reflections after an analysis class, part 1 of .. um .. N? (N ≥ 1)

grading finals today, i became introspective. between papers, i asked myself:

i had always wondered what teaching an analysιs class would be like. now the semester's over.

well? how did it go?
have i learned anything? [1]

i started thinking of analogies.

1. it's not unlike teaching someone tennis. often the student swings awkwardly, sometimes effectively. you can't help but wince.
   
   sometimes the ball is in play, the shot is bad, and the student knows right away .. but not every student chooses to learn why .. and so we keep on wincing.


2. it's not unlike teaching someone how to code (computer programming). the basics are, yes, basic.
   
   some students quickly become bored, and only bother you when they can't get something to compile. others are frantic, even ask you for your own code ..
   
   [sighs]
   
   .. and sometimes when you do, they still can't figure out how it works.


3. it's not unlike teaching someone a language. unless the student is fluent or has learned a similar tongue, (s)he may have no idea whether something sounds right.
   
   some students really want to speak well, and they'll ask you vocabulary unrelated to textbook stuff. they will meet you outside of class on occasion, and it won't even be about homework.
   
   during one of these chats, a student will say something which makes perfect sense, only you never thought about it that way, before ..
   
   .. and it will remind you of how cool you thought this stuff was, when you first learned it. (-:

[1] that is, other than the basic analysis that i had forgotten, when i first took such a course. (-: