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A good starting point for this discussion might be this quotation from the late Israel M. Gelfand, a pioneer of writing correspondence course materials in secon

A good starting point for this discussion might be this quotation from the late Israel M. Gelfand, a pioneer of writing correspondence course materials in secondary school mathematics in both Russian and English: "Students have no shortcomings, they have only peculiarities. The job of a teacher is to turn these peculiarities into advantages." Thus far the Stack Exchange discussion includes a lot of complacency along the lines of "some students just don't have the capacity to get it" that I never found when I was living in Taiwan. Over there, even the below-average students in seventh grade are all expected to learn quite a lot of algebra and geometry, which they consolidate knowledge of during junior high school. By the end of junior high, students in Taiwan and students in urban areas of China and students in Korea, Japan, Singapore, and Hong Kong generally know United States secondary school mathematics quite well. (I have heard Chinese graduate students in the United States, students in nonquantitative subjects, deride the mathematics section of the GRE general test used for graduate school admission as a test of "junior high math," and that is literally true in terms of the standard curriculum in China.) So how about it? What creative ideas do we have here to help the young learner learn how to solve proportions, an aspect of day-by-day reasoning that only secondary school graduate might reasonably be expected to know? How to reignite a spark of interest in mathematics after school lessons that may have been a turn-off, may have been flat wrong, http://www.ams.org/notices/200502/fea-kenschaft.pdf http://www.ams.org/notices/200502/fea-kenschaft.pdf and at a minimum have left the learner with an excuse to not keep trying to learn?

