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Topic: Learning and Mathematics: Papert, mathetics (repost)
Replies: 29   Last Post: Nov 19, 1995 4:46 PM

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 Tom Davis Posts: 13 Registered: 12/6/04
Re: Learning and Mathematics: Papert, mathetics
Posted: Nov 6, 1995 7:09 PM
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In article <pow-0611951644240001@olmo.swarthmore.edu>, pow@forum.swarthmore.edu (Problem of the Week) writes:
|> I have found it to be the case that the best way to test my understanding
|> of something is to discuss it, or even better try teaching it to somebody
|> else. It is this _discussion_ of mathematics that makes me want to be a
|> teacher as opposed to a mathematician who only gets to "do" math. What
|> are other ways in which we can test whether or not a student has learned
|> something?

I think teaching is by far the best way to learn something. In high
school in my Advanced-placement math class, our teacher, Mr. Hoffman,
never understood anything, and he was so pathetic that we students took
turns teaching him and the rest of the class calculus. At the end of
the year, the 14 kids in the class got 11 scores of "5", one of "4", and
two of "2" on the advanced-placement exam -- fabulous results.

When I came back to visit my high school the next year, I talked to a
student in Mr. Hoffman's calculus class, and was horrified to find that
Mr. Hoffman hadn't learned anything from our class, and that years'
class was also having to teach him every detail about calculus.

Mr. Hoffman also coached the tennis team, and years later, I met someone
who had played on his team. It turns out poor Mr. Hoffman didn't know
anything about tennis, either, and the stronger players had had to teach
him about the sport from scratch. The amazing thing is that nearly
every year, my high school won the state tennis championship!

Mr. Hoffman was clearly the best teacher I ever had in my life, but the
sad thing is that even knowing exactly how he did it, I can't imagine
myself emulating him. He was so good at feigning ignorance and getting
pity that none of us figured him out until years later.

When I taught math in college, I always volunteered to teach classes
that I didn't know much about. I probably did twice as much "homework"
as the students, terrified because every day I imagine so many questions
they could ask that I couldn't answer, and I studied like crazy so I'd
know the answers. Looking back on it, those were the classes where my
students learned the most, too -- having just thought very hard about
the subject, it was very clear to me what parts were difficult and
needed lots of explanation, and what parts were "obvious".

Date Subject Author
11/3/95 K. Ann Renninger
11/6/95 Problem of the Week
11/6/95 Tom Davis
11/7/95 Michael Keyton
11/7/95 Brian Hutchings
11/9/95 Ken Wood
11/9/95 Andrea Hall
11/9/95 Katie Laird
11/9/95 Katie Laird
11/10/95 Steve Means
11/10/95 Steve Means
11/10/95 Andrea Hall
11/10/95 Jim LaCasse
11/10/95 Steve Means
11/11/95 Andrea Hall
11/11/95 Steve Means
11/11/95 John Burnette
11/12/95 Lou Talman
11/13/95 Tarin Bross
11/13/95 Katie Laird
11/13/95 Steve Means
11/13/95 Kristina Lasher
11/14/95 David Weksler
11/14/95 Jane Ehrenfeld
11/15/95 Andrea Hall
11/16/95 Robin J Healey
11/16/95 Pat Ballew
11/17/95 Johnny Hamilton
11/17/95 Steve Means
11/19/95 Tarin Bross

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