Saturday, February 21, 2009

Homework as Exercise

This is a third post on the subject, related to wasting time on homework exercises. Another way to look at this is by analogy to physical exercises. In general, one does not gain the benefits of a physical exercise without completing a full cycle of motion. When doing chin-ups, for instance, it isn't enough to just hang from a bar for two hours -- that's called stretching, and it does something but doesn't have the intended effect. One needs to completely move through a range of movement to get the muscle fibers to grow. Getting stumped on a homework problem and struggling with it for hours is like hanging from the bar... you end up sore with little to show for it.

On the other hand, muscle is gained by consistently overloading by a little more than your muscles are able to handle repeatedly. But you want to work around 70% of the one-repetition weight, so that you can still repeat the motions several times. Forcing yourself to bring to mind facts that you are trying to learn and string them together into very long complicated deductions is only helpful if the length of a deduction doesn't completely overload your working memory. When it does, your working memory fails, and you feel a sense of disorientation and dissatisfaction even if you get the deduction right. I would doubt you could easily commit such a deduction to long term memory either; the facts aren't all there in memory to reverberate together and establish a strong association to one another.

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