The best "ultimately practical" resource on composition is the work of people like Atget, HCB, Walker Evans, Gene Smith, etc., etc. You can't teach composition with words.
But you can use words and your index finger to point out an element of a composition, or a relationship between elements, that your student might not have seen, or if seen, meght not have registered, or if registered, might not have realized its importance to the effect of the picture. And if that element, or combination of elements, is something that the works of the photographers you name treat in a similar manner, you begin to have a principle of composition that seems to hold true for the style, or styles, of those photographers. Other photographers might or might not treat that aspect of composition in the same way, adding evidence for that element as being more universal or more associated with a given style.
Either way, the words and index finger can help to produce an "aha" moment for a student for whom the issue might never have been seen, or might have been perceived at a pre- or non-verbal level but not crystallized into conscious awareness.
I would also like to state that some of what we do and value in photography works because of fixed principles of perception derived from our neurological makeup, such as seeing certain configurations more quickly than others, etc. These would underlie commonalities in the styles of various art and probably across cultures. On the other hand, ways of using (or not using) these underlying neourological realities of human sight and perception also vary from culture to culture as the meanings of the perceptions become more, or less, valued. Even within a culture, the meanings and values change over time...or not.
A musical example: I was taught as a child that "music is a universal language." I also was taught that music in a minor mode often represents sadness, while a major mode represents the opposite. After learning to hear and interpret that way I discovered music from the middle east which, more often than not, was composed in minor modes yet sounded happy to people of those cultures.
I had another shock when a professor from India taught me a lesson when I invited her to hear my collection of recordings from India. She asked if I thought I understood something about the music. She did not mean the musical theory of the music, but the emotional content. She gave me a "drop the needle" test (remember phonograph records?). When she asked "happy or sad?" I would respond. Even though I knew these recordings by heart, and despite the fact that I was a professor of muscal comosition and theory, my "score" on 25 musical examples was not only poor, but less than I would have achieved simply by chance! So much for the "universality" of "the musical language."
A problem in trying to teach anything about composition, musical or otherwise, comes in how elements of style are valued. We can find what appear to be common principles in a given style of art (or specifically, photography), but this is analysis of what certain people did in their photographs. If we then teach these elements of style, our students might learn that photography that does not follow those "principles" cannot be "good" photography, rather than learning that "this is what these photographers did in that style."
I think that Caponigro's approach to isolating elements of composition can, in the best case, give anybody from snapshooters to professionals, a way of learning to be more aware of what they potentially can see and how to explore the use of these elements to make something that works for them.
JPC has done a nice job of isolating elements of composition, without making value judgments about them.