Numbers as Language
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I recently also found that there might be some linguistic explanation too. The other day, my daughter (2nd grade) surprised her class by providing an answer for 7 times 8. She said she spoke in Chinese, and her teacher asked her to translate that into English and that turned out to be the correct answer. That surprised her class, though this was actually no big deal. It is supposed to be in your operating knowledge, period.
Back to the linguistic aspect of elementary math, I find it is much easier to recite and recall multiplication tables in Chinese then in English. For instance, all the 4s. In Chinese you say:
si si yi shi liu (5 syllables)
si wu er shi (4 syllables)
si liu er shi si (5 syllables)
si qi er shi ba (5 syllables)
si ba san shi er (5 syllables)
si jiu san shi liu (5 syllables)
It is a rather easy flow of facts that can be easily memorized and recalled. There is even a beautiful rhythm to that once the student becomes familiar with it. It’s just like Brad Pitt doing fly fishing in the movie A River Runs Through It. That’s why you often see Chinese kids reciting the table with body movements. It’s like a ritual, a chant.
It looks like it is more cumbersome to commit such to memory in English (unless there are some similar shortened forms that I don’t know of), for instance, “four times nine is thirty-six”. There are two more syllables. And reciting all the “times table” is very difficult from the beginning to the end because it lacks the symmetry and rhythm as the Chinese language does when it comes to the multiplication table. Reciting it in English seems to demand a heavier cognitive load for the learner’s short-term memory.
I am not sure if any of these make sense, or simply my stereotype, but today, after years living in the US, I still remember phone numbers in Chinese.
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March 13th, 2009 at 9:40 pm
I still count numbers in Chinese – do arithmetic in Chinese – and remember phone numbers in Chinese.
Not sure what language I dream in though…
The last dream I remember is of a tiger chasing me around my living room. Don’t recall whether it was an English speaking or Chinese speaking tiger …
March 13th, 2009 at 9:47 pm
I often wonder the same thing: What I think in when I am thinking. In English or in Chinese? It is really hard to tell. We may not think in any language at all. It is when we speak and write that the fuzzy, language-less thought crystallize into words.
March 13th, 2009 at 9:49 pm
@ Allen #1: Your dream reminded me of something that happened shortly after I was married. One morning after my wife woke up, I told her she had been talking in her sleep. She asked me what she said and I told her, “I don’t know, you were speaking Chinese.” That’s when I realized this was NOT going to be a typical marriage. 😛
It doesn’t matter if a tiger can speak English or Chinese, what matters is whether he can catch Allen ~
March 13th, 2009 at 9:59 pm
Believe it or not, one of my friends speaks Japanese when he gets drunk! It is his second foreign language.
March 13th, 2009 at 10:49 pm
Hey berlinf,
Shouldn’t it be “syllables” instead of “syllabus”?
March 14th, 2009 at 12:25 am
hehehe, that’s an interesting theory, I’ll have to let my former professor who has a phd in linguistics know about this. 🙂 But it is always an interesting question to ask someone who is multi-lingual in what language they think in. Nice post berlinf.
Oh yeah, this is an aside, but Lu Xun was known to say that the Chinese writing system was too hard to learn and was holding Chinese students back because it was taking too long for them to learn it.
March 14th, 2009 at 12:46 am
flags of the republic, thanks! I have corrected the mistake!
Yo, I would love to hear what your professor thinks of the issue. Chinese is difficult only as a foreign language, but I always think it is well worth the effort.
March 14th, 2009 at 1:09 am
“Obama noted specifically that in eigth-grade math the U.S. has fallen to ninth place. Coming in at number 1 in that category? Students in Taiwan, fourth graders in Hong Kong took the top spot among their peers”
http://www.bostonherald.com/news/opinion/op_ed/view.bg?articleid=1157930
March 14th, 2009 at 2:50 am
I am not sure if syllables are the main contributor to the difference. You can easily transform “ten times ten is one hundred” into “ten ten one o o.” “Nine eight seven two” would be “nine times eight is seventy-two.” and use T for thousand and H for hundred and so on.
