Chinese versus American Math Education

Seth Roberts

When she was in eighth grade, a Chinese friend of mine moved from Shanghai to upstate New York. (Her dad worked for General Electric.) In New York, she discovered she’d already learned eighth-grade math — in fourth grade. Her new school moved her to tenth grade math. It was still material she’d already had, but less absurdly easy.

If 80% of American parents knew this, would they abide it? Or would they decide that something is terribly wrong? Now, of course, almost no American parent knows this.

28 thoughts on “Chinese versus American Math Education”

  1. The Chinese students may have a higher aptitude for math that allows for a steeper learning curve than American students could tolerate. In my town, even the American born Chinese students seem to have a relatively high aptitude for math. This is evident even at early grade levels (kindergarten, first grade) where I assume differences in parental emphasis on education would not yet have a great effect.
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  2. Do you suppose that learning a particular language at an early age predisposes one for certain activities? Such as Chinese or Russian for math and German or English for physics?
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  3. “If 80% of American parents knew this… ”
    .
    Then nothing would change at all.
    Parents already know that American kids lag many other nations in math & science. It’s been a loud, consistent theme in the U.S. media for decades. yawn
    Secondly, “parents” are typically unable to analyze & understand the core deficiencies of the American K-12 school system. They are direct products of that miseducation system, and have been heavily indoctrinated by that very same “system” to accept it as is. The fundamental dysfunctional, and despotic nature of compulsory mass schooling is truly invisible to most Americans.
    Thirdly, parents have zero practical power/authority to improve that education system. Parental power was lost long ago to legions of government education administrators, bureaucrats, and NEA lemmings. Real power has consolidated at the distant state and Federal bureaucracies.
    Imagined parental-power over the vast calcified government school empire is extremely naive.
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  4. I once heard a math professor at a very large and well known university with a very strong math department say that, by the age of 12, most children have the necessary brain development to understand basic calculus.
    I’ve always wondered if that was true, and I’m curious if anyone else has any comments about it.
    In some countries, all high school students are required to take calculus in order to graduate. So, it seems that by the age of 18 many (most? all?) people have the ability to comprehend math at that level.
    There’s always the sneaking suspicion in US schools that we just aren’t teaching math properly/assigning enough homework problems/exercising the students’ minds/providing enough body armor/etc.
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  7. College professors are some of the least self-aware people I have ever encountered. That math professor is full of sh*t. My experience teaching high school students is that at the age of 12 many of them don’t have the brain development to understand basic algebra, let alone calculus.
    There is a big intellectual leap between “what do you have to subtract from 12 to get 7?” and “12 – X = 7; what is X?” It is a leap that some people (like “a math professor at a very large and well known university with a very strong math department”) make easily, so easily they don’t even realize it is a leap.
    I don’t know how many countries require passing calculus to graduate high school. If they are honest in their testing (a very big if), then nowhere near 100% of their 18 year olds are getting high school diplomas.
    Math doesn’t come easy to lots of people in the USA. Even if we’re “teaching math properly/assigning enough homework problems/exercising the students’ minds,” lots of them won’t “get it.” Education Realist has an interesting post on, “The myth of ‘they weren’t ever taught …’”
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  9. Robinson (of the Robinson Curriculum) had his kids teach themselves math from second grade on (among other subjects). They would finish calculus between the ages of 14 and 17. Although I don’t necessarily agree with all of Robinson’s methods it shows that people are very capable.
    Government schooling is a waste of time, even private schools. Best just to home educate if possible.
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  10. “Imagined parental-power over the vast calcified government school empire is extremely naive.”
    I didn’t say that — that parents have control over the “school empire”. I don’t know what would happen if parents had a better idea of how bad American education is relative to other countries that also engage in “despotic . . . compulsory mass schooling”. (My anecdote at least suggests that compulsory mass schooling is not the only problem.) I am much less sure than you that the answer is obvious.
    I think recent history supports your claim of powerlessness. Michelle Rhee, Diane Ravitch, Geoffrey Canada — none of them derived power from parents. But I also think most parents don’t understand how far America is behind other countries.
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  11. My 15-yr old son is doing AP Calculus along with some of his high school friends of the same age. I think he could have handled it a 2-3 years ago.
    He’s on the same curriculum path his 2 older brothers took. And our family isn’t even Asian.
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  12. “I don’t know how many countries require passing calculus to graduate high school. If they are honest in their testing (a very big if), then nowhere near 100% of their 18 year olds are getting high school diplomas.”
