Is AP Calculus BC (and AB) too easy?

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<p>Proof-Based is the way to go, but it requires much more natural mathematical aptitude. 99% of students will not be able to handle the material. It is, in my honest opinion, intellectually taxing. </p>

<p>Plug-and-Chug calculus, is quite frankly, a waste of time. Of course you need to learn integrals before progressing, but I feel in many high school and university courses, it stops there. </p>

<p>I will admit, I am horrible at proofs. I hate them. But that didn’t stop me from a 5 in AB Calc, or A’s in all subsequent calculus courses I have taken in college. Why? Because there were no proofs! :). And, I’m incredibly proficient at memorizing practice problem methodology and applying it to similar problems. So that’s how I got by with top marks.</p>

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<p>I would like to see a more proof based AP Calculus… But the whole AP system in general seem to “tolerate” bad teachers. Sure it gives guidelines and course goals but that’s all that my “math teacher” ever follows. All he ever does is click his remote for the next slide in the powerpoint, which is provided by the book publisher.
He gets his “homework problems” from the Princeton Review book or some other “secret” prep book and when I ask him, “How do you differentiate [insert function] without a calculator?,” he just stammers a bit and says “You won’t need that on the AP exam.”</p>

<p>It’s really ridiculous how the requirement for teaching an AP class, let alone AP Calculus, is that a teacher submits a decent syllabus. Personally, I doubt I can get a 5 from this teacher let alone skip first year college calculus if I do pass. Indeed, it’s AP TI89 Calculus</p>

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<p>Do remember guys, the problem of not providing a solid foundation is a pretty widespread problem with AP courses. College level chemistry involves more than the narrow set of concepts about the narrow set of reactions on the AP test, and the only programming courses that would actually be equivalent to APCS are the ones for people who never intend to write any program in their life. </p>

<p>Don’t even get me started on the “Memorize events, associate them with a general time period, and regurgitate them very quickly on demand” that is APUSH. It was actually a blessing to have a teacher who ignored curriculum guidelines for that course.</p>

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<p>I agree with this. My AP Chemistry teacher teaches to the test and actually tells us that we don’t need to worry about further explanations of certain topics because they won’t be on the AP test. The problem is that since I plan to be a Chemistry major (I’m going to Penn), I will have to take a placement exam for the two semesters of intro chem to pass out. I have taken a small look at an old edition of the textbook for the course, and it seems that it is a lot more physics based than what we have learned in AP. Since I have a strong background from my Calc and Physics C teachers, I hopethat I will be able to get the textbook and fill in the gaps which we did not learn in AP, but I may just take intro.</p>

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<p>Holy cow! Sorry guys. Didn’t get to read all the long posts. Just wanted to say though that at Caltech, everyone takes Calc I over again, except this time, the course focuses on proofs of the most fundamental tools and concepts rather than problem-solving given the tools (derivatives, etc). </p>

<p>So too easy? That’s subjective. But high school Calculus is certainly too much memorization-based rather than understanding-based.</p>

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<p>a = dv/dt
v(t) = 5t^2 + 6
a = dv/dt = (2-1)5t^(2-1)
a = dv/dt = (1)5t^(1)
a = dv/dt = 5t</p>

<p>Is the answer 5t?</p>

<p>I’ve been teaching myself Calculus from Calculus Made Easy by Silvanus Thompson.</p>

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<p>I think it’s 10t, because, if I remember correctly, you carry the two from the exponent for multiplication, not the 2-1. Although I could be wrong; I’m trying to study it myself as well.</p>

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<p>Yes, you’re right it’s 2 * 5t ^ (2-1)!</p>

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<p>Proofs build reasoning ability and help students see the applications of Calculus in many disciplines. </p>

<p>Understanding calculus is much different than knowing how to do calculus. The former is necessary for using calculus in a variety of disciplines, while the latter does very little for the majority of students. It certainly did very little for me, as I can’t fathom how to apply calculus to anything. </p>

<p>I wish I had been subjected to a more proof based approach to calculus. I’ve always wondered what kind of calculus is taught at Cal-Tech, MIT, Harvard, and other rigorous institutions and is it fundamentally different from what the majority of students are exposed to in high schools and mainstream colleges.</p>

<p>As for subjectiveness, I think most would concur that a proof-based approach is much more difficult mathematically than a memorization based approach, outside of the minority of people who reason and use logic brilliantly, but can’t remember he or she was supposed to wear pants.</p>

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<p>And that’s the problem right there, navyarf. </p>

