# remarks on AP courses in high school

by mathwonk
Tags: courses, remarks, school
 P: 347 EbolaPox: It depends on the school, but honors-level courses usually cover the same material as their non-honors counterparts but at a much more deeper and enriched level, and sometimes introduce more advanced topics. For example, at my school engineers and scientists have to take their own versions of calculus courses, which are as you would expect very application-oriented; mathematicians have the option of taking honors calculus or advanced honors calculus. The honors-level courses introduced calculus with a very light emphasis on rigor, so you would see things like epsilon-delta arguments, and the proofs of the theorems are more 'intuitive' than 'formal'. The advanced honors course, however, feels like an analysis course. Every theorem is proved formally, and the material is presented at a much deeper level. For example, the honors course will introduce sequences from the point of view of the real line whereas the advanced honors course will treat them in general metric spaces with the real line as a simple special case. And usually most first and second year courses have an honors-level equivalent. Of course, as I said, this varies from place to place. As for Apostol, I think his linear algebra section is lacking (at least in the first volume). I would seriously suggest you look elsewhere (e.g. Friedberg et. al). But that's just my opinion (and keep in mind that I'm not a big fan of his text, so I admit to some bias ). The introduction of integration before differentiation is historically more accurate, and you can see this in many other, older texts (e.g. Courant and, I think, Hardy). However I also recommend you read another book (like Spivak or Courant) for integration as a supplementary text to Apostol. Because if I recall correctly, he insists on using step functions to introduce the theory of integration, while the others use upper & lower sums. Both approaches are of course equivalent, but you might benefit from sampling both and choosing the one you like more.
 P: 555 Chroot, did everyone* in your IB curriculum courses make it out as well as you did? Oh, and the lazyness thing, AP Physics has 9 students right now, and the average number of them who do their homework on any given night is probably three.
 P: 101 From what I have seen of IB, the only classes worth taking are the HL level courses. I've looked at the material covered in the IB SL Mathematics course, and it is simply algebra II and some Calculus I. I tutored some friends in the class and found the material to be quite simple. The IB HL Chemistry course was on par with what I studied in AP Chemistry (which, according to many universities, is equivalent to Chemistry I and II. I suppose that all depends upon the university.) Although this is purely anecdotal analysis, IB seems to force students to do large quantities of pointless busy work and internal assesments and other nonsense assignments. When I was tutoring the mathematics students, they had no clue about riemann sums or limits with epsilon-delta definitions. I was rather shocked, as they had claimed IB mathematics was at least on par with AP Calculus AB. However, if one goes through the IB Diploma program, I'm sure they'll come out with just as much, if not more, work-ethic, experience, and knowledge as one that did an equal amount of AP work. So far, I've got around 45 credits from AP and am taking 6 more AP exams this year. With respect to the Linear Algebra, my friend happened to have Linear Algebra by Friedberg that he let me borrow (he was too lazy to read it apparently.) I assume it would be best to study LA out of Friedberg and not Apostol? I'll probably end up reading both just for the extra practice.
Emeritus
PF Gold
P: 10,426
 Quote by mathwonk so there is a huge difference between students whose goal is to get by, and those whose goal is to become mathematicians or scholars. i am there for the latter,
You seem to have this idea that every single student should have some deep, burning passion to become a mathematician before they ever grace the hallowed sanctuary that is your... high school math class. You've indicated this in many, many posts here over the years.

Bull****.

I often think you're more than just a bit presumptuous, man. Most US high school kids don't even go to college (it's a pity, but it's true). Probably fewer than one in a hundred of your students will choose to pursue math as a career. Few, if any of them know enough about mathematics yet to really have developed a passion for it, anyway. Most of them literally do want nothing more than just to pass your class, and that's okay! Some of them don't share your goals or opinions about the One True Path to living their lives.

You're teaching kids, man. Teenagers. People who don't understand how to drive stick shift cars, cook anything with more than two ingredients, or have meaningful interpersonal realtionships. These are not mathematicians, nor should be expected to behave like mathematicians.

Your job is decidedly not to focus on the kids who will one day prove the Riemann hypothesis. Your job, as you are paid by the state, is to provide a fair, reasonable education in basic mathematics that will serve the greater good of society. That's it. You apparently suffer from crippling delusions of grandeur that, in my opinion, probably make you a lousy teacher.

Get off your high horse and stop acting like you're teaching doctoral students at Oxford. You're a high-school teacher. Get a grip on reality, and teach the damn kids (even the dumb ones) some math.

- Warren
Emeritus
PF Gold
P: 10,426
 Quote by moose Chroot, did everyone* in your IB curriculum courses make it out as well as you did?
The program started with 400 kids. 42 took the IB exams. 32 got their diplomas.

