# a drunk penguin would do a better job than my math teacherNovember 6, 2005 4:13 PM   Subscribe

My BC calculus teacher is incompetent. This is a major problem.

First, she tends to assign homework without explaination, or with insufficient explaination. Our textbook is worse at explaining things than she is. (ex: it's directions on implicitly deriving y^2 were use the chain rule to get 2y*y' although this is true, it doesnt necessarily make sense to someone who has never seen implicit differentiation before) Usually I can find someone else to explain stuff to me, but not always. Do you have any suggestions for websites that can help me with this?
Second, How does this teacher still have a job? My friends and I have a new favorite activity of complaining about how terrible she is. For the sake of future students, is there something we can do to get rid of her? What could go wrong if I decide to complain about her, and is it worth the risk? Is there some way I can get access to AP test scores from previous years to enhance my point if I do complain to the administration? I've found my schools results for the SATs, stanford tests and the SOLs (virginia's standardized test's) but not AP or IB exams.
Finally, I was inspired to post this question based on the 3 problems she assigned us to do over the 4-day weekend, none of which I know how to do. I think I can use physics to figure out 2 of them, but this one has me stuck

an object moving along a curve in the xy plane has position (x(t),y(t)) at time t with
dx/dt= cos(t^3) and dy/dt =3sin(t^2) for )< t=3 at time t=2 the object is at position (4,5) a. write an equation for the line tangent to the curve at (4,5) b find the speed of the object at time t=2 c find the total distance i>(should this be a scalar or vector?) traveled by the object over the time interval )<=t<=1
d find the position of the object at t=3
posted by martinX's bellbottoms to Education (25 answers total)

Bad teachers are a staple of all high schools, everywhere. Teaching doesn't really pay that well, so it's nearly impossible to recruit hundreds of thousands of quality teachers. It only takes a few years of mediocre reviews to get tenure, then you're pretty much set, barring scandal. If she has tenure, "getting her fired" would be difficult, if not impossible. That said, depending on the other teachers in the mathematics department, you could prevent her from teaching AP Calculus in the future. First off, have you spoken with her about your problems with her teaching style? Perhaps she doesn't know that any of her students are having problems. Secondly, you should talk to your school counsellor (not the health and wellness counsellor, but your academic counsellor). If she's not tenured, an upswelling of student dislike will get a teacher fired (I've done it before), but you can't just dislike her - you need to talk to the principle directly with a few other students and voice your concerns in a clear and consise manner.

For online math help, I usually turn to MathWorld. You could also check out a different math textbook from the library, or convince your parents to hire you a tutor (I'm in college now, and several of my friends tutor for AP classes at the local High School). All of these solutions are more proactive than ask.me.

Finally, implicit differentiation: If z=f(y) (which means z is a function of y), then to get dz/dt, you need to use the chain rule - dz/dt=dz/dy*dy/dt. So for the function z=f(x)=y^2, dz/dy=2y and dy/dt=y'. Asking for explicit homework help is generally frowned upon.
posted by muddgirl at 4:29 PM on November 6, 2005

That should have been z=f(y)=y^2.
posted by muddgirl at 4:32 PM on November 6, 2005

The distance would be a scalar.

To find the equation of the tangent, you just need to find rise/run of the curve at 4,3, which you already know by simpliy substituting cos(2^3) and 3*sin(2^2), and the actual position (4,5).

The speed of the object would again use the derivatives you're given. It's just the square root of the y-component squared, plus the x-component squared, so sqrt(cos(23)2 + (3*sin(22))2)).

Remember, the speed is just the length of the velocity vector, which points in the same direction as the tangent line

Actualy, I'm not sure what they mean by distance, now. Do they want the distance between point A, where the object started and point B, where ended up, or do they want the total distance the object moved along the curve?

To find the distance, between the two points, you'll just need to figure out where the object is at both times, (do this by integrating the two derivatives. I don't have my calculator with me, so I can't do that. That's also what you'll need to do to answer the last question, which is just asking about the object a specific point in time).

If they want this distance traveled along the curve, well, that's something I learned in calc-2 in collage, and promptly forgot. It involves integrating along the curve, as if you were dividing it into an infinite number of straight line segments.

I'm sure someone else around here will know how to do it.

