That said, I know people who went to the same school middle and high schools I went to, but who were never able to get past the introductory algebra class I took in 8'th grade. Sure, some people probably got better or worse teachers, but I believe some peoples brains are just better at math than others.
Then why does the US look so bad at math? I don't know. I suspect that both of these statements are true:
1. Many countries have better alternate education paths for people who aren't that interested in college. People on these alternate paths are excluded from foreign statistics, while people who ought to be on them dilute US statistics.
2. Doing poorly in school is more acceptable to Amercan parents than it is to parents in many other developed countries. (Ironically, this may be because a lack of alternate education paths led parents to becmoe disillusioned with the value of school)
One of my daughters can hit anything thrown at her. My other daughter is more advanced than most kids her age at math, but I know that she has already learned more math than she will ever use in her life (she is in eight grade but is doing very advanced algebra). Her interests will never lead her to a career that requires more than she already knows.
The problem is pushing everyone to one standard, when they do not need it. It makes them feel stupid, and is a waste of time that could be used developing other skills.
*good in this context means AP level. This is not because AP is the correct measurement, it is because AP and the like is the measurement used to judge high schools
I think the intended preparation is actually really important. With AP the flow is Learn ch2 algorithm > learn ch3 algorithm>...> do well on test > not have to take calc in college. If you actually prepare a course for rigorous understanding, I suspect you might end up sacrificing your AP score somewhat for much greater gains later on. However, the system only cares about that short term result.
I believe high school students who take college courses can be a great asset for their high school for this very reason.
As a junior in high school I took college algebra at a community college in the evenings. As a result of the conversations with my math teacher, she made many changes to the subjects she covered in her pre-calc and algebra 2 classes.
To put things into perspective, there is zero AP credit offered at Caltech. The only way to skip classes is to pass Caltech's own placement exams. I took the first placement exam (after finishing the entire AP math curriculum, as well as the entire math curriculum at the local community college—through linear algebra, diff eqns, and multivariable calc), got a 96% on Caltech's placement exam, and was recommended to take an extra, remedial mathematics course in addition to the regular freshman load to help bring me up to speed.
A strange feature of the class was that the weeks where we studied derivatives were a lot harder than the weeks when we studied integrals. Although derivatives are a lot easier to evaluate than integrals, it's a lot harder to prove that they exist. Most of our problems were proving the existence of derivatives and integrals, not evaluating them, so it was a weird inversion in what is normally considered difficult in calculus.
If you want a sample of the problems, here's one of the problem sets from this year's class:
http://www.math.caltech.edu/%7E2011-12/1term/ma001a1/homewor...
(Note: I studied math as well as chemistry and CS at a state college so my background is a little unusual.)
Those program offerings are really important, they're like a parallel education track to public K-12. Now there's Khan Academy, the MIT and Stanford courses online, all kinds of resources, but you have to get motivated/gifted together with like minded ones.
Smart students with everything going for them get to make this decision:
(A) Dedicate their entire life at college to doing useless problem sets. No free time. No social life. No girlfriends. Spend all your time with stinky nerds drilling on useless sets. Then get out of school and make $80k doing the engineering slog. Max out your salary at $140k, 20 years down the road.
(B) Take easy classes while being a professional partier. At parties, have loads of sex and take lots of drugs while meeting many many people. Build up 1000+ Facebook friends and forge lifelong bonds with important well-connected people. Get your degree and use your connections to get hired for $80k. Have your employer then pay for your MBA. Max out your salary at $400k 20 years down the road, not including bonuses and side deal opportunities.
Phillip Greenspun was right. Unless you're a masochist or a social reject, engineering is for foreign students. A top American student from a good family has no incentive to do engineering: not lifestyle, not financial.
When it comes to software this is even more true because you don't even need an engineering degree to write software. Paul Graham has a philosophy degree and most of his wealth came from people skills: convincing Blackwell and Morris to hack for him, and later convincing young engineers to hack for him.
Steve Jobs vs Steve Wozniak is another perfect example. Woz did the work, Jobs got the glory. Woz stayed home nights hacking while Jobs was out fucking the prom queen and taking credit. Our society does not reward engineers so anyone with the ability and foresight to be a doctor, dentist, MBA, or clinical psychologist is not going to torture themselves.
Hacker News entrepreneurs are just a bunch of masochists who never learned that partying, taking drugs and having sex is more fun and pays better than writing Ruby apps.
If you're smart (and I mean really smart), finance is generally a good bet. Once again, adjusted for time input it's not great but it does have a higher expected value.
Just make friends with rich people and get them to hire you at their friend's giant corporation where their job is to undermine democracy and fool people. It's easy and pays well.
id think having a deep enough knowledge on lisp to fill two books probably had something to do with it as well.