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Re: Please remind me why -3^2 = -9
Posted:
Oct 19, 2012 9:07 PM
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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 video-based, community-education
("mathematical fitness"), basic-literacy program ... designed for
math-illiterate, math-fearing, non-student 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
K-algebra.
[Please e-mail 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 Mackey-prompted 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
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