I am a secondary school teacher in New Zealand and what is being described in the initial post is what we call "reflective practice". Good teachers must always look to better themselves for the sake of their students. I'm sure this is where beginner's mind fits in as well. Be open and attentive to new ways of knowing and you cannot help but become a great teacher.
In the sports community it is called deliberate practice. 10,000 hours of deliberate practice to "master" something. "deliberate practice" is that which is done while actually paying attention to what you're doing, and not having a side conversation about yesterday's party while looking like you might be practicing (say) Ikkyo.
I view a coaching position as one where the coach guides the athlete through discovering how to do something. To some extent, the system of showing a technique four times and then saying "please practice," with our without the name of the attack and technique, is an approximation of this observational (and perhaps "intrinsic") learning.
In my work, if a crew of beginning rowers is "sitting" angled down on one side or the other (an "eight" is 18 meters or almost 60 feet long and only about 60 cm or two feet wide), instead of telling them to move their oar handles to make the boat sit level, I'll ask them (sometimes repeatedly) "What do you have to do to make the boat level - look around, what do you (etc.)" They figure it out in a few minutes. I've found over the years that this works much better than telling individuals to raise or lower their oar handles. They've figured out the solution, rather than me telling them. FWIW, I've changed the way I coach rowing since starting Aikido in 1993.