I ask in all seriousness.

When I was a schoolboy in England one just needed to demonstrate mastery via O/A-levels and beyond that nothing else really mattered.

Over here, I am confused because it appears as though one must simply mark time in high school and that is about it. There doesn't seem to be any other yardstick other than having so many years of high school Maths,English etc to be able to 'graduate' from high school. And without that high school 'diploma' one is just about SOL when applying to go to university in the US.

From where I stand, it seems as though one could have stellar SAT/ACT/AP subject scores and still be spurned by any college here without a high school 'diploma'.

I ask because (and maybe I am the stupid one here) my DD is currently absorbing Maths like a sponge and I want her to a) proceed because she likes it b) keep her in her ZPD so we 'after school' Maths.

However, if she has finished AP level maths by the end of the sophomore year does that mean she will not be able to 'graduate' high school because she will not have the required years of high school Maths and therefore not meet matriculation requirements for colleges here?

I had been thinking that with Maths (up to Calculus BC) under her belt she would be free to delve more deeply into other interests if she still had high school years to go before university because CC's here are not great.

Am I wrong to after school Maths after all?

Yes, I agree with Portia-- figure out what strategy will work best when your child begins studying geometry or algebra-- the reason is that state requirements can shift UNDER YOU when your child enters high school.


That is, credentialling via something other than afterschooling probably isn't optional, firstly-- it's going to HAVE to go onto a transcript somewhere somehow--

but also, make sure that geometry and algebra II are on that high school transcript.

Why? Well, because "four years of math" is often the oversimplified version of the following:


Yes, this really can mean that your child with AP calculus can be denied a high school diploma if they took geometry as an 8th grader and it didn't get onto a high school transcript.

So in short, I agree with your set of concerns-- and I'd be wary of doing too much of this as homeschool/diy enrichment, because you'll lack the credentialling that is necessary. Please note that credentialling is no indication of quality, of course.

Yes and NO.. For math you can do this easier than English. And it depends on the school. To get into my local university one only needs to prove at least mastery of Algebra II. One can take the SAT II Math Test for this, or pass AP Calculus Test. (NO class is required to take the test.) Officially our school requires 2 years of math, at minimum passing Algebra to graduate. But you must take 2 years in H.S. But if you take A.P. Calculus as a freshman (as one of my son's classmates has done) I believe your math requirement is considered done as there are no higher math classes.

My son just told me that other freshman in his H. Algebra II class are taking the AP Calculus test tomorrow. Not sure what that accomplishes, perhaps they won't have to take any more math at the H.S.? In my district the math co-coordinator is strict and if you want to take the honors math sequence you MUST take it in order from the district and not skip. He does not allow any outside coursework to count. (He is not popular amount the gifted kids parents.) On the other hand it is possible to get on a track to take Calculus as early as a 9th grader but you have to start back in 5th grade.

On the other hand. English requires 4 years in class. You can take AP English classes, and you might be able to get a summer or online English course to count. But you can't just test out of it. And 3 years of Social Studies.

Foreign Language is the only other course that I know of you can test out of instead of sitting through a course. My son mentioned that a number of kids he knows are taking the AP Chinese test this spring. These are kids who speak Chinese since birth and have been taking Saturday school for years. Universities will usually count an AP Test or a SAT II test. For languages the SAT II test can be harder than the AP, I was looking into this because my son was interested in taking Japanese a class not offered at his school. My H.S. only required 1 year of a foreign language OR 1 year of performing arts so this isn't a big deal for H.S. graduation.

There are ways particularly in math. Some school districts have higher level math. Some private schools offer more flexibility. My district does accept online courses and classes taken at a community college or university to count. But only one or two of those courses per year will count towards graduation.

Good Luck. Keep in mind that what is required to GRADUATE from H.S. in the U.S. is different from what is required to get into university. Universities can be more open to accepting a test as mastery, and many U.S. high schools have very low requirements.

Check with your school district in your area. My son's Algebra & Geometry class will not go on his H.S. transcript and he will be allowed to graduate. Although what this might mean is that is GRADES won't show up on the transcript, it is assumed he passed both classes to be enrolled in Algebra II as a freshman.

For what it's worth, in California 30 years ago, I dealt with this by "testing out" of all the classes between Algebra I (taken in 8th grade) and Calculus (taken in 9th grade). I did all of the quizzes for every chapter of every math class, which was a lot of work, but nicely filled up the time after the AP test when everyone else was watching movies or cutting class. Looking back, I am very grateful to my calculus teacher for agreeing to grade all those.

And I had a ridiculous amount of math on my transcript for freshman year, since I got credit for all those "tested out" classes. I could easily have graduated in 3 years if I'd wanted to.

The recent tweet of the Davidson database updates includes a resource related to this topic of alternative paths. It is an encouraging article called Tips for Parents: Taking Control of your Child's Education (2014).