 Oh, and the lazyness thing, AP Physics has 9 students right now, and the average number of them who do their homework on any given night is probably three.
Things really, really must have changed in the last few years.

- Warren
 Sci Advisor HW Helper P: 9,406 Chroot: have you mistaken me for someone else? i am not a high school teacher i am a university research mathematician who agrees to teach high school honors classes for free, for those few students who want the best. if they do not want what i am offering they do not belong in my class. in particular i never teach regular classes and i am not paid one cent for what i do in high schools. As i have stated here before, i taught elite private high school students who applied to be in my course, writing a special NSF grant which paid them a salary to attend my class, while i did it for free. i like you, but you are wayyy... off base here. In particular everything you have said about me tonight seems to be totally false, and could have been known to be so from the mildest acquantance with my posts "over the years." i am sure you meant well, but before attacking someone you might bother to get at least some of your facts straight. please forgive me if i have embarrassed you, as your comments, although totally wrong and misplaced (except that I am an arrogant prick on a high horse, which of course is a given), were obviously meant as sympathetic to students. so you are probably a good teacher. but, surprize, so am i.
 P: 347 chroot: I think mathwonk is not talking about the average high school "kid" but instead those who DO have the "deep, burning passion to become [mathematicians]." He's talking about offering an advanced class to those who want to take it. And he's not a high school teacher, either. So yeah...
 Sci Advisor HW Helper P: 9,406 i must admit chroot, i have also written impassioned responses without having read the previous posts. may i suggest you read the earlier posts in this thread? i apologize for their length.
 Sci Advisor HW Helper P: 9,406 perhaps it was not clear that these notes were aimed at people who actually want to understand mathematics, e.g. to become mathematicians, or at least to master the subject as well as possible, rather than simply get by in school. i thought that was apparent by my citing the inspiration of zapper's essays on preparing to be a physicist. i might have titled them "so you want to be a mathemnatician" but it seemed presumptuous to pretend they would have the same value as his notes. at any rate, i hope the angry outburst they have inspired does not deter anyone from making a comment or asking a question. i have noted over the years that poeple who believe in and care about teaching, almost always argue strongly over how it should be done in theory. curiously these same people tend not to argue when they actually observe what the other is doing in the classroom. i.e. the difficulty is in understanding what is meant by what is said. moreover, most of us have buried memories of unpleasant experiences which are set off at times by someone else's comment. we may think "that XXX sounds just like the guy who made my life miserable in junior high." and off we go. anyway, all comments are welcome here, even contrary or critical ones.
 Emeritus Sci Advisor PF Gold P: 10,426 Okay, mathwonk, I apologize for my outburst. On the other hand, I *have* read a number of posts from you, over a long period of time, that bemoan the sad state of high-school students -- even the bright ones. If these high-school classes of yours inspire so much animosity in you, maybe you should just stop teaching them? It doesn't sound like you have (or permit?) many students in the classes anyway, so it wouldn't affect many students. You might be happier for it. Trust me, teenaged kids are generally not all that much fun to work with, even if you have a noble purpose in mind. - Warren
 P: 483 My AP Physics class has about 20 students. I'd say about 70% of them just took the class because they liked Physics I but took it for the purpose of interest only, with no desire to take anything more than Mechanics or something for their major at university. About 10% think that they want to be engineers, myself included, and no more than ten or so students from two AP classes making up a total of about 40 are extraordinary with AP level physics. Those ten or so students are the only ones taking the AP test in May, and that's all. My school district wants to make it manditory for students to take the AP test if they take an AP course, which I highly disagree with. Overall the AP courses in my district are top-notch. I believe AP courses are wonderful, and if it were up to me, I'd make them manditory! It's disgusting how many kids are just plain out stupid. Although, you look at kids who take Calc BC and compare them to schools in the 1970's where you had one algebra class and one geometry class. Now precalculus is manditory, calculus and statistics are optional. If anything, AP courses teach you problem-solving skills and prepare you for the college workload. I agree with Warren's statement about the IB curriculum preparing him for college, even if the AP curriculum is a bit different.
 P: 555 z-component, I do not wish them to be mandatory, at ALL. What I love most about my AP classes is that the students are generally smart. BTW, if you look at a good high school in europe, almost every single student will be able to pwn almost every student in any AP class in the US.
 P: 483 But that, of course, doesn't surprise me at all. It should be easy to pwn American high school students. But really, when will this change? We're a world superpower and the world's policeman, but we have kids dumber than a box of hammers.
 P: 736 That's where my public education reform solution comes into play