Oh yes, discussion of pedagogy -- you're playing my favorite song! (not that I'm such a good singer, I just love to think of what helps people learn statistics better)

I have to admit to being a hack, but my gold standard for good teaching has long been a friend of mine who is a professor over at NCSU (Dave Dickey, for those of you who know him). I've watched him teach and taught with him many times over the years, and I've observed one thing he does with every new concepts he introduces:

1. Present a simple, folksy analogy with no math. Talk about visiting Mars, or a mother snake, or earthquake-resistant buildings in San Francisco, or something that gets people's imaginations warmed up.
2. Dive into all the math of what you're teaching.
3. Present the applied statistical concept in a data-specific context to show why it works.

I've tried to use this approach in discussing new concepts and the beauty of it is that everyone in the room can respond to at least one of the 3 explanations.

So I'm a hack because I borrowed that strategy. but at least I'm borrowing from one of the best.