My oldest is only a sophomore, so I’m very early in this process, but haven’t found any good information on this question. How possible is it for college students to place into/out of classes beyond the AP level, and how can you possibly find this information when researching them.
She’s advanced in math – took AP calc BC as a freshman, multivariable calc and differential equations this year, will do calc-based probability and stats next year, and more as a senior. But, we live in the middle of nowhere, and don’t have access to do this at a college. These classes will be on a high school transcript, but not official college credit (a mix of online classes for homeschoolers and self study through things like MIT open courseware).
So, she wants to be able to place out of this stuff in college (not get credit, just be able to take higher level classes and not be forced to redo 3 years of math). I can’t find any information about this on college websites, so I don’t know if it’s likely to be something she could do at most colleges (by talking to the department and/or taking tests), something that would only work at specific colleges (which ones, and how to find them?), or something that’s pretty much not possible (in which case I don’t know what to tell her – just audit math classes in college?). She might well be in this position for science too, since she’s finishing up all the AP science classes this year.
I’d appreciate any tips about how to incorporate this kind of question into a college search.
My S25 is in a bit different position because he took college level math classes beyond what students typically take in high school, but it does seem like a number of universities we looked at would allow for students to test for placement into higher level courses, possibly by taking final exams for those courses to demonstrate knowledge.
I’m active in some homeschool circles (currently homeschooling my youngest), and I’ve definitely read stories about kids who self studied for higher level math and were able to test out successfully once they reached college.
Science might be more difficult due to lab requirements.
Are you open to online classes? That would be a way to get actual credit for the classes.
Prerequisite fulfillment for higher level courses. Some colleges or math departments enforce prerequisites more strictly than others. Having placement testing would be more needed when prerequisites are more strictly enforced.
Lower level courses listed as required for the major. Policies on placement testing for subject credit, or allowing higher level courses in place of lower level courses, can vary.
Search for “credit by exam” or “challenge examination” or “advanced standing examination” or whether the school’s math department enforces math prerequisites or if the course catalog lists “…or instructor permission” after the prerequisite.
Whether or not the department enforces prerequisites (and if so, how easy it is to get a waiver from the department) is something you will need to ask current students - of the school I know that do not enforce prerequisites, none publicly state that.
There are also schools where students can start with a proof-based single or multivariable calculus course that can still be challenging to those who have taken it before.
If she’s a homeschooler, check out Art of Problem Solving for math, and maybe competitions like the AMC or USAMTS
For science, she can move on to either study one of the three main sciences at a deeper, Olympiad level (if there’s a subject she’s passionate about) or even something completely different (Introduction — Neuromatch Academy: Computational Neuroscience )
Also, for the record, I have found math departments in general to be more flexible with taking advanced courses than science departments. Also, places like MIT are much more open to and familiar with the type of student who can take a graduate course at MIT freshman year and do fine
Some schools have students use placement exams like Northwestern. Purdue also is flexible with placement if a student has the course credits from somewhere. All the old math exams are available online and the recommendation is 80% or higher is enough to move ahead.
I looked at the Northwestern site, and it just mentioned placement for calculus (in math), which is what I found most other places I checked as well, not placement for 3 years of math beyond calculus.
It sounds from comments like it probably does vary between schools and departments, and some might be flexible even if they don’t spell that out on the website, but she’d have to ask. Would a department answer that question, or just students? And how would she even find the vanishingly small number of students in her situation at any given school to ask?(especially the non-lottery type schools – I’m sure she could find them at MIT, but it might be harder at more reasonable to get into places)
When is it appropriate for a kid to ask that kind of thing? In my ideal world, we’ll manage one college-visit trip sometime in junior year, and it would be nice to know this before choosing where to visit. Visiting colleges is a huge lift to do at all from rural Alaska, and if we can pull it off, it’ll be limited. Could she email departments when she’s a junior thinking of applying? Or will that just be annoying to them?
