<p>for math are we supposed to understand why things work the way they do? is it important? do most people understand why the different methods in math work?</p>
<p>say for polynomial division for example. you're taught a method to help divide polynomials in class. it's pretty easy to just follow the steps and it'd be easy to get 100% on a test. but is it bad if you don't understand why the method works the way it does? also take derivatives...i can derive something, but i don't understand why multiplying the coefficient by the exponent and dropping the exponent by one finds you the rate of change...am i supposed to know?</p>
<p>what im trying to say is i can do the math by just following the steps i was taught, but i don't really understand why it works. is this bad?</p>
<p>Lol... I don't know about college (Im in HS) but for me I don't really bother understanding why SOME things work.</p>
<p>For example, derivatives- know the basic concept behind it but you don't need to know how to derive the formals. </p>
<p>But let's say for integrals- this you should understand (Riemann Sums- what integrals are based on) but understand that the Integral operator was empirically (read: randomly) derived and you don't know how it neccessarily works either.</p>
<p>I think that it is a real foundation of why american students tend to do very badly in math: they are not taught to understand, but instead just to follow the steps.
No wonder math feels like a nightmare: you need to memorize tons of different algorithms for every possible situation. If, on the other hand, you just understand the concept and the logic of what you want to acheve, math becomes very easy.</p>
<p>And Fizik, how many people in the world do you think can derive how to find a derivative or integral? Or even better- deriving the fundamental principal behind Flux, Curl, Line Integrals or more?</p>
<p>My College Level textbook says for a lot of the material something along the lines of -> "Proof of the aforementioned concept is beyond the scope of this sequence", and this is Multivariable Calculus we're talking about. To a certain point, one can only hope to memorize.</p>
<p>What sort of math are you talking about? I mean, what is your question in reference to? I think it'd be difficult to be a math major, and not care about why things work, because it gets a lot more theoretical in college - more proofs, more abstractions.</p>
<p>Also, multivariable calculus is a continuation of calculus, and a nonabstract class... not representative of all future college math classes.</p>
<p>What's the point of memorizing how to do it if you don't understand it? If you don't understand it, you'll probably forget the process by next year, anyway :)</p>
<p>To truazn:
you do not need to be a genius to understand concepts, you need to be a genius to come up with the new ones.
And yes in my own class I very often tell my students: the proof is beyond the level of this class, but only because the students are very bad in math.
And to answer your question: quite a few people are capable of finding a derivative or integral, if you cannot do it after going through calculus you probably were not taught well. The reason that you need to memorize table integrals/derivatives is not because it is impossibly difficult to derive, but because it saves time. Just like multiplication table.</p>
<p>i'm not majoring in math or anything. the reason i brought up this question was that i was in 2nd year calculus last year, and since i blew off the last two years of math and high school in general i decided i didnt want to take the ap test. this means i have to take a placement test to get placed in a math class at college this upcoming year, and all of the topics on the test are things i learned years ago. </p>
<p>as i was reviewing i realized that although the topics i was reviewing for were "easy" stuff from middle school or early high school, i didn't really understand how the methods i was using worked. just out of curiosity i wanted to see if other people actually learned why they take the steps they do to solve a problem. i thought maybe as i was reviewing i should actually take the time to learn what everything actually means instead of just memorizing the steps to find the answers for the test.</p>
<p>i guess i wanted to know if the average math student was SUPPOSED to know why they do the things they do, or if it was good enough to just know how to do it but not know why.</p>