For most students, this choice is not made by the student; it is made by how the high school organizes its math curricula and tracking, and decisions made by the student’s parents and middle school teachers/administrators long before the student applies to any colleges.
While true, for the student who is misplaced or who wants to accelerate, there are usually options. A late-bloomer should not be penalized for a decision made in the 6th grade.
However, recent threads about students facing administrative and curricular barriers to changing math tracks in high school suggest that “should not be” is not always the case in real life.
Understood. I also know that there is no blanket phrase that will cover every student. While there may be resistance from the school initially, I also don’t think that the student/parents should just throw their hand up in the air and say “well, that’s the way it’s gotta be” without doing further due diligence. Maybe the outcome won’t change.
But in that case, for college admissions anyway, that’s the opportunity for a GC to write about school policies in the rec.
Our district made accelerating in high school possible by switching all schools to either the trimester or the quarter system. Students can take either 3 trimesters, or 3 or 4 quarters of math a year if they wish to accelerate.
Surely that depends on the individual student’s intended post-secondary plans. If a student is intending to pursue a math heavy STEM related field at an academically rigorous school, I would think that it would be advisable for them to complete Calculus in high school. A student intending to study English literature or foreign languages not so much.
As for repeating courses in first year for which a student has a high score in the AP equivalent, often times, AP courses are not in fact equivalent to first year courses. If a student skips the introductory class in a course they are intending to major in, they could be missing out on material not actually covered in the AP course. Also the adjustment to first year studies, especially if a student is away from home for the first time, can be difficult. Taking a course where the majority of the material is review can be beneficial for easing into the expectations of post-secondary studies. Add to the fact that many courses in high school are taught with the memorize/regurgitate model, a student may find that the synthesis/analyze and apply approach to university studies takes some getting used to. If they skip the intro sequence of a course where the professor is more apt to give an initial adjustment period and instead dives right into a higher level course where the professor expects the students to already know what is expected, they may find themselves at a disadvantage.
@ucbalumnus The idea of pushing toward calculus in high school might be more of a result of wanting to show the most “rigorous” course of high school study than one of being “behind”. If there is a track to allow a student to do calculus in high school and the student fails to pursue it, does that have an effect on rigor?
I agree totally that this idea of B- have the student repeat calculus in college- seems ridiculous for a student who excels in math. My daughter’s school allowed a small number of students to take Algebra Honors in 6th grade for high school credit. They were specifically targeted because they had shown particular math aptitude. In her class, there were 5 such students. All of them went through Calculus BC by 11th grade and then took Stats. None repeated Calculus in college and have all done well. My daughter took the next level math at her LAC for “fun” (she placed out of having to take math at all) and aced it Freshman year.
If this is true, then I think the college has the obligation of not accepting the AP course for credit in that major. Colleges know the AP course curricula, and they understand the requirements and approach that AP teachers are following. There are plenty of programs that will not accept certain AP credits for required courses in the major. AP Bio for Biology majors is the most prevalent example that I came across. Many colleges will offer credit for a Biology for non-majors course, but not for the course required of Biology or Biomedical Engineering majors. Why should parents and students have to blindly guess whether the material covered during their AP class will be of sufficient quality for that major?
However, as I’ve mentioned before, this creates a certain amount of risk. Even if the course has some content that wasn’t covered in the AP class, that content will almost certainly not be introduced at the start of the class. It may not come until the last few weeks. Therefore, the student may spend their initial time in the class reviewing material that they have already mastered, creating a false sense of security when testing time comes around.
It’s not just content, but also or rather approach, in-depth work right from the start, not to mention colleges with proof-based calculus. You can also look at the first year math curriculum at MIT or Penn or Williams and you’ll understand why many students who come in with AP Calc AB credit don’t skip ahead. (To be fair, those colleges also don’t necessarily give credit for Calculus AB 3 or 4). Some easier colleges will give a Calc1 credit for Calc AB 3.
I agree there can be a false sense of security in the first weeks of college, one that can hobble students later on - freshmen don’t grasp the level of mastery required, are still in the “memorize, more or less” HS mindset, and don’t move to the “synthesize/analyze/apply” model until they realize they need to, around the midterms. 
I did my undergraduate studies in Germany where calculus is mandatory in high school and university level calculus classes are called “Analysis” instead. From this perspective, I think its valuable that STEM students have been exposed to calculus before entering university.
