I had never heard of non-AP calculus before I read this site. Seems odd to me also. Our school has a few options once students complete algebra2. AP stats is popular among those who aren’t up to calculus or don’t want to take it, but there is something lower level also.
I could imagine up to three (not four) levels of high school calculus:
AP calculus BC
AP calculus AB – slower, so a subset of BC
non-AP calculus – perhaps modeled on a first semester calculus for business majors course
However, since any student who reaches calculus while in high school is good at math (at least one grade level ahead of normal), it is likely that s/he is ready for at least the AB course, so it seems unlikely that a non-AP calculus course would be necessary. So probably only two levels (BC and AB) at most would be needed. Of course, if this is a school district where there are many students who are pushed ahead beyond where they really should be in math, then it may be “necessary” to offer a non-AP calculus course for them.
Maybe some teachers here can assess the level of their calculus text. It’s “Calculus: An Applied Approach” Larson, Edwards, and Falvo. Houghton Mifflin Company. They skipped or skimmed the first few chapters. The homework is often not from the book, however, but consists of worksheets and teacher-created problems. That could be adding a level of difficulty…or not. Chapter 2 is entitled “Differentiation,” Chapter 7 is “Functions of Several Variables” and the final chapter is “Series and Taylor Polynomials.”
I am fully prepared to accept that as a family we are as not strong in math as we should be, especially relative to people on this site. Nevertheless, DS took Calc BC and Physics BC as as junior (no outside acceleration classes), so I don’t think that was too shabby. Her homework that even took him hours was a worksheet. DH said the number and complexity of problems assigned is more the issue than difficulty.
I get the issue of moving from one track to another. It is difficult to move up, especially in middle and high school. So parents try to put their child in the highest possible track because it is easy to move down.
The problem is being pushed too far too fast and remaining in an inappropriate level. This usually happens with very bright students who can’t keep up the faster pace in a particular subject, like math. By the time the child hits pre-calc and definitely calculus, she can have a difficult time because of a weak foundation. This was a problem in my school district. First, the district wanted to give students the opportunity to move ahead on math so started offering algebra I in 7th grade. Other parents saw this, wanting their snowflake in that very top group argued for their child be placed in the class. (The school system seems to capitulate quickly to a parent request/complaint.) Now, you a little arms race in one subject and sadly the bright but not tippy top students suffer.no matter what. My child was ridiculed and made to feel inferior when she entered the STEM program in ninth grade taking Honors Geometry. But three years later, we saw the pushed students fail the BC exam (1 and 2 were not uncommon among the juniors).
Multiply that by other subjects and grades, ratcheting it up over ten years and this arms race must create a learning environment unbearable to everyone. Our school system, after seeing juniors taking BC calculus falling the exam and teachers reporting poor performance from former students attending college (and not elite colleges), taking Algebra I in seventh grade is no longer a suggested or expected route.
There are still young students taking Algebra I but they are now the exception rather than the rule. I guess the school system will find out how well this works in five years.
"I say, calculus super-lite for high school juniors is a class that is right for nobody. "
@“Cardinal Fang” - I once taught a class like this, “Introductory Calculus with Precalculus” and I think the kids got a lot out of it. The sequence for them had been non-Honors Alg II, non-Honors Geometry, and then the class in question. We were able to do a lot of qualitative approaches to calculus ways of thinking and rates of change and limits. Were these kids headed to Caltech? No. But they became more broadly mathematically educated in ways that would allow them to understand the world.
You could say that they should have had a different math elective - they did have a selection of choices, and 20 kids chose that one.
At the school in question, the senior year was divided into other kinds of travel and projects that would have made the class less suited than it was in junior year.
With all due respect, that’s a pretty broad statement “…is a class that is right for nobody”.
I should say, though, that my Intro Calc/Precalc class does not sound like what has been described for @TheGFG 's daughter. Her class sounds much more rigorous and not necessarily appropriate for her (?) or for the population I taught in Intro Calc.
