If you wanted to learn how to do something --- fly an airplane, swim, play a violin --- you would probably spend a lot of time practicing. If you buy a whole bunch of Karate books and spend lots of time just reading them carefully, you will not become very good at Karate. You actually have to practice Karate ... practice a lot of Karate ... for many years ... before you become any good at it.

. Reading about doing something, or watching someone do something, is not the same as doing it onesself. Would you want to be operated on by a surgeon who had read about and observed but never done the operation? The brain is economical, and will only develop the ability to do things that it is regularly called on to do. So if a student reads and watches, he will develop the ability to ... read and watch. But not do.

Typically, I find that students who do most of the homework assignments do a lot better in exams than those who do just a few, and I don't mean by a little bit. Quite often in a calculus test, all the students who did most of the homework do better than all the students who did little of the homework. The graph of test scores sometimes shows two big mounds: one mound (mostly grade B-ish) of scores of students who worked hard on the homework before the test, and one mound (mostly grade D-ish) of scores of students who did not. The reality is this: while homework may officially count for little (if any) of the grade, unofficially homework drives the grades. This should not surprise anyone who looks at exams as performances, and homework as rehearsal: as any musician, actor or athlete will tell you, if you do not practice, you bomb on stage.

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