(btw, take all this with a grain of salt, I was always bad at math...)
posted by delmoi at 4:39 PM on November 6, 2005

I'm in BC now. I was a little confused at your description of the problem, but I am pretty sure I can help. Drop me an email, I'd love to help.
posted by daviss at 4:42 PM on November 6, 2005

For the sake of all of us who aren't in high school, and haven't been for quite a while, what is "BC Calculus"?
posted by NotMyselfRightNow at 4:45 PM on November 6, 2005

I think what you would do to find the length traveled along the curve would be:

∫√(x(t)2+y(t)2)dx from the two points in time. So if you want to find the length traveled along the curve at time t=1 to time t=2 you'd integrate from 1 to 2.

The syntax on a ti-89 would be

int(sqrt(cos(t^3)^2+(3*sin(t^2))^2),t,1,2)
posted by delmoi at 4:47 PM on November 6, 2005

For the sake of all of us who aren't in high school, and haven't been for quite a while, what is "BC Calculus"?

It's an advanced placement class (collage credit). There's calc AB, and then there's BC, which is harder.
posted by delmoi at 4:48 PM on November 6, 2005

There's only one place to go for intro-level calculus help: Karl's Calculus. Wolfram is probably way too formal and dry for someone at your level to appreciate.

I hate to break it to you, but Calculus is going to take lots of work. If you have a local university/community college nearby, you can drop by their math room for Calculus help.

As for the bogus teacher, I'd talk to the principal, but I suspect that there's not a whole lot that can be done. Accept the fact that this person will not be your primary source of learning and move on.
posted by onalark at 4:50 PM on November 6, 2005

The formula for arc length is the integral of dt*sqrt((dx/dt)^2+(dy/dt)^2) over whatever bounds you're asked about. If you think of it as parallel to the Pythagorean theorem, it's pretty easy to remember. Length = sqrt(x^2+y^2).
posted by wanderingmind at 4:54 PM on November 6, 2005

It might be the case that your teacher is actually "incompetent," I suppose. But nothing you've described is any unambiguous indication of that; what I see more of is you misunderstanding the role of the instructor and instruction in a supposedly college-level math course.

In college, it is common for people to assign a problem set after explaining a topic once, or after going through the relevant derivation once. This is because once is all it should take. If you have done the assigned reading and worked several example problems on your own to prepare yourself well enough to know when you stop getting it so you could ask relevant questions, and taken a solid set of notes during lecture, it should not take more than one instance of being told how to do it. The purpose of immediately assigning problems is to see what people are actually not getting, so that later meetings can be structured more usefully around the actual problems in understanding that have presented themselves.

You're getting homework assignments that you don't immediately know how to do. Get used to it. You should expect problem sets to not merely require you to apply a rote algorithm to a set of arbitrary equations a few times, but to force you to think about what you are doing, and why you are doing it, to require creative thought to see the answer, to require you to integrate what you have learned over the past several weeks, and to draw on a general scientific/mathematical literacy. If your teacher is actually teaching BC on an introductory college level, you should expect an average problem set to take around six to twelve hours to complete.

If you're not getting it, sitting around being bitchy about your instructor with your friends is not going to cause calculus to appear in your brain like some backwards Athena. Open the book, or another book, and bust ass. Be prepared. Work lots of problems on your own. Ask questions.

If you just want another source, Alpha Chiang's book on mathematical methods for economics is decent. Its primary focus is on econometrics, but the introductory sections on calculus and precursors are (IIRC) okay.

I am an actual no-shit college professor, and have taught several thousand people in various courses. In every class with more than 20 people that I have ever taught, at least one person has returned an evaluation that said that I was the devil and had ruined their life, and at least one has returned an evaluation claiming that I am the greatest teacher this side of Proxima. The point being, what you think of her really doesn't mean shit; it's all noise and no signal. Don't go fucking around with people's lives on bases like that. If she's really so horrible, her students' results on AP and other exams will reveal this, and she'll stop teaching the course. If her students do fine, then the problem is more likely to be with you than her. If you're still pissed at her instruction when you graduate from college and have a better sense of it all, complain then.
posted by ROU_Xenophobe at 5:06 PM on November 6, 2005

For yourself: get a tutor, a study group and another math book. You could probably find a good tutor from a local university. Your local library should have other calculus textbooks that you can cross-reference for better explanations. Otherwise, try a college campus bookstore for half-priced used textbooks. As a last resort, check out those "prepare for the BC Calculus AP exam!"-type books. Your friends will make a good study group (plus, it's better time spent than complaining about your teacher).
For the teacher: I've always thought that teachers should have a midterm review, as well as students. Send an anonymous typed note to the principal or the head of the math department. Be constructive about your criticism. Don't say "The teacher sucks!" but say something like "She doesn't offer help outside of class" or "She's unprepared for the day's lecture." (And has she been doing this, or have you asked her for help outside of class?)

