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Subject:   RE: Formulas
Author: rabeldin
Date: Apr 7 2005
On Apr  6 2005, Mathman wrote:
We avoid all of this writing, although the
> process of "invert and multiply"  is based upon it, and write simply
> the end result (2/3)(7/5) from the initial question, and carry on
> from there.

This is my point with transforming formulas.  The
> fact is that we "do the same to both sides", but having done so many
> times we see that we don't need to, and can simply transpose.  I
> believe that many students get frustrated by having so much baggage
> to carry around wit hall of that writing, and that it makes them
> more prone to error and disappointment.  A few examples would do to
> set the principles, then lots of graded [very easy to difficult]
> questions for practice applying the learned principles.  That is
> just my opinion and experience, and I do not challenge in any way
> that of others who prefer to keep on writing additional terms on
> both sides at every step.  However, I would suggest that it is not
> done in higher education where it would be far too much of a burden.
> But techniques learned with simpler problems would still be
> applicable.  To me, it is in a sense learning to "read" mathematics.
> So, after some preliminary work establishing the rules, I would
> concentrate on learning to resolve formulas and equations by
> transposing terms.  It is in fact what I did, and it worked well
> over the years.


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 one-on-one,
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.


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