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[Phys-L] effective teaching of scaling/ratio use



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?