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

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 Kaba Posts: 289 Registered: 5/23/11
Re: Maths pedagaogy
Posted: Mar 17, 2013 10:21 AM

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.

I'll concentrate on the type 1 writers; the type 2 writers hopefully
improve on their writing as time passes.

Speaking of books in particular, whose main purpose is to teach, one
quality metric for me is to count the density of weasel words in the
text. An unfortunate example is Lang's Algebra, where everything is
obvious, easy and trivial. This is almost always contradictory. If it
really is trivial, then why not write it down; it should take about the
same space as stating it trivial. If it takes more than a few sentences,
then it is not trivial. I find the advice in Strunk & White (Elements of
Style) relevant: "Do no inject opinion."

A contrasting example is to take any book from John Lee (Introduction to
Topological Manifolds, Introduction to Smooth Manifolds, Riemannian
Manifolds). These are masterpieces to learn from. No weasel-words,
precise, and minimum amount of errors of any kind. It shows that the
author is interested on transmitting knowledge as efficiently as
possible, and also knows how to do that.

To me, the use of weasel words reflect a lack of effort; that the writer
isn't interested on giving the reader the best learning experience he
can. They make a book confusing to read, and indeed, I have sometimes
missed important points this way. You can afford to be careless when
writing to experts, but not when you are writing to students (readers of
the book).

In my opinion, weasel words do not undermine the readers confidence. To
the contrary: they contaminate the reader with a false sense of
security, opinions of what is easy and what is not. What actually
happens to me is that, if the claim is not immediately obvious, I skip
checking that claim to get back to the flow of the text.

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. From the
helplessness of the start of not understanding, because information is
missing, the reader works through the proofs, and increasingly builds
confidence in himself. 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. I hope future writers avoid writing their books
this way; it's abuse in disguise.

--
http://kaba.hilvi.org

Date Subject Author
3/17/13 Paul
3/17/13 David C. Ullrich
3/17/13 Paul
3/17/13 David C. Ullrich
3/17/13 Paul
3/18/13 David C. Ullrich
3/18/13 Paul
3/18/13 David C. Ullrich
3/18/13 William Elliot
3/18/13 Paul
3/18/13 Frederick Williams
3/18/13 Paul
3/18/13 Frederick Williams
3/18/13 Frederick Williams
3/18/13 Paul
3/18/13 Frederick Williams
3/19/13 David Bernier
3/18/13 Frederick Williams
3/18/13 William Elliot
3/17/13 Kaba
3/17/13 Frederick Williams
3/17/13 David C. Ullrich
3/18/13 Kaba
3/17/13 quasi
3/17/13 Kaba
3/18/13 quasi
3/18/13 Kaba
3/19/13 quasi
3/19/13 Frederick Williams
3/19/13 Paul
3/19/13 David C. Ullrich
3/19/13 Frederick Williams
3/19/13 fom
3/20/13 David C. Ullrich
3/20/13 Paul
3/20/13 fom
3/19/13 Paul
3/20/13 Herman Rubin
3/20/13 Brian Q. Hutchings
3/21/13 Herman Rubin
3/20/13 Paul
3/21/13 Herman Rubin
3/21/13 fom
3/19/13 quasi
3/19/13 Frederick Williams
3/20/13 Paul
3/20/13 Herman Rubin
3/18/13 Shmuel (Seymour J.) Metz
3/20/13 Brian Q. Hutchings
3/17/13 fom
3/17/13 Shmuel (Seymour J.) Metz
3/18/13 Frederick Williams
3/21/13 Jesse F. Hughes
3/21/13 fom
3/21/13 Kaba
3/21/13 fom
3/21/13 fom
3/18/13 grei