March 14th, 2009 at 4:49 am
@Allen: Strange, I dream about big, furry animals chasing me too. A couple of months ago I dreamt I was in a university somewhere, could have been the US or China, when someone yelled “A panther is loose!”. People began to panic and run in all directions and soon the panther (which was 5 meters long) was after me. I tried to run into the entrance of the main building, but it was already barricaded… Then I tried to elude the animal by changing directions, and woke up.
I don’t remember what language people yelled in.
March 14th, 2009 at 9:49 am
Interesting post, but I agree with scl. I just think that Asian kids are just better disciplined (not physical punishment) in regards to science/maths-based subjects and their parents expect them to do well in it.
But in the UK at least I’ve noticed they generally don’t do as well with arts-based subjects like Art, English and History. Is it because they can’t do it? No, some do very well. I think it’s down to work priorities. When I was at uni hardly any non-Caucasians were studying arts subjects, even though there were a fair number of them around.
March 14th, 2009 at 2:19 pm
Raj, I think it is a combination of many factors, higher expectations, more time on task, confidence (which comes from positive stereotype) ,and, last but not least, language. Language does explain why it is more difficult for a foreigner to memorize a phone number in English. A few more syllables do not make worlds of differences, but these small strokes fell an oak.
When we took English listening comprehension lessons back in college, both the teachers and students experienced numbers as one of the greatest difficulties, to teach or to learn.
Besides, there is a disconnect between the numbers and language in both English and Chinese. After all, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 are arabic. The arabic representations are accepted worldwide. Why? Because human brains love simpler representations than complex ones. The single symbols (1 vs “one” with three letters) seems to be a more natural thing for human memory. And the Chines representation shares more similarity with that the arabic system than the English one:
1, 2, 3,4,5,6,7,8,9
零，一，二，三，四，五，六，七，八，九
Zero, one, two, three, four, five, six, seven, eight, nine
March 14th, 2009 at 2:46 pm
It is interesting and sth we do not aware of when there is nothing to compare. Who says ‘Beijing-style stuffing education – memorization’ does not work? Now I know why I think in English and compute in Chinese and look/speak/write like a FOB (fresh off boat). 🙂
March 14th, 2009 at 5:03 pm
Steve & Allen, maybe you two can go to a Freudian dream analysis session together 🙂
Anyway, I also have a theory regarding language and math abilities. Supposedly people with greater spatial skills tend to be better at math. Chinese is a much more visual language (and clearly demands the use of different brain faculties from European languages). I wonder if that helps Chinese children develop better spatial skills.
Now, if Chinese parents would only stop clipping their children’s wings by putting so much emphasis on test scores and taking piano lessons. Almost all the Chinese children I know are taking piano lessons. Why are Chinese parents so intent on raising cookie cutter kids?
March 14th, 2009 at 5:36 pm
confucius said that if you read a book a hundred times, you’ll understand it. i think that’s a nutshell of why people of confucian heritage cultures (CHC) do so well in maths, and so badly in (at least) English… i read a book about rote learning, asian style, ages ago, and one point made was that it does facilitate deeper reflection than we tend to give it credit for. that makes sense: if rote learning was so superficial, CHC kids’ maths scores would be in the toilet. getting back to languages, i think that the problem is not the focus on rote learning, but the curious absence of collaborative learning. i walked into one of my classrooms once, and my students were prepping for a conversational english exam the next day. all 40-odd students were conversing their bums off… problem was, it was 40 different conversations, with their books as their conversation partners. SAD times….. i guess between the lines, there’s a lesson for us westerners: stop being so touchy feely in the classroom and ram that maths down the kids’ throats….
March 14th, 2009 at 6:15 pm
To Allen #1:
I wonder if it was a crouching tiger that looked like Zhang ZiYi 🙂
I learned the times tables in HK, much in the fashion that BerlinF suggests. I think one difference is that you don’t use “times” and “is” when you do that. So it’s “six eight forty-eight” rather than “six times eight is forty-eight”. But I agree that it inherently sounds better in Chinese than in English. Whether that makes it inherently easier to memorize, I don’t know. I think another aspect is that you were expected to know the times tables in HK (and presumably in CHina) at an earlier age than in the US/Canada, it seems.
I used to think in the language I was speaking at the time. As time goes by, however, I find that, even when speaking Cantonese, I’m thinking in English and translating back. Oh well….
