<p>As appdad said, think about grad schools if it applies to your S. Med schools will not take AP credit over college classes in the subject – other types of grad programs may not, also.</p>
<p>I took these things a long time ago, so all of this may have changed. But when I was a kid, way back in 1974, I passed 4 AP tests, with 4s and 5s as I recall. The only class I took for them was US History - the only one my school offered. I didn’t take the Calc AP but I took Calc at a CC before going to college.</p>
<p>My feeling (and what I did) was use them to get out of required classes not in my major field. I used the History and English AP to get out of some university requirements. I passed Chem and Bio AP but would not have thought of using them for those courses. Instead I went into the honors Chem and took the normal first Bio course. I was right. The chem class was far and away more difficult than the exam.</p>
<p>As far as math, I would not rely entirely on the Calc AP exam to tell me whether to skip ahead or not. First, if you are a humanities major and passed the Calc AP I don’t see any reason not to use the exam to meet a math requirement.</p>
<p>But if you are going into engineering or hard science I would definitely take the introductory college calc at an honors level if possible. You want to be able to use basic Calc like arithmetic when you get into upper division math and science. I don’t know if anybody on here has seriously looked at the Calc BC exam - but I recall college calc being a lot harder.</p>
<p>One caveat - if your kid is a math genius, and you know who you are, you can safely skip. I’m not talking about someone who just passed a Calc AP test - I mean 5 on Calc BC, 800 on Math II, taking ODE or Analysis in high school and getting As, and scoring in USAMO or high in AIME. Then you could probably safely skip.</p>
<p>One other thing to think about. Take a school like MIT. I bet 99% of the kids (maybe 100%) admitted there got 5 on the Calc BC exam. If it was so advisable to skip the intro math class, why do they even have one? Or do they?</p>
<p>JHS: Is Honors Calculus at Chicago really a calculus course or something in disguise? Math 55 seems to have been renamed. It used to be called Honors Multivariable Calculus and Linear Algebra. Very misleading. Math 55a is now called Honors Abstract Algebra and Math 55b is called Honors Real and Complex analysis. I suspect that advanced freshman math courses at other institutions also have misleading titles.
Here is the link to the Harvard Math department’s guide to its various freshman post-AP courses.
[Harvard</a> Mathematics Department : 21, 23, 25, or 55?](<a href=“http://www.math.harvard.edu/pamphlets/freshmenguide.html]Harvard”>http://www.math.harvard.edu/pamphlets/freshmenguide.html)
I don’t know how many students who scored 5 on the BC Calc exam would take lower level classes, eg. Math 1a and 1b: Introduction to Calculus.</p>
<p>I agree on the deficiencies of the entire AP curriculum. Too much teaching to the test–and in the humanities and social sciences not enough actual writing unless the teacher requires it–it’s not a mandatory part of the curriculum. I think the IB is superior in this regard.</p>
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<p>I bet most don’t even take it. I know at Caltech that all of Single Variable calculus through Linear Algebra and Diff EQ’s are in a single year long class - and some even skip that (though they have to test out).</p>
<p>I took Calc BC and am now taking an Honors Calc 2 at UMich (which isn’t really “baby analysis” I don’t think, just a harder version. We’ve done some proofs in homework, but none on any tests.) and it is quite different from BC. Not necessarily harder, but the focus is put on very different areas (so far 2 HUGE focuses have been Riemann sums and work, each of which were very very minor in my Calc BC class) and we have done completely new topics (like center of mass, probability, a few others I can’t remember right now), and things which are repeated are taught in a completely different way. We did a lot of memorization (like of trig identities and integration formulas) in BC, and in this class we learn how to really do it and understand why we do things the way we do. </p>
<p>I took AP Chem and am taking Orgo and have not found any deficiency issue, but they are very different subjects.</p>
<p>Marite,
S1 started first year at Chicago w/IBL Analysis (he preferred the methodology to Honors Analysis) and graduate-level Discrete. Is currently taking Honors Abstract Alg and Complex Analysis. What’s called Functions at his HS winds up covering a fair bit of Calc I, which enables the Analysis I course he took soph year to finish the BC Calc curriculum before the end of first semester. They went deeper and wider from there. After that, he took lots of the other usual suspects, mostly As, but Bs in MV and DiffEq. The teacher uses old final exams from other top schools as HW assignments, so there is no disputing the difficulty of the course (and that when HW counts 35% of the grade, this can pose a problem for a disorganized kid!).</p>
