Discussion:  All Topics 
Topic:  Formulas 
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Subject:  RE: Formulas 
Author:  Mathman 
Date:  Apr 7 2005 
I don't disagree, but I would point out
> that mentioning such mental short cuts in class may short circuit
> the learning of some students. In a oneonone, we can tell pretty
> much whether the student is ready to seal up that principle. The
> desparate student may respond either by tuning out (That's too much
> for me!) or by learning the short cut without the justification.
> Both are likely to cause problems in the long run.
I will not argue the point at a junior level, Dick, since the capabilities of
students vary so drastically. I have taught all HS grades all levels in math,
and used both approaches to advantage. This is why I left it open. However, as
much as I wouldn't dream of trying to teach those with great learning problems
resolution by transposition, neither am I greatly impressed with a need to teach
it in any shape or form to them in the first place.
That said, I do not ever propose simply using transposition, but to approach it,
as I did successfully with "advanced" students, by *first* teaching the
underlying principles and constantly showing how each can be done more
succinctly; constant reminders of where it comes from with each problem
discussed. Then moving into transposition. One approach to this I found to be
successful was to teach the topic as I say here, leading into the idea of
transposition, then, a bit later in the semester, redoing the entire exercise
[new problems] using *only* transposition. Marks were based upon the best out
of the two sessions, the idea being to learn, not to punish [but I'd like a
dollar for every time they mixed those two up]. When given that background and
the opportunity to resolve a problem with a lot of writing or relatively little,
the students inevitably choose the latter.
David.
 
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