Re: Being careful with dimensions (was Re: i,j,k things)

[Stefan Jeglinski <jeglin@4PI.COM>]

> I think it is amazing that the unit vector thread has produced the
> divergent views it has, and also has produced some converts (me
> included) who realized they might not have been viewing things 100%
> correctly (or "positively pedantic" as Joel Rauber says).
>
> Here is something pretty basic in our everyday teaching, and we do not
> all view it the same.  That's amazing.


I agree. However, I can't help but have certain feelings while
pondering this thread. There have been many valid comments on the
details of why this vector beast should be written one way or the
other. Some descriptions have been argued as "less correct," and some
"more correct," and the notion of units as opposed to vectors per se
has been creeping in and out.

While I understand the point of being pedantic, the real goal is to
get the student from their side of the creek to ours, so to speak.
Everybody who has written in on this presumably "gets" it. That is,
we would be unlikely to make errors in the interpretation or solving
of a vector or unit problem, regardless of the many ways the notation
has been posed. We know what the pitfalls are, and defects in the
notation are accounted for virtually by inspection.

We got this way, presumably, by pondering vectors to such an extent
that we all finally had the "ah ha" response. We really got it on a
deeper level at one point or another. I myself was a stubborn
student, not getting many concepts, even after someone (or somemany)
had explained it in a variety of ways. I had to ponder it and roll it
over in my head until I could finally say "ah ha!" No amount of
"pouring it into my brain" was as successful.

To this end, the most effective learning experiences I had for
vectors and units and many other things were not tedious repetition
of pedantic notation (although it had its place), but the
presentation of well-chosen counter examples which produced either
absurd or subtle incorrect answers (that is, a solution performed
incorrectly on purpose). Ones which were eye-opening and tended to be
a surprise, and pointed out the pitfalls of not being careful, when
contrasted against the "correct" approach. The more relevant to
everyday experience, the better, at least for those who are not
physics oriented.

With simple vectors, it is difficult perhaps to come up with
"eye-opening" examples because they are pretty mundane (which is not
to say unimportant). Nevertheless, in general I recall single
counter-examples being worth more to me than entire texts of rote
examples and dry descriptions. I, like many others I think, actually
enjoy seeing a "wrong" solution contrasted against a "right"
solution. It is somehow satisfying and makes you feel empowered when
you "get" it in this fashion. Students that feel empowered are
difficult to stop. Those who are confused or bored are almost
impossible to motivate.


My 2 cents.


Stefan Jeglinski