I had originally planned to stay out of this round of this perennially
recurring topic. But after taking leave of my senses, I thought, "why
not contribute something?".
First off, I do side with the forces who want to restrict the use of
the phrase "acceleration due to gravity" when referring to the value of
g--esp. when in the company of beginning students. I would prefer,
initially, at least, "the strength of gravity", "weight-to-mass ratio",
"surface gravity", etc. (almost anything except phrases mentioning
"acceleration"). Later, I would relax a little, after the students
had (one would hope) safely understood the general difference between a
general acceleration a and a particular local value of g and then
maybe mention that g could be considered as "the freefall acceleration"
*after* the special case of ma = mg --> a = g for the *special case* of
freely falling bodies has been understood. When it comes time to
introduce fields to the students then we could be begin to refer to g as
the "gravitational field (strength)".
With all this said above, I have an important point of near agreement
with John D.concerning the use of the term "acceleration of gravity"
or similar "acceleration" containing phrases in connection with g. That
point concerns the time when the equivalence prionciple is to be
covered. It is a fact that -g (the "-" is important here) *is* the
*accleration* of the local frame of reference used (in whatever relevant
instance where g occurs with a nonzero value) with respect to the class
of locally inertial frames, i.e. freely falling frames. Similarly, we
*can* consider +g as the *acceleration* of the class of locally inertial
or freely falling, frames w.r.t. the frame actually to be used at hand.
Thus if a local nonzero value of g occurs in some useful frame of
reference and in that frame a very massive nearby body's surface is
locally at rest w.r.t. the origin of its coordinate system, then we can
consider g as being determined primarily by the gravitational effects
of that nearby celestial body, and we would have the right to consider
the above-mentioned local acceleration of the freely falling w.r.t. the
frame used as being their local acceleration due to the gravity (or
gravitation if one wants to use a longer word) of that nearby massive
body.