A Mathematician's Lament: An essay on mathematics education

  • Thread starter morphism
  • Start date
  • #26
6,814
13
Also if you really want to improve things, you have to get some people from East Asian with hands-on math teaching experience and bring them to the US. If you try to create a program from second or third hand information, you'll just end up with a "cargo cult" airplane that won't fly. You can exchange them for American writing teachers, since I do think that American schools are much better at teaching high school students to write than Asian schools.

I do know of a few parents from Taiwan that end up sending their kids back specifically because they want them to get a better math education.
 
  • #27
atyy
Science Advisor
14,003
2,285
Also if you really want to improve things, you have to get some people from East Asian with hands-on math teaching experience and bring them to the US. If you try to create a program from second or third hand information, you'll just end up with a "cargo cult" airplane that won't fly. You can exchange them for American writing teachers, since I do think that American schools are much better at teaching high school students to write than Asian schools.

I do know of a few parents from Taiwan that end up sending their kids back specifically because they want them to get a better math education.
My bias is to think you are right about Chinese maths - I'm a biologist and a biologist friend of mine from China can do derivations that US engineer friends of mine marvel at. But my bias is also to suspect you are wrong about American writing education. At least in biology, I've often been recommended Strunk and White, who have tin ears for style.
 
  • #28
6,814
13
But my bias is also to suspect you are wrong about American writing education.
If you've ever tried to help someone from East Asia write an essay, you'll find what a painful process it is. I don't mean the mechanics of grammar and spelling, but rather the essay form. In most East Asian education, written consists of taking the words of people in authority, showing that you've memorized what they've said in great detail, and then coming to the correct conclusion.

There are political at work here. Suppose you are a high school student in Mainland China, are you seriously going to wrote an original essay on what you really think about government policy? If you are an official in the Ministry of Education, are you seriously going to develop a curriculum in which high school students are encouraged to write about and discuss government policy? Of course not. Even things like history are a landmine. There is an officially approved history. Your grade is determined by how well you can repeat the official history. If you have any alternative ideas about history, you best keep them to yourself.

This causes huge problems with students from East Asia come to the US, because what is bad in East Asia (coming up with original thoughts and ideas) is good in the US, and what is good at East Asia (copying the words of established authorities verbatim) is considered plagarism in the US. In the US, you are supposed to write using your own words and your own style, whereas this is generally considered a bad thing in most East Asian schools. You are supposed to quote authorities and use the precisely approved sentences and phrases to come up with the officially correct conclusion.

This also has other implications. When someone in the US writes an essay, it's assumed that they are writing what they believe. When someone in China writes an academic essay, then the opinions expressed in that essay may have nothing at all close to what they actually believe.

Also while East Asian students do spend more time at math, students (at least in Taiwan) don't spend that much time writing.

I don't want to give people the mistaken impression that I think that education system in Taiwan is "better" than the educational system in the US. The US has a weakness in primary and secondary math education, but it has a lot of strengths also.
 
Last edited:
  • #29
atyy
Science Advisor
14,003
2,285
If you've ever tried to help someone from East Asia write an essay, you'll find what a painful process it is. I don't mean the mechanics of grammar and spelling, but rather the essay form. In most East Asian education, written consists of taking the words of people in authority, showing that you've memorized what they've said in great detail, and then coming to the correct conclusion.

There are political at work here. Suppose you are a high school student in Mainland China, are you seriously going to wrote an original essay on what you really think about government policy? If you are an official in the Ministry of Education, are you seriously going to develop a curriculum in which high school students are encouraged to write about and discuss government policy? Of course not.

This causes huge problems with students from East Asia come to the US, because what is bad in East Asia (coming up with original thoughts and ideas) is good in the US, and what is good at East Asia (copying the words of established authorities verbatim) is considered plagarism in the US.

Also while East Asian students do spend more time at math, students (at least in Taiwan) don't spend that much time writing.
But how about essays like "On the importance of gravity"?
 