What I have heard, is that when people get old and senile, they revert to their first language. That should be interesting, but by then, I probably won’t remember, and likely won’t care.
To Tony #13:
ahh, FOB. That used to be a term I was called…not so much anymore.
March 14th, 2009 at 6:31 pm
@Cheung #16.
You got promoted from FOB to OCI, old Chinese immigrant. Haha.
I remember the way we memorized the periodic table: PS. Call Ma… for potasium, sodium, calcium, aluminium, magnesium… I forget the whole phrase now.
March 14th, 2009 at 7:29 pm
@ 15
i read a book about rote learning, asian style, ages ago, and one point made was that it does facilitate deeper reflection than we tend to give it credit for. that makes sense: if rote learning was so superficial, CHC kids’ maths scores would be in the toilet.
I don’t agree with your conclusion. Rote learning doesn’t necessarily provide reflection because maths isn’t about reflection – it’s about learning methods/techniques that can be used in any scenario. For arts-based subjects reading the same text over and over and learning it by heart in of itself does nothing to help you understand it. Eventually you might understand it, but that would be from luck rather than design and is a very inefficient method.
Reading something more than once is useful in that you notice things you didn’t before, but only if you ponder. It’s much better in my book to spend more time as you read, make notes, etc rather than memorise and/or repeatedly read text.
March 14th, 2009 at 10:45 pm
I don’t think it’s a dichotomy of rote learning OR non-rote learning. Clearly, there’s room and need for both. Six times eight is forty-eight. There’s nothing warm and fuzzy about it, and you either know it or you don’t. So I think rote learning is vital for acquiring the “facts”, without which you can’t progress. However, once you’ve acquired the facts, you need to learn how to be flexible and fluid in applying that factual knowledge in solving problems at hand. Based on what others have said, that may be one of the drawbacks of a prototypical Asian education: the difficulty when faced with the need to think outside the box, or to respond to a scenario that you haven’t seen before.
The subject matter is also important. As a generalization, in the sciences, where you’re dealing with “facts”, there’s probably a greater need for rote learning. But in the arts, where you’re dealing with interpretation, there’s probably less such need.
March 15th, 2009 at 12:01 am
Bloom describes the types of learning most thoroughly in his taxonomy: knowledge, comprehension, application, analysis, sythesis, evaluation. China (and I heard Britain too) emphasizes on building a strong knowledge base which utilizes mainly the first two types of learning. Americans recieve more training in solving real-life problems, but in doing so, they may find themselves lacking in certain knowlege base items such as basic math. Unfortunately it is more likely for a wide-eyed Chinese college graduate to get lost in the real world once they graduate. But once Chinese learn of the American ways, they can be very powerful.
March 15th, 2009 at 2:34 am
oh dear this is morphing into a general discussion on education.
i did teacher training in new zealand and in my opinion bloom is used really extensively, and really badly, there. the approach of policy people and the teachers that teach the teachers is to look almost exclusively to research based theories, and they champion these approaches to education and sort of rubbish approaches that aren’t ‘scientific’ or whatever. but teaching is a craft, you can’t reduce everything to a zero or a one hypothesis (i forget the terminology). it’s like, to take carpentry, you can either do tests on a range of metals and woods and publish a book called “cutting wood: new approaches” or you can apprentice yourself to an old salty seadog who’ll say “first you need to plane this,” and he’ll look at you funny if you say “on what basis?” so, that’s how i feel about bloom, or at least, how he’s misused. research has its place, but it SHOULDNT be centre stage. on that note,
Raj: it wasnt my personal conclusion, i just read it in a book that was based on a study of different kids’ cognitive processing in mathematics. you disagree, and i’d say a majority of people would be with you in thinking that rote learning is pretty poor. the problem with that seems to be that it’s not borne up by the facts. and…. what’s the real world outcome anyway? chinese aren’t automatons, new zealand kids aren’t sages, despite all the reflective evaluation and syntheses and cross-disciplinary homework…. i meet a chinese person and i’m meeting a peer. i don’t feel like i have a distinct advantage because of my 13 years of free love vs. his/her 12 years of drudgery… i mean, i had a WAY more colourful earlier life cos it wasnt dominated by homework, but, my education doesn’t make me more or less capable, i don’t think….
