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Re: Please remind me why 3^2 = 9
Posted:
Oct 19, 2012 9:07 PM


I suspect that Alain is alluding to a substantial difference between how the challenges of mathematics instruction and instructology arise within curricular environments ... and how they arise through clinical instruction/research.
Clinically attending the *personal mathematical health* of individuals (who might or might not be enrolled in curricular programs) relies on viewpoints/perspectives which are quite different from what is required when trying to attend "classes" of students ... subject to the constraints of institutionalized curricular programs. Each perspective discloses things that the other does not. Neither is righter or better than the other.
Each deals with its own *managerial dimensions of concern*. Those concerns often overlap ... but often are independent of each other ... and their results sometimes are woefully contradictory. ["Covering the material" of a course, on time, often is at the expense of the conceptual understanding which is essential for personal mathematical health. Urging learners to strive for personal mathematical comprehension (Vs. rote "parroting") might sometimes inhibit students' scholastic success.]
Although the two perspectives are not fully "complementary" (even taken together, they hardly provide a "complete" picture) ... they nonetheless can enhance each other's perception of the nature and processes of the instructional guidance of mathematical learning.
As for the prospects for collaboration, the MALEI Mathematical Learning Clinic now offers unprecedented opportunities for educators' cooperative pursuits for furthering national educational progress. For over a year, the Clinic has been gradually developing a videobased, communityeducation ("mathematical fitness"), basicliteracy program ... designed for mathilliterate, mathfearing, nonstudent adults. Anyone who is willing to collaborate on that kind of effort surely can gain substantial insights into how to improve the effectiveness of curricular instruction, at least Kalgebra. [Please email me, directly, rather than through a ListServe.]
Cordially, Clyde
  From: "Alain Schremmer" <schremmer.alain@gmail.com> Sent: Friday, October 19, 2012 4:15 PM To: "Clyde Greeno" <greeno@malei.org> Cc: <mathedcc@mathforum.org> Subject: Re: Please remind me why 3^2 = 9
> > On Oct 19, 2012, at 12:22 PM, Clyde Greeno wrote: > >> A Mackeyprompted extension: >> >> "Below, insert parens to show two reasonable interpretations of ' x^y' >> ... and circle the one that is most commonly used in mathematical >> literature: >> x^y or x^y " >> ... then illustrate the difference, by evaluating both formulas, by >> choosing a value for x, and a value for y, and using those values in >> each of your two parenthesized formulas. Which of those values is >> displayed by your calculator ... with and without your parens " > > > Indeed, even nicer. > > I find it interesting that I very rarely have that kind of idea. But then > that's why people collaborate. Too bad, though, that mathematics > "educators" usually don't even want to consider the possibility. > > Regards > schremmer **************************************************************************** * To post to the list: email mathedcc@mathforum.org * * To unsubscribe, email the message "unsubscribe mathedcc" to majordomo@mathforum.org * * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 * ****************************************************************************