As for the comments on math and science options in high school, she did use AOPS through calculus, doesn’t like competitions, and is OK with live online classes, but not the asynchronous ones which are most of the meager offerings available, since she thinks that’s worse than self-study.
The departments of the subject (e.g. math) and her major (if different, and requires that subject as part of major requirements) would be the places to ask.
Students generally may not be the ones with or familiar with that situation.
Typically there’ll be clear guidance from admissions on using AP for credits and placement. So, as I understand it, she has Calc BC AP results and can assess that pretty easily.
Our experience beyond that was that it was usually a Math department decision and the Undergrad advisor can be helpful there. You’ll want to save all syllabuses, p sets, exams, etc. for each class. Yes, contacting as a prospective applicant would be fine.
She might find that this is all sort of moot. It’s possible her post-calc coursework just isn’t as rigorous as the sort of college level math she wants to pursue (the math-major course level, not the general student course level). Just for example, even the most well-taught HS Calc BC course is probably equivalent at best to the lowest level of Calc taken by engineering majors. There are levels above that for Math majors.
And, at top level math programs the math majors will typically move through a sequence that’s proof-based and/or doesn’t really overlap what she did in HS. So she might find repetition isn’t an issue.
You can get a sense of this by looking at the math major placement pages at different schools. Some do a better job than others (usually the better ones are those encountering more than a few students like yours). Princeton’s is a good example, and whether that’s a school of interest or not you might find the content helpful. For example, their info on calc placement might be interesting to you:
Thanks for the note to save the work and exams. Not sure we have it all for multivariable calc last semester, but can do it for differential equations this semester. The class she’s taking right now is an online live one for a handful of accelerated homeschoolers that the prof says is taught more theoretically and thoroughly than most university versions. I do not have the background to judge that myself. As for whether it’s moot, seems like there’s a bit of a catch 22. A place like Princeton, where you linked the info, seems like they are quite used to kids coming in at an advanced level, and have systems to deal with that. And also like their classes are probably run at a more advanced level in the first place, so placing out might not be as important.
But almost no one gets into places like Princeton! And all the more reasonable-to-get-into places I’ve looked at just list AP tests, and don’t mention further work, even though placing out of classes is probably more necessary at those.
She’s leaning towards data science/CS rather than pure math, and I’m not sure if she wants to take math all 4 years, but she definitely wants to do more math at college, even if she meets the major requirements already. As a data geek, she’s particularly interested in the probability/statistics side of things, and calc-based probability and stats also doesn’t tend to come up in the placement info.
My daughter had a handful of friends at Purdue who placed out of all those courses so there is a mechanism to do so. I know for DE classes they wanted the syllabi and they were reviewed by the department before they were approved. And the approval came very late…like a few weeks before classes started so it could t be counted on.
Yes, my reason for linking to Princeton was just that they encounter this enough to develop a guide. I thought some of that might be helpful in thinking through how math is taught at the university level.
I think for many schools, you’ll need to get this info from discussions.
If CS is the likely path, what is it that she’s concerned she’ll have to repeat? MVC? That’s possible, but she can take a proof-based version. She hasn’t taken linear algebra, correct?
Entry-level statistics courses come in various levels, depending on the rigor and math level of prerequisites:
Non-calculus, for general education requirements. AP statistics covers similar material.
Calculus-based introductory statistics.
Probability theory and statistical inference (typically a year long sequence) for statistics and data science majors, often requiring more advanced math than single variable calculus. Sometimes, one of the above introductory level courses is a recommended or required prerequisite (as well as math prerequisites).
That third option is what she’s planning to do next year. She found a pair of MIT open courseware courses that seem to do that (they require multivariable calculus as the prerequisite for the probability, and then the probability as the prerequisite for the statistics).
Yes, it is helpful, thanks. It seems like the same content is taught at different difficulty levels at different universities, and at the same university in different classes, so there’s probably no way to know what’s a repeat or not without asking a specific department. I’m not sure I get what you mean about ‘proof based’ – don’t all math classes involve doing a bunch of proofs? All hers have.