Ask the administration to send in someone to evaluate the class and grades from past year's classes. If all the students are doing poorly in her class, as your midterm grades will reflect, the administration will act on it.

Lastly, calculus isn't easy all the time. 3 problems for a 4-day weekend isn't unusual once you get to college. I found that working through the proofs of each theorem is useful. A good textbook will do this. If not, find another one.
posted by hooray at 5:16 PM on November 6, 2005

Five Free Calculus Textbooks
posted by glibhamdreck at 5:22 PM on November 6, 2005

Ha ha, if you think is this bad, wait 'till you're in college taking a class with a professor who's only interested in doing research.

Or worse, a TA who's only interested in going into industry.
posted by Eamon at 5:42 PM on November 6, 2005

I will grant you the benefit of the doubt for now that your teacher may not be the best. This is understandable, as finding math teachers is already hard, so, finding quality math teachers who can teach upper level calculus will be even harder (I think BC is upper level?). It should also be noted that upper level calculus is hard for a lot of people. I had a horrible professor for calc 2 in college, so I feel your pain. But, that doesn't mean I would not have struggled even if I had an amazing professor or teacher. An education professor of mine would ask us when we "hit the wall" in math - for a lot of people it was college level calculus. I managed to just barely get past that, but my level of understanding was low.

You never mentioned anything about asking the teacher for help...have you done this? In my high school calc class, we would always always ask during class time. Or when homework was being corrected. Instead of complaining with your friends, you need to let her know that you are NOT GETTING IT and the textbook isn't helping. If you have already done this and she didn't do anything, then say something to the administration, other teachers, or counselors.

Why does she still have a job? Possibly the reasons that muddgirl said, and also the fact that not every math teacher can teach this kind of math at all. Look around...are there other teachers teaching the same course at your school? I've heard of schools keeping mediocre math teachers around solely because they're the only person who can do the job.
posted by jetskiaccidents at 7:33 PM on November 6, 2005

For the sake of future students, is there something we can do to get rid of her?

I guess I'll rock the boat here.

You know, teaching isn't easy. The problem is that just because you know something doesn't mean you can teach it to people who don't know it. I learned this firsthand as a student of Saul Bellow. My favorite class with him was the one where he was sick and we had a TA.

Anyway, my point.

Here's the problem: this teacher may not fully understand how bad their teaching method is. Over time, you forget what it's like to learn something for the first time, you forget the various tricks and mental manipulations you needed in order to learn the material for yourself.

Believe me, it is not being presumptuous to approach them after class, sit down together, and explain why a lot of the students (yourself included) have problems with certain aspects of their teaching method. The problem is, nobody in high school ever thinks this way. They never think, "this is just a human being, just like me, who went to school, got a job, and now here we are together." No high school student wants to break that invisible "teacher/student" barrier. But they're human. You can talk to them. Really.

My Calc BC teacher was horrible. He would assign homework, then first thing the next day he'd have people write their answers on the board. If a student didn't have the right answer, he'd ask for a volunteer from the class to offer their answer. If no one had a solution? He'd get mad at the class because he thought they weren't doing their homework, and would stonewall our request for an answer with "I'm not going to do your homework for you!"

Thing is, he just didn't realize that sometime a concept would come along and stump the entire class, and that he'd have to go extremely slow when teaching them to make sure everyone was following along. We were honestly looking for him to be our teacher, yet his mistaken attitude prompted him to complain that we weren't acting like good students. It wasn't after a small group of us approached him afterwords (one of which was the class "smarty pants") to sit him down and tell him, "Look, we aren't lazy. We just don't understand, and if you won't go over it with us out of spite, we'll never understand."
posted by Civil_Disobedient at 8:42 PM on November 6, 2005

Ha ha, if you think is this bad, wait 'till you're in college taking a class with a professor who's only interested in doing research.

Or worse, a TA who's only interested in going into industry.

