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Fwd: Bloom taxonomy in Math
Posted:
Dec 6, 2010 11:28 PM
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I've inadvertently pressed "Reply" instead of "Reply All".
____________________________________
From: DCJLEE@aol.com
To: schremmer.alain@gmail.com
Sent: 12/4/2010 12:39:40 A.M. Eastern Standard Time
Subj: Re: Bloom taxonomy in Math
Before addressing Alain's points, I must express surprise
that this topic hasn't caught the attention of more people,
given that myriad school districts advertise the fact that
they use Bloom's taxonomy in curriculum design.
A) Your preoccupation with instructional material seems to
preclude the meaningfulness of assessment independent
of how knowledge was acquired.
B) There are strategic and tactical aspects to assessments.
In principle, why are you against the possibility or usefulness
of checking students' grasp of the material presented in each
class meeting?
C) I wonder if other subscribers to this forum agree with your
conclusion. I rather wait and see if someone cares to address
this point.
D) Of course, you're right. But, as announced, it was supposed
to be a simple example.
E) Again, you seem to conflate/identify knowledge/understanding
with the process of acquiring it.
F) Mental arithmetic was just a device used here to preclude
the use of calculator/paper&pencil. No time constraint was
imposed. The formula was explained earlier in class.
G) Please refer to A) and E).
Regards,
JL
In a message dated 12/3/2010 12:22:03 P.M. Eastern Standard Time,
schremmer.alain@gmail.com writes:
On Dec 2, 2010, at 12:25 AM, DCJLEE@aol.com wrote:
> Proposed levels may not come as sharply distinctive, yet well defined
> levels, illustrated by lots of detailed relevant examples, seem to
> be needed
> as a practical guide for designing assessment instruments,
A. Assessment instruments cannot really be designed independently of
the materials: Mathematical entities are connected in many different
manners and can be seen in many different ways. The materials have to
be designed/written with some particular conceptual organization in
mind, which implies a particular selection among all these
relationships and thus a particular viewpoint. As a result, their
conceptual understanding then necessarily depends, at least in part,
on this organization. Independent assessment tends to be limited to
the "mechanical" aspects which is not to say that the latter are of
no importance but only that they do not really relate much to
conceptual understanding.
> and may have implications for lesson planning.
B. One ought to plan at least a semester, if not a sequence;
certainly not a lesson. Moreover, "lessons" invariably devolve to the
students "taking notes" (just so as not to draw attention by
appearing idle). In developmental mathematics, with appropriate
materials read by the students before class, time is much better
spent discussing whatever comes up from said reading.
> One simple example. Consider the formula for the square of a sum
>
> >>> (a+b)^2 = a^2 + 2ab + b^2
>
> I've regularly witnessed the following five distinct scenarios:
>
> (1 ) Student knows this formula, and can use it to compute 103^2
> mentally (without assistance).
> (1*) Student knows this formula, and can use it to compute 103^2
> mentally (with the hint to use the formula).
> (2 ) Student knows this formula, and can use it to compute (100+3)
> ^2 mentally (without assistance).
> (2*) Student knows this formula, and can use it to compute (100+3)
> ^2 mentally (with the hint to use the formula).
> (3 ) A student knows this formula, and cannot do any of the above
> (even with the hint to use the formula).
>
> Haven't you experienced similar situations? Their daily occurence
> seems
> to indicate the existence of different "levels" of understanding of
> the formula,
> however "levels" are ultimately defined?
C. I do not see what impact the above "scenarios" can have other than
resulting in more drilling.
D. The above"scenarios" may just be "still photographs" out of a
whole continuum of possible behaviors.
E. The use of the term "level" would seem to imply a hierarchy which
I do not see the scenarios to imply. Consider the following: faced
with the same problem, my wife, whose field is on the analysis side
of differential geometry will get her ideas from the look of the
computations whereas I, whose field was somewhere between
differential geometry and fluid dynamics, would get mine from (a
considerable amount of) doodling. Are we still talking "levels"?
F. Mental arithmetic is a very special talent which many
mathematicians do not have. On the other hand, given any two numbers,
my father could give you what percentage of one number the other one
was and he was not even remotely a mathematician,.
G. The differences in the scenarios can be explained in ways other
than "levels of understanding of the formula". For instance, it may
be that the explanation didn't really "explain" at all so that the
formula became voodoo and ended up having to be memorized. Which in
fact is what "student knows this formula" seems to point at.
Regards
--schremmer
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