orf 13y ago
Lets base our curriculum on endless tests and see if that works.
shrikant 13y ago
I've taken the GRE once in India, and I can confirm that the math section was RIDICULOUSLY easy. I could ace it without breaking a sweat, and I'm (was) actually a fairly average student.
pyre 13y ago
I thought that the Chinese basically 'pruned' their student body. The students that can't keep up with the curriculum are kicked/weeded out.
- bane 13y ago
  I can't say about China particularly, but many school systems route students into entirely different kinds of schools pretty early. Those with good early (elementary or middle school) math and science scores go on to STEM focused high schools and are then routed into STEM programs in Uni. Other kids will end up on a "vocational" track and go to a High School with a strong trade training and essentially do a supervised apprenticeship, if they're really good there they'll go on to a specialized trade school and focus in some kind of trade, instead of changing oil in a car they might rebuild alternators or transmissions or something. I've heard China has done similar routing for several topics of national prestige, kids end up in an Olympic gymnastics or diving program and train in that program until they either make it into the Olympics, fail out or end up as a coach when they're in their single digit ages. I'm not sure about other areas.
munin 13y ago
> (I have heard Chinese graduate students in the United States, students in nonquantitative subjects, deride the mathematics section of the GRE general test used for graduate school admission as a test of "junior high math," and that is literally true in terms of the standard curriculum in China.) this is true for students educated in the US as well! it's super frustrating, because you're staring at trig identities that you last looked at ten years ago.
- dtparr 13y ago
  Agreed. I always assumed the GRE must have been designed to accommodate/calibrated to humanities and social science grad students (or other majors without a significant math component) more than STEM students. Almost every CS friend I had either scored a perfect score or missed only one. It was a little frustrating, as there's no room to differentiate students who are average from those who are outstanding.
  - B-Con 13y ago
    Same story here. I was actually a math major and took the general GRE (which I believe is what we are discussing) in my senior year. I only studied the night before, just to see if their prep guide included any funky vocab or other memorization questions. I looked at some vocab, spent 10 minutes reviewing geometry and trig identities, and called it a night. Turns out I didn't even need any of it. (I did get one question wrong, though, and looking back I definitely know which one. It was an easy one in the middle of the exam questions and I think I just messed up a concept like "less than" instead of "less than or equal to".) All my math/C.S. friends thought it was really easy and I think the worst score I heard from them was 720 / 800. Interestingly, though, back when I took it the average score for the math section was notably higher than for the other sections. Just by missing 1 question I think I was bumped down to about the ~90% percentile.
  - ajdecon 13y ago
    > I always assumed the GRE must have been designed to accommodate/calibrated to humanities and social science grad students (or other majors without a significant math component) more than STEM students. This is probably true. I mean, this is why we have GRE subject tests...
dxbydt 13y ago
gre general test has always been crap. I've had the unfortunate occasion to take it thrice (for each of my 3 graduate degrees) because the scores expire (what a scam!). Now the subject math gre, that's fucking awesome. I once challenged my math professors to take it with me & they scored less :) Its broad enough to envelope most math specialities & deep enough to stump you if you haven't been paying attention to your speciality. Here's a copy of the subject math- If you don't know any CS or math but can quickly code some ruby/js/whatever, try #44. otoh if you know some CS, try #33, #25,#28 & #30. http://www.ets.org/s/gre/pdf/practice_book_math.pdf http://www.ets.org/s/gre/pdf/practice_book_math.pdf
nate 13y ago
[Ricardo Semler](http://en.wikipedia.org/wiki/Ricardo_Semler http://en.wikipedia.org/wiki/Ricardo_Semler) is pretty inspiring entrepreneur with his work in democratizing his company. But he's also been experimenting with education at [Lumiar](http://www.telegraph.co.uk/education/educationnews/3326447/Learn-what-you-want.html http://www.telegraph.co.uk/education/educationnews/3326447/L...) in Brazil. In one article I've read about the school, instead of rote learning about pi and circles, they'll encourage the students to make their own bicycle. And through finding "projects" that the kids want to work on, the students bump into having to learn things like: "how do I measuring the circumference of a circle".
- mtdewcmu 13y ago
  Ugh. I would have hated that. I would have much rather learned a few simple math concepts than figured out how to build a bicycle. Not everyone has the same idea of fun.
chipsy 13y ago
I was an unmotivated math learner, who did not want to admit it. I essentially stopped at integral calculus(failed three times), although I did try a linear algebra course at the same time and had to drop it because the effort needed to complete the proofs was beyond me. On the other hand, I took well to immediate, CS-y applications. I liked graph theory, since I could write pathfinding algorithms with it. And I learned to like parts of Fourier analysis, since I could understand DSP with it. So I know I can enjoy the study, given the right context. However, I think it speaks to the difficulty of math education that nobody discovers exactly the same approach to its study. But perhaps this is the wrong way to frame it. Perhaps, to put it another way, other subjects allow students to cheat themselves more easily into getting answers without understanding. I think, with respect to current curricula, we focus far too much on computation, and on proof. Both are answer-oriented by nature, whereas in my self-study I was motivated by developing a process, and in understanding the process I was considering things with language and hasty spatializations of ideas, long before I was ready for the formal applications. And we give almost no credence to process development as part of mathematics education. A typical lecture begins: "Assume the following. We define..." And this is perfectly reasonable if you've already immersed yourself in the jargon and want to get to the point as quickly as possible. But if you aren't ready for it, it's intimidating. A tiny definition, a sentence or two long, can become something you struggle over for a week, which only compounds the intimidation factor. In theory the problem sets should help you explore further. But if they're unmotivated, the students can barely try at the problem sets.
bane 13y ago
The main issue I had in the US K-12 system was both a lack of obvious applicability (there are no math labs), and a complete lack of teaching to my particular learning style (visual-tactile, i.e. watch then do hands on). There's a boring lecture, some numbers on the board, then drills. This method works, but only when there's a huge pressure on the student to drill...something that the U.S. system just isn't structurally built to supply in the ways that East Asian systems are. My wife grew up in South Korea and came out of High School knowing the level of calculus I wouldn't even touch until the last semester of my Sophomore year in College in a STEM program. Her 10th grade math textbook looked like an advanced version of my University Calculus course. The problem I had, and the original question has is that there's just no connection made for the student in the U.S. system from math class to anything remotely useful. Abstract statements like "engineers need math" just simply doesn't mean anything to a bored out of their mind 7th grader. They have to actually use math to solve something they could solve with basic arithmetic and a calculator. Something with a reward at the end other than yet more notebooks full of drilled exercises: some flashing lights on a digital circuit, winning the pot at blackjack, launching a water balloon at a target, whatever. But modern math education doesn't just fail in making it boring, it makes math scary. Calculus becomes this "special" course only the tip-top AP students take...if your High School even offers it (those special students might even have to go take it at a local college). Basic calculus isn't really all that hard to learn the mechanics of. It shouldn't be treated as special. Just "yet more rules for algebra". Even Math teachers would talk about trigonometry in hushed tones. Modern Math education doesn't even show student how to apply math to critical reasoning skills. Something even students who go on to the most liberal of liberal arts can benefit from. Importantly, I don't think anything I could have learned in K-12 mathematics remotely prepared me for the kinds of upper-level mathematics I eventually became exposed to at University. K-12 math prepared me to be a carpenter or a cashier, but it should have left me at a jump off point to be a scientist, or a philosopher, an engineer or a physicist, or at the very least given me a small glimpse into those worlds, because I sure as heck got a glimpse into 17th Century Japanese poetry styles, Shakespearean Theater, Classical Orchestra performance, being a member of Congress, and other career paths I wasn't interested in pursuing. I made some suggestions here https://news.ycombinator.com/item?id=5858652 https://news.ycombinator.com/item?id=5858652