  • #30
ideasrule
Homework Helper
2,266
0
My wife was an elementary school teacher in Taiwan. Chinese students who intended to study in the sciences are expected to *know* formula off the top of their heads. They aren't expected to *memorize* the formula. I'm willing to bet that if you ask most Chinese science students how to derive the formula, they can.
I agree: Chinese students will almost certainly know how to derive it. They are also required to memorize it, but they probably use it so much that it becomes impossible not to remember it.

About American math: is it really focused on memorization? How many formulas can there possibly be to memorize?
 
  • #32
6,814
13
Hamster143's response is the sort of total utter non-sense when ever I bring up teaching math. I'm sorry to be harsh about this, but it has to be said.

It turns out that in any sort of East Asian math book, there are no "word problems" at all in the American sense. It's all conceptual. Conceptual does not mean easy. It is true that East Asian math classes are "harder" than US math classes, but if you make hard classes with stupid brain dead word problems, you aren't helping anyone at all. Why the hell are we talking about "wood". There is this concept called "x". And there is all of the non-sense about how wonderful things where in the past. US math education was never very good, and in the case of higher education, the US ended up just copying the Germans.

The other thing that I think is total non-sense is that idea that math is only for smart people. The important thing about East Asian math classes is that *everyone* is expected to learn the material, and if students can't then the curriculum and the teacher gets changed. The thing to notice is not how well the scientists and engineers do, but how well people that go through the Chinese equivalent of community college do. The only reason that we have this idea that math is for smart people in the US, is because of how badly it's taught, and how little resources go into math teaching.

And one more thing.... It's crucial in the global economy to be multilingual. If you go into any Chinese bookstore, you see *tons* of excellent math preparation books, and it's just a fact that if you want the world's best primary and secondary textbooks, you are better off being about to read Chinese, Japanese, or Korean. If you can read Chinese, and then get any Chinese math textbook, it quickly dawns on you how horrible US math education is, and how telling students to work harder at the wrong thing is just not going work.
 
  • #33
6,814
13
It is very good and I have used it with my daughter. It definitely moves faster than the Canadian curriculum. That said, it is still not the perfect system and requires a skilled teacher.
That's one problem with East Asian math, is that it requires tons and tons of very skilled teachers, which means a huge number of normal schools, which means the type of massive state bureaucracies which Americans tend to distrust.

One other problem is that as the economy improves it becomes harder to get skilled teachers. In the early 1970's in Taiwan, you could pretty easily get ambitious young women from the countryside to go to boarding schools, which were run something like military training camps. You really can't do that now, so most of the older teachers think of the younger ones as "soft".

However, the fact that both Mainland China and Taiwan got so far so fast is pretty amazing. I have older relatives in which someone was considered extremely highly educated because they graduated elementary school and could read. Getting from 20% literacy to 90% literacy inside a generation was not a small thing to do, but it turns out to be essential for economic growth.
 
  • #34
6,814
13
About American math: is it really focused on memorization? How many formulas can there possibly be to memorize?
It's worse than that. American textbooks tend to have people try to memorize specific processes. Memorize how to calculate this type of problem. Memorize how to calculate this other type of problem. Memorize how to calculate this other type of problem. One of the first thing that you notice about East Asian textbooks is how thin they are in comparison to American ones. That's because they focus on teaching a few concepts rather that a hundred processes.

The problem is that if you have people memorize 20 different rules which are actually part of the same concept, you are making things more difficult for the student and wasting their time and yours, but anyone that complains about this is accused of "dumbing down" the curriculum. It's actually the opposite. Because the entrance exams in East Asia are so tough, you do everything you can to make things simpler, because if you make things needlessly complicated then you are doomed.

Also the way the US does standardized testing makes things worse. It's not that standardized testing is a bad thing (after all, people in East Asia go through this trouble to pass the entrance exams), but the details how how the standardized testing is set up increases this bad aspect of US math teaching. One other thing that you quickly find about education is that it's political in a bad way. What happens is that certain styles of teaching are associated with certain political ideologies so what people really are arguing about is politics and not math. (It's true.)

