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Re: rote learning math facts
Posted:
Aug 12, 2002 1:17 AM
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Brian, I have a couple of questions.
When you speak of understanding, are you thinking of any particular
part of Boom's Taxonomy? Are you using it as a synonym for
Comprehension, which is the second step in the Taxonomy, or are you
using the term more broadly? When I say "understanding," I use it more
broadly, so as to loosely refer to a conjunction of all or some of the
steps beyond Knowledge.
Are you claiming that remembering and understanding are sufficient and
necessary for each other, even though neither one temporally precedes
the other? Regardless, I find this idea intriguing. Would this mean
that one cannot occur without the other? If so, then there would be no
such thing as rote memorization (defined as "memorization without
understanding," where memorization is defined as "committing to
memory"). Note that this relates to what Mark Houghton said, which is
that "the focus to the debate should be on the little word 'rote,' and
not the strawman 'memorization.'"
I think that BEHIND what Art is saying (and behind many of my prior
posts on k12.ed.math [on the subject of student solutions manuals and
on other subjects]) is this thesis: If what is remembered is
sufficiently well-chosen, then understanding can flow naturally from
knowledge - understanding can become a natural consequence of
possessing some knowledge (that exists in longer term memory and can
be held in working memory when recalled). And I believe that this
holds regardless of whether this knowledge temporally precedes this
understanding.
It's clear to me that "remembering" can be (to a practical degree)
scientifically defined and measured. It's also clear to me that
"understanding" is not as amenable to a scientific worldview, which is
why I (and perhaps others) prefer to focus on Knowledge and let
Understanding flow from it. In "Why just about any mathematics is hard
to learn," I gave an anecdote of this idea (regarding a struggling 9th
grader in Algebra I), so I'm not speaking here in some abstract
philosophical way, but hopefully in a way that practicing teachers can
find useful.
Paul Tanner
--
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