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Topic: Maths pedagaogy
Replies: 57   Last Post: Mar 21, 2013 9:47 PM

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Shmuel (Seymour J.) Metz

Posts: 3,315
Registered: 12/4/04
Re: Maths pedagaogy
Posted: Mar 17, 2013 10:23 PM
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In <ki4jfg$efu$1@news.cc.tut.fi>, on 03/17/2013
at 04:21 PM, Kaba <kaba@nowhere.com> said:

>17.3.2013 14:25, pepstein5@gmail.com wrote:
>> Maths texts and lectures often refer to observations as being "easy to check",
>> "trivial" or "obvious."


>I find two extreme situations for why someone uses such weasel words.

>1) The writer is an expert, and is bored of going around the same
>argument for himself for the thousandth time. The claim is probably
>correct.


>2) The writer is a novice, and does not have the energy to go into
>details which detract him from the main point he is trying to make.
>There is a high risk of the claim being incorrect, or of that the
>claim is correct, but has a tedious proof.


3) The belief that they are weasel words is a delusion.

>An unfortunate example is Lang's Algebra, where everything is
>obvious, easy and trivial.


Assertion contrary to fact.

>If it really is trivial, then why not write it down;

Because doing so would bore the reader.

>it should take about the same space as stating it trivial.

Assertion contrary to fact.

>If it takes more than a few sentences, then it is not trivial.

Assertion contrary to fact. If it takes more than a few sentences but
the details are obvious to the reader then it is trivial.

>I find the advice in Strunk & White (Elements of Style) relevant:
>"Do no inject opinion."


That applies to your "weasel words" characterization more than it does
to anything in Lang.

>Related, there is this effect which I call the Stockholm Syndrome
>for Mathematicians :) This happens when people read a book which
>leave large gaps in their proofs, and force the reader to fill
>them.


That's not Stockholm Syndrome; that's teaching. Learning Mathematics
is not memorizing proofs.

>After having mastered the book this way, his emotions have gone
>through a rollercoaster of frustration to a feeling of control. And
>suddenly those positive feelings are projected to the book; since
>I know this well, the book must be great. But it's not the book;
>it's the massive work that was done to recover the details and
>essential techniques.


Au contraire, it's the guidance that the author provided that enabled
you to fill in the gaps.

--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

Unsolicited bulk E-mail subject to legal action. I reserve the
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Date Subject Author
3/17/13
Read Maths pedagaogy
Paul
3/17/13
Read Re: Maths pedagaogy
David C. Ullrich
3/17/13
Read Re: Maths pedagaogy
Paul
3/17/13
Read Re: Maths pedagaogy
David C. Ullrich
3/17/13
Read Re: Maths pedagaogy
Paul
3/18/13
Read Re: Maths pedagaogy
David C. Ullrich
3/18/13
Read Re: Maths pedagaogy
Paul
3/18/13
Read Re: Maths pedagaogy
David C. Ullrich
3/18/13
Read Re: Maths pedagaogy
William Elliot
3/18/13
Read Re: Maths pedagaogy
Paul
3/18/13
Read Re: Maths pedagaogy
Frederick Williams
3/18/13
Read Re: Maths pedagaogy
Paul
3/18/13
Read Re: Maths pedagaogy
Frederick Williams
3/18/13
Read Re: Maths pedagaogy
Frederick Williams
3/18/13
Read Re: Maths pedagaogy
Paul
3/18/13
Read Re: Maths pedagaogy
Frederick Williams
3/19/13
Read Re: Maths pedagaogy
David Bernier
3/18/13
Read Re: Maths pedagaogy
Frederick Williams
3/18/13
Read Re: Maths pedagaogy
William Elliot
3/17/13
Read Re: Maths pedagaogy
Kaba
3/17/13
Read Re: Maths pedagaogy
Frederick Williams
3/17/13
Read Re: Maths pedagaogy
David C. Ullrich
3/18/13
Read Re: Maths pedagaogy
Kaba
3/17/13
Read Re: Maths pedagaogy
quasi
3/17/13
Read Re: Maths pedagaogy
Kaba
3/18/13
Read Re: Maths pedagaogy
quasi
3/18/13
Read Re: Maths pedagaogy
Kaba
3/19/13
Read Re: Maths pedagaogy
quasi
3/19/13
Read Re: Maths pedagaogy
Frederick Williams
3/19/13
Read Re: Maths pedagaogy
Paul
3/19/13
Read Re: Maths pedagaogy
David C. Ullrich
3/19/13
Read Re: Maths pedagaogy
Frederick Williams
3/19/13
Read Re: Maths pedagaogy
fom
3/20/13
Read Re: Maths pedagaogy
David C. Ullrich
3/20/13
Read Re: Maths pedagaogy
Paul
3/20/13
Read Re: Maths pedagaogy
fom
3/19/13
Read Re: Maths pedagaogy
Paul
3/20/13
Read Re: Maths pedagaogy
Herman Rubin
3/20/13
Read Re: Maths pedagaogy
Brian Q. Hutchings
3/21/13
Read Re: Maths pedagaogy
Herman Rubin
3/20/13
Read Re: Maths pedagaogy
Paul
3/21/13
Read Re: Maths pedagaogy
Herman Rubin
3/21/13
Read Re: Maths pedagaogy
fom
3/19/13
Read Re: Maths pedagaogy
quasi
3/19/13
Read Re: Maths pedagaogy
Frederick Williams
3/20/13
Read Re: Maths pedagaogy
Paul
3/20/13
Read Re: Maths pedagaogy
Herman Rubin
3/18/13
Read Re: Maths pedagaogy
Shmuel (Seymour J.) Metz
3/20/13
Read Re: Maths pedagaogy
Brian Q. Hutchings
3/17/13
Read Re: Maths pedagaogy
fom
3/17/13
Read Re: Maths pedagaogy
Shmuel (Seymour J.) Metz
3/18/13
Read Re: Maths pedagaogy
Frederick Williams
3/21/13
Read Re: Maths pedagaogy
Jesse F. Hughes
3/21/13
Read Re: Maths pedagaogy
fom
3/21/13
Read Re: Maths pedagaogy
Kaba
3/21/13
Read Re: Maths pedagaogy
fom
3/21/13
Read Re: Maths pedagaogy
fom
3/18/13
Read Re: Maths pedagaogy
grei

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