March 15th, 2009 at 11:24 am
Before I could write a proper essay in English, I used to have to memorize some article, and then made a few changes here and there before handing in my English essay homework or test papers. It was time consuming and brain wrecking at the time. It took me years to get to the point where and when, like learning to ride or swim, for the training wheels and floats to come off.
Today I hear students of Chinese or Englsih complaining way before putting in sufficient hard work.
Oh, we don’t have the English environment, is the most common gripe, then there are foreigners who are in the Chinese environment who even say out loud that the chinese language is illogical and their Chinese teachers boring and are too Chinese (Huh?!)
I agree there are good methodologies and some ways are not so efficient, but I still think ultimately the buck stops at the learner (special talented individuals aside) and not so much the teacher/system.
March 15th, 2009 at 2:01 pm
My common sense. We need to use the brain more and at a younger age to stimulate those brain cells/nerve fibers. Learning piano is one of the good exercises even most will not make it as a professional pianist. Memorizing the multiplication table is another one. Watching the Einstein’s Baby DVDs may not except for the pocket of the vendor. Memorizing those Chinese characters is a good exercise too.
When you pray, do you think God understands everyone or he has an interpreter for every language known on earth (ask your preacher today)? 🙂
Is the reason God taking a long time to preach his words to China is he has a hard time to learn Chinese, vice versa for Buhdda? 🙂
Berlinf, it is a refreshing topic. If you changed it to ‘Why Chinese is smartest’, this thread would be more controversial and generate more heated discussion. 🙂
March 15th, 2009 at 3:36 pm
to Tony: “Berlinf, it is a refreshing topic. If you changed it to ‘Why Chinese is smartest’, this thread would be more controversial and generate more heated discussion. ”
I once did write a post to that effect:
http://family.mblogger.cn/berlinf/posts/92169.aspx
However, whether being “smart” takes us anywhere is a different issue. I think we are not as assertive or agressive as Americans are, and qualities may help a person more than being intelligent.
March 15th, 2009 at 4:32 pm
HongKonger: Yeah. YEAH. discussion about education is mostly about the goods and bads of styles of teaching and methodologies. but at the centre is the learner…
people are wired to learn, that’s what neural networks do. we are literally learning machines. i strongly beleive that there are two lessons that educators can learn from this:
1. students will get on with learning regardless of the educational context… so, teachers aren’t fundamental at all to the process of education. they are at best only ever peripheral to the process.
2. the potential for schools/adults to assist students in their learning is MASSIVE, and in any regime around the world, largely untapped. so, we could all do with creative exploration and sensitivity to what works and doesnt… innovation needs to be a defining characteristic of pedagogy.
i think the worst thing a school/education system can do is make teachers busy. teachers need to be reflective animals, and a busy person is not a reflective person. teachers are learners too, but they can’t learn to be better teachers if they have no time to think about what theyre doing. i believe teacher reflection is the key element in innovative pedagogy. reflective=responsive. my concern is that the process of innovation is commandeered by labcoat clad researchers up the political foodchain. this is bad. also, westerners are very good at systems, policies and procedures, but all the effort that gets sunk into maintaining regimes of procedures can diminish a school’s core business… innovation in education needs to be liberated from programmatization. i’ll stop here.
March 15th, 2009 at 7:26 pm
Given the recent world history, racial discussing without smoothing over and emphasizing the environmental factors won’t be popular.
Sometimes you just need some common sense. Let’s say you pick a random couple in Copenhagen and another in Guangzhou. They each give birth to a baby. You raise the Danish baby in a subtropical climate with a constant Cantonese diet, and the Chinese baby in a subarctic climate with a constant Scandinavian diet. On average the Danish baby will grow up still taller than the Cantonese baby, though there is a good chance that the gap is smaller than their parents. If you repeat the process for hundreds to tens of thousands of years, the gap may be erased or even the difference may be reversed.
There were some studies that showed Asian kids adopted by non-Asian families scored better in math/science tests. It seems that there are more than just the rice-paddy work ethics and presumed linguistic advantage Malcolm Gladwell explained in his new book “Outliers”.
