Re: [Phys-l] crutches versus shoes

[John Denker <jsd@av8n.com>]

On 04/14/2011 09:39 AM, M. Horton wrote:
> I don't want to bring up a touchy subject again, but . . . "If FOIL is 
> taught improperly -- "do it this way because I told you to" --
>   then it is a special case disconnected from the general case.  It's just 
> one more thing to remember." is a marvelous example of the ills of teaching 
> algorithmically . . . something that you proclaimed the virtues of a short 
> time ago.  This is teaching an algorthm without an understanding of how or 
> why it works.  That's exactly how I described, and educators describe, 
> teaching algorithmically.
>
> It makes me feel better that, although we might use different terms to 
> describe it, that we agree that it is bad.

If that's all you mean by "algorithmic" then you personally are in 
the clear.  (I still think the world would be better off if people
would avoid this pointless and insulting abuse of the terminology, 
but that is a very small point, and not the point I wanted to address
in this thread.)

In any case, the larger point remains.  There is abundant evidence that
some educators -- whether or not they abuse the term "algorithmic" --
think that shoes and bicycles should be demoted to the crutch category:
 a) Alas, some folks think the factor label method is a bad thing as 
  a matter of principle, because it allows students to solve certain
  problems without necessarily having a deep understanding of
  proportional reasoning and scaling laws.
 b) Alas, some folks think Gaussian elimination is a bad thing as 
  a matter of principle, because it allows students to balance
  chemical reaction equations systematically and mathematically,
  as opposed to doing it by "intuition".
 c) Alas, some folks think that pilots should learn to fly at a 
  small airport (so as to develop spot-landing skills) before going 
  anywhere near a big airport (lest they use the VASI as a crutch
  and use all the extra runway-length as a crutch).

I invoke the principle that says don't confuse the presence of one thing
with the absence of another.  With a good instructor and/or a little bit
of self-discipline, you can land your C-172 on the middle 1000 feet of a 
10,000 foot runway.  Knowing a systematic approach to reaction equations 
does not prevent you from understanding what the equation means, nor vice 
versa.

It is also possible to go off the reservation in the other direction;
some folks think crutches should be promoted into the shoe category:
  x) Alas, some folks think the "density triangle" is OK.
  y) Alas, quite a lot of folks think it is OK to pretend that there
   are filled "Lewis octets" in molecules, because that allows students
   to calculate the right answers to a certain limited set of questions
   ... even though this allows and indeed _requires_ students to form
   wildly wrong models of what is actually going on.