I would recommend anyone going into STEM, especially engineering or physics to repeat Calc at college. perhaps starting with Calc 2. As others have said, it gives you an opportunity review the material and learn it their way in preparation for a math intense and rigorous major. For business majors, I would use the AP credit to skip the class in college.
This thread seems to have two parts to it: what to take in high school, and what to take in college. This question for the discussion focuses on the latter issue.
What if your college gives a specific breakdown of recommendations for four levels of calculus—
- one level for kids with no prior calculus background,
- one level for kids with lower scores on the AB or BC AP test,
- one level for kids with a 4 or 5 on the AB test, and
- one level for kids with a 3, 4 or 5 on the BC test.
- And then there is a lower level non-calculus class on mathematical reasoning with no prerequisite, but a fun-sounding description. It is probably mostly taken by non-STEM majors.
Imagine you are a future major in something other then STEM (history or poli sci or English or something). You enjoyed math well enough in high school, and it was a rigorous high school with an excellent calculus teacher. You got a 4 or 5 on AP Calculus AB, the highest math course offered by your high school. But you probably would never choose to take a math or science class… except that it is a distributional requirement, so you have to take a math or science at some point, and you enjoy math reasonably well.
It sounds like choice 2 would be a repeat of material you have learned, and you actually would need special permission from the math department to take it, according to the catalog, because they expect people with your background to take choice 3. You would need to make the case that you do not feel your high school prepared you well enough- which probably is not true.
Choice 5: any reason not to go with it?
Choice 3: Any reason not to go with it?
Would you say the same for precalculus?
Would you say the same for those who took more advanced math at a college after a 5 on BC?
Would you say the same for those who got a 5 on BC in 11tg grade and have tho opportunity to take more advanced math at a local college in 12th grade?
What ucbalumnus said.
I could add more to what was said above but really that nails it.
ucbalumnus has raised multiple questions on this thread, and has made some statements about what “behind” in math really means. To provide my opinion on a few of these:
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A student who has not had calculus in high school would be at a serious disadvantage in the honors first-year chemistry and physics courses at my university. The student would also be at a pretty considerable disadvantage in the honors math sequence, even if the student started with Honors Calculus 1. So it depends. If the student is just interested in the regular course sequences in math, chemistry, and physics, it is probably okay (though unusual) not to have calculus in high school. We permit students to keep AP credit and start in the first-year honors versions of the courses in chemistry and physics, because they are different enough from the AP courses. (I am not sure about math.)
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I very, very strongly recommend that a student not take any serious electricity and magnetism course in physics without having completed multi-variable calculus, including vector analysis. This would be true both for the honors sequence and for the regular physics for scientists and engineers sequence. (It is not needed for the non-calculus based physics sequence taken by many pre-meds).
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I would not recommend re-taking a calculus course in which a student had a 5 on the AP exam, provided that the student actually understands the course content. The difficulty comes in assessing whether the student really understands the course content or not. For those of us who use math all the time, it is not so difficult to tell from a conversation with the student. If parents don’t use math all the time, it may be much more difficult to discern.
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Calculus BC does leave out some topics that are really essential for beginning calculus, in my view. Examples would be: the epsilon-delta definition of a limit, the idea of uniform continuity, and the Heine-Borel theorem, all likely to be covered (and assumed to be mastered) in college calculus classes that are any good.
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The issue of “racing ahead” needs to be evaluated relative to the alternatives. I know that the people at AOPS are enthusiastic about not having students rush ahead to calculus. However, the pre-calculus courses that they envision are nothing like the pre-calculus courses in our local school, and I know that many local schools are far worse, when it comes to standard high-school math.
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The heavy reliance on GPA for med school and law school admission (without much attention to the details of the transcript) causes many students to take a route through college that maximizes their GPAs, rather than their learning. I think this is regrettable. I know a few 3.5 and 3.6 GPA students that I would be happy to put up against a lot of the 4.0 students I have seen.
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When it comes to college language courses, I have seen some awful practices by GPA-maximizing students, whom my husband calls “sandbaggers.” Here are a few examples: heritage speakers starting in the first year, first semester course; a student who had lived and worked for a year in a country where the language is spoken enrolling in the first year, first semester course; a native speaker of Korean, who grew up in Korea and spent her entire pre-college life in Korea, taking first-year, first-semester Korean to pad her GPA. I knew a brilliant student at Princeton who took first-year Russian there, and found himself in a class that otherwise consisted entirely of students who had Russian (and often multiple years of the language) in high school. He found his feet in the language eventually, but with a C in the first-year course.
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A number of colleges (including mine) used to have the requirement that a student take the course the placement exam indicated, if the student had any prior class work in the language. We also used to require that a student who had transcript credit (anywhere) for a first-year language had to start in the second year. This became a problem for students who returned to school after many years away, if they had started a language. It turns out that having French 1 twenty years ago is rarely adequate preparation to start in French 2 now. So we abandoned this requirement, and abandoned placement exams.