This might not be a problem. We are in PA. Middle school Algebra I and Geometry do not go on the HS transcript. Every year there are a few 8th and 9th graders that have taken all of the HS math courses (through Linear Algebra), and they attend classes at a local university (fortunately, there are three 4-year schools within walking distance). No one goes to the local CCs, because they are further away and they are not as good as the nearby colleges. It is fine at our district HS if you never even take a math class there - you just need three years of math somewhere.

Linear algebra in a high school?

Yes, Linear Algebra. Because if you take AP Calc BC as a junior (not uncommon here), what would you take as a senior?

Hopefully nothing Mathy unless you really want to but can delve more deeply into other interests instead. Am I being pitifully naive?

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.

The way school teaches it, you don't actually need to be conscious in calculus class to get a 100%.

This makes school plays much more intellectually stimulating.

Ditto to everything kcab said -

polarbear

My district is very proud and stubborn that THEIR honors math classes are the most rigorous classes around. I'm not completely convinced but I am not unhappy with their rigor either. My son's been struggling to get good grades, I've heard the teacher uses problems out of AoPS on her tests. My son's High school has multiple kids who get top scores in the country in USA(J)MO, although I'm not sure if that isn't more because of all the outside tutoring these kids have been in for years than the districts curriculum.

I am still confused as to what the kid who is a freshman and in my sons Algebra II class and taking today's AP BC Calculus test is planning. I don't believe our H.S. will give the kid credit for the course. Perhaps he plans to enroll is math courses at university? I expect he wanted to skip to Calc this year but the school wouldn't let him? Years ago my husband took maths classes at university starting in 9th grade, and I know it can be done. But most of the kids who finish Calculus early around here, just don't take math for a year or two.

This reminds me that my son asked last night what one learns next year in Pre-Calculus anyway? In his mind if it was like Pre-Algebra there didn't seem much point.

My short answer to him was that is was more trig, some more geometry, a hodgepodge of other topics helpful to know before taking Calculus and some basic beginner Calculus.

The issue is IF they have a strong foundation in Trig., and this comes down to what the particular per-Calc class involves. His Algebra II class seems to only have 2 Chapters of Trig. and they haven't even started it yet. Still 6 weeks of school left. So I expect a lot more Trig in next years Pre-Calc.

Also worth noting that no, actually, the problem that I mentioned is one that local B&M kids are up against, as well. At least with a virtual school, middle schoolers don't require transportation to and from the high school to enroll in higher level math class as seventh graders. In fact, it's a BIGGER problem for students who take EPGY independent study, because you have to get the local high school to agree to give credits for it. Sometimes they won't.

Seems kind of random, truthfully, as I know two local students this happened to, and both parents are proactive-- one of them wound up sleeping through geometry again as a senior for the specific purpose of obtaining a regular high school diploma. Yes, really. The school couldn't be bothered to seek an exemption with the state, and that was the only other solution.

Completely agree-- except that most modern Algebra II and Geometry courses aren't rigorous enough to constitute a truly adequate foundation in and of themselves. Still, very strong and motivated students shouldn't need it either way, given what I've seen of it (I've now looked at no less than four different textbooks for this course).

Thanks everyone for your comments - alarming and reassuring simultaneously LOL

Personally, I see Maths as something to be used not studied for the sake of it so I would fully support my DD dropping Maths once she had demonstrated that she would have no trouble with further Maths at college and devoting more high school time to other subjects potentially requiring the Maths that she had learned up to then, e.g. Physics (obvious), Statistics, Chemistry etc.

I would much rather she did something she found interesting than a stultifying high school Maths class covering material that she already knew.

I posted the first post in this thread to try to see if it would be possible. I have learned:-

a) it would be potentially possible to graduate without 'token years' of high school Maths.

b) paranoia will be the only thing keeping me sane, I must stay on top of local/state requirement and that obsessive collection of documents and transcripts from online courses is essential.

c) some here think that *not* doing maths for the sake of it (taking a break from pure maths) is a bad thing - I am not convinced.

d) many quality universities do not require a high school diploma

e) eligibility for state aid with tuition may be compromised if a high school diploma or equivalent is not obtained.

Thanks again all!

The question of C) is one you can review for yourself and in terms of your kid. How much is retained from year to year; then say after five years without practice. Will courses with applications of math or specific math be required come college?

Also a means of a work-around for item C) is the notion that your child, provided that s/he has the right temperment and inclination, might enjoy tutoring other students on the material while in high school-- this has helped DD keep the geometry skills sharp while she works on other things that don't use the skills.

This is a worldwide issue - it's not just the US. Personally I think that the majority of mainstream schooling systems are like this and therefore outdated and rather pointless.

