Re: How not to teach mathematics

In article <efcqqr$dcn@xxxxxxxxxxxxxxxxxxxxxxx>,
Bob Pease <Popester@xxxxxxxx> wrote:

"Herman Rubin" <hrubin@xxxxxxxxxxxxxxx> wrote in message
news:efcks7$2uou@xxxxxxxxxxxxxxxxxxxxxxx
In article <1159316964.800871.59280@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
William Hughes <wpihughes@xxxxxxxxxxx> wrote:

Michael Press wrote:
In article
<1159286786.180020.82350@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
tgdenning@xxxxxxxxxxxxx wrote:

Michael Press wrote:
In article
<1159277968.221146.286570@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
tgdenning@xxxxxxxxxxxxx wrote:

I have removed talk.origins from the list.

..................

I still do not feel I understand analytic function
theory. I know how the objects work, and that, at
least at this time, the domain must be the complex
numbers. I know how to prove the theorems and to
use the results. But what is the concept?

This talent, alas, seems to be rare.


As I see it ( having taught Math at levles grade seven through @00 grad
level, and in computer school to adults with below third grade math
skills)::

Mathematics consists essentially of three different skills

1. Computaion (Being able to perform algorithms when presented wth them)
2. Reckoning ( Numeracy, estmation. )
3 Analysis ( the rest)

The "rest" covers far more. However, it is not a
collection of skills, but involves understanding, which
seems to have been eliminated from the educational system.
I have left one paragraph from my previous posting in.

Unfortunatly JQ Public has some of the first, liittle of the second, and
none of the third.

There seems to be a belief that #1 1and #2 are all that's needed,

These two are necessary, but by no means sufficient conditions.

Are these even necessary? If one knows which algorithm
to use, and has a machine to do it, is it necessary to
be able to carry it out? It is most important to know
what it means (concepts), and of some importance, in
some cases, to know how it is carried out, but of little
importance to be able to carry it out unaided.

I cannot fly, so I use airplanes.

Analysis is essentially a VERBAL skill, and with a general shortchanging of
students in all areas of mental development. it is difficult for analysis to
develop. yet alone to prosper. ,

You have put too much in the rest.

" I can't DO word problems" means that somehow verbal skills have not been
well ennough developed to cross over into analysis."

It is not verbal skills, but the lack of knowledge of
suitable language. The use of variables, which is
essentially a very simple language with little fixed
vocabulary, and not too complicated grammar, and
this certainly can be taught with beginning reading.
One should not DO word problems in general; this is
equivalent to mentally applying several steps, or a
sometimes sophisticated search; instead, and this is
what the requirement should be, one should be able to
formulate word problems in any subject in which one
understands the concepts involved; this part of what
you have called "analysis", which is the use of
"mathematical language", is the minimal requirement.

If someone has a statistical problem, what is needed
is to understand probability, and the field of the
problem, to formulate it. Then someone who has the
appropriate solving skills can provide the solution.

My 3.14 cents worth

RJ Pease




--
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
.