John Denker recently wrote “. There is no law that says pedagogy must recapitulate phylogeny. That is, retracing history is rarely the best way to teach a subject or to solve practical problems.”
I’d like to see comments of a proposed re-ordering of topics that I’ve been thinking about. In the topics of gravity and electricity we usually introduce the forces first. For gravity we start out with the force that a planet (usually Earth) exerts on a mass, m, and state
F_ = mg_ (the “_” indicates a vector).
Aside: Unfortunately, most books call g_ the acceleration due to gravity, or worse, the acceleration of gravity. I’m starting to call g_ the gravitational field (fighting the book language in Knight), and if the gravitational force is the only force acting when we apply Nt 2nd Law, we get ma_ = mg_, and a_=g_, so the acceleration of m, because it’s in a gravitational field, happens to have the same magnitude and direction as g_. I think it’s much more powerful conceptual language if we call g_ the gravitational field.
Now, back to the main idea. These forces involve the interaction of two items, either 2 masses (for Newtonian treatment of gravity) or 2 charges. Then, we “back-door” the ideas of fields and students are much confused. Would it be better pedagogy in the long run to introduce the field associated with a mass or a charge FIRST, then talk about the force when a 2nd item interacts with the field?
As an example: In the space surrounding a charge there is something called a field. It is a vector. The direction of that vector is either toward the charge or away from the charge. It’s magnitude is |E_|=|kq/r^2|. Explain each term. Emphasize the sign of the charge tells us whether direction is away (q>0) or toward (q<0) [You could do this in terms of r-hat if you want and stay away from absolute values, etc]. If there are two charges, calculate the vector for each charge at a point in space then add the vectors. That’s the electric field, E_, at that point. When a charge Q interacts with an electric field that is not it’s own (must come from other charges, but right now we don’t care where), it experiences a force F_ = Q*E_ . Then say, historically there is a relationship called Coulomb’s Law which looks like |F_| = kqQ/r^2. Talk about various detailed relationship of signs of charges.
If we want to build the idea of masses or charges interacting with gravitational or electrical fields, resulting in forces, shouldn’t we introduce fields first?
Enough rambling… ready, aim . . . (Looking for comments on the main question, not rabbit trails about the details of the example).