This is unbelievable even to me, but...I think I would most enjoy teaching a secondary-school math class. Things like algebra, trigonometry, maybe even a little intro-level calculus.
Math can be hellish when you have a bad teacher, or when there's too much pressure on you to understand things immediately, but if you're lucky enough to get through to the other side with a real understanding of what you've learned, going back to that older stuff is actually kind of fun.
It's only now that I'm halfway through college that I realize the significance of some of the "nonsense" I was forced to memorize back in high school...if I knew now what I knew then (and there isn't a whole lot of difference, tbh...) things would have been a lot easier. I'd like to share that perspective with people who don't have it yet.
Besides, as someone who struggled with those topics, I understand people's frustrations. ^^; I also understand that people learn math in different ways.
Some people are good at memorizing 'nonsense'; some people really won't get it until they have a concrete understanding of what that stuff on the paper actually means.
Some people ace concepts right away; some people need more time to digest them...and those roles can reverse depending on the concept.
Some people need visual aids; some people would rather be stabbed than draw a graph...I've been in both camps. XD I used to love graphs; I still draw li'l unit circles and triangles for trig stuff. But on the 3-dimensional plane, graphs stop being fun REAL quick. 6_6; I guess that also depends on the concept.
In conclusion, I guess I'd like to teach that kind of math because I understand it well AND YET I still remember what it was like to not understand it at all.
...Besides, nothing in this icebreaker says anything about teaching in an actual school, or for a whole year, or to actual children. I could be teaching an online GED course to adults for 6 weeks; I'd be okay with that. ^^