She hasn’t taken linear algebra yet, but was planning to, probably senior year. She’ll need some math senior year, and it seems like a logical choice? But she wants to take more math even if she doesn’t strictly need it for CS, so some of those other things like differential equations might be prerequisites. So I guess she’s worried about repeating anything past calc BC (which is usually straightforward to place out of), including 2 semesters she’s already done, and 4 more she will do.
The focus on proofs in math courses does vary. “Regular” calculus (and AP calculus), multivariable calculus, linear algebra, and differential equations in most colleges has to include some focus on application and computation as well as proving theorems, for students who will apply the math to other subjects. At some colleges, there may be “honors” versions with greater focus on proofs and logic than the “regular” versions, where the expected students in the “honors” versions are math majors who come in with strong backgrounds in math. Also, “honors” versions of courses may include generally harder problems than “regular” versions.
Discrete math typically has a greater focus on proofs than the “regular” versions of other frosh/soph math courses. Some math departments also offer a proof techniques and practice course to prepare students for upper level math courses, which mostly focus on proofs and logic (e.g. real analysis, abstract algebra, theoretical linear algebra, complex analysis).
CS majors usually have linear algebra and discrete math as major requirements; multivariable calculus may be required for engineering-based CS majors or those that require physics (E&M typically uses multivariable calculus). Upper level CS theory courses tend to be like math courses with a focus on proving theoretical CS theorems.
The concern about needing to repeat something because it’s listed as a prerequisite for an upper level course will be more difficult to predict but generally probably less of an issue. Faculty can almost always override prerequisite requirements; they list them to make sure students have the proper preparation. Usually this can be as simple as an email or a meeting with the professor, who might ask about background or even give some sample problem sets.
If it helps, my kids were in a cohort on roughly the same timeline as your daughter. There are 15-20 kids per year at our HS on that timeline. None of the students I know of were stymied in college by prerequisites, meaning that none had to retake what they viewed as the same course or were later prevented from taking upper level math because they hadn’t taken particular 1-200 level courses at the university (or received official university recognition of having taken them). There were discussions with faculty and some digging on their preparation but the result was always satisfactory placement. Now, there were cases where something like an independent study of LA wasn’t sufficient to fulfill a BSE requirement, but those kids just took a more advanced version (which felt to them like a totally different class).
None of that answers your initial question but sharing just FWIW.
On a side note, with the interest in cs, math, probability, she might have some interest in courses in operations research and optimization.
ABET-accredited engineering majors must require a minimum amount of math and natural science (math and natural science must be at least 1/4 of the usual number of credits to graduate), although departments of those majors may choose to be flexible in allowing the substitution of more advanced courses for students with knowledge of but not credit for typical courses like single variable calculus, multivariable calculus, etc..
Brown’s CS department handbook addresses the issue of credit for advanced math taken in high school and differentiates between classes taken for college credit vs high school credit.
They mention math a couple of times, so keep reading until you get to the section about nuances for joint concentrators:
If your HS sophomore attends a school that attracts high-quality students (a much, much larger set of schools than just Princeton), then they will have a math department that can meet her needs, and she will not be the first student they will have seen who will have taken what are typically college-level courses. They will all have some mechanism for placing her at (what they dem to be) an appropriate level.
That mechanism may not be the one that, if compared with all other schools and all other mechanisms, puts her in the most advanced math class - but that’s where I would say that mathematics education in particular is a marathon, not a sprint, and I wouldn’t spend too much time (or really any time) worrying about this. She will be academically challenged and have the opportunity to grow over her 4+ years of mathematics education.
You can certainly ask a question like “how does mathematics placement for advanced students work” and you’ll get an answer. I’d just not worry about comparing the methods and trying to draw conclusions, because I think that’s a quick way to get wrapped up in something that feels big and will end up being very small.