    “The Chinese students may have a higher aptitude for math that allows for a steeper learning curve than American students could tolerate. In my town, even the American born Chinese students seem to have a relatively high aptitude for math.”
    I have counter-examples for both of these statements. I am an Eastern European – schooled there up to finishing high school. We did high-level calculus in grades 10-12 and most students were pretty good at it. Most of them were white. I don’t think you have to be Chinese (or Asian) in order to understand it. Most Eastern European countries have similar math courses in high school and do high level math for grades 5-8. Testing is fair. I don’t know much about Western Europe.
    I went to college in the US. In my first year I was taking differential differential equations and doing fine while most American peers were seniors. Eastern European friends that moved to the US during high-school often mentioned how their math and science classes were “so easy” because they did that material 4-5 years previously. I don’t have direct experience with this but tend to agree.
    I’m not blaming parent involvement or teacher or anything. I have a distinct feeling that US education was on par with most European schools in terms of difficulty (pre-undergraduate) but schools started to focus on standardized tests and what not and started to “teach to the test”. The SAT only has very basic math in it. The GRE also deals with pretty basic math. I got really high scores in both on first try without years of standardized testing experience or preparation. I am in no way a genius; most of my high school classmates probably would have scored similarly.
    P.S. Something that might contribute to this – Eastern European students tend to “specialize” before high school. Some of them go the math/science route, and take exams to get into those courses, and follow a mainly science curriculum, others do art/music and all that implies, and others do humanities. The students themselves have to discover their aptitudes and needs and apply for the route to match.
    Most humanities students only take basic math and are never expected to take calculus for their final graduation exam for example. While science route students have to and their work is mostly centered around scientific subjects. Maybe that focus has something to do with it?
    Seth: Good comment. Including correct use of “steep learning curve”, which is rare.
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  13. “I have a distinct feeling that US education was on par with most European schools in terms of difficulty (pre-undergraduate)”: no. I can remember the debates in Britain in the late sixties when the Forces of Progress were determined on “comprehensivisation” in the secondary schools. “We want to copy the US” they said. Their opponents howled with anguish: everyone with experience of sending children to American schools seemed to leap into the fray, dismissing American standards as hopelessly undemanding. It was, such people said, the Germans and French from whom we should learn about secondary schooling – it was only at graduate school level that we needed to learn from the US.
    I’ve spent most of my career in good universities and everything I and my colleagues have seen – on academic leave, on teaching Americam visiting students, and so on – says that the Forces of Conservatism were right in the sixties. Indeed, in spite of decades of the dragging down of British standards, American schoolchildren still manage to be more poorly prepared for undergraduate studies, it seems.
    Nor is the problem remotely confined to STEM subjects: colleagues have reported the problem to be worse in languages, with Americans expecting to work from translations into English rather than reading in the original tongue. The fact that few Americans seem to know much history or geography is also remarked on.
    The tragedy of all this is that the American exchage undergraduates that I’ve taught have been clever, unusually keen to learn and very hardworking. By God they’ve been let down by the schools, and it would seem to have been a problem for generations.
    Seth: I agree with all this. The mere fact that it has to be said is one sign of how poorly Americans grasp how badly their education system works, compared to many other places. Why education reformers don’t pound this — American kids much more poorly educated than other rich countries’s kids — into us is a question I can’t even begin to answer.
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  14. “If 80% of American parents knew this, would they abide it?”
    Of course. They know it now. How is you think most parents aren’t completely aware of this fact?
    But of course, by “American parents” you mean suburban, probably white, parents. Asian parents living in this country are well aware. That’s why many of them came here, to avoid the hyper-competitive atmosphere back in China and Korea–and it’s why most of them pay for hagwons over here.
    But then, it’s only a tiny fraction of “American parents” that delude themselves into thinking that students could be learning more, if only we bothered to teach it to them–or that the brightest kids are suffering by not learning material they could have learned in 4th grade in 8th.
    Cheating is rampant in China, and while they cover rote material quite well, it’s very obvious that they aren’t encouraging their kids to think critically. So distrust what you hear that “most” Chinese students are doing, because “most” of them cheat. And those who aren’t cheating are desperately memorizing. That’s why the Chinese have largely taken over the top 20% of most elite US universities without having even begun to start taking over the country.
    And many, but not most, American parents know all that, too. Especially the ones who live next to lots of Chinese, Koreans, and Indians (who cheat, too).
    Some overstatement in this comment, but nowhere near as much as in your single “most American parents”, so we’re even.