Or worst of all, a TA who does not speak English. I'm not talking about people with accent. I had a computer science TA who actually did not speak English. At a state school in the US of A.
posted by callmejay at 9:13 PM on November 6, 2005

Nobody said Calc was easy. In college I took the first semester 3 times before I passed. It is very difficult material to understand if you are not used to thinking in that way. Don't expect an easy ride in math, this twists the limits of your brain. But if you make the extra effort to get through this with a good understanding of the material, then that teacher has done a damn good job to prepare you for the demands of a good college program. Don't always assume that a teacher's job is to spoon feed you all the info that you need, you have to be an active participant in understanding. If you do succeed in getting rid of the teacher, I think you will do a great job in dumbing down future students.
posted by JJ86 at 12:58 AM on November 7, 2005

Could you and several of your friends get together and see the teacher after class? Explain that you're struggling with the course and that you have some ideas that might help her communicate the concepts to you. Point out what you do find helpful right now and how you think you need to be supported. Do NOT attack the teacher or show hostility in any way. Do not go overboard with criticisms. And do make sure there are several (not 1, not 2) of you present, so that it doesn't look like you're the one wingnut. If you are absolutely diplomatic, emphasize good points, and even offer a few of your own suggestions, you may be surprised at what happens. I've been part of this in high school (Grade 10 Social Studies), undergrad (English Lit) and grad school (Marketing). In every case, the teacher responded positively and made changes to improve their techniques. One even brought the dean to discuss the issue further. YMMV.
posted by acoutu at 1:10 AM on November 7, 2005

Calculus requires an intense amount of abstract reasoning that isn't always there up until 22 in some people. It's also later, typically, in men than women.

Now as to teaching calculus. I suspect your teacher is trying to set you up for the reality of college/university life. The only people who will hold your hand are the other students and, if you have one, a TA or department tutor. After a certain point, it is your responsibility to be your own teacher. To do that, you need to know who you are, how you best learn things and how to best get that out of the circumstances you're in.

A good teacher will understand that there are diverse learning styles (visual, aural, kinesthetic, tactile, etc) and will try to map the problem space onto a few of these learning styles, but that isn't always possible given the time constraints of a teacher's day.

My wife used to teach calculus and precalculus and she would spend at least an extra hour after school every day to help lost students. I'm surprised that's not available. If you approach your teacher with a closed mind ("you're incompetent; change your teaching style."), you'll create an adversary. If you approach your teacher with an open mind ("I need examples and one-on-one work--what can we do?") you'll more likely find an aly.

I took calculus AB in HS and decided to re-take it in college. To my surprise, the textbook was written by the same guy ("Who could forget a name like Swokowski?"), but to my surprise, the college book had 3 times as much material in a slightly larger tome. In other words, the college text was good for three semesters. One of those is about what your entire year is.

Now, I know this sounds harsh and I could just say, "suck it up and work through it." Instead, find what you need and find a way to get it.
posted by plinth at 5:01 AM on November 7, 2005

Calc isn't fun. There are a select few who really thrive on it, much like there are a select few who really love molecular bio, deconstruction of 18th century literature, or chemical engineering. If it's not your thing, you're going to have a hard time with it.

Like ROU_Xenophobe I'm a college prof (OK, a relatively new one, but with 6+ years of teaching experience under my belt). I've had my share of good and bad teachers from high school on up. In my experience there are three situations in which a student and instructor don't work well together:

1) Instructor is incompetent. It happens, sadly, but again bad teachers don't stick around long, especially not when (as is the case in many states) school funding is directly tied into student performance on standardized exams.

2) Student is lazy (no offense meant here). Quite often students don't get the material either through lack of effort or insufficient practice. I include in this section those students who are unwilling to ask the instructor for help, which is of course the job the instructor is paid to perform - so don't be one of these people!

3) Instructor's teaching methods do not mesh well with student's mode of learning. This is a tough one. An instructor will develop a specific teaching method over time, and it will not work well for all students. In this case again refer to the instructor for extra help, or find an outside source.

Last thing to mention on topic here is that if you think this is hard to deal with in high school, wait until college. You will be faced with horrible profs. You will be faced with incompetent, inexperienced TAs. You will be expected to learn the material in spite of this. In high school you can take comfort in the fact that your teachers actually had to earn a degree in education and then do a student teaching internship before they were given the chance to teach you. All your TA is likely to have is an undergrad degree and hopefully some experience. With profs it's a crapshoot: some are good, some could care less about teaching and don't give a shit if you know it or not, because they have tenure and can't be fired.

