One particular part of a story about the teaching experience of a graduate student in math at Dartmouth College in the fall of 1996 resonated with me. It articulated something that I had only an intuitive but often a skeptical understanding of; when you learn something as opposed to simply memorizing a pattern or algorithm, you don’t need to study it again to remember what you learned.
…I was lucky enough to talk to some of my students about the experience a few months later. The general consensus was that the material really stuck. Furthermore nobody studied for the final. No joke. As one girl said, “I tried studying because I thought I should, but I gave up after a half-hour because I already knew it all.” That is how I think it should be – if you study properly through the course, then you won’t need to study for the final. Because you’ve already learned it. And you’ll have a leg up on the next course because you still remember the material that everyone else has forgotten.
Sometimes, even a decade after I’ve last thought about an obscure topic, I’ll recall everything I’ve read about it including arcane details and problems I’ve work out and the reasoning that brought me to conclusions.
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