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Topic: Is logic part of mathematics - or is mathematics part of logic?
Replies: 6   Last Post: Jul 10, 2013 6:54 AM

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Clyde Greeno @ MALEI

Posts: 220
Registered: 9/13/10
Re: Is logic part of mathematics - or is mathematics part of logic?
Posted: Jul 8, 2013 11:53 PM
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My responses by ##

- --------------------------------------------------
From: "GS Chandy" <gs_chandy@yahoo.com>
Sent: Monday, July 08, 2013 1:19 PM
To: <math-teach@mathforum.org>
Subject: Re: Is logic part of mathematics - or is mathematics part of logic?

> Responding to Clyde Greeno's post of Jul 8, 2013 6:39 AM (Dr Greeno's post
> is pasted below my signature for reference):
> As noted earlier, I am 'broadly in agreement' with most of your approach.
> I've checked out your web-pages:
> - -- "The American Institute for the Improvement of
> MAthematics LEarning and Instruction" (http://malei.org/index.html)
> - -- "The Tulsa-OK Mathematical Literacy Project"
> (http://malei.org/mathliteracy.org/index.htm)
> (http://malei.org/mathliteracy.org/clinic.htm)
> - -- "The (MACS) Project for Teaching and Learning
> Mathematics As Common Sense" (http://mathsense.org/index.html)
> (http://mathsense.org/clinic.htm)
> A couple of links did not work (they are, I believe, under development).

### Thanks for visiting. The website is sorely in need of cleaning up. We
are seriously under-staffed.

> OK - as noted above, I 'agree broadly' with your approach, the underlying
> philosophy. I am NOT giving my full and unconditional agreement till I am
> more convinced that you are ACTUALLY doing/able to do what you're
> promising).

### Oh my, please! "full and unconditional"? Perish the thought! I doubt
that my communicates are sufficiently comprehensible to warrant that. One of
the beauties of scientific clinical research is that others can help to
patch up the weaknesses.

> Are you in a position to guide, say, a student who wishes
> "To understand, thoroughly, all topics of my math syllabus, and THEREBY to
> improve, very significantly, my results in my math exams, tests, quizzes"
> ??

### YES, guide *A* student (call it "S", for brevity) ... but perhaps to
somewhere other than where S thinks S wants to go. [*A*, meaning "one"
(maybe), because the MALEI Clinic presently is serving only a handful of
teachers, parents, and students ... all of whom are cooperating on the
clinical R&D activities of the Mathe-Literacy Project. But I presume that
your own inquiry actually is about how the proceedings of an adequately
staffed, mathematical-health oriented clinic would respond to S.]

### It seems that S is caught up in the usual SCHOLASTIC GAME of being
enrolled in a "course" for S to transit, provided with a course "curriculum"
of instructional prescriptions and instructive experiences for S, and
challenged to earn performance "scores" on "math exams, tests, quizzes" ...
in which S has a substantial stake. One pertinent "usual personal trait"
might be that S's goal is to substantially improve such scores [because they
were "lower" than acceptable to S] ... using [what seems to S] to be an
optimal means of doing so. In that context, S might be interested in
clinical mathematics instruction only as a means to that end ... improving
"scores" ... and hopes for the most cost-effective means of doing so ...
without due regard for personal mathematical health.

### Students who are thus disposed often want a "thorough understanding" of
how to irrationally execute whatever curriculum-prescribed performances
will result in higher scores on "math exams, tests, quizzes." No
mathematical-health clinic would offer that kind tutorial service. The
clinical response to such students is to try to quickly enlighten them about
the rational, common-sense nature of functional personal mathematical
intelligence ... and about its healthy development and achievement through
reasoning things out for themselves. When that mathematical-health
orientation is not accepted, clinical mathematics instruction cannot
succeed. [Instead, the traditional "parrot-training" kind of
"understanding" can be got from traditional tutors or, for free, from The
Kahn Academy ... which explains its popularity.]

