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preface: I took AB and not BC but I feel both are similar in nature.

By bad course, I mean that I feel as though Calculus AB/BC sets students up for 'failure,'

for starters, how successful are BC students in the future multivariable course?

To get a 5 in BC, one needs to pass with almost a 60% of questions correct on the exam. The exam is also all computation (which to be fair is much of Calculus II anyway), but because a lot of the exam is computations, proofs are magically handwaved or ignored in favor of computation (which gives students a bad impression of what math really is). For example, delta-epsilon is never touched on and so when I first encountered delta-epsilon, I was very confused.

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    $\begingroup$ (This pertains to the U.S.) Aside from honors level college courses, you're also not going to see much in the way of proofs in college Calculus 1 (differential calculus) or Calculus 2 (integral calculus). Typically, proofs are postponed to advanced calculus (traditionally this has been a Junior-Senior level 2-semester sequence) or in undergraduate real analysis. $\endgroup$ – Dave L Renfro Aug 29 '18 at 23:51
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    $\begingroup$ I'll say that faculty at my college are not happy about being forced by administration to give college credit for these courses. $\endgroup$ – Daniel R. Collins Aug 30 '18 at 0:29
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    $\begingroup$ that's not true, I went to a 'mediocre' school and, in calc I, we had to prove all the limit laws, linear approximation, IVT, MVT, limit of sinx/x, l'hopital. In calc II, we had to prove arc length, parametric and polar work, sequences (limit n^(1/n)), the Taylor series, etc. $\endgroup$ – Lenny Aug 30 '18 at 19:11
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    $\begingroup$ @TommiBrander: I've edited the question to include a Wikipedia link on Advanced Placement Calculus. For more background, see also the Wikipedia article on the Advanced Placement program in general. $\endgroup$ – J W Aug 31 '18 at 8:05
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    $\begingroup$ There is a middle ground between requiring epsilonics and completely ignoring proofs. We can have analysis without going all the way into the technical details. I think the question is whether or not we see questions which are novel and require thinking based on concepts. Or, is the expectation of the course that the tests be just like the homework with almost everything falling into the PSQ category. I have students who are genuinely confused when I lecture in the style of discussion as opposed to: "here is a problem... here is how you solve it". AP test format does tend towards thinking deep $\endgroup$ – James S. Cook Sep 4 '18 at 4:50
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Yes the AP exam is bad and not an adequate substitute for a rigorous college class at, say, a state flagship university. This is for two main reasons:

  1. The exam allows calculators and the calculators are really good at Calculus, so you can answer many of the questions just by learning how to get the calculator to do calculus.
  2. The grade range is too small. As you point out a 5 is 60%, which at most strong colleges would be a failing grade. Of course the vast majority of students go to schools that are weaker than state flagships so maybe a 5 is an A at most schools, but the cutoff for credit at my university should be something more like a 6 rather than a 4.
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  1. I don't think there is traditionally much need for epsilon-delta in third semester calculus. After all, it is not a real analysis course.

  2. When I took calc in the 80s, there was a short section on epsilon-delta. But who cares. It's not like you need it to do hard calc problems. Euler didn't.

  3. The 60% is more troubling, but all that said, I bet ETS has plenty of statistics to back up the idea that a 5 is like an A for a typical (GA Tech, not Cal Tech) calc course.

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    $\begingroup$ The typical AP BC calculus course is nothing like as demanding as the typical first year calculus course in a university like Ga Tech. Students who place out of first year calculus are often done a disservice, because they never learn calculus well, as they would have had they taken the first-year course. $\endgroup$ – Dan Fox Aug 30 '18 at 11:48
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    $\begingroup$ The remark "When I took calc in the 80s, there was a short section on epsilon-delta. But who cares. It's not like you need it to do hard calc problems. Euler didn't." seems to me absurd. Any serious use of calculus requires understanding it's basic definitions. Students who never understand epsilon-delta argumentation have not developed basic intellectual skills adequately to understand things like ordinary differential equations that make heavy use of calculus. They may not make rigorous arguments later, but they do need to know how to think. $\endgroup$ – Dan Fox Aug 30 '18 at 11:50
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    $\begingroup$ If my Calculus students understood calculus as well as Euler did, I'd be thrilled! I actually agree with this answer on point 2. What I disagree with is point 3, which is factually incorrect, and honestly somewhat insulting to Georgia Tech which is a very strong university. $\endgroup$ – Noah Snyder Aug 30 '18 at 17:07
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    $\begingroup$ Dan, I took BC, using an AP text (Thomas and Finney, the book you see in Stand and Deliver). But the content was almost the same as the college edition of the text. I had zero problems after validating out of 2 semesters of calc at USNA with a 5 in further math and science courses. I suspect USNA and GA Tech are similar caliber. Again, I am the opposite of an ETS defender. But I would also not assume that individual snipes on the Internet are the same as their systemic psychometric evaluation and proof that a 5 is equivalent to an A in a standard calc course. $\endgroup$ – guest Sep 1 '18 at 1:07
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    $\begingroup$ Dan, regarding ODEs, I have 4 common ODE texts on my shelf. Standard books used at USNA, NU, etc. None of them require the use of epsilon delta to learn diffyQs. Most classic ODE solution methods were developed very fast after the calculus itself (before 1700). The people doing that and using the diffyQs for applications afterwards, did not have modern analytical theory. See this retrospective: citeseerx.ist.psu.edu/viewdoc/… $\endgroup$ – guest Sep 2 '18 at 15:09

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