Numbers in indian languages are very much similar to english. Indian students have to learn new words for numbers for 1-20 and then for 20,30 and so on.. ! 🙂
Prabhu, interesting. I wonder if it’s principally Chinese or if other languages (Korean, Japanese, etc.) have a similar dynamic.
Japanese and Korean are very interesting. They both have two sets of numbers, one native and one borrowed from Chinese.
For the case of Japanese, the Japanese numbers exist from 1 to 10, so that is arguably 10 more numbers to be learnt (although there is the strangeness of having two words for each of those numbers, and figuring out when to use one and when to use the other – they are not always interchangeable).
In Korean, native numbers exist for 1 to 10, and then for 20, 30, 40, … 90. There are also native Korean words for 100, 1000 (and maybe beyond). Again, as in Japanese, the native set of numbers and the Chinese-derived set are not always interchangeable.
So I don’t know what this means for the hypothesis …
Another side note: languages like Chinese, Japanese and Korean have counters – so you can’t say “three apples”, you need to say “three of apples”. English only requires counters for uncountable nouns (“three pieces of paper”). One could argue that this makes learning harder for languages where counters are obligatory (or perhaps not, if one takes the view that learning the counter words does not interfere with acquiring numeracy skills).
Also, it just occured to me that the numbers from 13-19 and 20-90 in English aren’t completely idiosyncratic – they follow a pattern (only the words “eleven” and “twelve”, plus the morpheme suffixes “-teen” and “-ty” are new). This is in contrast to the Korean numbers for 20-100, which do seem like completely new words.
I did think about the “teen” and “ty” suffix dynamic YYY and ultimately decided that while we look at it as a number with a suffix, I think when a kid learns it, it is a distinctly new word to them. None of the Chinese words are numbers with new suffixes, they are just the basic numbers themselves.
I think it is actually a subjective what constitutes and prefix/suffix and what constitutes a new word. When a child learns the words from 13-19 (assuming he already know 1-10), is it a new word for each of those numbers (given they have a common suffix) or is it just one new word for the bunch, or something in-between?
Why do I say this? Consider for example Korean numerals (I am referring to the set that was borrowed from Chinese). For the numbers 11-19, they all go “ten one”, “ten two”, … “ten nine” … However, the pronunciation of “ten” is not the same for all the numbers 11-19. (In particular, there is a phonetic change in the number 16.) So there is a question now: when a Korean child learns the number for 16, what is going on? Does he/she learn it as a new word because of the sound change, or is the sound change learnt as a separate rule. or something in-between? Does this mean that the “ten” in the numbers 11-19 is more of a prefix in Korean?
In linguistics there is a technical distinction between morpheme (smallest unit of meaning) and words (definition not so clear, considering German and their ultra-long compound words). Morphemes may or may not function as standalone words (i.e. they may have to be combined with another morpheme). So “-teen” and “-ty” would be morphemes and not words in English.
In Chinese, there is almost a one-to-one correspondence between morphemes and characters (although there are exceptions – the Chinese word for spider has two characters which have no meaning in and of themselves). However. in modern Chinese, most nouns are actually polysyllabic – very few Chinese characters can be used standalone as nouns. (Note that this is not the case with classical Chinese.) The pinyin romanization of Chinese recognizes this, and as a rule, words in Chinese are written without spaces in between the characters when transcribed into pinyin (eg Beijing not Bei Jing). What makes this complicated in this discussion is that the Chinese words for one to ten are exceptions in that they are morphemes (characters) that can function as standalone words.
So I don’t know what really goes on here. Is the the number of morphemes that must be learnt the determining factor, or the number of “words”? As I alluded to earlier, there isn’t a really good definitiion of what a word is, especially from a language acquisition perspective. (I am sure no one taught you the word “antidisestablishmentarianism”, but you can figure out what it means.)
Even in your Chinese example, the Chinese words for 11-19 are actually somewhat irregular. If you compare them with the words for 20-99, you realize that to be truly regular, the Chinese words for 11-19 should be “one ten one”, “one ten two”, etc. So a Chinese child needs to at the very least learn this fact – that 13 is “ten three”, not “one ten three”. I actually think (not sure though) that this is a common mistake that Chinese children make. So there is an additional piece of information here (just like in English one needs to learn to add “-teen” to make numbers from 13-19).
Sorry for the long post – I didn’t major in linguistics for nothing, I guess.
I’m skeptical. It sounds appealing, but I suspect that Asians do better in math because their cultures demands it more than in America. They’re not touchy-feely about self-esteem. If a kid can’t hack it, he is told to work harder. Period. If he won’t work harder, he is stigmatized and shamed. That’s pretty powerful incentive. But in dysfunctional urban schools in America we have 9th graders who can’t do the multiplication times tables (a guy I know who teaches 9th grade math in a Philly told me this directly). I also also suspect that if we got rid of teachers unions in America our math scores would improve. If a teacher can’t get his kids to do basic math, then fire him/her, and get somebody else who can do it. In America we can’t do this, but in China, Korea, or India such incompetence probably wouldn’t be tolerated systemically.