<p>He is currently a junior tutor (TA) for a 130s (non-honors) level calc class – he said there are not JTs in the two higher levels of Calc. He says folks come in with some Calc background; some are pre-meds looking to meet the calc requirement without going crazy, some didn’t get 5s and are looking to hone their skills. He wound up helping a lot of folks with Honors Calc (160s) last year, as it is heavily proof-based and if folks didn’t have any Lin Alg background, they were catching it on the fly in the course.</p>
<p>Clearly he is one of those exceptions – but I will also say that he only placed into Honors Calc based on Chicago’s placement exam! He talked to the math dept. advisors at Chicago and they agreed based on his coursework and outside enrichment, he was ready for analysis, and he never looked back.</p>
<p>S2 took Calc AB as a junior. Got a four on the exam, 760 on SAT and 770 on Math Level II. At his school, this makes him a solid B+ math student. Is taking AP Stat this year. Says that if he needs calc in college, he’ll go back to Calc I and at least have a clue – though other posters’ points about the quality of teaching going up as one moves beyond the basic courses rings very true. He is also in IB – which we have found less-than-satisfying for math instruction. He will take the SL Math Studies exam – but he actually took the course as a soph. Since them he has taken the AP courses, which should help with the IB exam. At least as his school does it, the curriculum tends to be fractured. His GF chose not to take HL Math and is taking MV/DSiffEq instead – at their school, MV/DiffEq is the tougher course.</p>
<p>IB was a total non-starter for S1 because of the difficulties in getting substantive subject acceleration in math and CS. S2 chose not to accept the offer at the math/science program his brother attended because he feared he’d have trouble with the math. Both made excellent choices.</p>
<p>My feeling is that if the AP course went well beyond the AP curriculum and a student got a 5, there should be some level of confidence into placing above or beyond the first level in college. (The physics course S1 took senior year was sufficient for 50% of the class to make the top 150 in USAPhO. The AP Physics C exams were an afterthought.) Short of a five or if one plans to major in the subject, and if the course was taught strictly to AP standards, give it more thought.</p>
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<p>One of my high school-era friends went to MIT and did use his AP scores to skip. This was all part of a plan to finish undergrad in 3 years due to money issues. I credit his success to the caliber of his high school, his innate smarts, and an impressive work ethic. No idea if such a thing is possible now. Kids, don’t try this at home. ;)</p>
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<p>I’d be more liberal in my assessment. 5 on Calc BC 800 on Math II, general facility with math even if not at the scoring at USAMO level should be good enough to skip, even for math/science majors, at most schools, where the majority of students aren’t at that level. Caltech/MIT et al wouldn’t fit under this rubric.</p>
<p>Actually, your point is a good one. However, many of you desire to send your Ss &Ds to the top schools in the country. At many of these institutions the goal is to generate life long independent learners. I have seen several advises withdraw because of their failure to make the transition from the ‘supportive’ environment of HS. Al deadlines are hard there is no extra credit and in some cases we expect students to deal with material not covered in class. We do offer support, office hours, facilitated study groups, tutors etc… Student outcomes on the whole are very good as measured by number graduating in 5 years, and matriculation to graduate professional school.</p>
<p>ESL TAs can be a challenge. However, all courses at my institution are taught by faculty. Graduate TAs are used to run smaller discussion sessions. We make every effort to support all ESL TAs (minimal English proficiency scores, special training program). Our tracking data indicates that having an ESL TA does not negatively impact a student’s performance in a course. By the way all this costs money!</p>
<p>Countingdown:</p>
<p>Thanks for the detailed explanation. It’s so hard to know what courses at one institution are equivalent to other courses at another institution. I had heard that Honors Analysis at Chicago was equivalent to Math 55. </p>
<p>I remember a study that suggested that the IB curriculum in math and science was not as strong as the AP curriculum. S took MV-Calc and LA the year after he took the BC-Calc exam and had no difficulty. He did less well in an advanced freshman physics class, but that may be because he had taken the AP exam three years earlier.</p>
<p>I think that most colleges offer support in the form of drop-in math centers, individual tutors, office hours, etc…
These types of support, however, are external to the class. In high school, the support comes from the teacher. It also takes several forms. First, a longer school year; second, more class hours weekly (an AP math/science class, in our high school meets four times per week for a double session of 90 minutes each. Compare this with the typical college class which meets three hours per week).
