I definitely agree that teachers in many areas are underpaid, but I think a single nationwide minimum wage for teachers is a bad idea. There is just way too much variability in cost of living between different locales for a single amount to make sense. Would much rather it be based on some localizable metric, e.g. X times the median apartment rent or some such (don't want to get caught up on the details, other than to say it should take some form of regional COLA into consideration).
See this is something I wish people would understand more when talking about economics things like a federal minimum wage in a place like NYC or Cali may not sound like much but in rural Missouri or Arkansas that could bankrupt most of the businesses overnight.
If only we divided the country into geographical areas that could each be responsible for administering their own issues for the most part, so they would have a better understanding of the costs and tradeoffs, and be able to live they way they want without enforcing their way of life on people halfway across the country, and instead of the people in a few big cities and Washington DC ruling everyone from afar each regional area could be self governed.
Oh well that sounds like nonsense anyway after all the same things that are good for NJ are obviously the way things should be run in Montana .
I don't see why this couldn't be done on a smaller (state or county) level instead. If someone starts offering an attractive starting salary and that leads to better educational outcomes you would expect others to follow (at least make it easy to campaign on it).
Edit: And obviously adjust the salary to match local conditions as you point out.