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When it comes to grad school admissions in math, physics, or chemistry, the admissions decisions are generally made by the faculty, not by admissions staffers. At this point, the quality of the curriculum does come into play, and so does research experience. With a decent GPA, but not pre-med level, one can get into many high quality graduate research programs in math and the physical sciences.
Re: #64 @QuantMech
On point 7, does your college offer language courses for heritage speakers?
On point 8, wouldn’t keeping the placement tests (without the requirement to take a more advanced course based on old college records) handle the “French 1 twenty years ago” and the heritage speaker situations, as well as the “four years of French in high school, but no AP or SAT subject test” situation?
My D ran into the language thing at her HS when taking AP. Other than herself, every other girl spoke the language at home. She dropped into a lower lever after 4 weeks.
WRT to calc. I would not suggest anyone who has taken precalc skip even calc 1 in college, regardless of the major. If they took more advanced math at a college after a 5 on BC or got a 5 on BC in 11th grade and have tho opportunity to take more advanced math at a local college in 12th grade? Sure, why not, if they did OK in the advanced math, MVC?
But, in general, engineering and physics and math heavy and I would want my kid well grounded in the basics.
@Massmomm we are also in Massachusetts and only about 10% of the current 250 8th graders take algebra and of those, there are usually four or so who are required to repeat it again in 9th grade based on grades. For the other 90 or so percent, they can opt to double up sophomore year with geometry and algebra II, but most don’t. A student moving into an engineering curriculum or any other math heavy college program will be running to catch up. My three kids have been part of the 10%, but I still wonder if after taking AP Calc next year it might be worthwhile to repeat in college. Especially since S19 plans in engineering.
Kids can be well grounded in the basics without repeating. Really depends on the kid and the school.
I’m a bit biased. My kids don’t have to take a math class beyond a stats course in college for their engineering degrees unless they want to take one. There was never a question to take the credits and run. Sometimes that’s the best calculus to make as it allows room to breathe by not having to take a math class for the first term or two (or more.)
If they don’t have a good grasp on calculus then physics will be a bear. If they’ve gone ahead in math and have a good grasp, continuing down that path will continue to be a benefit.
@QuantMech I agree with almost all of your points. However, I do believe there is a difference between knowing the theory and knowing the practice of calculus. By the theory, I mean the some of the topics that you call essential in your point 4, such as the epsilon-delta definition of a limit, some of the finer distinctions of continuity and differentiability, and so on. A mathematician needs to know these points, but a chemist or engineer generally does not, since most real-world applications involve functions that are continuous and differentiable. Also, the widespread availability of graphing calculators and graphing programs can show us the domains and ranges of functions. Therefore, for STEM majors other than math majors, I would say that if a student is truly comfortable with the practice of calculus (derivatives, integrals, and Taylor series, and knowing when to apply them), they will be adequately prepared to take multivariate calculus and differential equations. I think this is what you mean by your point 3.
Would you suggest that such a student who completed precalculus in high school repeat precalculus before taking calculus 1?
So are you saying that a student who completes calculus BC in 11th grade should move on to multivariable calculus when choosing college courses to take while in 12th grade, but a student who completes calculus BC in 12th grade should repeat calculus when choosing college courses as a college frosh?
MODERATOR’S NOTE:
Let’s not muddy the waters with discussion about foreign language progression (or indeed, any department other than math), please.
@nypapa Calculus is mandatory in Germany for Arbitur students (German students get tracked in about 4-5th grade and go to different schools…Arbitur(Gymnasium) being the most rigorous…pretty much every student that goes to college goes to Gymnasium. Realschule ends in 10th grade and Hauptschule, the least rigorous is more like vocational school.
In the US, of course, we track too but most people stay in the same HS.
@QuantMech
“ For those of us who use math all the time, it is not so difficult to tell from a conversation with the student.”
D1 had a 5 in BC, and an A in MV Calc in high school. Her college faculty advisor (a PhD in EE) recommended she retake MV, but tried it, but said she was bored.
He did exactly what you suggest. He asked her to come to his office, and the “test” was an hour and a half discussion of the main topics and concepts covered in MV. He said he doesn’t give a written test because crunching answers is often not the same as understanding something.
I was very pleased and impressed that a professor would invest the time to do a careful one-on-one assessment like that to ensure she was properly placed. You don’t see that type of diligence much any more.
I am not sure how many students raced to calculus in HS **so that ** the student can repeat it in college. As OP also pointed out on post #20 that this choice is not made by the student, and in most cases, not even by the parents. Therefore, for majority of the students in the calc track, the placement in calculus in the normal curriculum decided for them by the school.
