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Re: [Phys-L] mass, energy, and spacetime



Here is a big educational misconception. While students may have seen such
plots, they really did not understand them. If you have HS seniors or intro
college students measure X vs t using a constant velocity car and then plot
the data, they invariably make a plot of Y vs X. This happens even when
they are told to use the actual measured variables. Then when presented
with X vs t they have difficulty writing the equation. They do not
associate Y=mx+b with any plots that have other variables than X, Y. It
takes at least a semester to break most students of the idea that the only
variables are X and Y.

So while it may be standard, it does not connect with math very well. Then
they start writing equations like X(m) = 5 t(s) rather than X = 5 m/s t.
They do not understand functional notation and move it over to writing
specific equations. Of course they are given some specific instructions and
show how to write the specific equations for a lab experiment.

Part of the problem is that just seeing something is passive, while writing
something is active. It is like the difference between passive and active
vocabulary. Students have to learn to write equations rather than just be
consumers of equations. A good calculator can solve or give the results of
substituting into an equation, but at present it requires human intervention
to write good equations. Math is teaching them the obsolescent skills
rather than the skills that still require human intervention.

John M. Clement
Houston, TX



"The idea of plotting x versus t as we have done here is
completely standard. It's something you should have seen in
8th grade (if not before), and seen many times since then."