Tuesday, May 17, 2011

Thoughts about a class about proofs (Part 2)

two weeks later, i still think about that intro-to-proofs class.

i'm still without firm conclusions,
only guesses and impressions.

when i was structuring the course, i added in two weeks of propositional logic and truth tables, because the syllabus i was given didn't include it. i was hesitant about this decision at first. it would mean that i'd lose 2 weeks of lectures.

looking back at it now, i wonder if i did enough.

there were a few lectures about "techniques of proof" --
for each type (direct, contradiction, contraposition, induction), i gave an example,

then in later lectures i gave more complicated examples that combined multiple types,

and then for the next two weeks, every time i proved something, i either
  1. stated what kind of proof it would be;
  2. verbally explained how one method of proof fit the situation better than another [1].
so yes, i think that's plenty to explain what a proof is ..

but when i think about it, though, i never gave a single lecture about problem solving. perhaps i regularly explained a strategy behind a proof, where it comes from, but i never formalised the approach.

to be honest, i don't know exactly how i would do such a thing.
it just seems like so much common sense, a few guiding principles.

[1] in one student's evaluation, there was a complaint that we didn't cover enough basic proof techniques. my best guess is that many students only wrote what i wrote on the board, and didn't record what i said in relation to it.

to be fair, i tried to write everything i spoke on the blackboard. that, of course, gets very tedious after a while. it probably explains why i used to be able to cover 5 pages of my own notes in a single 50-minute lecture; now i usually cover 4.

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