It's not that education is less political in East Asia, but you have *different* politics.
 
Last edited:
  • #35
6,814
13
Also problems about piles of wood are pretty stupid. No one gives a damn about piles of wood, and if you talk to a professional logger they'll tell you that the problem is bogus anyway. Since I've taught at the University of Phoenix if I have to come up with a word problem it would be something like.

1) You just lost 40% in your 401(K) last year. Assuming that your employer doesn't/does match contributions this year, how much do you have to contribute to reach your retirement goals assuming the Dow goes to 12000, 10000, 8000, 5000?

2) If you were to get laid off tomorrow, how much money in the bank do you need to survive for X months?

3) What increase in salary do you need to make your tuition in UoP a positive investment?

4) How much money will you save if you pay off your credit cards?

All you have to do is to mention three or four of these sorts of questions, and then Algebra 101 is no longer boring or montonous, and at that point you focus on concepts so that people have the skills to answer those questions, and other questions which life throws at you. Again, if the US had a decent math education system, my students would have learned all of this in the 7th grade, but better late than never.

I sometimes wonder if the reason that Chinese are huge savers is that most educated Chinese in China can do basic algebra whereas a huge fraction of Americans can't. If you can't do math, you are going to have to rely on the bank to do the math for you, and you are likely to get screwed since the guy at the other end of the table knows how much money he can squeeze out of you, and you don't.

(How much is this adjustable rate mortgage going to cost me, if interest rates go up to 8%? How much do house prices have to go down before I'm underwater?)
 
  • #36
708
7
It turns out that in any sort of East Asian math book, there are no "word problems" at all in the American sense.
While I admit ignorance of other countries, the Singapore math system is very word-problem heavy. The ones I did with my daughter were generally well thought out, required thinking rather than plug-n-chug, and were appropriate for a 7 year-old. I know there are strong opinions about word-problems (I have mixed feelings), but I think the Singapore primary system was successful because of them.

I think this changes dramatically in secondary-school, though, and might be what you are referring to.
 
  • #37
atyy
Science Advisor
14,003
2,285
While I admit ignorance of other countries, the Singapore math system is very word-problem heavy. The ones I did with my daughter were generally well thought out, required thinking rather than plug-n-chug, and were appropriate for a 7 year-old. I know there are strong opinions about word-problems (I have mixed feelings), but I think the Singapore primary system was successful because of them.

I think this changes dramatically in secondary-school, though, and might be what you are referring to.
Is it true that the Singapore word problems are meant to be solved without algebra? I once looked at them and found them ridiculously hard - maybe Singapore's system is deteriorating.
 
  • #38
708
7
Is it true that the Singapore word problems are meant to be solved without algebra? I once looked at them and found them ridiculously hard - maybe Singapore's system is deteriorating.
The grade 2 and 3 ones I have seen are not that hard - just a little challenging compared to Canadian school. What grade level were you looking at? I cannot see how you are supposed to solve anything in math 'without algebra.' That is like running without breathing.

In what sense is it deteriorating?

http://en.wikipedia.org/wiki/TIMSS

http://nces.ed.gov/timss/results07_math07.asp

http://nces.ed.gov/timss/table07_1.asp

http://nces.ed.gov/timss/figure07_2.asp


While curriculum is somewhat important, I have come to believe that a culture's attitudes toward learning are even more important. Twofish's comments about Taiwan seem to support this. Willingness to work hard and respect for achievement are just more universal than in the West.
 
  • #39
ideasrule
Homework Helper
2,266
0
While I admit ignorance of other countries, the Singapore math system is very word-problem heavy. The ones I did with my daughter were generally well thought out, required thinking rather than plug-n-chug, and were appropriate for a 7 year-old. I know there are strong opinions about word-problems (I have mixed feelings), but I think the Singapore primary system was successful because of them.
In mainland China, elementary school textbooks certainly have plenty of word problems. I've never gone to high school there, but the Chinese calculus textbook I have has few word problems and the Chinese university entrance exams that I looked at online have none. That said, I'll ask my cousins whether they did word problems in high school; it's better to get some info than to assume things.
 
