Re: motivating * knowing the subject

["John S. Denker" <jsd@MONMOUTH.COM>]

I wrote:
> > Teaching is maybe 10% knowing the subject matter and 90%
> > motivating the students.  They could have gotten the subject
> > matter from books.

... which was more-or-less OK in context, but won't withstand
detailed scrutiny.

John Clement wrote:
...
> Incidentally there have been several studies that showed that students learn
> much more when the teacher has better mastery of the subject.  So content
> mastery is actually a very large factor.

Good point.  The percentages I gave are not right in general.

Interestingly, changing the percentages doesn't fix the problem.

The key word here is "factor" (in contrast to "term").  That is,
motivating_the_students (M) and subject_area_knowledge (K) are
!!multiplicative!! not additive.  Both are required;  neither will
make up for a lack of the other.  We have
  success ~ M*K
(not M+K) so the idea of percentage is not directly applicable.

================

If we now make the (questionable) assumption that things are
differentiable, we obtain
  d(success) ~ M dK + K dM
which is additive, so percentages might apply in particular cases.

I suspect the 90%/10% numbers made sense to me only because of
my narrow experience -- I've taught only in situations where I
was very much in command of the subject, so the "K dM" term was
dominant for me.  In contrast, if you made me a major-league
baseball pitching coach, or asked me to teach sculpture, I'm sure
I would get a brutally keen reminder of the importance of knowing
the subject.