[chrisseaton]

But your college courses seems to be so high quality. How does a student in the US go from what sounds like quite a limited education in maths at high-school to doing so well in maths at college? What connects the two up?

[barry-cotter]

Individual school districts and occasionally schools have enormous autonomy compared to the norm in Europe. So two schools in the same state can each have a class called Algebra II, with literally zero overlap in the material covered. Yesterday I read about a high school math teacher who decided to teach partial differential equations, normally, I believe what Americans call Calculus II in university, as an elective. There are good schools, but the system is very far from uniform. Partly this is because it wasn’t designed from the ground up to teach nationalism with education fit in around that goal. Puritan New England was the first society with mass literacy. Schools were locally funded, run and organised and that organisation of local rather than state administration persists, possibly in every state, certainly in most. Education came before nationalism so there was never a state system designed from the top down to turn everyone into Americans, nationwide, though many reformers gave it a good try.

[tropo]

No, partial differential equations would be the fourth semester.

Calculus I is differentiation. Calculus II is integration. Calculus III is vector calculus, with stuff like curvature in 3 dimensions. Differential Equations would be the next class.

The AP test covers differentiation and, optionally, integration. It's the first semester or two. This is what a good high school student will do unless the school itself is really bad or really small.

[rmah]

I remember Calc I (1st semester) being limits, differentiation and integration. And Clac II (2nd semester) being partial differential equations. This was in the engineering school though... it may have been different for other schools in the university.

This is the original poster's point. There is no consistency. Even in university. Some schools use quarters, some semesters, some trimesters. Some have letter grades, some percentages. Some are pass/fail freshman year, but are graded in subsequent years (e.g. MIT). What makes up "Calc I" at university varies tremendously.

[scott00]

One thing to keep in mind is that although there are a lot of elementary and high schools that do a bad job teaching math in the US, there's also a lot that do a good job. Kids that struggle in math in high school and/or come from high schools with poor programs mostly don't even try doing it in college. One other observation I've made is that people who do poorly in what I would think of as engineering math (calc 1-3, linear algebra, differential equations, probability and statistics, CS theory classes) often have more trouble doing the algebra error free than doing the "complicated" parts of problems. It's possible spending more time on algebra is actually beneficial to doing well in college level math.

[maxlybbert]

My high school math teacher had spent years teaching remedial math at a university level. We thought she was being a curmudgeon when she complained that universities even offered remedial classes.

Nowadays, I think she was right: university students should be ready for university-level work. Many people aren’t at that level the moment they graduate high school. The US really doesn’t have a place for those people, aside from remedial classes.

But, anyhow, for many people, there’s an intermediate step that doesn’t get talked about.

[nradov]

The US has a place for those students: community college. Universities shouldn't waste resources on remedial courses.

[cat199]

for the US student:

they went to private schools or, alternatively, they went to the wealthier public schools which teach these sort of courses, although usually on a 'tracking' system which segregates the 'smart' from the 'not so smart' at around 12/13.

for the US university (at least the more elite ones):

the above, in combination of the fact that a big chunk of the of the students are international students.

[xvector]

Selection bias - self-motivated kids, or kids with good teachers, will take some of the amazing STEM courses our colleges have to offer.

The rest don't even bother, if they go to college at all.