Chinese Math Students vs. English Math Students
April 26th, 2007 by MarkThis is a recent test used in England:
Royal Society of Chemistry
Here’s a Chinese math test:
The BBC also has an article talking about how many students are actually being discouraged from taking math classes:
Chief executive Richard Pike also said universities were increasingly having to run remedial classes in maths.
The Department for Education and Skills said more pupils were studying maths.
Dr Pike said: “Schools and students are reluctant to consider A-level mathematics to age 18, because the subject is regarded as difficult, and with league tables and university entrance governed by A-level points, easier subjects are taken.”
BBC: Pupils ‘are urged to drop maths’
Understandably, some UK educators are upset by reports such as these, and point to possible weaknesses in Chinese education. Still, I think some criticism is valid. I know that many of my students here in Taiwan are far ahead of what I remember students doing in US schools. I think that one reason Asia has developed so quickly over the past several decades is simply recognizing the value of mathematics. Obviously political systems play a huge role, but the fact that it’s very easy to graduate from a western high school with only two years of math isn’t a good thing in my opinion. The fact that it’s so common to graduate with a 4-year degree with little further mathematics study is even more disturbing.
Gian-Carlo Rota of MIT explains why:
When an undergraduate asks me whether he or she should major in mathematics rather than in another field that I will simply call X, my answer is the following: “If you major in mathematics, you can switch to X anytime you want to, but not the other way around.”
Alumni who return to visit invariably complain of not having taken enough math courses while they were undergraduates. It is a fact, confirmed by the history of science since Galileo and Newton, that the more theoretical and removed from immediate applications a scientific topic appears to be, the more likely it is to eventually find the most striking practical applications. Consider number theory, which only 20 years ago was believed to be the most useless chapter of mathematics and is today the core of computer security. The efficient factorization of integers into prime numbers, a topic of seemingly breathtaking obscurity, is now cultivated with equal passion by software desigers and code breakers.
I am often asked why there are so few applied mathematicians in the department at MIT. The reason is that all of MIT is one huge applied mathematics department; you can find applied mathematicians in practically every department at MIT except mathematics.
Gian-Carlo Rota: 10 Lessons of an MIT Education
As an English teacher, obviously I feel that English is an important subject. Still, I’m more concerned with people undervaluing math. I’ve never met anyone who made it through high school with only two years of English classes, or completed college with no further English.
Related article: Chinese and English speakers’ brains handle math differently (MSNBC)
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April 26th, 2007 at 10:34 am
The comparison is slightly misleading - the diagnostic exam assesses whether a student needs remedial math, while the “pre-entry” test is the gaokao and is supposed to be challenging. No doubt there are differences in math education, but this example is a bit overdone.
April 26th, 2007 at 11:21 am
I agree completely. I’d also wager that the UK Royal Society of Chemistry hand picked the problems in order create the most embarrassing comparison possible. I still think their concerns have merit, though.
April 26th, 2007 at 1:02 pm
I think the bigger point is that it is becoming harder for places like the US and the UK to stay competitive with some other nations that have a stronger focus on math. Science and technology are increasingly important, and other nations are doing a better job at preparing their students for jobs in these fields. Besides, math isn’t only helpful in learning how to solve mathematical problems, but it’s also an exercise in logical thinking.
In my university back home, I taught a remedial math course for college freshmen, and tutored students who were studying to be elementary school teachers. It was disturbing to know that they had difficulty with “simple” math like percentages and fractions. Now I am teaching math to Taiwanese high school kids who could be teaching me, if only the subject weren’t taught in English. Whether or not the examples given here are exaggerated, I think it still highlights a topic to which places like the UK and the US need to be giving more attention.
April 26th, 2007 at 6:40 pm
Allow me to ask the burning question asked by many math students when I was in high school “When are we going to use this if we don’t go into Math in university?” I am NOT downplaying the need for better math skills in western countries but am curious to hear your answer.
PS- Your blog has been a goldmine of interesting stuff the past few months even if I don’t always understand what you are on about.
April 26th, 2007 at 11:27 pm
I’m not sure I understand your point. If math was really as important as you infer, wouldn’t society have corrected this imbalance? If not, maybe English is more important than math in terms of general success in US society after all.
Honestly, I know of no one among my university/grad/law school classmates who complain of not taking enough math courses.
After all, the current logic is that we can still import the mathematical/scientific know-how we need from India and China (and to a lesser extent, the former Soviet Union.)
I would also be very cautious about attributing Asia’s economic development to ‘math’. ‘Appreciation’ of math had far less to do with it than Cold War geopolitical realites.