  • #40
6,814
13
While curriculum is somewhat important, I have come to believe that a culture's attitude towards learning are even more important. Twofish's comments about Taiwan seem to support this. Attitudes toward hard work and achievement are just more universal than in the West.
I don't believe this at all, and I don't think for a second that Americans *are* particularly lazy.

When given a choice people in Taiwan can be just as lazy as Americans, it's just that people that work hard do so because they really don't have much of a choice. Once you grow up rich, it's much harder to work hard when you don't have to, but that's nothing to do with nationality. But what happens in the US is that once you have a group of immigrants become rich and lazy, you have a group of poor and hungry one's come in right afterwards.
 
  • #41
708
7
I don't believe this at all, and I don't think that Americans *are* particularly lazy.
I don't think any culture in the world is particularly lazy. I do think that some cultures put a stronger emphasis on achievement through hard work, though. Whether those cultures work harder becuase they are not rich is a different question.

The suggestion above to read 'Outliers' is worthwhile. While I doubt that Gladwell will win any awards for scientific rigour, I think his basic premise covers a lot of this ground (including why Asian countries succeed at teaching math). It is an easy book to read and gives plenty to think about even if you don't agree with all of it.
 
  • #42
ideasrule
Homework Helper
2,266
0
I don't know about Taiwan, but mainland parents are certainly much more concerned about education than Western parents. Maybe this is due to the fact that in China, there's not much choice: there's no hope of getting into university without working your butt off, and there's certainly no hope of getting a tolerable job without getting into university. However, even Chinese parents in the West seem to have this kind of attitude.

This is not necessarily a good thing. Plenty of their parents force their children to study 24/7 and participate in a bunch of useless contests so they have something to show off when applying to university. People don't become good scientists/mathematicians because they're forced to study; they become good scientists/mathematicians because of their natural curiosity or thirst for knowledge, and I'm not sure China's education system is conducive to either.
 
  • #43
34,017
5,672
I don't think any culture in the world is particularly lazy. I do think that some cultures put a stronger emphasis on achievement through hard work, though.
I think the culture plays a very important rule. In the US, people tend to think of mathematical ability in binary terms: either you have it or you don't, and if you don't have it, why work at it. The East Asian cultures tend to think of this ability as being learned through effort, and that if you don't get it, you need to work harder, the same as becoming proficient at a musical instrument or in athletics. Sure, not everyone has the ability to become a mathematical prodigy, but a much larger proportion of people have the potential to become mathematically literate (or numerate, in John Allen Paulos's terminology - see "Numeracy").
 
  • #44
atyy
Science Advisor
14,003
2,285
The grade 2 and 3 ones I have seen are not that hard - just a little challenging compared to Canadian school. What grade level were you looking at? I cannot see how you are supposed to solve anything in math 'without algebra.' That is like running without breathing.

In what sense is it deteriorating?

http://en.wikipedia.org/wiki/TIMSS

http://nces.ed.gov/timss/results07_math07.asp

http://nces.ed.gov/timss/table07_1.asp

http://nces.ed.gov/timss/figure07_2.asp


While curriculum is somewhat important, I have come to believe that a culture's attitudes toward learning are even more important. Twofish's comments about Taiwan seem to support this. Willingness to work hard and respect for achievement are just more universal than in the West.
Instead of algebra, one is supposed to use "bars" or something weird, isn't it? http://www.nychold.com/art-hoven-el-0711.pdf.

I find the bars method ridiculously hard, so I can't do the problems, so I conclude the Singapore maths system is deteriorating (of course I could also conclude my maths skills are inadequate :smile:).
 