    Seth: “They know it now”. They do? They know education is other countries is better as measured by standardized tests — and some of them wonder whether the test scores coming out of China (comparing Chinese students to students in other countries) can be trusted. I don’t trust them. I don’t think most parents know concrete examples like this one. This example cannot be explained by cheating.
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  15. dearieme – you might be right. I was basing my assumption on my professors’ stories and impressions. I don’t know how it was in the past. The more modern trend of standardizing everything certainly doesn’t help.
    I have a similar experience of American undergraduates – they are quite clever, hardworking and keen on learning. My friends and I used to envy them on their “fun” experience with school. For us it was a very formal environment; american students pre-undergrad get to have more fun. We didn’t have a well-stocked chemistry lab, so we did very few experiments and many more paper and pencil problem sets. My American friends did many more experiments. I guess the answer might be somewhere in the middle? I do appreciate Seth’s continuous efforts towards finding better ways of learning.
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  16. I’m reminded of an NPR piece I heard a while ago– it claimed that elementary math in American schools is based on a theory that it should be dabbed at repeatedly in the hope that students will eventually pick it up, rather than thoroughly understanding a concept and then moving on.
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  17. This probably has something to do with Chinese education being completely focused on their college entry exam, the 高考. Chinese education emphasizes rote memorization above everything else, which I imagine is useful in math. They don’t learn how to derive the answers, they just memorize which equation to use for which problem and that’s that. While Chinese are able to do well in certain areas based on all of this, it doesn’t foster creativity and Chinese children’s lives are Hell compared to American children. After school they go to after school school and continue memorizing material for the next test. Very few of them play sports or have time to “just be kids”. I remember when I was a kid I would go out in the forest behind my house after school & just play around, build forts & stuff for hours at a time. They say “time in nature” is highly correlated with empathy. Aside from creativity, another thing greatly lacking in Chinese culture is empathy.
    Don’t get me wrong, this seems like a scathing rant about Chinese. I’m married to a Chinese woman & have lived here for 3 years. I do like aspects of China, but the price their kids pay to be “good at math” & to pass a stupid test is not worth it.
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  18. I don’t understand what they get for all this.
    I can use myself as an example though I’m not Chinese.
    I spent a lot of time on math growing up. All I could really do, however, is solve a given type of math problem fast. And then, over time, I’d probably forget the lesson that I’d learned. I was also part of the math competition team.
    I didn’t really do anything useful or interesting with the math I learned. I didn’t use it to solve any real world problems.
    I don’t really use any of the math I learned at my job. In fact, when I look back on it, I wish I’d spent less time on math. I took way too many classes. I wish I’d looked ahead to figure out how much math I’d need later on in life and only done that.
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  19. A co-worker from China told me that the reason they are better than us at math is that they teach their kids to count on their fingers.
    We have been using the fingermath method to homeschool our kids.
    https://www.amazon.com/The-Complete-Book-Fingermath-Scientific/dp/0070376808
    The book was meant to be a textbook (in the 70′s?), but it never caught on.
    It is essentially a “finger abacus”. Right hand is ones, left is 10′s, thumbs are units of 5. You teach the kids how to transition (once you put all four fingers down, you pop them up and put down your thumb — thumb and four fingers down, then you pop them up and put down a finger on your left hand). They are the ultimate math manipulative.
    My daughter is starting second grade math. All the topics are redundant – carrying? It is obvious with finger math. Borrowing? Obvious. having the numbers written horizontally instead of vertically? No need to rewrite.
    Moving on to multiplication–skip counting by 5s? By 10s? No need to drill, just show it to her.
    If all or most Chinese learn like this, a chunk of our basic math program is redundant. On top of that, the Chinese kids would probably have a better “number sense”, and less math anxiety.
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  20. “I don’t understand what they get for all this.”
    That’s a good question. I was good at math as a kid. Now it’s helpful with statistics, which I use all the time. Many psychology professors seem afraid of statistics. This is a huge problem for them because they often let other people analyze their data. It inevitably gets analyzed badly but they are unaware of this.
    Chinese students who get a perfect score on the math GRE, as many do, find it easier to go to graduate school in America. I think math ability makes engineering more of a possible job. A friend of mine at Berkeley wanted to be a doctor. She changed her mind after her first science class. Maybe better math would have helped.
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  21. I often asked myself what will I do with all that math/science I took as I child. And trust me it was a lot. Often times we would skip sports class and do math. As a child I did find it sometimes useless.
