I haven't been instructing for very long, but my students thus far have been pretty mainstream and predictable. Some are good, some need a lot of hand holding. I think this weekend I had one of those rare, magical occurrences that just make you go "wow". 
My student: a 20-something Asian girl driving a new-ish BMW 328xi, like this:
With different, cooler wheels and some carbon fiber look stuff. It's an automatic. She's had one prior track day, at a different track. She's autocrossed some. She's so thin, I'm not sure she weighs enough for the seat to detect her for airbag activation. So what would you expect your weekend to be like?
Our first session we go out. The transmission does all the shifting. She figures out the general line quickly, and we work on hitting individual marks. I can tell right away she is FOCUSED and BRAVE (not to be confused with FEARLESS). I can tell her to do something once, and she does it. She effs up, and self analyzes. Hmmm. This is looking like it's going to be fun. Too bad about that wonky autobox though, as it's fighting her on corner exits.
So I offer her to ride with me in the instructor session in my Spec E30. Loud, harsh, brutal. She's all over it. I tell her like I'm telling you, I'd be lying if I didn't admit there is a bit of showing off when instructors take students out. I don't go 10/10ths, but if they aren't screaming during the warm up lap, I turn the wick up to where it's fun for both of us. I hear not a word from the right seat. Do a "thumbs up" check and get the affirmative, so we keep going. I point out a few things and also fess up when I do wrong (which is often enough to keep my ego in check). We come in and I get "awesome". 
So after my "don't try what I did" speech, we got out for session two. She's done sandbagging. Her hand uses the autostick. She's hitting apexes like they are a bad ex-boyfriend. The traction control is off; the X-drive makes this a non-issue. She's smooth, fast, and totally serious. I'm in awe. Every little squiggle of pushing it a smidge past where it should be is corrected with the precision of a ninja.
She's got The Gift.
It is rainy for our second day and she adjusts perfectly. As the track dries out, she's driving this giant pig as fast as I probably would, and in total control. She is Master of her universe. The last session, I say almost nothing. I just let her drive, enjoying the dance, watching one of my buddies chasing her in MY car (far lighter, far stickier but less power). If we had been able to work on her late braking she would have smoked him, but it's wet and we agree today isn't the day. When our day is done, I do my best to tell her how good she is without making her cocky. Yeah, the car is really, really good and makes some of it possible, but the car isn't nailing the shift points, throttle application out of turns and corner entry points. I basically plead with her to keep pursuing this sport.
In the course of our conversations throughout the weekend, I learn that she only got interested in driving after purchasing the 328. She's a highly educated, very smart girl (probably with a super IQ) and quickly found the internet forums, local BMW tuner shops, etc. She tells me the autobox was a compromise for the urban driving she does and that it fought her when she first got it, so she took it to the dealer and told the service department to "reflash the berkeleying thing so it works right". 
She's totally got it bad, and she's loving every minute of it. Oh, and she bought a E36 M3 to turn into her track toy.
