Thank you Drew for this question. I have pondered this often and hope that I reflect what I am about to say in my own classroom. In no particular order than the order they tumble from my mind:
1. Always continue in your own curiosity. Never stop wanting to know more about stuff in general and things your students might want to know about in particular.
2. Follows from 1. Share your curious thoughts with your students. (I suddenly hear Crosby, Stills, Nash, & Young..."Feed your children well...upon your dreams...").
3. Be fearless in the face of not knowing the answer yourself. And if you can't be fearless, be brave enough to live with uncertainty yourself. Teachers are not required to be the source of knowledge, rather they should be the source of questions, ideas on how to get to the answers sure, but not the repository of the answers.
4. (You asked about maths teachers specifically I will try to focus there) Love your subject, get lost in it. Right now my co-author Sunil is writing a book he is titling "Down the Rabbit Hole..." a phrase we chose for a chapter heading in Math Recess. He is doing so to allow himself the space to get lost in the maths. Be curiouser and curiouser about things you thought you once knew.
5. About that last point in #4. I have found through my 30+ years that there are always new ways to see the things that I once thought I knew completely. For instance, when I met Dr. James Tanton and started to experience Exploding Dots I came to a much fuller and richer understanding of the ideas of polynomials in general and the specifics of arithmetic. Two subjects I could have argued I knew A LOT about before. Or like in the past few months, Dr. Po Shen Loh revealed a method he was clarifying for himself for the first time, regarding solving Quadratic Equations, you can watch this here. Both of these mathematicians found new ideas for themselves within what is arguably "Elementary" mathematics. Never diminish the power of mathematical thinking.
6. Study the history of mathematics. This is far more critical than I once believed. But maths are a human creation, and therefore have human stories that surround them. Knowing those stories helps to contextualize and demystify mathematics. Also, studying the history of maths is a fabulous means to celebrate the diversity of cultures within your classroom. This process is known in some circles as re-humanizing maths and I am fond of that characterization.