John D. mentioned spacetime graphs in passing, and that reminds me of
another problem students have with the way they think about graphs.
When determining the location of a point in relation to the axis of a
coordinate system, students appear to have been taught they should construct
a line through the point and perpendicular to the axis of interest. That is
not correct. Rather, they should construct a line through the point and
parallel to the other axis.
Of course for a coordinate system with orthogonal axes, either method works.
But if the axes are not drawn orthogonally (such as on a spacetime graph)
you have to do it the parallel way rather than the perpendicular way. I
can't begin to tell you how this messes up relativity students even after I
warn them about it.
It is interesting that if you look up abscissa and ordinate in Wictionary,
it is stated correctly... "the abscissa of the point is the distance cut off
from the axis of X by a line drawn through it and parallel to the axis of
Y." It has to be viewed that way if there is any possibility you might
sometime use non-orthogonal axes. However, I have asked the math professors
here, and they admit they teach their math-education students the
perpendicular construction. They are considering switching, but they say
most math textbooks explain the perpendicular construction. They say it
isn't exactly wrong since they are clearly discussing a system with
orthogonal axes. It seems to me that if you are trying to teach the concept
of locating something with respect to two axes, and maybe even drawing a
grid, you ought to teach it in a way that allows non-orthogonal axes, and
that the "grid" might be parallelograms rather than rectangles.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
1 University Drive
Bluffton, OH 45817
419.358.3270
edmiston@bluffton.edu