### Clinical mathematics instruction eductively guides learners (students or
otherwise) to knowingly advance their functional personal mathematical
intelligence ... toward meeting the learners' own immediate and imminent
needs for it (that being the major criterion for personal mathematical
health). Such intelligence includes whatever mathematics one owns as
rational, personal mathematical theories (informal, intuitive, or even
subconscious as those might be), together with the creative, analytic,
rational, metaphoric reasoning entailed in developing those theories. [In
language that can be understood by the lay public: whatever mathematics is
learned and owned as "common sense" ... usually including only a fraction of
what is encountered in school. More technically: "theoristic learning and
knowledge" in mathematics.]

###Clinical mathematics instruction is NOT geared to curricular proceedings,
syllabi, or "math exams, tests, quizzes" ... which tend to be very poor
(and often very unhealthy) measures of students' knowledge or progress.
Nonetheless, students' personal mathematical-health often depends partly on
how well they can cope with the demands and opportunities presented by the
curricular programs in which they are enrolled. If S actually wants to
improve S's personal mathematical health ... including better grasp of the
mathematical sensibility of S's curricular topics ... S's so-increased
mathematical powers surely will enhance S's potentials for faring better on
"math exams, tests, quizzes." But, "THEREBY improve" the scores? ... as with
"if ... then ...." ? There are too many influential factors for assurance of
better scores.

> Are you in a position to help, practically, a teacher who wishes "to
> become a 'first-rate' math-teacher" (based on his/her current abilities as
> a teacher)

### Teachers and math-coaching parents who are being served by the MALEI
Clinic continually improve their practical knowledge about
mathematics-as-common-sense learning and instruction ... and thus improve
their abilities to invoke those clinical advances. In fact, the Clinic's
contributions to the (MKTE) of Mathematical Knowledge for Teachers'
Education are gradually being released for worldwide access. But that kind
of help it is far too specialized to span "an action plan" of the kind at
which you are driving.

- -- Can you help him/her to put together an action plan for this Mission??

### Only insofar as that plan would include participating a "MACS Project's
Constituents' Group" that has yet to be activated. Especially for persons
engaged in in-person, class instruction within curricular institutions, most
other dimensions of teacher-excellence and growth lie far outside the scope
of the MALEI Institute
> Are you in a position to help, say, a group of 'stakeholders' in US
> education (i.e. including students; teachers; parents; administrators;
> politicians; others) who wish "To improve, very significantly' the US
> public school system" ???

### Yes, but only insofar as they would be helped by scientific
enlightenment about healthy educational practices in core-curricular
mathematics. In 2013, how many want that kind of help?

> I am not able to see, from your web-pages just how you would help the
> respective stakeholder(s) noted above to accomplish any of the above-noted
> aims.

### Hardly surprising! Read *The MALEI Mission*! It does not encompass any
of your "above aims." Our mission is concerned with advancing and using
scientific knowledge about personal mathematical health ... NOT otherwise
about curricular education mechanisms ( schools (public, private, or
home-based) colleges, vocational programs, or others ... and most certainly
not about any "reforms." For sure, much of curricular mathematics
"education" is unhealthy, and MALEI can assist organizations and communities
wishing to make it healthier ... but that is not what you are asking for.

> If I am mistaken, please accept my apologies - but do let me know just how
> you would accomplish any or all of the above - and do please have these
> potentialities reflected in your web-pages.

### You are badly mistaken. You are wandering around in quite another
ballpark. MALEI is NOT into educational reform ... any more than it is
geared to curricular proceedings. It has no intention of accepting
responsibility for whatever the U.S. schools already do, or will do ... only
for enlightening the nation and world within which they operate.

### Scientific mathematics instructology is strictly about how learners
internally and progressively accrue functional personal intelligence ... and
about how instruction strives to navigate their progress. Such studies might
or might not be pursued within the context of personal educational health.
Gradually, technology will re-form most systems of curricular education. But
growing concerns about the personal mathematical health of all Americans
will continually increase the importance of learning and instruction in
mathematics as common sense to the learners, themselves.

### Your apologies accepted. Priorities and resources permitting, we will
try to improve the communications-effectiveness of the websites. Thanks for
prompting some interim clarifications.

> ==========================
> Clyde Greeno posted Jul 8, 2013 6:39 AM:

>> 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

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