orf 13y ago

Lets base our curriculum on endless tests and see if that works.

shrikant 13y ago

I've taken the GRE once in India, and I can confirm that the math section was RIDICULOUSLY easy. I could ace it without breaking a sweat, and I'm (was) actually a fairly average student.

pyre 13y ago

I thought that the Chinese basically 'pruned' their student body. The students that can't keep up with the curriculum are kicked/weeded out.

bane 13y ago
I can't say about China particularly, but many school systems route students into entirely different kinds of schools pretty early. Those with good early (elementary or middle school) math and science scores go on to STEM focused high schools and are then routed into STEM programs in Uni. Other kids will end up on a "vocational" track and go to a High School with a strong trade training and essentially do a supervised apprenticeship, if they're really good there they'll go on to a specialized trade school and focus in some kind of trade, instead of changing oil in a car they might rebuild alternators or transmissions or something. I've heard China has done similar routing for several topics of national prestige, kids end up in an Olympic gymnastics or diving program and train in that program until they either make it into the Olympics, fail out or end up as a coach when they're in their single digit ages. I'm not sure about other areas.

munin 13y ago

> (I have heard Chinese graduate students in the United States, students in nonquantitative subjects, deride the mathematics section of the GRE general test used for graduate school admission as a test of "junior high math," and that is literally true in terms of the standard curriculum in China.) this is true for students educated in the US as well! it's super frustrating, because you're staring at trig identities that you last looked at ten years ago.

dtparr 13y ago
Agreed. I always assumed the GRE must have been designed to accommodate/calibrated to humanities and social science grad students (or other majors without a significant math component) more than STEM students. Almost every CS friend I had either scored a perfect score or missed only one. It was a little frustrating, as there's no room to differentiate students who are average from those who are outstanding.
- B-Con 13y ago
  Same story here. I was actually a math major and took the general GRE (which I believe is what we are discussing) in my senior year. I only studied the night before, just to see if their prep guide included any funky vocab or other memorization questions. I looked at some vocab, spent 10 minutes reviewing geometry and trig identities, and called it a night. Turns out I didn't even need any of it. (I did get one question wrong, though, and looking back I definitely know which one. It was an easy one in the middle of the exam questions and I think I just messed up a concept like "less than" instead of "less than or equal to".) All my math/C.S. friends thought it was really easy and I think the worst score I heard from them was 720 / 800. Interestingly, though, back when I took it the average score for the math section was notably higher than for the other sections. Just by missing 1 question I think I was bumped down to about the ~90% percentile.
- ajdecon 13y ago
  > I always assumed the GRE must have been designed to accommodate/calibrated to humanities and social science grad students (or other majors without a significant math component) more than STEM students. This is probably true. I mean, this is why we have GRE subject tests...

dxbydt 13y ago

gre general test has always been crap. I've had the unfortunate occasion to take it thrice (for each of my 3 graduate degrees) because the scores expire (what a scam!). Now the subject math gre, that's fucking awesome. I once challenged my math professors to take it with me & they scored less :) Its broad enough to envelope most math specialities & deep enough to stump you if you haven't been paying attention to your speciality. Here's a copy of the subject math- If you don't know any CS or math but can quickly code some ruby/js/whatever, try #44. otoh if you know some CS, try #33, #25,#28 & #30. http://www.ets.org/s/gre/pdf/practice_book_math.pdf http://www.ets.org/s/gre/pdf/practice_book_math.pdf

nate 13y ago

[Ricardo Semler](http://en.wikipedia.org/wiki/Ricardo_Semler http://en.wikipedia.org/wiki/Ricardo_Semler) is pretty inspiring entrepreneur with his work in democratizing his company. But he's also been experimenting with education at [Lumiar](http://www.telegraph.co.uk/education/educationnews/3326447/Learn-what-you-want.html http://www.telegraph.co.uk/education/educationnews/3326447/L...) in Brazil. In one article I've read about the school, instead of rote learning about pi and circles, they'll encourage the students to make their own bicycle. And through finding "projects" that the kids want to work on, the students bump into having to learn things like: "how do I measuring the circumference of a circle".

