<p>In high school calc I find myself bored out of my mind watching the teacher do a problem and then doing it 10 more times with different numbers. This requires 0 thinking and for the most part you don't actually know what's happening because you're just doing the same thing over and over and over again. I'm struggling i guess because i have no motivation and don't even think in that class ever because all I know is copying what the teacher does on the board. I have a feeling if I would have taken ap calc it would be the exact same thing with double the hw.
I just really hope college isn't like this because I don't think I can deal with it anymore.</p>
<p>^And that is my #1 problem with most of the American education system. Not enough emphasis on solving challenging problems or how to think.</p>
<p>As a current math/CS major, I can say that very few of the problems are simply rote memorization. You actually get to apply things you learned in high school, such as using Newton’s method to write a program to compute the cube root of a number, or using anything you’ve learned in computer science, math, art, etc. to write software.</p>
<p>They’re better in the sense that the professor isn’t going to do the same problem over and over again on the board, but you’re also expected to learn a lot of things on your own. I’ve sat through a lot of lectures where I had no clue what was going on, and that’s equally boring. The homework problems are more fun, though.</p>
<p>I think memorizing formulas and doing rote problems can be useful because it gives you familiarity with a topic before you learn it for real (probably in college). I usually don’t fully understand anything the first time I see it, and it helps if I’ve seen it in some cursory way before. </p>
<p>If you’re using a college level textbook for calculus then just go to the last ten problems of the section and you will be plenty challenged. The thing is that it sounds like you may be on power rue or product rule where you just take derivatives. It’s fine if you do that stuff a million times because guess what? It’s important later on in physics and multivariate calculus. It’s like with algebra, You did a million addition, subtraction, multiplication, and division problems before you ever saw an X. It’s the same thing here, you have to do hundreds of straightforward differentiation problems before you can start proving theorems and working with physical applications.</p>
<p>No we’ve been finding the limit of equations for over a week. I don’t think doing the same problem over and over again will help me understand or remember anything by the time i get to college. Id rather learn by figuring the equation/method out myself if possible. Then I would actually remember it. </p>
<p>You’re pretty much on pace for a regular high school calculus class. A typical AP calc AB class would be doing the things I mentioned before. Calculating limits is three sections in my textbook and would definitely require at least a week to master. You could learn difficult problems like squeeze theorem, greatest integer function, and delta epsilon proofs. Basically it will get a lot more rigorous and faster pace in college, but you’re in high school enjoy it while you can. If you really feel the need to be challenged like I said before you can do the last problems at the end of each section or you can try and dual enroll in college calc 1 or take an online AP course.</p>
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At most colleges you’d have to take a real analysis class to really learn the theory behind calculus (although you might learn epsilon-delta proofs in your class). The curriculum is structured the way it is because most of the people in your class don’t yet have the “mathematical maturity” to learn real analysis, which historically wasn’t developed until after calculus anyway. </p>
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It’s supposed to help you remember. I still remember how to do all of the arithmetic operations I learned as a kid a dozen years ago even though I rarely use them, presumably because I spent years drilling them into my head. In contrast, most of the stuff I learned even a few months ago that I only spent a few hours pondering about because that’s all I needed to learn the concepts is all gone from my memory.</p>