While the HS might not require math courses once a kid gets past a certain point, US colleges do not like to see the student take off a year (or more) from math. Someone might make a similar argument to stop taking foreign language after a year or two if the kid knows what he wants to study and foreign language is not needed. However, the decent colleges don't like to see this. It is a silly game, but we all need to learn to "play the game" to get what we want (and that extends well beyond HS).

As for the tutoring, middle kid's friend just recommended her for a position at a (paid) tutoring program where this friend works - I'm a little concerned since she could potentially be tutoring classmates or older (and I know I wouldn't want to pay and find some kid is tutoring my kid - but this is for another thread.)

But gap years between school and uni are blessed?

Bizarre and somewhat absurd if that is OK but doing using the time to explore interests in more sciences instead of just doing Maths for the sake if it is frowned upon.

Personally, I do not consider any AP courses a substitute for college level classes at any college worthy of being called a tertiary level institution.I do not see AP classes as a route to duck out of or save money on any college classes, myself. I just want my daughter to have a chance to do more sciences while still at High School if she is so inclined when the time comes.

I'm not going to say that AP courses match college level - they do not. My middle kid is taking AP Bio this year, and while she loves the teacher, she is disappointed with the coursework. She knows it is not college level. She even attended a 200 level course (just one class) at a nearby college and was disappointed. This is a well known, highly regarded school, and she was still disappointed by the level.

AP courses are good for getting credit in college. My eldest is debating graduating early, or doing two majors in four years - all thanks to AP credits. The credit give the kid options when they get to college.

This is dogmatic. I earned a 5 on the AP Calculus BC exam. When I went to Harvard, I glanced a few times at the homework and exam questions being given to Harvard's "regular" calculus class (the one taken by biology, economics and other non-math majors). The questions were on material I had seen and were not above the level of my high school calculus class. In fact, the calculus textbooks authored by Harvard instructor Deborah Hughes-Hallett have often been criticized for their lack of rigor. I started with multivariable calculus and was not hampered by not having taken single-variable calculus at college.

I doubt that Harvard's "regular" calculus class is much more difficult than that of other colleges. Its Math 55 course probably has counterparts at only a few selective schools. Harvard et al. are so expensive that it makes sense to take courses at them which are not offered at other places (including high schools).

I had a similar experience as Bostonian with my engineering math and science courses.

The first year was mostly a repeat and required no actual class attendance or work.

This depends entirely on how the H.S. Class is taught. All AP Classes are not of the same rigor. There is a huge variation of quality this depends on the teacher & how they teach the class.

And what you mean by substitute for college level classes varies. Depends on what college class you want to replace, and at what university. Typical AP course is only a one semester/one quarter not an entire year. Non calculus AP Physics doesn't really help you unless all you need is a Gen Ed Science credit. AP Calculus can replace anywhere from the first semester to the whole year, it depends on what your going to do with it. Are you a Engineering Major or studying pre-Med?

My experience with AP courses (me taking them) is like ancient history at this point, but as my ds is moving into high school I've been a bit surprised at how they seem to have evolved since I was in high school. It's disappointing to me to see that so many of them seem to be the equivalent of 1 semester's worth of a college course rather than a full year's worth, and my dh and I are now seriously rethinking - do we send our ds to the high school program that allows for the most AP courses or do we send him to a program which will allow him to start taking college courses earlier and just skip the AP courses.

Back when I was taking AP courses, my one year of AP Calculus was equivalent to what I would have had in my first year Calculus course at my very highly respected engineering college, and getting a 5 on that test allowed me to place out of that first year of Calculus, which worked out a-ok. My AP Physics course was the full first-year Calculus-based physics course typically taught at engineering and science university programs, one semester mechanics, one semester ee. Credit for AP courses at my college was determined by individual department heads, so for whatever reason my 5 on the AP Physics exam only earned me one semester credit - for the mechanics semester. There was absolutely *nothing* new presented in the semester of ee I had to sit through - and again, I was attending a very rigorous highly respected engineering college. (and I'll be honest here - I didn't mind sitting through one class that first semester where I already knew everything lol!)

Personally I'm just a bit bummed about what seems to be available for my ds to take in terms of rigor and pacing with AP courses. There are a lot of them out there now, but I'm not sure the choices (where wer'e at) are all that great for a kid who is really capable of working at a college level. Even for kids who aren't DYS-level in ability but who are one-two years ahead academically, I don't understand why the AP courses need to be watered down? Is there something that is supposed to happen overnight developmentally when a student receives their high school diploma that makes them all of a sudden ready for a twice-as-much-material in one year course?

Stepping off my little soapbox for now!

polarbear

Just be careful of the college courses versus AP courses. Sure, AP courses are not that rigorous, but around here, my older kids would say that the local CC courses were okay for their 9 year old sister, but not for kids much older than that. If you have decent four year colleges near you, that may be a good option. However, the HS may not want a kid taking college courses until he exhausts the courses at the HS.