This is interesting, touches on something I’ve wondered for a while (and I’m sure is covered if I tried to study up on some linguistics).
I wonder what the complex alphabet in Chinese compared to the simpler English alphabet does to the patterns of learning written language and how it might be a hindrance for certain tasks. At a simple level I would think it makes typing and using a computer difficult. From simple things I’ve read it seems that there are issues with Chinese keyboard design, and I wonder what is lost by having to expend mental energy on the typing issues of the language.
The parallel I think of is the Arabic numeral system versus Roman numeral system, and how which system you use controls what you can accomplish easily. For instance, long division with roman numerals strikes me as being incredibly complex. However it can be handled pretty easily on paper by 4th graders (probably younger outside US!) because it can just be done algorithmically with a simple procedure.
Gladwell discusses this at length in his third book, Outliers. Chapter eight, “Rice Paddies and Math Tests.” While in Outliers, check out chapter two, “The 10,000-Hour Rule” to learn why it is significant that Bill Gates, Steve Jobs, Steve Ballmer, Eric Schmidt, and Scott McNealy were all born within 12 months of each other.
Very interesting. Although this idea has opened my mind up to the possibility, I’m feeling that I side more with SooSang. Just knowing this culture and the way things work from being here my entire life, I believe what SooSang is correct. A major problem in the education system here is the unionization of teachers. I revere educators as something that should be held just a little bit higher than an average job/career. These people are in control of the future’s education and intellect. If you were a teacher and your class’ scores kept going down, or never improved, you need to be fired. Period. No question about it. Teaching obviously is not for you. A couple of years ago, I worked as a Florida State Teacher Exam Coordinator for a college here in Central Florida. And I must tell you that some of those educators that came through there to take that test (which by the way is basically the Law BAR exam but for teachers) were some of the most ignorant people I have ran across in my entire life. It was absolutely appalling that these individuals are the same people sitting in the classroom teaching the youth of our Nation! Absolutely ridiculous.
Sorry for the rant… Happens from time-to-time! 🙂 Great post Larry.
-Blake Gates
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We are a group of tutors, each with many years of professional tutoring experience in their respective academic subject, especailly in Math and Chinese language.
We believe that to be good in Math, one has to be strong in mental skills. Asian languages with root in Chinese are memory-intensive language. This is the reason why students from these countries are doing well in Math.
However, we believe that this is not going to be the same in next 10 to 20 years for 2 simple reasons:
1) The proliferation of calculators in schools is weakening the mental skills of students. Taking Singapore as example, caculators are allowed at the age of 10. Many students are now finding it hard to handle concepts such as fraction, decimals and percentage without calculator. As they move on to higher levels, they find topic such as algebra even harder to understand, since concept such as (x-4)/3 cannot be handled caculator.
2) Chinese language skills are also weakening in many countries, even in China. During my recent trips to China, I found many Chinese not familiar with idioms and phrases that we used to memorize when we were young. In Singapore, many students are opting a simpler syllabus of Chinese for their high school (known as Chinese B).
In summary, the overall weakening of mental skills is having the same impact on Math learing and Chinese learning.
Is there any data on second generation Asian children in the US? My daughter has friends who I think would be considered native speakers of English, but they are still very good at math. Here is a study of brain regions (fMRI data) involved in solving math problems for speakers of English and Chinese.
http://www.msnbc.msn.com/id/13560741/
Gladwell’s chapter is self contradictory – first claiming it is language, then claiming it is just stamina.
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No one mentioned about mapping? I don’t think it has much to do with the mathematical vocabulary, but more likely the ability to map actual numbers in language and numerical representation:
365
Three hundred, sixty-five
three | six |
hundred (百) | ten (十) | five
—————————————-
3 | 6 | 5
For children new to abstract ideas like numbers, it’s probably harder to visualize the relative positions of the numbers in words like fourteen, eleven, fifty, twenty-three as opposed to ten-four (14), ten-one (11), five-ten (50), two-ten-three (23).
The only discrepancy I see is the omission of “one” for 10-19 as opposed to other units: ten-five (15), not one-ten-five, unless it’s preceded by a higher magnitude: two-hundred-one-ten-five (215).
When I was teaching remedial math classes to English-speaking children (ages 9-12) and they struggled with place value, I found that teaching them 一二三四有五六七八九十 and 百, 千 helped them immensely. Even first grade (ages 6-7) did better with place value when I taught them place value using Chinese.
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