April 27th, 2007 at 12:18 am
Elliot,
If your question is how much math people need to use after high school, the answer is very little. If they don’t want to use math past arithmetic, they can pretty much avoid it for their entire lives. The same would also be true of poetry, music, literature, history, and just about anything else taught in high school, though.
If your question is how much math people can use to further themselves after high school, then I would say that they would be very hard pressed to find a discipline in which math couldn’t help them in some way, or a branch of mathematics that couldn’t be used for some discipline.
Personally, my math skills helped me get a job doing 3D graphics engines before I had a degree or much of a background in computers, they paid for my college, they helped me enormously with my poker game, and they’ve helped me with my investing, too.
April 27th, 2007 at 2:34 am
Prince Roy,
I think society actually helps create this imbalance. Think about it. Most of the people teaching in elementary schools are the very same people who weren’t very interested in math themselves. It’s only natural that the opinions of elementary schools would have an effect on their students.
It’s true that law school is another haven for the non-mathematically inclined, but I would still be shocked if your classmates regretted not taking enough English (or any other subject) as uniformly as Gian-Carlo Rota’s students regretted not taking enough math.
You’re right that talent can be imported from China and India, though. Over the past decade, Immigrants were the founders or key executives of 52 percent of tech and engineering companies started in Silicon Valley, and Indians alone accounted for 26 percent. I’m not sure how good of a long term strategy this is for the US, though.
April 27th, 2007 at 11:59 am
You may never use math as you did in school, but there are important concepts that can be learned from math, such as extrapolation, abstraction, critical thinking and what not. Unfortunately, math teachers often fail to explain real-world application or benefits, but that is a topic for a different time.
All of those proofs you might have had to battle with in geometry might seem pointless, but a proof is much like a term paper, you need to prove your argument by providing evidence. It is another approach to critical thinking. Solving equations may have been pointless, but if you understand the relationships that the equations represent, the relationships can helpful when you analyze a graph and extrapolate from it.
Math is really a just a language, a very concise language that holds a lot of information through strict relationships and grammars. I suppose that one could express the same ideas using regular languages, but it would be very hard to follow as it would go on for pages and pages.
I guess my argument for why math is needed would be that it reinforces critical thinking and problem solving skills.
April 27th, 2007 at 6:54 pm
“You may never use math as you did in school, but there are important concepts that can be learned from math, such as extrapolation, abstraction, critical thinking and what not.”
All of which I learnt in language and literature classes. Conclusion: Maths is not as important as some like to think.
April 28th, 2007 at 12:53 am
All of which I learned in math, not literature. Literature is not as important as you think. Believe me I am doing fine in my career as an electrical engineer without literary criticism and the “body of literature” in the English language, just as people in non-technical fields probably are doing fine without math in their career. Can you not see the value in learning a different way of approaching an issue/problem though?
I read plenty of prose and enjoy a good book as any one might, but I’d have rather spent the 4 years of literature in the electronics lab, music room, or in art class rather than reading Milton and all of that. I wish my classes had focused more on English grammar and rhetoric rather than British “classics”. Perhaps yours were better than mine, I don’t know. However I do appreciate that in criticizing the literature, I was exposed to a different way of critical thinking. I never use it directly, but I can appreciate it.
You do, however, highlight another important issue in that learning styles vary from person to person. That is another topic though.
April 28th, 2007 at 8:56 am
Sorry, Bryan, I was over-tired last night and it seems I didn’t express myself so clearly: I certainly did not mean to suggest that one field of study is more important than another. As you say, learning styles vary, and that is another topic, all I’m saying is that everything everybody claims to have learned in maths I learned in different subjects, therefore I find it hard to believe maths is in any way more important than other fields of study. Having said that, I wouldn’t for a second pretend that a solid education in literary criticism is in anyway necessary for a successful career as an electrical engineer. So in fact, I agree with you completely.
April 28th, 2007 at 1:11 pm
I am sorry too, I think I misread your post. Sorry about that. I agree with you 100% that math is not more important than any other subject. In fact I feel that being able to write one’s native language is probably the most important.
However, exposure to math is certainly important, just like literature and art and basic science. As Holly pointed out, some people are walking away with advanced degrees in education yet they cannot add one third and one half if given some paper to work it out. All students don’t need to take calculus or advanced maths, but at least one course in algebra is important because it teaches a new way of thinking. I think a course in applied statistics and discrete math would be more valuable to students who don’t plan to go into science or engineering would be helpful. That is also another topic though.
Requiring stricter math requirements for all students though is certainly not going to fix the problem that western countries face when it comes to lack of people working in science and engineering. Financial incentive, affordtable training and education, more free time for students to explore in the laboratory, as well as access to mentors and professionals would certainly help. I don’t see any of those being realized though, so until it gets too expensive (and then it is too late) to import the skilled labor, I guess it is all we have.