Do you have a school in your area that will allow him to take college courses early? That really isn't an option in my area. One can take community college classes, but the H.S. has to approve these courses and they are unlikely to approve courses for courses they already teach unless there is a major scheduling conflict.

BTW my knowledge of what AP Courses cover what comes from college catalogs, parents of current college students (many at top universities), and UC college professors.

I'm finding a lot of useful information here. I've been drawing up comparison charts and trying to track exactly how much college DS11 can manage to get under his belt while the school is still paying for it, and I've come to the conclusion that we may have made a mistake in skipping 6th grade. If he could have done Algebra I this year as a 6th grader instead of a 7th grader, he'd be that much ahead of the game. But it's only one class (actually only 1/2 of a class, as he started at semester with the 2nd half), and I guess it will work out.

I'm looking at the classes at the e-school, at his regular school, and at the two colleges they work with, and trying to figure out a course of action that will get him the most paid-for college credits along the way. I thought he might still have two years' leeway because he'll be a senior at 16 and could still stay in, doing college classes, as long as he didn't let them graduate him, but I'm not sure now -- it looks like he can do one year of college after his senior year if he doesn't graduate, under the concurrent program, but possibly not two.

But the tossup is AP classes vs concurrent college classes, and the hangup is how many at which school are allowed, and in which order.

DS8 is on track to take AP Calc BC in 6th grade. We've been warned about some silly rules that he may not be able to graduate from high school because of this, but we're just not going to worry about it. We'll do what is pedagogically best (not too fast, not too slow, covering a wide range of topics, doing challenging problems). He'll take a bunch of college math courses before finishing high school. If a college would really reject such a student due to supposed lack of high school math credit, then they should not be taken seriously as an academic institution.

I have read several posts here on this site reporting how good grades on AP this or that allowed people to qualify out of course X in during the first year of college or that course Y in their first year was basically a replay of their AP class. Only now has the penny has finally dropped on why a bachelor's takes a full year longer year here than in England and Wales. The academic level of a typical US high school leaver at 18 is apparently a full year behind its peer, an exiting 6th former, in England and Wales.

I have been having unrealistic expectations of what a typical exiting high schooler in the US is supposed to have under their belt. Good to know, thanks!

22B, it isn't that the college would reject him for lack of math, but a HS might not let him graduate (need to check local rules). Do you have a decent four year college near you? Near the MS and HS so it is easy for him to get back and forth? If he is in third grade now, is he in Geometry? I found it more common around here for a third grade kid to be maybe two years accelerated in math, then the kid suddenly raced through the math around age 12. I think it has a lot to do with brain development of abstract thinking skills.

I have read that outside the U.S., students apply to college to study a specific subject. American colleges have distribution requirements requiring you to take classes outside your major, and you may not need to declare a major until the beginning of the sophomore year. These differences may explain why a BA takes 4 years in America. Quoting the Wikipedia:

http://en.wikipedia.org/wiki/Undergraduate_education
In many other, particularly continental European systems, an "undergraduate" degree in the American sense does not exist. Because students are expected to have received a sound general education at the secondary level, in a school such as a gymnasium or lycee, students in Europe enroll in a specific course of studies they wish to pursue upon entry into a University. In the US, students only specialize in a "major" during the last years of college. Specializing in a field of study upon entry into a university means most students graduate after four to five years of study. The fields available include those only taught as graduate degrees in the US, such as law or medicine.

I think 22b is saying they will just apply for admission to college without a high school diploma citing extenuating circumstances of a stupid rule nature. You can always attend high school until senior year and then graduate as a homeschooler and apply as a homeschooler or some other creative approach.

Just to note, in our district, I know kids that took only college math courses from 8th grade on, and there was no problem with HS graduation. They just needed to take three years of math while in HS - it was fine if those were graduate level math courses. I also have reservations about kids taking courses such as Algebra II, Geometry and Pre-Calc before age 11 - while they might get an A in those courses as an eight or nine year old, I also think that they would have a better, deeper understanding if they waited until age 11 or so. I truly think an 11 year old gets more out of rigorous proofs than an eight year old. Just my opinion, as I know others would disagree.

And there are potential issues with homeschooling in senior year, especially if the kid is involved in HS activities. In our state, the public schools must let homeschooled kids participate in ECs (sports teams, academic clubs, music programs). However, it is not this way everywhere.

With respect, I think it's not helpful, on this board of all places, to have opinions on what works for "kids", "an eight year old" etc. We of all people should know the damage that can be done by people who don't know our kids pronouncing on what's best for them on the basis of what works for other kids.

FWIW, the way it's currently working for my kid is that the maths he's done for the last year or two hasn't taken him forwards by a year or two in school syllabus terms, and at 10.5 he still has some school maths left to do. (Still, he did Alg 2 a long time ago, and he's more than happy with rigorous proof, thank you very much.) Most of his effort lately has gone into improvement in his ability to solve harder problems, rather than learning more syllabus. That's been right for him. But I have had to decide year by year, and perhaps small differences in him might have led to me deciding differently.