<p>At a first glance, your idea makes no sense. In the AP calculus curriculum, you learn “find the displacement of this object, whose velocity is described by so-and-so function”. In a proof-based curriculum, you learn “prove that such-and-such rule for integration of functions with form so-and-so is valid”. The first is a real-world problem, the second is not, so how can the first NOT be more useful?</p>

<p>What people don’t get is that with a curriculum based on applications, you learn only those applications which are taught. “Find the charge of this object, the current into which is described by so-and-so function” should be a trivial problem for anyone who has learned integration. But as I found out in my AP calc class when we did that problem, that’s not actually what happens. People have no idea what integration IS; they only know what it can DO, and in their world that is restricted to finding areas under curves and finding displacements given velocities. </p>

<p>As I mentioned above, I’d love to show how ridiculous this is by making a comparison to how some other subject is taught. But in my high school at least, every subject is taught that way. Understanding things is too hard for the poor kiddies, we must only teach them how to DO things!</p>

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<p>I just wanted to say that I love everyone in this thread. These arguments are so logical and eloquently made!</p>

<p>And so that I might contribute a little more to this discussion than a passing compliment, I will add that AP calculus AB is too hard for most students… and that even applied calculus is above and beyond what is required of the majority of hs students. It would be fantastic if a proofs-based course were available to hs students, for those that genuinely excel at mathematics and desire a more solid theoretical foundation in calculus, but the fact of the matter is that this course would not be in high demand and thus would not be practical to replace applied calculus with outside of magnet schools or rigorous private schools. If all calculus courses were taught theoretically, many students may choose to avoid calculus entirely.</p>

<p>I value understanding over memorization, just as the rest of you, but such an emphasis would likely be too esoteric. If it is between memorization-style calculus and no attempt at calculus at all, I think it better that students learn at least memorization-style calculus.</p>

<p>To more directly address the main issue of this thread, perhaps it would be better if AB were replaced with a theoretical, proofs-based exam, while BC is preserved. Then, there would be two options, each clearly delineated from the other. This distinction would not only cater to students of both persuasions, but also help attract teachers that are capable of teaching theoretical calculus.</p>

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<p>And the more powerful the overused calculators get, the more removed the understanding is from the doing. :)</p>

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<p>It is probably far too hard for most students. And they should never be compelled to take it, but increasingly are, as it (in CC forums at least) is seen as necessary for a chance at elite institutions. A lot of students who are good, but not exceptional at mathematics, are pushed to take AP Calc, because it is simply the next level of mathematics available. They would be better served pursuing other subjects. I would suggest college-level accounting (not HS rubbish) as a possible alternative, because it allows students with excellent memorization skills and good (but not genius) mathematical skills to apply their talents and learn something useful (can we get an AP?). </p>

<p>If it is between memorization-style calculus and no calculus at all, it should be no calculus at all, simply because memorization-style calculus is of extremely limited utility outside of the AP test, especially with the powerful graphing calculators available today. By allowing students to pursue and succeed in memorization-style calculus, you are giving them the false impression that they are good, or proficient at calculus. They can use the 5 on the test as a credential, a badge of honor, or whatever they may choose, but most will fail to see its numerous applications in the real world. </p>

<p>I reiterate, 99% of students will not be able to handle proof based calculus. The top 1-5% might be capable of it, but those students must be taught by an excellent math instructor (majoring in math, superb teaching ability, preferably from a respectable institution/program) ,who are almost impossible to find. </p>

<p>Proof-based calculus can be too esoteric at times, so the exam should not be entirely full of proofs, but a mix of application (high-level) problems and proofs. </p>

<p>On aesthetics, calculus is beautiful and illuminating when seen from a proof-based and theoretical standpoint, it is downright ugly and pointless when seen from a memorization standpoint.</p>

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<p>Even my University is guilty of such credential bumping behavior. All Business/Economics students must take two semesters of calculus (never proof based, standardized departmental tests). This allows the business school to claim its dubious superiority (they love to advertise this fact) because all of its students take calculus (unlike most business schools), when in fact the majority of students get the credit (some at easy-peasy online course or CC), move on, and then find they have absolutely no clue how to use it, because they never understood it. Professors in upper-division economics classes, often teach the basics of calculus again as it applies to their discipline, because they know that most students will not be able to convert their “knowledge” into an economic context. Furthermore, on an economic standpoint, this is blasphemously inefficient. I have personally seen students who have made excellent grades in calculus, come up to me and ask how to solve economics problems, geometrically, because they really didn’t know that calculus was necessary, even when the problem was as simple as finding an area under a curve presented in economics. </p>

<p>Thankfully, I’m teaching myself calculus again, for understanding this time.</p>

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<p>It’s a high school course.</p>