    From what I can tell so far it’s that it does “shape” your brain somehow. People who take the math/science route from my country have some aptitude in it, but for the most part, they end up at the end of it all thinking in a more analytic manner. It was very easy for us to pick up new science subjects in college, or to get good at programming fast, because of the way our brains were “re-wired”. Even in our current jobs it’s much easier for us to grasp certain scientific subjects or understand things that seem to baffle the humanities folk. We’re not doing math exactly, but I am pretty sure we are using those connections that we formed in the past.
    I don’t have any scientific proof of this, it’s more of an observation. Wish somebody could do a study at some point to look at how school shapes your mind:)
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  22. I had to take 20 hours of advanced math for my computer science degree, earning high grades in each class. In my work, I used a little bit of set theory but no other math concepts. So from my personal experience, I’m not convinced that America would be a better place if all kids learned more math. The Computer Science department grew out of the Math department. It was obvious they forced all those required math hours just to keep their math department employed.
    I am more worried about two related issues, both of which I have seen happen to kids I know. (By kids, I mean I knew them when they were friends of my children when young and now they’re grown up and in their twenties.)
    The first: why are so many boys failing in school?
    The second: why do so many smart girls choose unemployable degrees?
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  23. Seth, I’m curious as to the value of taking algebra by 4th grade?
    In my own socialist/”Communist” country (not China), 4th grade included Geometry and Algebra content–stuff beyond anything most US students learn till high school. I thought this was great, because I loved mathematics.
    But other kids, those who didn’t love mathematics, didn’t think it was so great. They fell behind pretty quickly. Then again, this was a system that did not try to educate all of its students. So it didn’t matter if some kids were held back for a while because they couldn’t master linear equations by 5th grade. China, I understand, is more similar to this than United States (where we try to educate every child).
    Given that most students simply do not need this knowledge, what is the value of this type of education? To produce “useful” citizens? If it’s product is me, I have to tell you, I’m not particularly “useful”–my pure mathematics degree isn’t really gonna help me do anything useful.
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  24. One more thought. It seems that Seth and most of the commentators are aware of some international comparison studies I am not when they draw the conclusion that “most parents don’t understand how far America is behind other countries.” I guess I don’t either!
    The standard, which I take to be TIMSS, shows U.S. 4th and 8th graders are doing fine, on average. Could be better, yes, but a far cry from what media and politicians tell us. For example, many people I talk to seem shocked to learn that we do better than Germany. In fact…
    In 8th grade, the 11 education systems with average mathematics scores above the U.S. score were (South) Korea, Singapore, Chinese Taipei (Taiwan), Hong Kong-CHN, Japan, Massachusetts-USA, Minnesota-USA, the Russian Federation, North Carolina-USA, Quebec-CAN, and Indiana-USA. Note that 4 of those 11 were states in the US!
    The countries which do outscore us are very different than the United States. Education-focused culture, homogeneous, and/or not interested in educating the bottom 20% of students. Given that United States cooperatively downplays the importance of education, is heterogeneous, and attempts to educate all students, I genuinely don’t see how we’re so far behind as many here assume.
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  25. “This example cannot be explained by cheating.”
    No. It could possibly be explained by rote learning. It could also simply be that your friend’s daughter was smart. By no means does it mean that the Chinese are that much more advanced than we are.
    And most parents would know, I hope, not to think one concrete example was evidence of what’s going on in a huge country like China.
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  26. ” It could also simply be that your friend’s daughter was smart. By no means does it mean that the Chinese are that much more advanced than we are.”
    I will find out if my friend was in a special school or class.
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  27. S.M.,
    I think you may be agreeing with me. I said, ““I don’t know how many countries require passing calculus to graduate high school. If they are honest in their testing (a very big if), then nowhere near 100% of their 18 year olds are getting high school diplomas.” You said that your fellow students took calculus but they had specialized before they entered high school and the non-science specialists didn’t take calculus.
    I don’t doubt that some high school students can handle calculus. Even some 14 year olds can (e.g., the kids jon mentions). However, most American 17 year olds simply cannot. And I feel fairly sure that there is nowhere in the world where close to 100% can.
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  28. It is not only the Chinese children. I am from Spain and was an exchange student in Iowa where I did the 11th grade. Math was really easy for me because I had already learnt everything they were teaching two years before. But it was not only math, the same happened with Physics and Chemistry where I got the best grades of my class without even trying for the same reason, everything they were teaching I had already learnt before.
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