Thanks, Bones. Your explanation was pretty much what my intuition was telling me. From wandering around these forums, I get the impression that there is no agreement among the experts on which approach is best.
My impression, from this and other sites and lots of reading and conversation, is that there is something of a consensus around this idea: unless you are coaching athletes with great natural speed, and especially if you are coaching beginners as you and I are, short to long is the better approach.