April 28th, 2007 at 1:15 pm
Ha ha, perhaps I should have worked harder on my English though.
April 28th, 2007 at 5:28 pm
[...] further to a discussion at over at Mark’s…. Find x. Posted by wangbo Filed in [...]
April 29th, 2007 at 3:56 am
Bryan said:
Very true. This is probably why philosophers started using mathematical notation for symbolic logic long ago. Even now, symbolic logic courses are cross-listed as both mathematics and philosophy courses in most universities.
April 30th, 2007 at 2:56 am
这条消息的发布恰好与一些废除高考的主张重合, 因此引起了网络和传统媒体的广泛的关注. 普遍认为, 在高考制度下, 由于考生高强度备考, 为达到选拔的目的, 出题者不得不加大难题, 怪题的比例, 多年来形成恶性循环, 导致数学教育脱离实际.
遗憾的是, 解数学难题三十年(2007年是恢复高考30周年)之后, 大部分人并没有认清数学的重要性. 最近有报道说, 教育部准备降低数学的难度, 压缩教学内容. 而针锋相对的, 理工类高校则普遍指责高中数学教育失败, 大学生数学水平太低, 需要在大学”回炉”.
教育部与高校的矛盾根源在于, 中国的数学教学一贯重计算而忽视逻辑. 一方面是传统使然(中国古代数学家的著作普遍以计算为主), 一方面计算题在批改时比证明题方便很多. 中国中学生从来没有接触过形式逻辑, 高校也普遍重视高等数学而轻视数学分析, 除数学专业外, 近世代数不被归入本科教学计划. 这导致了中国学生思维缺乏严谨性, 不能有条理的考虑问题. 高考制度实施30年, 没有为世界贡献一位有影响力的数学家, 足以说明这些年来的数学教育基本上是不成功的.
April 30th, 2007 at 2:20 pm
Serw, I think the problem of having too many questions that involve calculations and not enough proofs is going to happen anywhere. Proofs are just far more time consuming to grade. I wouldn’t say that there aren’t any well-known Chinese mathematicians, though. 曹怀东 and especially 朱熹平 are well respected for their work on the Poincare Conjecture, a problem that has baffled the top minds for over a century. 朱熹平 has published quite a bit of respected work, actually.
Maybe the real issue is that none of the contemporary mathematicians are well known to the populace at large. For that matter, few academics of any type are.
May 5th, 2007 at 9:13 am
It’s friggin sad. Remember a report a few years back showing how much more advanced in math and physics Chinese Middle School students were compared to US high school students. As a fomer one of the latter, that makes me sad. But, hey, I suck at math too.
May 12th, 2007 at 1:24 pm
for me, math and physics are so much easier than literature..:(
with math/physics.. everything is logical and predictable if you know the rules and all factors;
Literature, on the other hand, invovles many unknowns - one need to understand the cultural/historical/xxx contexts before they can comprehend a language
June 8th, 2007 at 10:13 pm
Apparently you are not aware of the size of Chinese population… If you were, you would know that even if the two problems presented were for the same circumstances in both countries, China still needs to increase the level of competition to afford such a high number of students they will get, so I guess you need higher standards because you will have a larger number of students that will know how to solve that… just out of the number of the population, and placing the “American” problem in a selection exam in such a big population would lead to a high number of people with good scores.
August 28th, 2007 at 4:46 am
it s ok, these 2 tests are not that hard. i am from china, i think since i was born there, i should get used to it. dont u guys think american students are eazy. i am a college student in america now, and i found the math, chem, ps were tough , even though i had studied in china for about 12 years.
October 18th, 2007 at 5:21 pm
I was reading an article from another source and they mentioned that in china most of the problem solving and talking is done by the students in class. Every single class I have had (Being an american student) has been mostly focused on lecture. What is the point of attending a lecture without any requesite knowledge of what is being presented? There is none. How is a student supposed to familiarize themselves with concepts without engaging in them (In the exact environment where the Maximum amount of learning is supposed to take place; namely the classroom with the professor)?
The next series of steps involve the teacher/professor finishing the lecture, assigning homework (which is usually due the next class), then ushering the students out of the room. The students can the go home and work on the homework assigned; but they may have an unanswered question, which of course they can ask in the next class. This process leaves the student who “does what they are supposed to” by the class design perpetually behind.
According to the standard class design, a student is supposed to ask a question about something he/she doesn’t understand while in class (during the lecture.) But asking questions hinder the process of “delivering the lecture” to the students.The goal of the professor/teacher of course is to deliver the lecture.
I think the chinese method of teaching is outright superior becuse it is based on reason. It places students in an active and engaging learning transaction, taking advantage of the proper role of the professor.