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Topic:  upper middle schoolers that haven't yet mastered multiplication facts 
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Subject:  RE: upper middle schoolers that haven't yet mastered multiplication facts 
Author:  Mathman 
Date:  Jan 28 2005 
2. it is more important to
> understand the situation as a complex set of factors requiring
> analysis of the issues of the students and a professional assessment
> of the learning situation in order to come to the appropriate
> approach. Perhaps more drill, perhaps other methods.
I know of no
> silver bullet.
Nor do I. What I'm driving at is the fact that the student body varies in
capabilites between VERY wide extremes, and that the process of teaching and
learning will vary widely accordingly. Although I know and greatly appreciate
the advantage of knowing theory as well as prcatice, and promote that myself in
general, there is the occasion when there is no other route but by brute force,
if you will. Either way, the answer lies in "whatever works." For, if that
hurdle is not passed one way or another, there is nowhere to go without the
greatest of difficulty for all concerned.
Concerning the importance of theory and understanding vs strict rote learning, I
don't know if this is a good example, but let's consider the following [the
knowledge and development of rational number arithmetic relies heavily on having
acquired skill and proficiency in multiplication]: How do you teach division of
one fraction by another? Students will inevitably "invert and multiply". Why
do they say, and do that, aside from "Teacher sez so."? I can tell how I
approached the subject, that question in particular, but am interested in other
opinions and approaches to a topic that confounds so many needlessly. So, there
can be a thousand sample problems which require the learned process for
practice, but that does not lead to the understanding that enables simple
solution to more difficult, or slightly out of the box solutions to problems
otherwise more tedious. However, there are those who will go beyond the normal
textbook [well, that textbook] approach, and those who most definitely will
not.
Thanks for the invitiation for private conversation on the subject. I am
amenable if you would provide your address. However, I'd rather keep
conversation here, since it is a public discussion, and others have just as
valid opinion, and I value theirs as I do your own. If you want to switch this
now to a new thread [perhaps ...Dealing with fractions], please do so.
David.
 
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