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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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
Read Learning and Mathematics: Papert, mathetics (repost)
K. Ann Renninger
11/6/95
Read Re: Learning and Mathematics: Papert, mathetics
Problem of the Week
11/6/95
Read Re: Learning and Mathematics: Papert, mathetics
Tom Davis
11/7/95
Read Re: Learning and Mathematics: Papert, mathetics
Michael Keyton
11/7/95
Read Re: Learning and Mathematics: Papert, mathetics
Brian Hutchings
11/9/95
Read Re: Learning and Mathematics: Papert, mathetics
Ken Wood
11/9/95
Read Re: Learning and Mathematics: Papert, mathetics
Andrea Hall
11/9/95
Read Re: Learning and Mathematics: Papert, mathetics
Katie Laird
11/9/95
Read Re: Learning and Mathematics: Papert, mathetics
Katie Laird
11/10/95
Read Re: Learning and Mathematics: Papert, mathetics
Steve Means
11/10/95
Read Re: Learning and Mathematics: Papert, mathetics
Steve Means
11/10/95
Read Re: Learning and Mathematics: Papert, mathetics
Andrea Hall
11/10/95
Read Re: Learning and Mathematics: Papert, mathetics
Jim LaCasse
11/10/95
Read Re: Learning and Mathematics: Papert, mathetics
Steve Means
11/11/95
Read Re: Learning and Mathematics: Papert, mathetics
Andrea Hall
11/11/95
Read Re: Learning and Mathematics: Papert, mathetics
Steve Means
11/11/95
Read Re: Learning and Mathematics: Papert, mathetics
John Burnette
11/12/95
Read Re: Learning and Mathematics: Papert, mathetics
Lou Talman
11/13/95
Read Re: Learning and Mathematics: Papert, mathetics
Tarin Bross
11/13/95
Read Re: Learning and Mathematics: Papert, mathetics
Katie Laird
11/13/95
Read Re: Learning and Mathematics: Papert, mathemaatics
Steve Means
11/13/95
Read Re: Learning and Mathematics: Papert, mathetics
Kristina Lasher
11/14/95
Read Re: Learning and Mathematics: Papert, mathetics
David Weksler
11/14/95
Read Re: Learning and Mathematics: Papert, mathetics
Jane Ehrenfeld
11/15/95
Read Re: Learning and Mathematics: Papert, mathetics
Andrea Hall
11/16/95
Read Re: Learning and Mathematics: Papert,...
Robin J Healey
11/16/95
Read Re: Learning and Mathematics: Papert,...
Pat Ballew
11/17/95
Read Re: Learning and Mathematics: Papert, mathetics
Johnny Hamilton
11/17/95
Read Re: Learning and Mathematics: Papert, mathetics
Steve Means
11/19/95
Read Re: Learning and Mathematics: Papert, mathematics
Tarin Bross

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