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.

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April 14, 2009 at 7:44 pm

okay. this is pretty great.

it was high time i said something

about the 151 class around here

and now i don’t have to walk down

to the coffeehouse to get this up

by tonight.

December 1, 2010 at 8:52 pm

https://calciii.wordpress.com/2009/04/14/sometimes-the-system-works/

motivating earlier post