Yesterday a student asked me "why do you teach?"
Another student said "He wants to know why you don't go live your life?" and the first student said "No, I want to know why you teach."
I said I like the subject - math - because it was always fun. (A certain set of rules, different ways of getting the answer, but a specific answer. And I told them the joy was when you make a difference to someone.
It doesn't happen in every class. Some just want to be shed of you and move on. Some make so little effort in the class that they make no impression on you and you make little on them. But every now and then you connect with a student and make a major change in who they become.
I told the class about a boy I taught in 9th and 11th grades. In 9th, he was headed noplace in particular. In 11th, we connected and I started to make a difference.
Last year he asked me if I knew he was supposed to graduate form high school - because that was the path he was on in 9th grade. Now he has graduated from college, started his own business and has served as an inspiration for others.
And that is why I teach.
Is he a mathematician? No. But he is an awesome human being and I played a small part in that.