Re: "I only truly understood this material when I started teaching it."
- From: hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin)
- Date: 4 Nov 2008 18:37:16 -0500
In article <f8c3c23f-02e4-4daf-bd2c-290792e2769a@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Kenneth Bull <kenneth.bull@xxxxxxxxx> wrote:
This is what my complex analysis prof said at one point today:
"Do you guys really understand this? Because I sure didn't when I
first took this course. Then when I was in grad school I thought I
finally truly understood it, but I was wrong. I only truly undrestood
this material when I started teaching it."
Where one gets understanding varies. One does not get
understanding by learning to compute, or even to prove
theorems. Mathematical concepts, when learned, are
clear and simple, and almost need explicit presentation
to be really learned.
(A few people laughed)
"What? It's true of everyone."
Is he right? He was implying that his understanding took a huge leap
when he was in grad school (obvious),
There was no point that one could say I started in grad
school, but much of my understanding came from either
seeing the explicit concept, or deducing it. I am
reasonably good at the latter.
but then it took another huge
leap after he started teaching as a professor- is there a huge leap
between getting a Ph.D. and teaching (for most people)?
Not for me. I was able to teach, with understanding, most
of what I learned, either from courses or from my own reading.
I have taught courses not in my field from a class or two or
outside reading, and had no difficulty if the students did
not want the computation and regurgitation type of material.
If so,
wouldn't it be so much easier to do research work in grad school after
teaching a few classes in the subject matter? Maybe force Ph.D.
students to do a simple research paper, then teach for a while, then
do serious research work while teaching.
It was four years from the time I started doing serious research
that I got my PhD, and a little more until I started teaching.
I occasionally developed improved ideas from teaching, almost
despite the attempts of those students trying for grades and
no understanding to derail. Teaching elementary courses will
not help anyone understand concepts, unless he is forced to
develop them in opposition to the text and standard methods.
--
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
.
- References:
- "I only truly understood this material when I started teaching it."
- From: Kenneth Bull
- "I only truly understood this material when I started teaching it."
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