Don't know if DS is HG+ but he is in first grade and very advanced with math in particular (for instance can do long division word problems) and his current teacher is giving him the correct level work. The last teacher was a disaster. Current teacher did a lot of assessments to find out what he knows/doesn't know and prints out advanced level worksheets based on what he needs to work on next. I didn't ask for this, although I'm sure she figured out there were problems in the other school and that's why we switched schools. Although despite this she seems to be the type who is very involved, differentiates for other advanced kids, and would have done it if he had been there all along.
That is just this year though. Who knows what will happen next year, although she said she is going to pass on what she's been doing to the next teacher and talk to the teacher.
I think in public schools, unless there is a special gifted program, it all depends on the teacher and the attitude of the teacher. Some of them can't be bothered, and others totally get it. If the principal gets it, then the principal can help to make sure the child has a teacher that "gets it" each year. In our last school, no one seemed to get it. The principal's bad attitude trickled down to the teachers.