An artist is invisible in their work.
Despite this, I can wander around art museums with my mom guessing at the particular Impressionist who painted something and we get it right often enough to earn a solid B.
A masterful performer is one who makes it look easy.
If you don't know what's going on, dressage looks like the easiest equestrian sport. Somebody sits on a horse, doesn't move much, and the horse backs up and walks sideways and maybe dances around a little. What you can't see, but can probably guess at, is the incredibly amount of training that goes into preparing a horse for this sort of competition. You can't ask any old hack to do a capriole and expect results. The riders, too, must be the best. A beginner can get on a horse and yank its head around and kick it and get it to go the right way at a trot, but it takes someone who knows their stuff to communicate with miniscule movements of feet and hands while looking relaxed.
I was going to keep going, but I think the analogy is obvious. The masterful invisible teacher does a lot of work to become invisible. Their presence, in fact, is necessary for the creation of the masterwork, the classroom full of independent students engaged in their learning. You can't get the same result from throwing a bunch of kids into a classroom with some computers and a vague goal any more than you can get that dressage performance from throwing me on a camp pony.