mtdewcmu 13y ago
Ugh. I would have hated that. I would have much rather learned a few simple math concepts than figured out how to build a bicycle. Not everyone has the same idea of fun.

chipsy 13y ago

I was an unmotivated math learner, who did not want to admit it. I essentially stopped at integral calculus(failed three times), although I did try a linear algebra course at the same time and had to drop it because the effort needed to complete the proofs was beyond me. On the other hand, I took well to immediate, CS-y applications. I liked graph theory, since I could write pathfinding algorithms with it. And I learned to like parts of Fourier analysis, since I could understand DSP with it. So I know I can enjoy the study, given the right context. However, I think it speaks to the difficulty of math education that nobody discovers exactly the same approach to its study. But perhaps this is the wrong way to frame it. Perhaps, to put it another way, other subjects allow students to cheat themselves more easily into getting answers without understanding. I think, with respect to current curricula, we focus far too much on computation, and on proof. Both are answer-oriented by nature, whereas in my self-study I was motivated by developing a process, and in understanding the process I was considering things with language and hasty spatializations of ideas, long before I was ready for the formal applications. And we give almost no credence to process development as part of mathematics education. A typical lecture begins: "Assume the following. We define..." And this is perfectly reasonable if you've already immersed yourself in the jargon and want to get to the point as quickly as possible. But if you aren't ready for it, it's intimidating. A tiny definition, a sentence or two long, can become something you struggle over for a week, which only compounds the intimidation factor. In theory the problem sets should help you explore further. But if they're unmotivated, the students can barely try at the problem sets.

bane 13y ago

The main issue I had in the US K-12 system was both a lack of obvious applicability (there are no math labs), and a complete lack of teaching to my particular learning style (visual-tactile, i.e. watch then do hands on). There's a boring lecture, some numbers on the board, then drills. This method works, but only when there's a huge pressure on the student to drill...something that the U.S. system just isn't structurally built to supply in the ways that East Asian systems are. My wife grew up in South Korea and came out of High School knowing the level of calculus I wouldn't even touch until the last semester of my Sophomore year in College in a STEM program. Her 10th grade math textbook looked like an advanced version of my University Calculus course. The problem I had, and the original question has is that there's just no connection made for the student in the U.S. system from math class to anything remotely useful. Abstract statements like "engineers need math" just simply doesn't mean anything to a bored out of their mind 7th grader. They have to actually use math to solve something they could solve with basic arithmetic and a calculator. Something with a reward at the end other than yet more notebooks full of drilled exercises: some flashing lights on a digital circuit, winning the pot at blackjack, launching a water balloon at a target, whatever. But modern math education doesn't just fail in making it boring, it makes math scary. Calculus becomes this "special" course only the tip-top AP students take...if your High School even offers it (those special students might even have to go take it at a local college). Basic calculus isn't really all that hard to learn the mechanics of. It shouldn't be treated as special. Just "yet more rules for algebra". Even Math teachers would talk about trigonometry in hushed tones. Modern Math education doesn't even show student how to apply math to critical reasoning skills. Something even students who go on to the most liberal of liberal arts can benefit from. Importantly, I don't think anything I could have learned in K-12 mathematics remotely prepared me for the kinds of upper-level mathematics I eventually became exposed to at University. K-12 math prepared me to be a carpenter or a cashier, but it should have left me at a jump off point to be a scientist, or a philosopher, an engineer or a physicist, or at the very least given me a small glimpse into those worlds, because I sure as heck got a glimpse into 17th Century Japanese poetry styles, Shakespearean Theater, Classical Orchestra performance, being a member of Congress, and other career paths I wasn't interested in pursuing. I made some suggestions here https://news.ycombinator.com/item?id=5858652 https://news.ycombinator.com/item?id=5858652