In some schools, students don’t take AB and BC–they just take one of them after precalc, depending on how well they do in precalc.
No one takes AB and BC in D’s school either:
• AB tends to be the senior level class for kids who are bright and generally competent at math but not really enthusiastic about it (a lot of very bright humanities kids end up in the track).
• For the next level up (where D is), the material covered in Calc A is part of the trig/pre-calc course that is taken junior year. This is sort of the middle-high math track (ending in CalcBC) at her school—for good math students who tend to see math as a tool rather than a course of study in and of itself (premed/life science types). I t’s the same sequence that the more mathy kids take, except they take it in sophomore or junior year (so there are 10th, 11th, and 12th graders in that class).
• The higher track (more math/engineering/CS/physics types) currently ends in multivariable calc. But since there is a growing number of sophomores in the BC Calc class, there are plans afoot to add another option to insure that the best math students don’t run out of math track courses as seniors.
BC Calculus covers two semesters of a typical basic college calc course. Many high school think high school students don’t need more than two semesters to cover the material. It’s not that you skip AB material or do AB after BC, that would be silly.
At our school, BC covers the second semester, AB covers the first.
BC as originally intended was to replicate a two semester sequence of college calculus. Fall would be Calc I (ie the AB material) and Spring Calc II. Some HSs wanted to make Calc II accessible to the students that couldn’t keep up with that pace. What these schools have done is instituted a AB before BC policy where they take a year to teach what is essentially the first half of the BC curriculum and then they have a full school year the next year to teach only the second half of the BC curriculum.
OP, the fee for each AP exam in 2015 is $91, not $150.
I don’t know if the OP is still reading this, but I’d agree that if her son is interested in a STEM major, it can cause big difficulties to be “out of practice” with math for a whole year (and two summers) between 11th grade and college. I would also point out that the topics covered in calculus are pretty much the same all over, and AP follows that set for calculus. It’s not like History or English APs, where the topics covered and the essay styles are somewhat arbitrary. The AP version of calculus is probably less proof-heavy than the calc-for-scientists sequence at some colleges, but otherwise, it’s the regular calculus students take anywhere. Except for the addition of more word problems, DS17’s calculus text doesn’t look much different from the ones I had 30 years ago.
@SAHMof2 You mention that you have “opted him out of AP courses for honors/Adv as the teachers don’t teach the subject they only teach to the test.” Did you opt him out of AP sciences, or just of AP humanities? If he is considering a non-biology STEM career (and maybe even for biology), he really should take one or more math-based sciences. In practice, that is usually one of the AP Physics classes. Some kids “like science” until they get to the level where science is really just math with word problems about throwing and dropping stuff, etc. Unless they take a math-based science course, it is difficult for them to tell whether they will love it or hate it.
I realize that the block schedule can make things difficult in math. The other HS near here has a block schedule the is probably similar to the one you describe (4 classes in fall, 4 different classes in spring). Kids mostly take one semester of math a year, and it is difficult for them to move that fast when they haven’t done math in usually 8 months. APUSH is supposed to be just an awful grind with that schedule.
Moving on to where the thread has drifted…
At DS’s school, one can take the full-year Calc AB class as a junior and then Math 160 (2nd semester calculus) the spring semester of senior year. Some kids may need to do that because of scheduling issues if they aren’t willing to take a zero period calculus class junior year.
Calc BC here is technically 2 semesters of a dual-enrollment CC class taught on the HS campus. However, many of the kids who take the first semester (Calc AB equivalent) during their senior year drop it spring semester because they have already sent grades for college applications and either have senioritis or are on the FRC team with takes up most of their time for 6+ weeks.
My sophomore son is taking Calc BC now, and his class is much smaller this spring than it was in the fall.
There is a huge range of when kids take calculus at DS’s school. I know a kid who took the 1st semester of calculus at the CC during the summer before 9th grade and another who is taking Calc BC freshman year. A couple kids each year skip Precalc so that they can take Calculus in 10th grade. (Trig is part of Alg II here, so there is not a lot left for Precalc.) So, some kids could conceivably get to Differential Equations at the CC by the end of senior year.