As I said, just my opinion. And my opinion often runs counter to others everywhere I go - from this forum, to forums on medical conditions my kids have, to Township committees I serve on. I suppose this should give me a clue.

And my kids are not advanced in math, or really anything else...just my observations of the smart kids I know (I certainly don't count my own among them - in fact we are trying to use athletics to give middle kid a leg up on college admissions). I have seen some smart kids rushed through various subjects, only to find it has hurt them later on (for US college admissions). The ones that have been successful (of course, I'm only considering kids I have seen) waited for Geometry until around age 11 - then blew through Algebra II, Pre-Calc & Calc BC in a year.

I'm not very smart and yet someone taught me how to do derivatives when I was 10. I could certainly get the right answer but I did not fully understand the applications. Just my opinion that kids will more fully appreciate/understand the concepts when they are a bit older. And I didn't have the chance to see those applications until I took a Physics course - but the school wouldn't let me take Physics when I was 10.

Also, the OP asked how asinine the US system was. College admissions are different in the US than elsewhere - just having really rigorous coursework and perfect standardized test scores doesn't guarantee admission. I know kids with perfect scores that were rejected at a number of colleges.

Maybe I'll stick to the athletic forums, even though my kids have no natural athletic talent. I'll be vilified there too.

The thing is that gifted kids (especially highly gifted ones) are very, very different from other kids (even moderately gifted ones). Kids with very high IQs can learn in ways that seem impossible to people who haven't spent time around them or learned about them. These kids are also very rare, and most teachers either aren't gifted or haven't had classes on gifted students. All this makes it very difficult for us as parents to convince the schools that our kids really did start to read when they were 2 or 3, or that they really can do algebra when they're 7 or 8 or 9, or whatever. Even harder is to convince others that our kids enjoy doing this stuff and get a lot out of it.

Also, when only looking at the surface, it's very easy to see "high achiever" as "gifted." Sometimes kids are both, but they often aren't. This table has a lot of information about the differences. Some high achieving kids may indeed be pushed into classes they aren't ready for, which may be what you've seen. I don't know.


That's up to you, but if you look for vilification wherever you go, you'll probably find it.

My ds11 is a hodgepodge of that chart. I would have no way of nailing him in anyone one of those catagories.

You don't have to. People can be all three!

If you dig around a bit on the site linked, you'll find an explanation that this chart was developed with the idea that Val mentioned - people can be all three or a mix of each. The person who developed the chart did so because she felt a previously published comparison on high achievers vs gifted individuals was too black and white, saying things like all gifted people are creative thinkers etc.

I'd say that each of my children is a mix of all three!

polarbear

My kids aren't as dumb as I make them seem. Middle kid typically could figure out Algebra before it was taught to her (teacher would let them try before she taught something, and middle kid could figure it out with no instruction). Same for when she was forced to take a Chemistry final without taking the HS Chem course and wasn't allowed to borrow the HS Chem textbook - she figured out how to do the pH problems just by taking the logical route and applying what she did know. But I don't think that makes her gifted or anything special, just rational and logical. We have never tried to accelerate her and she wouldn't go teach herself math on her own...she probably would watch Netflix.

There have been a few odd reactions to her. One kid wouldn't go out with my eldest because his younger brother said middle kid was scary (not in looks, in intelligence). And some kids kind of avoid her because of stuff she likes to discuss, though she certainly has friends that are like her.

I deal with enough politics and drama in sports. I have had to deal with some school politics (including that Chem final), but I try to avoid it. She is bored out of her mind in HS, but I think that will change once she gets to college - I have seen it change for the PG kids I know (who went where there were others like them). Only two more years - she can just concentrate on improving the athletic skills for her two sports.

And as for the OP's original question - delving more deeply into other subjects - unfortunately there is only so far you can go in certain subjects in US high schools. Maybe the kiddo can take a few foreign languages, since they might not have the chance to do that if they go into a STEM college degree program. Or take additional history courses. My older two always have/did take six core courses - one more than normal - to keep themselves busy.

They have no natural athletic ability, but they have certainly worked on their skills. They weren't absolutely awful at athletics, just nothing special. Eldest worked at it and had some DIII interest and made Honorable Mention All-State for her position. Sure, we're proud of that, and that middle kid was just accepted to one of the well attended college recruiting camps for one of her sports. But that didn't come easily to them. Not like academics.

I didn't vilify you.

There seems to be a use of "just my opinion" to imply "you are not allowed to argue". That might, I suppose, be a useful usage when attached to something that is a matter of taste "just my opinion, but this soup needs a touch more salt"; this could be heard as leaving open the possibility that someone else's taste might differ and theirs might be just as valid as yours; it's a qualia issue!