There were posts where parents asked how to place their kids into accelerated Math and but I doubt they intended for their kids to repeat it in college. As many have responded that it really depends on the kid, the HS and the college.
My kid was placed in the pre-calc track. She asked to skip Algebra 1 because she wanted to be with her friends. She successfully took the Algebra 1 exam (with no help from her HS) and was able to skip the course. Looking back, I found out it was helpful for her as she was able to take ACT/SAT and Math II in junior year with good enough scores. It also allowed her to take AP Physics C in senior year. It was never our intention so that she could repeat in college.
She is going to college in the Fall and based on what I know about what she learned in High School if she were to only need one Calc in college, I will suggest her to use her AP credit, but if she needs higher level Math, I may suggest her to take Calc 1, I will have to look at the curriculum. What does not make sense to OP, does not mean that it does not make sense to my DD.
As to kid who finished up to pre-calc, should they repeat pre-calc. Again, it depends on the kid and the college.
@bopper: It’s interesting to compare the college math progression in countries where calculus is part of the usual high school curriculum with US students that took an accelerated path. US colleges respond to the wider range of math experiences of incoming US high school graduates by also offering different levels of first year entry points, from basic algebra or beginning calculus to proof based calculus and even more advanced tracks. Depending on the individual student and the math course selection both scenarios are possible, either to backtrack and repeat material from HS in the first college semester or to fully apply the AP credit to jump further ahead.
What I see around me is that the race is on because college admissions have become more competitive. Parents who want their kids to have a chance at selective colleges or even just the better state campuses realize calculus by senior year is pretty much necessary. In our district, if the kid is leaning towards a technical major, they will be competing with kids who will be taking AP Calc BC Junior year at the latest. The kids I see getting into Berkeley for engineering were two years accelerated in middle school, then went to a high school with the quarter system where they accelerated even more, ending with two years post CalC BC math at minimum. The kids that were accelerated more moderately are “only” getting into UCSD and below. Parents are putting pressure on the schools to allow acceleration in math. For example, this coming school year, a high school in our district that runs on the trimester system is switching to the quarter system for math only.
@infoquestmom: that is NOT a norm at all in 99.9% districts though. Colleges do NOT expect post-AB/BC calculus. Many tippy top colleges expect some form of calculus but nothing “beyond”, and even they accept 4 years of math without calculus whatsoever for non Stem students if they show something else (like advanced foreign language proficiency, proficiency in two or more foreign languages, philosophy/logic…)
I know all parents like to think their kid is highly gifted and can start calculus in 9th grade but what you describe sounds like a nightmare of non-developmentally appropriate pressure for 99% kids and why Stanford says not to confuse rigor and crazy (well, they have officialese for this but check their language about “rigor”).
Honestly if this were the pressure in my public school system I’d pull my kids out.
BTW, I think this system of seeing math as a path to calculus (aiming for/going beyond) is wrong. I like curricula where other branches of math are explored (linear algebra, discrete math, stats&probability, even the logic of CS language).
In particular, I really think that the norm shouldn’t be precalculus + calculus for the endpoint in high school, but rather Algebra2+Statistics integrated with precalculus, if necessary spread over two years or accelerated with both in a year for STEM kids to get to calculus and calculus-based statistics, and with schools offering advanced math students a variety of advanced math choices from the different “dimensions” of math (analysis, algebra, geometry, statistics, discrete, etc.), perhaps with a link to an online college course or something.
Applied statistics is a very useful field to understand regardless of major, academic interests, etc, whereas precalculus and calculus train the brain and are basic building blocks for STEM majors so they’re necessary and useful, but not as “essential to understand the world” as statistics. Some school districts or universities don’t even count it as their required “4th math class”.
The result is that we have a high percentage of students who never take statistics and have no understanding of ratios or averages and such basic concepts that they forgot from 5th grade, let alone anything else that is necessary to understand the news (polls!) and the world around them. 
This really aggravates me and I wish there was a way to integrate basic statistics into the regular math curriculum without making it a separate course. (The separate course could still exist of course, but as additional knowledge.)
"The kids I see getting into Berkeley for engineering were two years accelerated in middle school, then went to a high school with the quarter system where they accelerated even more, ending with two years post CalC BC math at minimum. The kids that were accelerated more moderately are “only” getting into UCSD and below. "
This is just not true, it may be accurate for the kids you know but you can’t generalize like this. You’re assuming that every high school offers Calculus or Stats and has opportunities via a community college to take the advanced classes. Berkeley does not assume this.
Not really believable overall, since that would mean that UCB students would largely have completed the math requirements for most majors while in high school. Next fall, there will be 950 spaces in MATH 1A (first semester single variable calculus), 697 in MATH 1B (second semester single variable calculus), and 962 in MATH 53 (multivariable calculus). If so many UCB students have already completed these courses in high school, why would there need to be so many spaces in these courses?