Oh and the argument doesn't have to be (exclusively) verbal. It can consist of diagrams and symbol manipulation.
The only method I've seen work for a large set of students is to show lots of examples of what "good" and "not good" versions of "show your work" look like. Preferably on problems that look similar to the homework problems. And emphasize this during lectures.
E.g. after doing a derivation on the board: "by the way, this is what I expect to see when I say 'show your work' on a <insert problem type> problem."
Nobody ever explicitly tells you this, but a few lucky students guess it at some point, preferably long before they get to college.
Teaching is an art. To some extent, "show your work" is an art as well. The techniques of art are never perfectly well defined, and are always somewhat arbitrary, but people do manage to learn it. Learning an art by imitating the masters is as old as the hills.
Perhaps my biggest frustration while teaching the algebra course, was not that I was confused about "show your work" means, but that there was such a gaping hole in the preparation of my students.