AP Stats is only a single-semester course at our school. My son will probably take it spring of senior year while he is doing the FRC robotics thing because it lets him stay on campus rather than commuting.
Sorry, @attorneymother if I sounded ‘off.’
Wow, I learned a lot about what is available out in the bigger world. It is wonderful to hear how accomplished so many kids are out there. We hear so many negative stories about SAT/ACT scores and international tests. I wish these kinds of stories of kids doing great work in math and science (and other subjects) were more in the news. I’ve been pushing for higher level math classes since my kids were in elementary school and now I see what kids can do when the bar is set high.
On the subject of time passing between math courses - you know how British schools kind of exported the idea of gap years? Well, math majors are the one subject that is basically excluded from an automatic gap year option. Cambridge told me (with reference to their college system of application):
Realistically, this is likely to mean that virtually all of them would require immediate entry, and we do not have a list of those that may possible consider an applicant for Maths with a Gap year.
This was copied from an email exchange about math majors and which of their colleges might accept a math major taking a gap year. The implication being that math concepts need to be used, routinely, to be maintained.
Relevant XKCD: http://xkcd.com/447/
@numbersfun
No apology necessary. 
Frankly, I was in your camp until D disabused me. I told my D I’m glad she stood her ground but she has graciously not told me so.
The good news is that your child is going to be compared to the kids at his/her high school. Don’t be daunted by accounts of kids who are doing Calc III in 9th grade. I’m happy those kids are out there and I hope that they are putting their exceptional math skills to good use.
No true. This is a very broad statement. Again, depends on the school. Yale does not have a General Ed requirement, though it does have general distribution requirements. They are 2 quantitative courses, 2 writing, a language and 2 science. There are hundreds of classes that fit into these categories. My D, the Literature major, is getting one of her quantitative courses in a course called Geometry in Nature. Obviously this is not a course for STEM types, pre-med types, engineering types, etc because it would not meet the requirement for their major. I am sure a STEM type would not take one of the advanced Literature majors she would and would take a “soft” class to meet the requirement.
Not necessarily. My math major kid enjoys advanced spanish better than gen ed type spanish course. It has more “meat” to it.
I am sure one can teach a lot in Geometry in Nature type course. I just hope it’s not an excuse not to learn geometry.
I disagree. The students who can take such a sequence are two years ahead of the normal math progression. In other words, they should be among the top students in math, so they should be easily able to handle a one year BC course after completing precalculus (getting an A grade in the class and 5 score on the test without much difficulty).
It does not make sense to force the best students in math to take calculus at a slower pace than they are capable of handling. After all, the not-as-strong students in math will be taking calculus at college pace when they are college frosh, so the best students in math should be able to handle that pace (BC over one year).
My STEM-type D not only took advanced Lit courses, she picked up a second major in that discipline. But then she was able to pull that off bcos she took BC in HS, freeing up some college electives.
Some students do prefer to take advanced breadth courses, rather than just introductory level ones. Granted, this may be more common for STEM majors taking advanced H/SS courses than the other way around, since H/SS tends to have shorter prerequisite sequences (and H/SS student would likely have to take several frosh/soph level courses before taking an advanced STEM course).
Note that some schools or engineering divisions require that some of the H/SS breadth courses be at the advanced level.
With regard to ucbalumnus’s post #68, I think it depends on the university, whether a student needs calc-based E&M for various majors. At my university, all majors in Engineering and Science require at least one year of physics at the college level. I am essentially certain that all of the engineers have to take calculus-based physics, even the ones who are majoring in Engineering Tech or Engineering Arts or the equivalent. That means an E&M course in the second semester of the physics sequence. The engineering majors are extremely credit-heavy, with very little room for electives. There are pre-planned course sequences, which make it difficult to postpone basic physics, even if the later courses in a specific engineering major do not require E&M.
At my university, your comment is correct with regard to biology majors. They can take the non-calculus based physics. In fact, I don’t think they even have to take multi-variable calculus.
I agree that it can be financially prohibitive for students to take an extra year in college. That is why I would strongly suggest that a student who is in a position to take (and understand) single-variable calculus in high school should do it. Even if the student only places out of one semester of calculus, that is usually enough to permit a favorable math/physics course sequence.
