Wellll, I don't see the problem with scheduling
a time to sit and observe in your child's classroom - this was actually suggested to me by our principal when we had some issues with DD's teacher a few weeks ago. But, just showing up, IMO, is not really every appropriate - even if it's just to visit b/c you truly miss your kid during the day (me - gosh, the day goes by too fast
). If you don't trust your child's school enough that you have to show up unannounced, well, then, you should find another school.
I don't think most teachers mind volunteers - again, assuming you have signed up and scheduled this in advance, but that's entirely different than just wanting to hang out with your kid while they are at school. That is distracting to the kid, the other students, and especially the teacher.
In preschool, it's a bit different, IME. The kids are playing most of the time they are there, and there are usually plenty of things for parents to jump in and do. My DS's pre-k teacher was completely okay with parents just randomly showing up - not that I ever did this, though. But I think once they are in kindergarten and beyond, and even younger depending on the program (such as with Montessori, it wouldn't be helpful or appropriate for me to show up to visit in my DS's 3-6 M class), that pretty much ends.