  • #45
atyy
Science Advisor
14,003
2,285
Also problems about piles of wood are pretty stupid. No one gives a damn about piles of wood, and if you talk to a professional logger they'll tell you that the problem is bogus anyway. Since I've taught at the University of Phoenix if I have to come up with a word problem it would be something like.

1) You just lost 40% in your 401(K) last year. Assuming that your employer doesn't/does match contributions this year, how much do you have to contribute to reach your retirement goals assuming the Dow goes to 12000, 10000, 8000, 5000?

2) If you were to get laid off tomorrow, how much money in the bank do you need to survive for X months?

3) What increase in salary do you need to make your tuition in UoP a positive investment?

4) How much money will you save if you pay off your credit cards?

All you have to do is to mention three or four of these sorts of questions, and then Algebra 101 is no longer boring or montonous, and at that point you focus on concepts so that people have the skills to answer those questions, and other questions which life throws at you. Again, if the US had a decent math education system, my students would have learned all of this in the 7th grade, but better late than never.

I sometimes wonder if the reason that Chinese are huge savers is that most educated Chinese in China can do basic algebra whereas a huge fraction of Americans can't. If you can't do math, you are going to have to rely on the bank to do the math for you, and you are likely to get screwed since the guy at the other end of the table knows how much money he can squeeze out of you, and you don't.

(How much is this adjustable rate mortgage going to cost me, if interest rates go up to 8%? How much do house prices have to go down before I'm underwater?)
Hey, these are great! What about something for kids?
 
  • #48
708
7
Instead of algebra, one is supposed to use "bars" or something weird, isn't it?
Those exercises are visual training for kids to prepare for algebra; they are not 'instead' of algebra.

If you ever teach math to children, you will find physical blocks ('math manipulatives') to be very helpful in conveying concepts. This is just a paper version of making the question out of blocks. Remember the age level of the kids this is aimed at.

http://en.wikipedia.org/wiki/Cuisinaire_rods

Once kids can do the algebra, you don't need stuff like this any more. If a teacher is saying that you 'can't use algebra,' that is a problem with the teacher.
 
  • #49
atyy
Science Advisor
14,003
2,285
Those exercises are visual training for kids to prepare for algebra; they are not 'instead' of algebra.

If you ever teach math to children, you will find physical blocks ('math manipulatives') to be very helpful in conveying concepts. This is just a paper version of making the question out of blocks. Remember the age level of the kids this is aimed at.

http://en.wikipedia.org/wiki/Cuisinaire_rods

Once kids can do the algebra, you don't need stuff like this any more. If a teacher is saying that you 'can't use algebra,' that is a problem with the teacher.
Why not just teach algebra, wouldn't that be easier - ie. why not teach the easy way right from the start, instead of teaching them the hard way first? Wouldn't a kid pick up bad habits by thinking in blocks rather than algebraically? (Or is this preparation for powerful diagrammatic methods like Feynman diagrams and graphical models?)
 
  • #50
708
7
Why not just teach algebra, wouldn't that be easier - ie. why not teach the easy way right from the start, instead of teaching them the hard way first?
Do you teach algebra to 8 year-olds? If you do, then I want to learn your secrets.

This IS teaching them algebra. It just takes a little time to transition from concrete examples (blocks) to abstract reasoning (x). There are other ways of teaching algebraic concepts to young children, but they almost all use something concrete as a bridge to 'doing it right.'

We could ask this: Why don't we just teach primary school kids about fields and rings? Well, in fact we are - using ideas that they understand and building up to more abstraction as they have enough experience to make sense of it all.
 

Related Threads on A Mathematician's Lament: An essay on mathematics education

  • Last Post
Replies
17
Views
14K
  • Last Post
Replies
23
Views
3K
Replies
3
Views
8K
Replies
19
Views
13K
Replies
2
Views
4K
Replies
15
Views
645
Replies
1
Views
972
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
3
Views
10K
  • Poll
  • Last Post
Replies
13
Views
9K
Top