Unfortunately, I couldn’t find data on how many students take AB followed by BC the next year. However, I found some relevant data that might be interesting -
http://launchings.blogspot.com/2013/08/maa-calculus-study-effects-of-calculus.html
http://www.maa.org/external_archive/columns/launchings/launchings_06_09.html
This just confirms the opinions that have already been expressed in the thread. It also seems pretty clear that students who do well enough on the AP exams can safely skip Calculus I or II, though personally I think this has as much to do with the caliber of the students who self-select into AP Calculus.
A few personal opinions –
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Although I couldn’t find good data, I think the system in most high schools is to offer a choice of either AB or BC Calculus after pre-calculus – i.e. only a minority of schools mandate that students take a year of AB followed by a year of BC. Good math students who haven’t had any calculus before can definitely cover BC Calculus in a year. The class does need to move briskly to cover all the topics, so students need to be quick learners. Less able students should take AB Calculus if this pace is too quick - it’s the pace of BC that’s the issue, not the difficulty of the material.
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For those high schools that mandate a year of AB followed by a year of BC - there really isn’t that much extra material in BC Calculus vs AB Calculus. Even allowing time to review old material, I think it can be comfortably covered in 1 semester – there isn’t a need to take an entire extra year. I personally wouldn’t structure the curriculum this way, but of course all this depends on the size of the high school, its resources, and the population it serves.
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In our high school, a lot of students who take AB as juniors will take AP Statistics or AP Computer Science A as seniors (a few take BC Calculus). Both Statistics and Computer Science are year long classes, but there’s probably only a semester+ of material in each class. However, it’s still a good way for seniors to learn some neat stuff without working too hard while they’re enjoying their senior year.
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Overall, I think it’s wonderful that over the last 30 years schools have moved Algebra I down to middle school so that bright math students can take BC Calculus as juniors or seniors. My one misgiving is that rigorous, proof-based geometry seems to have almost entirely disappeared. I might be old fashioned, but classically the reason that mathematics was studied was to develop habits of rigorous thought that are important for students in all fields of study, from writers and philosophers to computer programmers and mathematicians. I’ve seen many good math students hit a brick wall in college once they leave the calculus sequence when they encounter rigorous mathematics while also dealing with new structures and levels of abstraction. Maybe more could make the transition if they already understood formal logic and how to write a proof. Personally, I’d think about using a 30% of the pre-Calculus curriculum (which doesn’t seem that crowded) to try to fix this.
Lastly, to my horror US News is publishing a “STEM Achievement Index” that they use to rank high schools: http://www.usnews.com/education/best-high-schools/articles/2014/04/21/2014-best-high-schools-for-stem-rankings-methodology
Someone should buy US News and shut it down. I think colleges, students, and parents would all be better off.
Actually, BC is not any brisker than calculus in college, which students who are not advanced in math may have to take after completing precalculus as high school seniors. So the better at math students who are advanced by a year or more should be able to handle BC in one year.
What do they do in high school geometry instead now?
I had assumed that our school used a fairly rigorous proof-based approach to geometry because that’s what D had. But I was wrong! There are actually four levels of first-year geometry taught:
M212: Explorations of Geometric Topics (Sophomore level—remedial) “Sampling of topics”; not proof-based
M214: Plane and Solid Geometry (Sophomore level—general) “Overview”; limited writing of formal proofs
M218: Accelerated Plane and Solid Geometry (Freshman or Sophomore level—slightly accelerated) Comprehensive study; proof-based)
M248: Advanced Geometry and Trigonometry (Freshman or Sophomore level—accelerated/Honors) Comprehensive study; additional emphasis is placed on the integration of algebraic techniques in solving geometric problems.
Approximately the top 10-15% of the class take 248 either in high school or 8th grade. Another 20-25% take 218. But I’d say that 2/3 of the kids have only limited experience writing formal proofs or none at all.
@al2simon is right—that’s not good.
Scantron in our public HS. Yeah, fill in the bubble representing the next line in the proof.