Children's education is not a qualia issue. On a forum where it is a central topic, if you make a statement applying to other people's children and others disagree with the statement, they're going to say so, even if you preface your statement with "just my opinion". If you don't like that, you should certainly go elsewhere.

A good thing about this forum is that boasting isn't a thing, and I hope you won't read this as boasting: it is unlikely that your "smart kids I know" include even one child as mathematically exceptional as my son, let alone enough of them for you to have observed a pattern in the consequences of different ways of educating them. Because this place is such a honeypot, the same applies to several parents who may be assumed to be reading what you write. Please be aware that there are variations in parents' experience beyond those you can easily imagine.

Wikipedia says that the nature and existence of qualia are controversial.

http://en.wikipedia.org/wiki/Qualia

Well, we might rather say that the usefulness of the word is disputed. I don't think anyone disputes that I may feel that my experience of eating some soup might be improved by adding some salt, and that (assuming we are concerned only with my pleasure and not with my health!) it would be incorrect of you to assert that I am incorrect in saying that I should prefer the taste of the soup with more salt.

Well-- I'm going to save Jon the trouble here and point out that such a notion deprives others of that valuable sense of deep, though non-abiding self-worth that only comes with WINNING.

Ergo, someone needs to be wrong, so that someone else can be righter than the rest.

Oh, and for anyone curious, DD14 is a eye-watering mixture of all three types, with heaviest emphasis on the right and center columns (gifted and creative)... and I completely agree with MoN's post on the preceding page-- there does seem, for many of us here, to be a point at which "least worst" looks rather unthinkable to outsiders who don't know our children personally (or can't see them for their biases, in the case of educators).

Heck, my child's own grandmother was an educator like that. She truly felt that if we'd just quit treating DD like she was unusual, she'd be more "typical." And that we HAD to by lying and, I guess, teaching DD phonics on the sly as a baby... or something. Because CLEARLY she didn't really believe that DD2 had every single sign of reading "readiness" that my Mom looked for in 6-7yo first graders. She expressed in no uncertain terms that we should keep her from learning to read. Truly not kidding. What is more astonishing is that we listened for nearly two more years.

I can definitely see some of the harm that such things have done to my DD, who will now struggle with task-avoidance and perfectionism her entire life. She hasn't learned that WORKING to learn is normative, because for her-- it isn't.

First you have to get to the point that the other person thinks that there is an "you" who can "experience" or have "preferences".

I'm pretty sure that there are people out there who dispute that.

Yes, there is a label for people like that, but most of them are so thrilled to be themselves that they don't really seek out such labels to start with.

This is true.

For instance, if I think that the only appropriate way to experience soup is with a certain level of saltiness, then to the extent that you think that you want something else is simply profoundly *wrong*.

And in order to fix your wrongness in terms of what you want, I must endeavor to correct your error for your own good.

Ding ding, task avoidance and perfectionism detected.... Maybe she will work hard at acquiring a growth mindset, and succeed in overcoming her task avoidance and perfectionism...

There's a similar problem in some Buddhism-esque practitioners too.

Me shadow <-----> you shadow

So, neither I nor you are real.

Yep. I'll leave it at saying that these kids aren't really all that smart. No need for me to give details as that would likely ID some of these kids.

I can't imagine every possibility...I realize that. For example, I know one kid who is the most exceptional athlete I have ever seen. My father, who has been around a lot of sports, says the same thing. Kid can pick up a sport and in a few weeks can surpass those that have played for years. Is in HS now and has verballed in the chosen sport, but kid could really have played any sport at a DI level. Unless I had seen this kid, could not have imagined such ability.

But all of this is off topic...how can we help the OP's kid? As I mentioned, my kids have taken additional courses - they take/took two foreign languages. Middle kid has applied to a selective math camp, eldest participated in stuff like Model UN (and chaired a committee this year when her school hosted a HS Model UN event). What might be interesting to explore?

She's done better there in the past 24 months since we've been truly pushing her to work at it, take risks, and improve her failure tolerance, yes...

BUT.

She was a kid who was extremely keen on algebra at 6yo, and then the school spent the next THREE YEARS teaching her... well, fractions, I guess. Because the rest of it? She knew at 6yo when we turned her over to them.

By the time she was nine, she was sloppy in her work habits, and tended to assume that mistakes were an indication that she should give up doing math, and that learning was painful and best avoided entirely.

Also-- I wouldn't assume that high-level thinking the way some have mentioned it here (rigorous proofs, etc) is even taught in high school curricula at this point in the US. Seriously-- do NOT make that assumption. Val and I can both attest that whatever higher level understanding our kids have had (up to calculus) has been gleaned via interactions with us, not with the curriculum or their teachers. Sad but true.


