The point is that if <i>all</i> you do is drill, by the time you get to the beauty, your students have already made up their mind that math is the most useless crap in the Universe. Motivation is a powerful force and unless people see that there's any point to what they are being ordered to do, they will comply with the smallest amount of effort they can get away with.<p>And to say that they want to fall back on "what works" sounds a little funny given how dismally American students in general are doing. If people are so afraid to make the mediocre worse, they'll never discover what works better.<p>Besides, I'm not even sure I agree that you need to be able to multiply numbers before doing algebra.