I identify as a teacher and a mathematician, but I only get paid as a teacher. I'm sure that I do less research than if I were paid as a researcher (for reasons of akrasia if nothing else), but I do enough to sustain my personal sense of identity. (I do it here, if anybody cares. If I were a little more organised and active, I'd do it here too. Mathematics journals are no longer used to disseminate information, but only to advance careers, so I have no need of them, although some yet further effort in that direction could get me published too if it mattered to my sense of prestige.)

On the other hand, I'd like to shift more out of teaching in classrooms into tutoring individuals, which is even more fulfilling. (It's arguably less efficient, although given how the normal college curriculum is designed, at least here in the U.S., I don't really believe that. People in classrooms are mostly studying what they do not want to learn and what will be of no use to them except in the next class, and I'm starting to feel a little dirty working in this industry. Tutoring does not entirely solve that problem, but at least the students are interested at the moment that I interact with them.)

But tutoring doesn't pay nearly as well as classroom teaching, and my budget is thin as it is. So although (for personal reasons) I'm very unlikely to move to Australia (eta: plus I'm over 30), I read all of this discussion with interest.