Knowing what I know now, I'd have pressed harder to get her into algebra a LOT sooner-- probably at 7yo-- and searched out the applications-oriented material that she was so clearly keen on, rather than relying upon the school to take care of that stuff. We pulled back later to allow for some math-specific unschooly time, but what she really needed was competent higher level instruction. University level, not this test-focused baloney in AP coursework now.

Maybe this goes over into the underachiever thread instead of here.

Maybe-- but MoN and I are pointing out that taking the well-traveled road has a price, too. I also stand by the statement that once that kind of thing is learned, it is something that one tends to struggle with, much like an eating disorder. It's just always there in the background, and it's hard work to force your thinking away from it as a default mode.

I think you have to consciously rebuild new habits and force them into place over significant periods of time so that the new habit becomes the default.

I agree. It's hard, but it's possible (and the decision to do it has to come from within). Parental units can set an example, but the child has to decide s/he wants to change, or it almost certainly won't happen.

Agreed-- but I've been working on that for nearly 25 years, and it's still my default to avoid tasks where success isn't certain in my mind. I have learned to enjoy learning, however, as opposed to "knowing."

Anyway. Tangential either way, I suppose.

My personal preference is for collegiate instruction, when moving beyond high school algebra and geometry. I feel that college instruction is better able to accommodate students who are divergent/creative thinkers with respect to material. High school teachers who lack graduate degrees (and, with no small frequency even a regular undergraduate emphasis in the subject) may simply not be ABLE to answer questions which exceed the scope of the curriculum. Now, that isn't to say that adjuncts or teaching assistants always can do so-- but the odds are certainly better, IME. This is still my number one reason for believing wholeheartedly that AP isn't college level.

Back on the topic of "ridiculous rules" we'll just do what we think is educationally best for our kids, and assume (or hope) that common sense will prevail.

Here's a fun yes/no question. Did your child learn to read in Kindergarten?

No - because both already knew how to read (self taught) before they started pre school.

Number 1 yes, learned to read in K

number 2 learned to read before k

No, DS2.5 has already self-taught.

And the analogous yes/no question. Did your child take high school geometry during high school?

DD6 has learned just this year in first grade, but she is grade skipped, so she is bang on target for learning at K age.

Guess I never heard it called high school geometry, but middle kid took geometry in middle school. Always at least a couple dozen who do this in our district. You can only take it in middle school if you are on the highest track or accelerated in math.

Both DSs learned how to read halfway through first grade. Just as I was getting ready to look for LDs, their readings light clicked on, and they were suddenly 3 years ahead.

Geometry, both in high school. In our district, geometry comes after Algebra 2, which DS#2 took at the high school before his 8th grade day began.

I remember doing Euclidian Geometry including theorems and their proofs up to the 4th postulate and the definition, at least, of parallelism at junior school before I was 11 in England back in the early Seventies. It followed right on from Arithmetic and after that we started with basic Algebra (simple linear equations).

I have never understood, given the sheer parsimony of it, why US schools wait so long to cover it.

It was cool and we got to learn to use compasses to draw and explore the properties of circles, chords, sectors, tangents, triangles, create perpendicular lines and bisect lines etc long before we learned how to use a protractor. Maybe people are afraid of injuries and lawsuits now given how discipline in schools has all but disappeared in many schools.

I should have realized this, since my kids went to a French immersion school, but math (and science I think) is different in the US than many other places. For some reason, in the US educators treat math and science as if there are neat, distinct subareas which do not depend upon or intertwine with other subareas. Algebra I is distinct from Geometry and Algebra II, Biology has nothing to do with Chemistry, etc. After seeing the European way of teaching math and science, my kids think the US way is stupid since we know these subareas cannot be used in isolation.

By the end of HS, the US kids may have covered the same math and science as their European counterparts, but if you look at things prior to then, the US kids may cover some topics earlier while the European kids cover other topics earlier.

I think my kids bisected a line around third grade, but that was at the French school. Didn't get back to that until 8th grade in the US public school.

In case anyone missed it, the point of these questions is this. Although there are 2 answers, yes and no, they cover 3 cases:

No, earlier.
Yes, during.
No, later/never.

The two "no" groups are at opposite ends of the range, but they are lumped together.

I don't think I studied geometry past the basics. I may be wrong but a lot of the stuff you talk about I have never done - trig yes, stats yes, algebra and calculus yes but very little geometry.

What one learns in U.S. High School Geometry has changed over the years. When I took it as a high school students, we learned Euclidean Geometry and learned how to do proofs properly. My DD's (regular) Geometry class was mostly a "how to" manual, that basically showed how you used these lemmas with some algebra to solve a lot of basic geometric problems. The difference with my son's "Honors" geometry class was that he was expected to learn how to do standard proofs.

