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Re: Is logic part of mathematics  or is mathematics part of logic?
Posted:
Jul 8, 2013 11:53 PM


GSC: My responses by ##
  From: "GS Chandy" <gs_chandy@yahoo.com> Sent: Monday, July 08, 2013 1:19 PM To: <mathteach@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 webpages: > >   "The American Institute for the Improvement of > MAthematics LEarning and Instruction" (http://malei.org/index.html) >   "The TulsaOK Mathematical Literacy Project" > (http://malei.org/mathliteracy.org/index.htm) >   "TULSA'S MALEI MATHEMATICAL LEARNING CLINIC" > (http://malei.org/mathliteracy.org/clinic.htm) >   "The (MACS) Project for Teaching and Learning > Mathematics As Common Sense" (http://mathsense.org/index.html) >   "TULSA'S MALEI MATHEMATICAL LEARNING CLINIC" > (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 understaffed.
> 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 MatheLiteracy Project. But I presume that your own inquiry actually is about how the proceedings of an adequately staffed, mathematicalhealth 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 costeffective 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 curriculumprescribed performances will result in higher scores on "math exams, tests, quizzes." No mathematicalhealth clinic would offer that kind tutorial service. The clinical response to such students is to try to quickly enlighten them about the rational, commonsense nature of functional personal mathematical intelligence ... and about its healthy development and achievement through reasoning things out for themselves. When that mathematicalhealth orientation is not accepted, clinical mathematics instruction cannot succeed. [Instead, the traditional "parrottraining" 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 mathematicalhealth 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 soincreased 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 'firstrate' mathteacher" (based on his/her current abilities as > a teacher)
### Teachers and mathcoaching parents who are being served by the MALEI Clinic continually improve their practical knowledge about mathematicsascommonsense 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 inperson, class instruction within curricular institutions, most other dimensions of teacherexcellence 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 corecurricular mathematics. In 2013, how many want that kind of help?
> I am not able to see, from your webpages just how you would help the > respective stakeholder(s) noted above to accomplish any of the abovenoted > 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 homebased) 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 webpages. ### 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 reform 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 communicationseffectiveness of the websites. Thanks for prompting some interim clarifications.
Cordially, Clyde > > GSC > ========================== > 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, responsable >> selfmanagement 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 >> commonsensible. 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 >> knowhow consists partly >> of *mathematical methods* that math majors gradually >> begin to acquire. >> >> Aside from those, the selfmanagement of >> learningfactors 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. >> Reshape 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 >> [boxprescribed] >> performances on which you will be "tested" ... >> whether or not the tutor >> actually can get outside the box, to disclose and >> impart the >> commonsensibility 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 >> commonsensibility of each >> troublesome topic. There presently is no such >> 'MACSipedia." But the MALEI >> Clinic's TulsaOK 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: <mathteach@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



