Date: Jul 7, 2013 9:09 PM
Author: Clyde Greeno @ MALEI
Subject: Re: Is logic part of mathematics - or is mathematics part of logic?

Apologies to GSC for not including a response to his thoughts about students 
" ... constructing models showing how (one's) own characteristics (can be)
hindering (one's) learning of math - and by enabling (one) to construct a
realistic action plan...."

In all areas of personal endeavor, respons-able self-management is a major
key for avoiding being victimized by ineffective habits and by
"circumstances" ... including being enrolled in some particular curricular
course that fails to make the content common-sensible. Mathematics
educators have badly neglected the students' needs for effective instruction
in HOW TO LEARN mathematics. [I cannot say that educators "have failed" in
that area, because they rarely try!] That kind of know-how consists partly
of *mathematical methods* that math majors gradually begin to acquire.

Aside from those, the self-management of learning-factors is of clinical
interest, but not yet of concern to leaders of the industry. That kind of
enlightenment awaits a highly visible demonstration that education in that
area makes important and significant differences. The ground is fertile,
but the crop won't "sell" until the market clamors for it.

The case that Chandy cites is of interest because it appear to lie within
the same arena that enshrouds most American students, and that so protects
the industrial traditions. "The curriculum presents you with a challenge.
Re-shape your thinking and your modes of operation so that you can get the
best results possible ... under those circumstances." [The student is
thereby led to stay within that curriculum's "box" while trying to learn
the mathematics ... rather than to get "outside the box" to better see the
mathematics, itself.]

One commonplace "realistic action plan" is to acquire the services of a
tutor who can empower you to better execute the [box-prescribed]
performances on which you will be "tested" ... whether or not the tutor
actually can get outside the box, to disclose and impart the
common-sensibility of the underlying mathematics.

How great it will be when the first step in the student's "realistic action
plan" can be to "click here" to learn the common-sensibility of each
troublesome topic. There presently is no such 'MACS-ipedia." But the MALEI
Clinic's Tulsa-OK Mathematical Literacy Project initiative aims to produce
such a resource. One "sampler" is on www.mathliteracy.org.

To find your own niche within that initiative, contact the
registrar@mathsense.org.

Cordially,
Clyde

- --------------------------------------------------
From: "GS Chandy" <gs_chandy@yahoo.com>
Sent: Sunday, July 07, 2013 1:20 PM
To: <math-teach@mathforum.org>
Subject: Re: Is logic part of mathematics - or is mathematics part of logic?

> Further my post (dt. Jul 7, 2013 1:01 PM:
>
> A: The link to a document referred in that post was inadvertently left out
> there.
>
> The document's title: "Mental Models: a gentle guide..."
> The omitted link is as follows:
> http://icos.groups.si.umich.edu/gentleintro.html
>
> My regrets for having left this out earlier.
>
> B: 'Mental models are crucial background to develop an adequate and usable
> understanding of the 'Warfield approach to 'systems (and the 'One Page
> Management System [OPMS]).
>
> GSC