Looking for example at math courses offered by Stony Brook, http://www.math.stonybrook.edu/mathematics-department-course-web-pages, a student that already took high school calculus could start with Analysis I and Analysis II. Analysis courses typically take a more systematic proof based approach than high school AP or college introductory calculus classes. That way a student does build upon what’s already learned in high school without skipping over university level calculus altogether.
Basically all of math before calculus gets repeated multiple times. I think I “learned” the quadratic formula like 4 times in 4 different classes. I saw a study once that claimed that about 70% of the math taught in grades 6-8 is review. So compared to that, repeating calculus again does not seem so unreasonable.
I got a 4 on the AP calculus test. I decided to repeat the class in college and I’m glad I did. It made a lot more sense to me the second time around! I really needed to understand the concepts well to go on to tough engineering classes.
But no one seems to suggest repeating AP credit if the college/department recommends using it to take advanced placement in other subjects (e.g. English composition, foreign languages). A student with an AP score of 5 in French may be recommended to take 4th semester French language courses at some colleges (e.g. http://french.berkeley.edu/undergraduate/placement-guidelines/ ). Would those here who recommend that students with AP scores of 5 in calculus start in calculus 1 regardless of the college/department recommendation for advanced placement also recommend that such a student start in French 1 in college?
DS19 and I attended a local university open house recently and we were speaking to the head of the chemistry department. When I mentioned to her DS19 would be taking AP Chemistry she stated that most of the material would be review for him then. I asked if she recommended that he accept credit for first year Chem and move onto second year and she said she strongly advised against that, that the adjustment to university was such that having a course be a bit easier would help ease him into the demands. DS19 in addition to taking AP Chemistry will also have AP Physics I, AP Calculus BC, and AP European History. The only course he may potentially accept credit for is AP Euro as it will be an elective course.
As a matter of interest, Engineering programs at the schools here will not give credit for AP courses. In addition, the majority of STEM programs and Commerce, all require grade 12 calculus for admissions.
@ucbalumnus I see people suggesting to repeat AP credit for other classes all the time. I think the analogue to your comparison with French is recommending someone who has a 5 on the AP Calculus test start in college algebra, which I have never seen.
I was talking to my parents recently about the courses I took my first semester freshman year. I took two courses that people recommended me not to take because they would be too hard (including my advisor), and two courses that no one batted an eye at. I got easy A+'s in the first two, and hard-earned B’s in the latter. So overall, I think it’s really important to realize that what might be good advice for one person, might not be for someone else.
But in most cases, it is because the college/department recommends that (or just does not allow advanced placement by AP score), or pre-meds thinking that they can get “easy A” grades repeating their AP credit instead of taking the more advanced course that their college/department allows them to start in.
If a student scores a 5 on AP Calc, they should usually move ahead. In engineering, having a few AP credits can allow the student to manage their workload to get through the math & science death march of the first two years.
In Massachusetts, the majority of kids take alg 1 in 8th grade, so they do end up in calc their senior year. It’s only rushing if a kid really isn’t read for algebra in 8th grade.
Where we are (in Ontario) we have an integrated math curriculum, which spirals. The math progression for those in the high school university track leads to Calculus in 2nd semester of grade 12 (though because most schools are semestered it is possible to fast track if a student desires). In addition, some schools offer AP, though that is not the norm. Streaming for math (or any subject) does not begin until grade 9. Prior to that, all students follow the same curriculum. While it is difficult to change streams, there are pathways to allow students to switch to a higher stream though after grade 10, that would most likely require the student to extend their time to graduation (which many students do for a variety of other reasons). If a student is moderately good at math, it is not difficult to get to (honours) Calculus in grade 12.
There has been talk recently of postponing streaming until grade 11 so that all grade 9 and 10 students follow the university stream curriculum so as to not lock them into a specific pathway so early.
@Massmomm that is not true in our MA high school. We have 4 math tracks. Only the top one leads to calculus in high school. To get on that track you must take Algebra 1 in 8th grade (maybe a third of our kids do that), and you must get a high A in it (obviously something less than a third). If you don’t get a high A you repeat Algebra 1 in 9th grade. I’m not sure how many end up taking calculus in high school but it is a minority of students. Neither of my kids got there. They both tracked to precalc senior year as is the norm for most.