There is a great deal more structure in high school than in college. Many students find that they lack the self-discipline to attend class regularly and to make their homework the focus on their activities. Many resist asking for help either from a prof, a TA or a tutor (even if it’s totally free). When my S was Course Assistant, he would often report that those who showed up for sections were often the better students rather than the ones who most needed help.</p>
<p>Unfortunately, once you are a physician or a NIH scientist there will be no teachers available to offer support. At some point need must ask to what extent our kids are ‘independent leaners’. Some students are precocious others require more time. To a certain extent this is the trait admission officers are looking for in a potential applicant. This is why they will often select a student with a lower GPA and SAT scores over one with perfect scores.</p>
<p>I took Math 1a and 1b at Harvard and they covered exactly the same material as Calculus BC. I flubbed the Calc AP and it had been three years since I’d looked at Calculus so I was glad to start over, but it was a very, very easy course for me, I even took it self paced which meant I skipped all the lectures. I’m no math genius though I’ve always liked math. I remember finishing the final before the halfway mark. I even ended up grading homework for calculus the following year. Anyway, I’d say most kids who got a 5 on the BC AP and feel comfortable with the material should be ready for Math 21. Everyone I knew did that. Other schools may operate differently. There was a drop in math center that was great for help. </p>
<p>I’ve been interested to see that my older son who I would have pegged as one who might not go for help often went to the office hours for the computer courses he was taking. It seems to be part of the culture of the school. I never went to office hours.</p>
<p>Appdad:</p>
<p>I agree completely. that is why whether a student who scored a 5 on an AP should or should not take the equivalent introductory course is such an individual matter. And you are right, too, that adcoms look for independent learners.</p>
<p>appdad: I second your reservations about APs. I’m one of a minority of humanist faculty members on a university-wide committee of faculty that works with primarily Honors College students who are applying for prestigious scholarships in the U.K. and elsewhere. When it comes to applying for these scholarships, the science majors with serious lab time have the advantage over the humanities majors except that … because they “got rid of” their humanities requirements by taking AP exams, they are seriously challenged when it comes to writing personal and project statements. When I look at their transcripts, the reason for this deficiency becomes immediately clear: there is a growing number of science majors who, after taking AP credits, have not had a single humanities or social science course in their entire undergraduate career. They have studied four years of high school language and never plan to expand their minds in that direction again. </p>
<p>What a shame! Well, I am very glad to hear that Med Schools don’t think highly of AP credit replacing college level courses.</p>
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<p>Uhh, this isn’t true at all. There are a lot of people that have not taken calculus, definitely more than one percent, and I know people here that have credit for their intro calc class that have tried to take it again, but they’re greatly discouraged from it. Of course, MIT only offers credit for actual classes for their intro calc and their mechanics classes, but there are other ways to test out of other classes. But the basic point is that if you’re ready, then you can skip classes, and for calculus and physics at MIT, the AP tests can show you’re ready, while they can’t for other classes.</p>
<p>My son is looking at majoring in either Mathematics or Engineering in college.</p>
<p>We asked both departments if he should skip to Calculus II after taking AP Calc this year.</p>
<p>Mathematics department suggested if he scored a 5 on the AP test AND did well on the university’s math placement test (a few points above the cutoff score) he would be fine in Calc II. They felt Calc I would be a repeat for him and he would be bored.</p>
<p>Engineering department felt that he should retake Calc I within the Engineering department. My understanding is that the Engineering department focuses much more on theory that is generally skipped over in AP Calc. My son’s AP Calc teacher told us the same thing.</p>
<p>EngProfMom, your explanation is precisely why my S ultimately chose UChicago > MIT. He knew there were things he’d get at Chicago that he couldn’t get at MIT as an undergrad, and those were the Core’s emphasis on the writing, critical thinking and the differnt ways of approaching problems and ideas. He felt he’d be challenged to grow more as a person at Chicago vs. the very fun, nerdy comfort zone MIT provided.</p>
<p>Shravas – so why on earth does MIT make USACO finalists/IOI medal winners take the intro class for Course 6? Boggles the mind.</p>
<p>Marite – there is Honors Calc (160s series) at UChicago and there is Honors Analysis (20700 series). The HA course is indeed as tough as Math 55. S took the Inquiry-Based version of Analysis and found they covered just as much as HA, only it wasn’t in lecture format. </p>
<p>What I’ve found interesting this year is that as a Junior Tutor, S must also attend the prof’s lecture with his students! Essentially, it means he’s taking five classes a quarter this year.</p>
<p>At S2’s IB program, I’d agree that the sciences and math aren’t as strong as their humanities. (Their English is just flat-out killer. Pre-IB 9th grade English was tougher than S1’s AP Lang.) OTOH, the strongest math/science students in this area generally attend the separate math/science program, so until recently (due to boundary changes) there was not a screaming need for math beyond a basic MV/DiffEq course at the IB. S2’s HL Bio course is pretty impressive, though. I hear a lot of grumbling about Physics (not much of IB Physics correlates to what’s on the SAT-II or AP, as S’s GF has discovered), and unfortunately none of the IB programs in this area offer HL Chem.</p>
<p>Agree that self-direction is an important factor, Appdad. I suspect that helped S a lot in admissions because he talked about the kinds of things he taught himself for fun and amusement, it was clear he loved it, and admitted that it sometimes cost him in other classes.</p>
<p>For anyone interested in precisely which math MIT freshman start with, here is a link:</p>
<p>[Rethinking</a> the Math Core](<a href=“http://web.mit.edu/fnl/volume/214/sipser.html]Rethinking”>Rethinking the Math Core)<br>
to summarize…</p>
<ul>
<li><p>Roughly 1/5th take the basic Calc 1</p></li>
<li><p>Roughly 1/6th take a half-semester acceleration
(which is equivalent to starting with Calc 2 at many other schools)</p></li>
<li><p>Roughly 1/3rd start with Multivariable Calc</p></li>
<li><p>7% choose calculus with extra theory or extra applications</p></li>
<li><p>1/10th choose an interdisciplinary approach</p></li>
<li><p>Less than 100 students place out of the Institute Requirement for math</p></li>
</ul>
<p>Of those, many are in differential equations (a requirement for most majors).
A few handfuls start with the math majors analysis series, or with the algebra series.</p>