As I continue to re-educate myself on Grade 11 Functions in preparation for a new tutoring engagement that starts this week, I'm struck again and again by just how much I've forgotten since my high school days. I look at some of the proofs that are included in that particular subject's curriculum - such as "show that 1 - cos^2 x = cos x sin x tan x" - and I die a little inside. Oh sure, I can still put pencil to paper and work my way through to a solution, but it takes me longer than it ever did when I was in school. In those days, I had so many rules and identities memorized that it was usually just a matter of mentally flipping through them until I found the right one for each situation. Now, I'll try one thing, have it lead to a dead end, and then go a second or even third route before I hit on the right approach.
Maybe if I do enough of this, with enough different students, I'll get back to that lofty level of mathiness... but right now, I grieve for my lost memories!
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