It comes with experience, which can be gained by working with higher-level formulas right away. Think of it like using a hammer; there's no point in spending hours perfecting your swing, just build something that uses the hammer a lot. The hammer can be any basic idea, and the thing being built using it is a higher-level idea that incorporates it. We do it that way in chemistry. We are given the periodic table and that of the cations and anions, and don't need to memorize it. However, by constant use in many areas I have ended up memorizing the atomic numbers, masses, families, and positions of a good number of elements. Drilling that wouldn't have sped me up that much, and the time was spent on learning more subjects in greater depth.
Do you guys agree that incorporating basic concepts into higher ones is a better option than drilling them for subjects like math and chemistry?
-Penguin
Math and chemistry are two different subjects and need to be taught differently.
Even the packet that you're given to use on the AP test has a periodic table and a
lot of formulas on it.
That said, there's still a lot of stuff you need to memorize for chemistry. Just less equations and stuff, as the important thing is to remember how to apply the equations.
In math, you're not given equations/formulas so much as you're given rules. And rules need to be memorized, plain and simple. When I took calculus my teacher (probably the best teacher I've ever had, and I was lucky enough to have him two years in a row) had given us several sheets that were printed front and back with formulas. At the beginning of the year they were all gibberish... halfway through we'd memorized around two of the pages front and back. Most people had lost them as we never used them. Finding something on there is a nightmare, as even being printed front and back there was a lot of information condensed in a little space. But at the same time, it all seemed like it was obvious and didn't need to be said... because that's just how math works. I guess I'm muddling this a little bit but there's a point... and I guess it's that there are no 'big' and 'small' concepts in math, it's just a pyramid that progressively gets bigger and bigger, and if you're like me or any of my friends, it's something that clicks around the time you get to calculus... and all the ways that you've been taught math all of the sudden make sense, and you never ask 'when will I ever use this?' ever again, because you realize that even if something doesn't really seem to be very useful at the moment in a year or two it will be essential, and even if something seems hard in another month it will be step 1 of a 5 step problem and you'll be able to do it without thinking, and you begin to appreciate (to a degree) when your teacher makes you do it 'the hard way' or doesn't give you the shortcut. Math's funny like that.
