The American math curriculum is embarassing to even explain to most europeans. An “advanced” high school senior in the US might be taking Calculus 1. Most students graduate barely able to explain what a linear function or a quadratic equation is.
What American math curriculum? Every American state has its own curriculum and every school district has very broad autonomy, right? I’m no expert but most states don’t even have state exams at the end of high school that are exactly comparable. There are many states that have more internal variety in their education system than most European nations.
The closest the US comes to having a national curriculum is the College Board Exams.
This has changed with Common Core and the pushing of standardized testing to the lower levels (elementary and middle school), though high schools still tend to have more variation.
I grew up in a European education system (Scotland) and subsequently emigrated to the US. I have two kids in the school here. Although your sentiment was my initial expectation too, it wasn't borne out by some time I spent studying the two curricula (present-day Scotland vs the classes my kids have). What I found was that they pretty much matched up age for age.
I was taking ap calculus bc in 9th grade (calculus I). There were 2 other students in 9th grade with me. 6 were in 10th grade, many were juniors or seniors.
I left high school soon after 10th grade started so I don’t know what track I would have been on. But there are tons of overachievers taking on as much advanced stuff as possible in high school. So I think it’s a little unfair to say an advantages student only might be taking calculus I as a senior, because my personal experience and observations don’t suggest that.
On the other hand, what you are saying might have been true a long time ago. My wife’s father is a professional economist and he only took Calculus in college and he’s pretty smart. So I think education has improved in the US in that time.
American schooling is centered around standardized testing, and you can get a perfect score on the SAT Math without knowing the quadratic equation, so of course it's just a footnote in Algebra education.
The other problem with Calculus in American schooling is the number of students who took and aced their AP Calculus classes only to completely flunk their college-level multivariable calculus. I remember it always being recommended that, even if you took AP calc in high school, you should re-take calculus in highschool if you were going into Physics, Engineering, or Computer Science. Is that still the case
Americans seem to make a really massive deal out of calculus. I wonder if that's counter-productive and puts people off.
You give it a special name, you talk about other topics purely in relation to calculus ('pre-calculus') as if calculus is the central big thing, and people talk about dreading it at college.
In the UK we never used the term 'calculus' when we learned it at school - we were just introduced to differentiation one day without any fanfare as part of an ongoing maths course, and then integration later. You didn't get a chance to get apprehensive about it and build up a mental block because you didn't know it was coming and it was no big deal.
FWIW, prior exposure to calculus is really helpful for tackling introductory undergrad engineering classes. If you can't do derivatives and some basic integrations without thinking, then you will really struggle in the subject-specific engineering classes (e.g. Circuits, Statics, etc.) that you start to take in your 2nd year. Not sure if pre-college calculus experience is as helpful for other fields, though.
Our high school physics teacher pushed for alignment of math schedule with physics lessons, as basic mechanics is much more intuitive with the understanding of derivatives, and derivatives get a clear illustration (of the principles, and also of the reasons why one might care about derivatives) in these physics lessons, so it makes sense to teach these topics hand-in-hand.
In the UK, differentiation and integration aren't taught for GCSE maths (to ~16 year olds, last year of compulsory schooling) [1] but are for AS-level maths (to ~17 year olds) [2]
However, students select which AS-levels and A-levels they want to study; students can drop math entirely if they so wish. And some CS departments will accept such students, putting them through a high-speed remedial math course.
> They explained derivatives to us on the first year of UK university CS degree
That's done partly as a refresher for those who didn't do maths at A-level (so would be 2 years out of not doing maths at all) and to take into account some systems that don't teach it.
At least that was the case for my UK university CS degree.
Yes this was my experience in Australia as well we did not have separate "Algebra", "Geometry", "Calculus" etc classes it was all just 'Mathematics'.
From memory I think concepts from Calculus were first introduced in year 10/11 via geometry (plotting curves and finding points of inflection) from there derivatives just made a lot of sense - slopes as a rate of change and all that.
OK so I started calculus at 15, IIRC, but I was in the advanced class at the young end for my year. Most people who are going to do it start it at 16-17, if doing maths at A-level.
Everyone else drops maths at 16, never having encountered calculus.
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?
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.
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.
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.
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.
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.
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.
An advanced high school senior in the US will take Calculus 1. An advanced high school senior in the US might take Calculus 2. (Yes, I am intentionally implying that taking calculus is what defines a student as advanced.)
My high school don't go beyond Calculus 1 (edit to add: this was two semesters and covered differentiation and integration).
That was years ago (pre-internet) and if a student wanted to take other college-level math they were released to take it at the local university campus. Today, I guess online classes are an option.
Calc 1 (Calc AB) is basic derivatives and integration without too many frills. Calc 2 (Calc BC) adds advanced integration (by parts, partial fractions, etc), L’Hopital’s rule and indeterminate forms, coordinate transforms, and basic Taylor Series.
There's 300M people there, you're bound to find 6 who are pretty good at it. And there's definitely resources somewhere to teach them stuff, it's the richest big country in the world.
The question is more how does the system work for average kids.
The US not only separates smart kids into different classes, eg AP and IB programs and early admission to community colleges, they separate the elites into whole other schools, eg private boarding schools, magnet schools, and technical schools.
This is ignoring the huge baseline variance in quality, due to funding and cultural variations.
Yes, I recall that very basic sets topics (e.g. unions and intersections),might have been introduced in 3rd or 4th grade? Definitely was in there somewhere before middle school.
This is in the UK, at a private school. Worked for me!