>All too often, students have no idea of what such "expressions" are talking about. So they are forced to view such formalisms as meaningless text with they are expected to perform data-processing tasks as prescribed by authors and teachers.
I think you hit the nail on the head - going back to Hansen's original questioning of how "X" was introduced in a fourth grade text book. A fourth grader may very well ask "Why? What's this all about?" -- the only answer that can be given in that textbook would be: "You'll understand later" -- a really crappy answer.
Instead, students should be introduced to formulas and become very comfortable that "expressions with variables" are much like a language to express meaningful things, long before they are asked to "solve for x".