Some school districts do teach a "Coordinated Math" curriculum rather than the more standard Algebra I, Geometry, Algebra II. This curriculum just takes the standard topics and rearranges the order. Each year you get a bit of algebra and some geometry. I'm not qualified to say if either ordering is "better" or not.

What bluemagic said. ^

My DD started to do geometric constructions in about 5th grade, I think-- around pre-algebra, anyway. However, she did not have the kind of rigorous instruction in proofs that DH and I both vividly (and very very fondly) recall from geometry instruction. Even honors didn't do much of it-- though they were exposed to the idea, unlike the non-honors peers.



I was also (pleasantly) surprised by just how much molecular biology and biochem is in high school biology coursework these days.


22B's point is the one that I was attempting to make, btw-- at least, that is how administrative bureaucracy can see the answers to those questions if you live in a state that has very particular graduation standards. It's bizarre, and yes, asinine to have to jump through many additional hoops in order to prove that you're not in the "no, never" group... seems like burden of proof ought to be nicely satisfied by doing higher math, after all, but it's not about logic or rationality, I'm afraid.

It's about PROVING it to those who frankly could care less about my family in particular.

This is pretty much my memory of geometry.

Granted, I have no idea what was actually taught in a geometry class.

My father simply pushed the "master system override" button, slapped a tutor on me for a few weeks during the summer, and the class was credited to my record.

Actually, your assumptions are not true and have not been true for at least a decade in my children's district and many other districts (in different states) of which I am aware. There is even the term "elementary geometry" sometimes used to describe the geometry routinely covered in the elementary curriculum. Circumference, area, volume, parallel/perpendicular lines ,translating/rotating/flipping figures, and compass/protractor use are just some of the topics routinely covered in elementary school. In our district's pre-algebra curriculum, easily a third of the curriculum would be more properly classified as pre-geometry and further extends coverage of geometry-type topics. "High school" geometry, which my DS will study in 6th grade will be routinely taken in 8th grade by "GT" students(maybe about a quarter of students as the label becomes more inclusive in middle school). That "high school" geometry course will require the ability to write proofs.

Back to the original question, the answer is no. I knew and/or knew of a few students at elite colleges who did not have a high school diploma. One kid got into trouble for creating an explosion at his private school so they withheld his diploma but the college (an Ivy) still wanted him.

As for the high school graduation requirements,as long as the district approved the original coursework, there shouldn't be an impediment. Of course, your DD may be subjected to additional "assessments" and other hoops, particularly if the original coursework was not arranged with the district's blessings.

If your DD completes Calculus BC by her sophomore year, I think it is unlikely that her interest in math will then terminate. Some high schools allow/facilitate enrollment in differential equations and linear algebra. Of course, AP statistics would be invaluable in sciences and economics, etc.

I read once that some high schools will give credit for college courses after the student has left high school, so someone could earn a high school diploma after the first or second year of college. This would be a form of dual enrollment.

The community college that my son attends will give a high school diploma to anyone getting an associate's degree if requested by the student. I think this is the case statewide (WA).

Sorry, you lost me which assumptions are incorrect?

My eldest attended a charter that was supposedly oriented toward math and science and supposedly understood gifted kids. The geometry class there never got past fill-in-the-blank style proofs. This was only two years ago.

Sorry for the lack of clarity. I don't mean that all your assumptions are incorrect. My point was that the situation has changed in the U.S. Euclidean geometry is now incorporated far earlier in many U.S. math curriculum than it was decades ago (when I attended). My oldest DS is 18 and I remembered being shocked that I had to purchase a compass/protractor for him in 4th grade (GT math so covered 5th grade topics). Furthermore, the same spiraling occurs for geometry topics as for arithmetic topics in elementary school. For example, they were calculating volume and translating and rotating objects in 3rd grade GT math (4th grade topics).

I think it is possible that my district might be a bit more vigorous than the average district but the spiraling mindset is the same. If you look at the ALEKS math courses, which I assume is fairly representative of U.S. curriculum, their 6th grade (one year before pre-algebra) topics include creating angle bisectors with a virtual compass.

I assume your junior high refers to 7th and 8th grade whereas our middle school include 6th grade as well as 7th and 8th. Most students in our district would take pre-algebra either in 6th grade (GT) or 7th grade (regular). Pre-algebra has quite a bit of geometry topics presented at a higher level than back in elementary school.

Now you did mention doing proofs up to the 4th postulate in junior high. That would be in line with GT geometry for 8th grade GT students. However, that would be beyond the regular math students who would not be required to produce proofs until they take geometry in 9th grade. Furthermore, the regular students start by filling in missing steps in the proofs before having to produce one from scratch. I also agree with a number of posters who mentioned that producing proofs aren't as big a part of geometry courses compared to several decades ago.

Maybe someone has already said this, but I think one reason fill in the blank style proofs are the thing now is that they are far easier to grade than the real thing. Of course, they're also far easier to do than the real thing as well.