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As John Denker routinely points out, using scaling laws (or
ratio and proportion) is extremely valuable and powerful.
This tool has great value beyond physics, reaching into
carpentry, economics, and even flying airplanes :).
My quandry is how to get students to actually use it. I
demonstrate it in class, I give exercises and show solutions,
but when it comes time for a test or quiz, about half my
students act like they have never seen the technique, even
when I tell them "use ratio and proportion like you did on
the homework and classwork."
The other half can't seem to grasp how to use the general
concept on a new law. For example, after using the technique
on the electric field of a point charge I then tell them (and
show them) the far-field distance behavior of the dipole
E-field. This isn't the only situation. It seems they don't
really understand the concept of scaling.
What methods have any of you found which are effective in
having students grasp the concept of scaling and apply it to
a "new" relationship they haven't been drilled on before?
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