Here is another example about how I think students view equations.
Consider the equation typically referred to as Ohm's Law. Should we
write it as R = V/I, V = IR, or I = V/R? Note that some textbooks
introduce R = V/I as the definition of resistance.
Of course all permutations are the same equation, and all permutations
are useful for calculations. When I want to know the resistance of an
operating light bulb I measure the voltage and current and calculate R =
V/I. When I want the voltage drop across a resistor and I already know
the current, I calculate V = IR.
However, when students first encounter this, what experiences, if any,
have they had? They know that batteries have a particular voltage and
they most likely have been taught to think of this voltage as a type of
pressure. They also know that wires and other electrical devices have
resistance to the flow of current. Therefore, if we present the
equation I = V/R it immediately makes sense to them. They view the
voltage as causing the current, and they view R as restricting the
current, so voltage in the numerator and resistance in the denominator
makes intuitive sense to them.
Therefore I first introduce it as I = V/R so they can see the logic of
it. Then I discuss the fact that if we know the current through and the
resistance of a resistor, we can calculate the voltage that must be
across it. Then I refer to this as the "voltage drop" explaining that
if we measure voltages in a circuit with respect to some reference
point, that when we traverse a resistor in the current direction, the
measured voltage is higher on the current-in side and lower on the
current-out side, and the difference is IR, and that is called the
voltage drop. If, on the other hand, they first read or hear there is a
voltage drop IR when current goes through a resistor, it doesn't quite
sink in what is going on.
It's not a matter of one permutation being more correct, which, of
course, is not true. It's a matter of asking if one of the permutations
will make more intuitive sense to the students, and therefore it might
be beneficial to start with that one. I may be fooling myself, but I
think I = V/R and a = F/m are the more intuitive permutations of these
equations.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu