I know there are a variety of opinions on follow-up emails after interviews. I tend to side with "do it", because it probably won't hurt and in some cases you might be able to add something key that you didn't get to in the interview.
Which I think applies in this case. I interviewed for an elementary teaching position earlier today and one of the questions asked was how I would implement a specific STEM program they would want me to teach. I'd never heard of the program, and it wasn't listed in the job ad either, so I'm not sure how I WOULD have heard of it. I was honest about the fact that I had never heard of it, and then gave a sort of generic response about how I'd implement a STEM program without really addressing the specific program they use. To be honest I kind of rambled a bit without saying much and it felt like the low point of an otherwise solid interview for me.
Now that I've gotten home I've been able to research the program they use and have a much better sense of what they are going for and how I would implement it. I was thinking of sending a thank you follow-up email anyway, so I thought I might also write a bit informing the interviewer (principal of the school) that I've looked into the program and give him some ideas I have for implementing it. (I'd keep it short, just a line or two, I know no one wants to read an essay in a follow-up email.)
The problem is, I don't have his email. Everything was set up through the phone. Being the principal of a public school, however, his email was easy enough to find, as it is right on the home page of the school's website.
I'm just wondering if it would be viewed as odd or unprofessional for me to send a follow-up email to that email account since it was never actually given to me personally. Is this common practice or frowned upon?