I took a calc course from a professor who told us on day 1 that half of us would fail, because that happened every time he taught the course (what's the only constant in that equation, Professor Brown?). I re-took the same course with Igor, an Eastern European TA with a thick accent, and thanks to his dedication to teaching I actually learned something. For every bad TA or prof you have, you'll also have a brilliant one who makes your life that much better. Get used to it, and value the instructors who actually like teaching and don't suck at it.

callmejay writes "Or worst of all, a TA who does not speak English. I'm not talking about people with accent. I had a computer science TA who actually did not speak English. At a state school in the US of A."

I had a TA who couldn't write English. No shit, ideograms on the board, and although he recovered, erased them and then re-wrote it in English, it was still illegible.
posted by caution live frogs at 6:30 AM on November 7, 2005

Long ago when I was in high school, I took a couple years of German. Somehow the German instructor had been tagged with the tag of 'incompetent' by students in years past. The tag was passed from year to year so that every class came in believing she was incompetent. The kids never gave her a chance. They openly mocked her and ignored her and made her life a living hell. She was a nice old German woman and her real problem was that she had no classroom management skills. She let the kids run roughshod over her. Despite what my peers beleived, she was not incompetent. In fact, while they fucked around and bitched and moaned, I paid attention and actually tried to do what I could to help her out. (I wasn't a brown-noser, but I felt terribly for her plight.) You know what? I learned German. My classmates did not.

Education is a type of communication. It is not a one-way path. It is not simply the teacher lecturing to the student. Education requires the active participation of the student, and it almost sounds as if that's not happening in your case.

I hated my Western Civ class in high school, but that's because I didn't meet my end of the educational bargain. I listened to the lectures and then complained about the instructor, as you are doing now. I loved my AP English class. Why? Because I shouldered my share of the burden, asked questions, did extra work outside class. Education is a two-way process.

I wish I had learned to be more involved in my own education before I went to college, had elected to use those skills I'd developed in AP English rather than those I chose not to use in Western Civ. At the university level, it's important to take the initiative, to perform additional work outside class, to carry your share of the education dialogue. The same is true in college prep courses.

Cut your instructor some slack. Look at things from her point of view. Don't be a jerk. Study. If you truly feel your instructor is incompetent, you won't need to do anything; the consequences are bound to catch up with her. It's more important, though, to make sure that you're not incompetent. If you're lost, seek help outside class.
posted by jdroth at 7:36 AM on November 7, 2005

I'll jump on the band wagon recommending spending some after class time with the instructor is possible. It's been my experience that schools put their best instructors in AP courses. Though it maybe that this instructor is taking up either the slack of an over loaded primary or that she was the original champion of the AP program at your school and therefor the course is hers even though she's not the best person to be teaching it. Though if the latter she's probably a good teacher, poor teachers rarely expend the additional effort to bring high level courses to their schools.

callmejay writes "Or worst of all, a TA who does not speak English. I'm not talking about people with accent. I had a computer science TA who actually did not speak English. At a state school in the US of A."

My third year multi variable calc instructor not only had a very thick accent, he wrote with an accent as well. Type written stuff was fine but handwritten stuff almost required an interpreter. And I don't mean it was doctor hand writing messy. Each letter was fully formed; however, it was written with a weird slant and form. We were half way thru our second class (and totally lost for the most part) when a classmate almost yelled out "that's an r". At which point the last 1.5 hours of lecture almost clicked into place.
posted by Mitheral at 7:51 AM on November 7, 2005

The formula for arc length is the integral of dt*sqrt((dx/dt)^2+(dy/dt)^2) over whatever bounds you're asked about. If you think of it as parallel to the Pythagorean theorem, it's pretty easy to remember. Length = sqrt(x^2+y^2).

Oops, you're right. I was thinking that x(t), and y(t) was a shorthand for the derivitive functions that martinX's bellbottoms's wrote out (cos(x^3) and 3*sin(x^2)).

That's why I was always bad a math, little mistakes. Ah well.
posted by delmoi at 10:29 AM on November 7, 2005

Now I remember why I became an Art Major...
posted by raster at 10:36 AM on November 7, 2005

By the way, thank your teacher for giving you a heads-up on the university experience. You may want to consider small, private liberal-arts universities for your undergrad experience, if you really found this to be a "major problem."
posted by ikkyu2 at 1:39 PM on November 7, 2005

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