March 15th, 2009 at 7:45 pm
Chinese kids are smarter? It could be due to Chinese (Koreans too) emphasize on education for the next generation. A lot of professionals help/supervise their children to do home work. Using black as an extreme example, they have a high percentage of single parents to start with and they do not have a lot of good examples of hard working that leads to rewarding professions.
March 15th, 2009 at 8:31 pm
Actually Gladwell in his latest book did more than just attributing Asian students’ math/science overachievements to environmental reasons. He also attempted to largely reduce the success of Jewish immigrants in the early to mid-20th century (and the subsequent generations) to luck, i.e. the choice of their main trade. Even the innate difference in IQ, in his mind, may not be that useful.
I wouldn’t mind the egalitarian society Gladwell wants to build, but if in the real world, an Asian kid with a resume that would otherwise put a black or Hispanic kid to a first-tier university, gets rejected by a 2nd-tier university, you are not really building a racially blind society, but rather a society that disincentivizes personal achievements and personal accountabilities.
March 15th, 2009 at 8:32 pm
I don’t think it has anything to do with genetics, that’s where Racism comes in. Those children adopted from China have parents who are ususally familiar with the Chinese ways of teaching and learning, so they may not be like the typical American parents.
The adopted kids also may associate with other Chinese kids, thereby raising the bar for peer comparison. Families with kids adopted from China also form all sorts of support groups which helped them to exchange ideas and information.
Chinese parents hang out together pretty often using occasions like Chinese schools to share information, resources, and exchange ideas. These parental communities of practice help too.
March 15th, 2009 at 8:35 pm
Ever hear of the Sapir–Whorf hypothesis?
http://en.wikipedia.org/wiki/Sapir-Whorf_Hypothesis
“The hypothesis postulates that a particular language’s nature influences the habitual thought of its speakers: That is, different language patterns yield different patterns of thought. This idea challenges the possibility of perfectly representing the world with language, because it implies that the mechanisms of any language condition the thoughts of its speaker community.”
Not to speak of understanding each other….
March 15th, 2009 at 8:36 pm
Besides, expectations are different. An American parent may take pride that his/her child get into a football team or even a cheerleading team. Chinese parents would not have taken too much pride in that. They would be more satisfied their kids get better scores in their exams. An American parent would praise a school child if he or she gets a B. Chinese parents have to see As.
Of course these are all generalizations. There are many exceptions on either side.
March 15th, 2009 at 8:41 pm
Regarding affirmative action; doesn’t China do it too, with regard to ethnic minorities? I look on it as less of a matter of being unfair and as more of a matter of bribing disenfranchised minorities not to riot or turn into a disruptive interest group
March 15th, 2009 at 8:57 pm
to ecodelta: Thanks for sharing that information. I definitely think that language shapes the way we think. Language does more than just “represent” our thought (which is just electrons cirlcling in our skulls anyway). Language changes thought. My favorite example about vehicles. In China, we have the word “che” to symbolize a whole lot of vehiciles. No matter how different they are, they are a type of “che”, such as steaming che (car), fire che (train), three-wheel che (tricycle)….
When it comes to scientific terms, Chinese terms also start from the familiar CO2 for instance is “one carbon two oxygens”. These explains why the average reader can read a math and scientific article at the basic level.
March 15th, 2009 at 9:30 pm
#25
Vam,
Good post.
I am a simple man with simple ideas. I grew up listening to the radio. I loved the Beatles, Elvis, the Rolling Stones, Led Zeppelin, Bob Dylan etc. But about half of time with many of my favorite songs, I had no idea what they were singing about, especially with Dylan’s poetic political lyrics and most Hard Rockers’ mumbling and or screaming out their lyrics. Same with movies, James Bond, the Longest Day, the Great escape, Ben Hur, walt Disneys, etc. Couldn’t comprehend most of the dialogues, but so what? Took me forever to go from understanding 20% to now nearly 100% of song lyrics and movie dialogues. The final hurdles were pertinent cultural understanding, humor, and political references, and those took a lot of crosscultural experiences, reading, speaking, listening and oh, very important: Singing: I learned about class struggles from singing John Lenon’s “The working class hero,” “Imagine”etc. I learned about the pains of war from Dylan’s, “Blowing in the Wind,” general love affairs and infidelity from, well in most songs, like Rolling Stones, you’ve got ” Angie,” the Eagles’ “Lying eyes,” a bit of theology from “Sympathy for the Devil,” etc.
