I think that is a spectacular explanation, DAD22.
I had not one bit of trouble "showing work" in calculus and beyond-- but prior to trigonometry or solving simultaneous equations in high school mathematics, I was always sort of flummoxed by what was intended by that statement.
I preferred-- as a teacher of college chemistry, I mean-- to suggest that students should "demonstrate THEIR process" for an outside observer/reader so that the observer could replicate that problem-solving strategy.
That's basically the basis of scientific (and mathematical) communication at those higher levels anyway. It just happens that it's also convenient for catching errors in a pedagogical framework, too.
