professing vs. teaching

I cruised down to teh math class I'm sitting in on, a bit late 'cause students were asking questions and 'cause they just had a test so that I figured initial time would be spent returning it.
Was it the right class? I checked faces; the students were the same, but a different teacher was expounding on exponential rules. He asked whether the regular teacher went through the notes step by step or skipped around... he skips around.
It's funny, it wasn't at all a bad delivery, but it truly highlighted the way the teacher who knows the students would "read" them. This fellow's "skipping around" was to summarize the rules... basically get straight to the "conclusion," without the development experience. Anything to the zero power is one, and zero to the zero power is undefined.
He asked what 2x^0 was... and they discerned that it was 2. (6x)^0 would be one, of course... but when they gave the expected wrong answer to 6x^0 + x^0, he slapped his thigh with his paper impatiently and pointed out that they'd just correctly said 6x^0 was 6... but the other subtle difference was the way he simply rattled off mathematical terms, whereas their regular instructor somehow phrases things with an awareness that no, they don't speak this language in their sleep... they don't know offhand what 15 squared is (this guy ... barked is a *tad* too strong a word, give me time... "no calculator, what's this?" to a problem including that, and yes, a student could rattle it off but yes, you just alienated five more.)
'Tis that delicate path of having high expectations but maintaining sensitivity. I loathe and despise the idea that we should abandon either.