So today I finally steeled myself to ask for an proof as homework (that’s “epsilon-delta”, for all you non-Calculus people; a famous sticking point in the introductory course). And I’ll bet at least a few of ’em’ll be substantially correct, too… but have to admit I won’t bet much…
Anyway, I’ve got a pretty good feeling about it and Thursday we’ll see how it actually went. Best-case scenario: several students confident enough to work out a problem like “Prove using the definition that the limit at 13 of 2x – 7 is 19” (I had this as a formula but the computer ate it and I’m impatient), at the board (very best case: such a student leads a discussion of the problem… this is rare but I’ve seen it done and it sure makes me proud [so I’m saying it]).
This class has stepped up with blackboard work quite impressively, with students at the front of the room calculating derivatives using the definition of “derivative”—i.e., “the hard way” (we will soon develop rather a large collection of techniques for avoiding these calculations; they are nevertheless considered essential material for a first course in Calculus [and rightly so in my view]). One of the themes in my work as a learner of The Art (of teaching math) is “the less I talk the better I like it” (which is, alas, not entirely true… but I’ve found it a nice slogan to express my firm conviction that the student often learns best when the student is moving the pencil [or chalk] and talking about it…); I’m pretty excited about the presentations I’ve seen out of this group (hence the guarded optimism of my first paragraph).
I haven’t even begun what I was planning on saying. But now I want to see if it’ll post. Here goes.