ETA: After looking at the book described by @TheGFG, I can say with assurance that my Intro Calc course was nothing like this one! The Larson & Edwards book seems geared toward college level kids who are filling in math gaps for a business or economics degree (?). If I ran the zoo, so to speak, it would not be a book I would choose for the less accelerated HS student. It loses so much of the beauty of mathematics without getting much useful for such a student in return. But I don’t even run my own zoo, much less another district.
Are you familiar with her text, fretfulmother?
I have an older edition in the office, but I just read the editorial reviews of the latest one this morning. If you want me to be more educated I can request a review copy! 
Do you disagree that it seems less focused on the theoretical beauty of calculus, though?
When we looked into the possibility of algebra in seventh grade for frazzled kids, we decided that this would not be the best idea. This had not seemed to work out well for many participants, either because they were not selected properly by placement test and teacher recommendation or because they became burned out by the acceleration.
It seemed to us that except for a very rare student, it was not something that anyone “needed” at that age. So, frazzled kids took AB calc (which at our school seems to cover most of what is covered in calc 1 and 2 in college) during their senior years.
Lots of students do catch up with and sometimes surpass the students who are accelerated early, by doubling up or taking a summer class, as their interests evolve. My own kids did not go this route.
Also, the last I heard, our high school does run an unweighted calculus course for students who are not recommended for AB calculus or do not want that class, but want to take a math class. There is no unweighted BC class, and I do not know if a student can enter the BC class for senior year if they do very well in the unweighted class.
However, knowing what I now know about how many college calculus classes are managed (or too often, mismanaged), and the typical preparation of students entering calculus classes at elite schools and highly-regarded state schools, I think I would have arranged for frazzled kids to have entered college with calculus through multivariable and differential equations already under their belts, probably by taking summer classes at a local college during high school or immediately after graduation.
OTOH, it seems to me that the high school class that @TheGFG’s D is taking is not being managed very well at all, so ymmv. The teachers who taught high school calculus to frazzled kids were excellent.
@frazzled2thecore you have me thinking now. My oldest was admitted to his lottery school as a math and engineering major and has had no differential equations or multivariable calculus yet! When he finished the math in our high school, he did an independent study of real analysis and one of linear algebra. Well hopefully that will be fine too, but can you elaborate on your feelings about needing one or the other at college entry?
Our school district is one of those that requires Calc AB before Calc BC. This means very few kids make it to Calc BC since the accelerated track kids take Algebra I in 8th grade. Only the kids who are very advanced take Algebra in 7th. They are now offering a class that combines Algebra II and Pre calc in one year which will allow more kids to get to Calculus whether that be the kids who were “regular” math kids who did not get to Algebra until 9th grade or accelerated kids who want to get to Calc BC by senior year. Jury is still out on how well kids with the combined Algebra II/Precalc class do in Calculus and on the AP exam.
There has always been an option to double up Algebra II and Geometry in Sophomore year for those who got approval.
Only a handful of kids are accelerated enough to get to multi variate calculus.
For those that do not want calculus, AP stats is available as is a non-weighted college algebra class.
So her textbook is college level? Hmm, too bad the high school course description colleges will see describe it as “preparation for college calculus.”
@TheGFG it’s more that to me, the approach is more of a sophisticated “fill in topics” applied math book. More for an older learner. Less accessible to a high schooler and less interesting from my POV. I’m not thinking the math per se is “college level” but then “college level math” is not well defined, because college level for MIT is not the same as college level for somewhere else. (I don’t want to fill in specific other colleges for comparison because someone will get upset.)
." In reality, a jump up to a higher track is strongly discouraged by many teachers behind the scenes."
Isn’t that a good thing for students like your younger daughter? She doesn’t need jumps to higher tracks. Though I suspect that’s difficult to swallow.
“First, the district wanted to give students the opportunity to move ahead on math so started offering algebra I in 7th grade. Other parents saw this, wanting their snowflake in that very top group argued for their child be placed in the class. (The school system seems to capitulate quickly to a parent request/complaint.) Now, you a little arms race in one subject and sadly the bright but not tippy top students suffer.no matter what…”
We also have this situation. The problems start much earlier than high school. Many of those kids find algebra to be pretty hard and when they move on to geometry, it’s clear they didn’t fully get algebra. The problems worsen in high school.