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<p>Are high school courses not allowed to be difficult?</p>

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<p>Of course they are, there’s just a limit as to how difficult. High school students are not fully directed toward one subject, and so an extremely difficult course would be far too time consuming for many and thus irrational. I’m sure many high schools offer independent study and/or higher level classes beyond that of what AP classes are offered (such as my high school does).</p>

<p>Another thought to think about is that the amount of course material must be compressed into a school’s schedule, and for many schools teachers are rushed to fit the required material as it is now.</p>

<p>It just does not seem beneficial to make a course extremely difficult if a student has far too many other things going on and with time restraints.</p>

<p>However, I don’t see why the Collegeboard could not look into extending some of their courses for some of the elite/more interested students.</p>

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<p>Don’t know where you live nigcrunch, but from my experience most schools don’t offer anything beyond AP/IB. In fact, many schools don’t even offer AP…</p>

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<p>I disagree. I think this occurs because people believing that it’s okay to be bad at math (and thus they stop trying), and it snowballs. This is something more of an American thing. We just have to break that mentality. </p>

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<p>Whoa! What applied Calculus? Find the acceleration of a car with velocity v(t) = 5t^2 - 7? Good luck finding such a car! The fact is, none of this calculus is really applied. Applied Calculus, as we know it, is usually NEVER this pretty. I’m talking about things that are not analytic, things where knowing the all-powerful “power” rule won’t help you. Things where you have to use numerical analysis. Now see, that’s Applied Calculus. Like, REAL applied calculus. And if they taught you that, I’d be okay with it. At least they can say “Hey! This is actually used in real life!” As we have it, we have very pathetic and artificial examples that appear to be like real life. This is not applied calc. This is watered-down Calculus with examples dealing with objects of real life, in no way similar to how they work. </p>

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<p>As it stands, those who take Calculus take it because they think they need to. If you make it theoretical, same amount of people will take it (at first), then gradually weed out those can’t handle. People will still take it to get that “prestige” of saying “I took AP calculus!”</p>

<p>But like I said, the AP Calculus exam is not applied. So, as stated before in thread, either turn it into AP Numerical Methods for Calculus (and thus be REAL Applied Math), or make it more theoretical. I’m not saying make it a Real Analysis class. Maybe something along the lines of a Spivak-based course. </p>

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<p>If seeing “AP Calculus” on transcripts wasn’t “impressive” or apparently “Required”, many students would avoid it entirely, theoretical or not.</p>

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<p>Agreed on the anti-math American mentality. We need rigorous training, especially at the algebra/geometry/precal levels. Excellent training and skills development at these levels is necessary to succeed in REAL CALCULUS. You can pass the AP without knowing next to anything. </p>

<p>We need to challenge students to excel. I went to a rigorous international school in Asia (average math SAT 700+), took geometry, struggled with the proof-based exams, and scraped by with a C+. It was excruciatingly difficult. I spent 2-3hrs a night tackling homework/studying and still ended up with tests and assignments full of red X’s and scratch marks. I returned to a private high school in the US, where the counselor saw my C+, laughed at my “deficient math skills”, and put me in the regular Algebra II class. One look at the homework and the test and I laughed even harder than she did. I was moved up to “honors”, if you could call it that, did about 10 minutes of homework a night, never studied, and made an A+ (110 average LOL). </p>

<p>They get good (hard) training in Asian countries. They spend hours upon end studying at home or in cram class while we are doing “extracurriculars”. (Though I have to admit, the Asian kids could stand to get out a bit) </p>

<p>I left that high school to attend a better prep school, where I took pre-calculus and then AP Calc. More difficult, but I was still able to make A+'s on around 30 minutes of homework/studying a night. I made a 5 on the AP, A in multivariable in college and yet, I STILL DON’T know what integration IS (like a previous poster mentioned), only that it can solve a few “real” problems that I knew I would see in the AP or on exams. </p>

<p>I’d rarely get back homework or exams in America that were not full of :)'s, “good job’s!”, and check marks. </p>

<p>A previous poster suggested that it might be better for calculus to be reserved for college. Most high schools in the Asian country where I resided, did not offer calculus. They instead focused on a rigorous approach to algebra/geometry/precal. Much better than the American system of speeding kids through math “levels” without really imparting any real knowledge upon them. </p>

<p>Somebody mentioned a Spivak book as a great tool for learning calc? Is it worth it? I’d love to get my hands on a real calculus book. </p>

<p>If anything, I’d say the American math-education system has failed me. They’ve handed me A’s and 5’s. If I was ignorant, I might assume I knew calculus and was good at math. But I know little calculus and don’t think I’m too great at math.</p>