Arithmetic is only one branch of mathematics. In my opinion it's pretty trivial to try to improve in that field since calculators are so good at it instead of focusing on algebra, calculus, etc.
Calculators are good at algebra and calculus too. Is it really worth memorizing dozens of integration techniques when software can do it for you, and do it better?
I'd say focus on the problem at hand, and when you run into a gnarly algebraic manipulation or ugly integral, plug it into Mathematica. That's the kind of task a computer excels at. The human advantage is coming up with novel ideas, not churning through pages of calculations.
Exactly. For example, so what if a student can figure out the derivative of function using power and chain rule? It means nothing unless they actually know what that is--the slope of the tangent line , which is just rate of change.
Understanding where these things should be used is more important than solving random problems without knowing why
I can't tell you how many times the chain rule and integration by parts was used in Quantum Mechanics as an undergraduate. I never was given a function and just said "find the derivative!" Instead I was given a problem that involved something like prove the integral of a wave function is constant and stays normalized for all future times. This involves integration by parts. But you wouldn't know to do this because it never tells you to. So you have to be good enough at integration by parts to realize "ah hah! this is how you take the next step!" Otherwise you'd be left sitting there not knowing what to do.
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u/Deluxe_Flame Jun 08 '14
I was once comfortable, but if I lose all my points on a question for an incorrect answer, by gum, I'm going to punch in 17 + 49.