Re: "I only truly understood this material when I started teaching it."

In article <5dcc6a21-e58a-4070-9687-0629b77b00ba@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Cory Knapp <thestonetable@xxxxxxxxx> wrote:
Indeed. As far as I know though, most universities ask that you show
evidence of your teaching ability when you apply. PhD students are
often graders, TAs and at large universities, they do actually teach
lower level classes. I've heard from a lot of people that they didn't
actually learn calculus until grad school... when they needed to teach
it.

Nobody learns calculus from a standard cookbook or from teaching
from such. A course in real analysis teaches the concepts; some
unpopular calculus books do a fair job. One can teach real analysis
without "college" prerequisites, and should; the usual way provides
lots of interference in understanding.

In my experience (I'm also an undergrad...) I don't know what I'm
doing until I explain to someone else what's going on. And in the
process of figuring out what they're having trouble with and trying to
explain it, my own understand increases greatly.

There are some who really understand, but who would have great
difficulty in explaining. Explaining how tgo use the tricks
in computing derivatives and anti-derivatives only teaches that.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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