So, I agree with you teachers are learners too, they need to reflect and adapt. I often find myself humming “All you need is love,” when I get discouraged, and apply that concept to the universal axiom,
“Treat others as you would like others you.”
Like I said, I am a simple man with simple solutions. Learning from mistakes most of the time.
March 27th, 2009 at 2:12 pm
Hello all 🙂
From my persepctive as a former teacher of a classload of lovely Taiwanese kids aged 4-7, I have to say they really do have *lots* of extra schooling in maths (amongst other things) from a really young age and I believe this is why they would hve been streets ahead of a class of UK kids of the same age. I can’t believe that this base for knowledge ever really leaves them in later life either..not having watched a 7 year old use ‘head abacus’ to work our multiplications faster than I could type them into a calculator. However I would not go so far as saying this is a racial difference – after all I’m sure there are masses of illiterate and disnumerate kids in poorer parts of China / Taiwan, I only ever met the nicely brought up ones with aspirational parents. When talking of Chinese kids adopted by western parents…these are exceptional cases. (especially as so many adoptees are female..you could be looking at a female/ male difference instead).
@25 point 1#- I think teaching method is important, as is teacher ability, as is also the attitude of the child to what they are learning (largely influenced by the parental attitude). The Taiwanese kids in my class, having been educated by English teachers from as young as 2 spoke English with great confidence, showed as much creativity as you would find in any classroom of English speakers anywhere in the world – things against the stereotype of Asian kids. point 2# – is this not contradictory? maybe i have misunderstood.
As for language…yes I definitely believe that the way one expresses oneself and the linguistic kit one has to hand influences ones thought processes. (as described by Hongkonger in 34# and indeed the original post).but not *that* much. Whilst a professor I knew once wrote a paper disproving the validity of arithmetic (Godels proof) in four languages for this reason- he felt formal logic needed Latin, arithmetic French (as it flowed better), Greek for the verbal proof (for the simplicity of the language) and English for the desription of aims and conclusion – he could equally have written it all using any one of these languages.
After all, within English-language speaking nations there is quite a range of national sterotypes.If you look at the stereotype for a Brit, we are aloof and reserved , the stereotypical ‘septic’ as the Aussies call them is overfriendly and undereducated and the stereotypical Aussie is sporty, positive and chauvinist. I would say what you might call ‘national experience’ counts for more in affecting attitude and aptitude alike in generating those slight general differences that create such stereotypes, much less than the language used. Education systems are part of this ‘national experience’.
Incidentally, Hongkongers post puts me in mind of a guy in Indonesia I met who learned English listening to Bob Marley. He always smiled when he spoke English.
March 27th, 2009 at 3:47 pm
OOM, thanks for the insights from the “frontline” of teaching kids in different languages. Language may play a very small role, but a role nonetheless, in making certain learning content easier. But I agree that after a certain point, all developed languages are equally capable for the teaching purpose.
Time on task can make more difference. Sometimes I wish that US schools will prolong the hours for kids. Now kids go back home at 2:45. Then it is up to parents to decide whether they will learn or watch TV (sometimes learn from watching TV, but that’s dubious).
March 27th, 2009 at 3:50 pm
Not all stereotypes are bad though. I just ask my kids to live up to the stereotype of Asian kids being good at math as a way of pressing them to learn:-)
March 27th, 2009 at 4:09 pm
@ OOM & Berlin: I’ve never taught English overseas so I’ve enjoyed reading everyone’s theories who have more experience in this. However, I was wondering what you all thought of the Mormon (LDS) language program. I’m not Mormon but they seem to turn out language proficient speakers in a very short time period using methods that seem to work really well. I’ve often thought that rather than re-invent the wheel, the American school system should use the Mormon training to teach language.
Are you familiar with their teaching method? Is it something that is already studied and utilized?
April 30th, 2009 at 5:31 pm
I just made a post on Malcolm Gladwell’s chapter on this phenomenon, but from a perspective of someone who loves languages:
http://translation-blog.trustedtranslations.com/the-chinese-la…bility-in-maththe-chinese-language-numbers-and-ability-in-math-2009-04-30.html