Gifted Issues Discussion homepage Forums General Discussion How asinine is the US educational system?

Oh, I don't know...statistics? Proofs in secondary school mathematics? Problem solving in secondary school mathematics? Perhaps these courses aren't sexy enough because they merely create a foundation and don't come with a sparkly sticker saying, "Dear IVY LEAGUE admissions officer, I did college-level mathematics when I was only 16! " Or, my cynical side is saying, because the latter two are actually very hard, and we can't have hard classes bursting our bubbles.

I did a web search and found that we have high schools offering multivariate calculus and differential equations in high school, too. Either everyone is highly gifted or maybe (just maybe) a lot of these kids aren't actually learning this stuff in a meaningful way (though they can probably do the homework problems), and acceleration-itis continues unabated in American schools.

All I know for sure is that a lot of university professors in mathematics, engineering, and science are saying that students who took calculus in high school are failing the pre-calc placement exams in colleges. Well, I also know that the secondary school math courses I've seen offered around here and read about don't exactly fill me with confidence.

We are moving forward recklessly with a plan to find a high school or hybrid setup that will continue to add to DS8's math knowledge if his interest persists. Which means I'm perfectly fine with him starting geometry now (glad I didn't sign him up for the algebra summer class after all.) There always exist situations where it won't be a barrier.

Val,
Not saying that everyone takes Calc BC here (because that is not the case), but I don't think that Linear Algebra in our district is a "sparkly sticker" course. There are enough kids that excel in math (and other subjects) that such courses are warranted. The average AP score (on all APs, not just math) for last year's class was slightly over 4, so most kids know the material. Very, very few kids score under a 3. And my eldest had more than one kid in her class that did mathematical research with professors at elite schools (and had their name on published papers).

Again, not every kid, and certainly not the majority, but those who are capable are encouraged to take such classes.

NSG, I was really just trying to point out that acceleration-itis is out of hand in US high schools in general. Sure, lot of American kids pass the AP exams, but passing an AP exam doesn't mean that a student honestly understands the concepts in calculus or even pre-calc. That's what I meant when I wrote that they can probably do the homework problems but don't get the ideas. I suspect that this is the case for a great many students.

Our education system is increasingly defining rigorous as meaning a) taught at an earlier age and b) more homework. This approach rushes students through a superficial curriculum as they try to grab more golden math rings, and they end up with a shaky foundation or, for many, pretty much no foundation at all.

I have no doubt that there are some kids who can get to multivariate calculus or differential equations when they're 16 and really understand the subject and what came before it. But their abilities are almost certainly in the top 1% (or maybe even well into the top 1%). I doubt very much that there are enough of them to fill a high school class on the subject. I doubt even more that I'd want them taking these courses in a high school.

What bothers me most is that these classes are seen as being more worthy of a student's time than problem-solving classes that ask a student to connect concepts in order to solve a problem.

Check not only local district-- but state Dept. of Ed.

Also know which way the wind is blowing up there at the state level. The reason that I have this caution is that many states have become more controlling about which specific courses are "high school" standards, and they don't always write escape clauses into policy.

The real problem if your child is 6th grade is that while you can get assurances that it won't matter... you can't get a written guarantee that it won't change under you in another 4 years, and there's no way for you to go BACK and do things differently to meet the requirements at that point, if you see what I mean.

So sure, our school would happily admit that to be taking AP statistics, my daughter must have taken geometry. Sure. But the state says she gets a "modified diploma" unless that class appears on her high school transcript. Since she took it in middle school, unless we'd insisted, it wouldn't have been part of her high school transript. Yes, this also means that she took her first high school math courses at nine years old, which wasn't ideal from our perspective... but from a credentialling stance, it was the safe move.


Our paranoia about this and our cover-all-the-bases approach was later vindicated when (during DD's freshman year) it suddenly happened that now, to satisfy our state's phased graduation requirements, she was going to need to have "Geometry" on a high school transcript.


I'll also second what Val is stating above. DD observed with horror last night; "How on earth do you get to be in ALGEBRA without having a firm grasp of how to work with basic fractions??"

She sees students like that quite regularly-- it's not that they are dumb, or that they can't do the material, and superficially, if she shows them the procedural method of working some type of problem, they can follow the scripted method, but the real problem is that they don't understand the foundational skills that came three or four years previously. They can't really understand what they are doing in the here and now in Algebra or Geometry because they don't understand stuff they should have learned in 3rd and 4th grade (but didn't).

I am curiously watching this thread.
Our DS in 5th grade will take Honors Algebra 1 next year in 6th grade. He seems to be very up to the task. We know he is on a fast track and could quite possibly be the only freshman at his H.S. at this level. The outline is to have him take pre-calc, AB, BC/multivariate and then see what the school has for Senior year.

I am not sure what else to do. We will cross that bridge when we get there.

He is in a private middle school that starts with 5th grade.

Yes, exactly. I hear and read this sentiment frequently, and the problem isn't just in mathematics. People who teach in the humanities have the same complaint: student thought processes are linear. We had the highest rejection rate ever at our college last year, yet nearly all of my freshman English students think in a one-dimensional way. Many American students have no concept of how to think about something and come up with a solution that hasn't been scripted.

For example, in English, they're hampered by the kinds of problem that Master of None outlined here. DS's AP US History class expected essays written in a particular format that regurgitated material in a particular way. A private school we toured a few months ago proudly announced that they teach students how to write by following a script: exactly n sentences per paragraph, structure the paragraph exactly this way, and so on. Follow the formula.

Too much stuff and too little substance.

Wow you have classes through Linear Algebra? Do you also have multi-variable Calculus or Differential Equations class? I ask because college level Linear Algebra class shouldn't even need to require Calculus.

The highest level math class in my district is B.C. Calculus that despite the fact that 10% of kids take Geometry in 8th grade. The school just suggests AP Statistics (non Calc Based) or AP Computer Science in the senior year. And they don't offer the calculus based physics AP. A few students take classes at a local university. Other districts and a local private school do offer multi-variable calculus.

Most kids who take Linear Algebra have taken Calc, though it is not required. Colleges would rather see Calc following Pre-Calc instead of Pre-Calc then Linear Algebra. Unfortunately, the school does not offer Calc III or Differential Equations. You need to go to a college class for these (though many fine colleges are nearby, and some students take this route).

The highest level sequence of math courses in our district requires proofs and critical thinking. College Prep courses do not. Middle kid got cut down a math level this year due to a scheduling issue (still Honors Pre-Calc), and she has complained about the lack of critical thinking problems given in the class. Kid is upset when she doesn't score a 100 on a test (typically due to a dumb error, not lack of understanding). She included this in an essay required to apply to math camp (yet to see if she got in). She isn't particularly a "mathy" type, but she isn't challenged in the math class.

Guess I am surprised by the reactions here, as I thought most posts complain about the lack of challenge - now we seem to be stating that the supposed challenging courses are just fluff. I am certain that is the case in some schools. I have read plenty of articles about schools pushing AP courses, then no one scores higher than a 2. Yes, those courses are fluff. But that isn't the case everywhere.

As I said, the problem is that the students are rushed through math courses in a race to get them into college-level courses as soon as possible. This approach necessarily sacrifices depth and foundation in favor of surface area. The schools, the textbook companies, and the testing companies will all tell you that their courses and tests are rigorous when in fact, they are not. I never said the AP courses were fluffy. That was your word (please don't distort ).


Scoring a 3, 4, or 5 on an AP test does NOT require you have a deep understanding of the concepts underlying calculus and pre-calculus. It requires that you have a decent understanding of basic and intermediate procedures (depending on score), but nothing more.