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Topic: Bloom taxonomy in Math
Replies: 2   Last Post: Dec 3, 2010 12:21 PM

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Posts: 28
Registered: 12/6/04
Re: Bloom taxonomy in Math
Posted: Dec 2, 2010 12:25 AM
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Proposed levels may not come as sharply distinctive, yet well defined
levels, illustrated by lots of detailed relevant examples, seem to be
as a practical guide for designing assessment instruments, and may
have implications for lesson planning.

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
however "levels" are ultimately defined?

In a message dated 12/1/2010 1:45:59 P.M. Eastern Standard Time, writes:

On Dec 1, 2010, at 8:59 AM, wrote:

> From:
> To:
> Sent: 11/7/2010 7:34:40 A.M. Eastern Standard Time
> Subj: Bloom taxonomy in Math
> Hi everyone,
> I'm interested in your views on the applicability of Bloom's taxonomy
> (or a revised version of it) to math education. Also, I would be
> grateful
> for pointers to studies on this subject that go beyond repeating the
> description of the various levels of achievement in the generic Bloom
> taxonomy, and provide a specific, nontrivial example of those levels.
> Thank you in advance for your help.

In order to respond, it would be useful, at least to me, to know a
bit more precisely what the issue(s) actually are that you want to
deal with.

While there obviously are "levels" at which mathematics is
understood---my level of understanding is certainly not that of, say,
Grothendieck or Thurston---I would argue that the notion of level
doesn't concern our students just like, while there are levels that
are meaningful for, say, sprinters or long distance runners, the
concept seems a bit useless both for children learning to walk and
for adults walking.

Beyond that, I would argue that while, for instance, Anderson and
Krathwohl (2001)' pyramid


might look good, it is not really relevant: In those few fields in
which I have some small competency---mathematics, building
construction, political sciences, mechanics, ... ---all six verbs
have all always been there and thus did not characterize levels and
if the mix changed a bit over time, it certainly was not monotonically.


P.S. Lot of interesting stuff on

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