“Our school system, after seeing juniors taking BC calculus falling the exam and teachers reporting poor performance from former students attending college (and not elite colleges), taking Algebra I in seventh grade is no longer a suggested or expected route.”
Our school experienced the same thing, and calculus became a 2 year AB-BC sequence and algebra2 became a 2 year algebra2-trig sequence (for most students). We now have the world’s slowest high school math program, thanks to middle school administrators who just cannot bring themselves to say no. Your school administration has more of a spine. The students who really belonged in algebra1 at 7th grade are forced into doubling up on slow-moving math classes if they want to complete BC calculus.
In my opinion, the top 10% or so of students are really ready for algebra1 in 7th grade and placing 30% or so as is done in our system just causes a lot of problems down the road. I think the best solution is to be more stringent about placement, and to have an expectation that students who try algebra1 in middle school and don’t receive an A will simply repeat algebra1 the following year with no shame. After all, if they hadn’t taken algebra1, they would have been repeating pre-algebra, There is no point in turning bright kids into struggling B and C students.
@fretfulmother - I sent you a PM.
Thank you @frazzled2thecore
Yours is probably an older edition, but the descriptions for all editions say things like:
http://www.cengage.com/search/productOverview.do?N=0&Ntk=P_Isbn13&Ntt=9781133109280&Ntx=mode%2Bmatchallpartial
http://www.amazon.com/Calculus-Applied-Approach-Textbooks-Available/dp/1133109284/ref=dp_ob_title_bk
I.e. it is for a less rigorous calculus for business majors course, not a calculus for math, physics, and engineering majors course. This should not be a hard course, even if it covers a full year of calculus for business majors.
Here is a placement test at Berkeley to help advise students who have not had calculus in high school on whether they are ready for Math 1A (calculus for math, physics, and engineering majors) or Math 16A (calculus for business majors), or need to take Math 32 (precalculus):
https://math.berkeley.edu/courses/choosing/placement-exam
Here is one at Tennessee Tech, but it has more levels of remedial math courses that it tests for:
http://math.tntech.edu/e-math/placement/index.html
Here are some “are you ready for [math course]?” tests for students whose colleges do not have their own:
From the stories on this thread, I wonder how many schools are limiting the access to their version of AP needlessly?
(before anyone jumps on me, hear me out.)
If a less advanced calculus course is working from a college-level text, what are the more advanced courses doing? Is the school dubbing the most advanced stream “AP,” and then working down from there? In other words, shouldn’t the most advanced group’s course description match what they’re actually doing, (Beyond AP, or whatever), rather than dubbing it “AP Calculus BC?” So instead of a lineup which reads,
AP Calc BC
AP Calc AB
Honors Calculus
College Prep Calculus.
One might see courses listed as,
Advanced Math
Multivariable Calculus
AP Calc BC
AP Calc AB
Honors Calculus
College Prep Trigonometry
It may be as prosaic as district contracts with the union which specify bonuses for teachers willing to teach AP courses. In a district filled with tech-connected parents, it would be quite likely that a far larger percentage of students than the norm are capable of taking calculus at the AP level in high school, but the budget won’t stretch to pay the bonuses for teaching AP.
As to the lab placement exam, I think the inability to type quickly should not disqualify a student from taking a lab. If the answers need to be entered in within a certain time limit, slower typists would be disqualified. I have worried for some time that the use of timed answers on machine tests could create a new category of disability: the smart hunt and peck kid.
And by the way, dyslexics can be very good at math.
@frazzled2thecore I believe a very small percentage of students enter college having taken differential equations. And, most kids do get through the math sequence. My daughter is at a tech school - not at the MIT level. They said the vast majority come in with Calc-AB credits. I’m guessing that statistic is different at MIT. I just don’t want parents thinking they have to send their kid to a local college to take a few additional semesters of math in order to be successful in college. Certainly, if they have run out of math classes because they are a few years accelerated, enjoy.