Here is a case of a public school teacher getting fired for expressing political views. The teacher, Deborah Mayer, said in response to a student question, "I honk for peace," and "People ought to seek out peaceful solutions before going to war." Apparently some students (or their parents, more likely) were upset that Mayer was "bashing Bush," and Mayer lost her job.
This is a tricky topic, because it is difficult to say that public school teachers have complete free speech rights; they obviously shouldn't be politically or religiously indoctrinating children. But, can they express opinions in response to questions? The lawyer for the school board certainly doesn't think so. He argues that, "teachers don't have First Amendment rights in the classroom because they teach a curriculum decided by state and local officials."
This is also too extreme. This would imply that teachers are, more or less, robots that simply enforce the will of those who determine the curriculum. The only speech that is protected is that which supports the curriculum. The lawyer for the board noted, "If they disagree with the curriculum, they can go somewhere else." Real mature. That sounds like a redneck who says "hey you lib'rals! If you hate America so much, why don't you just leave!?" Of course, I don't think teachers should be able to ignore the curriculum, but teachers aren't just robots to enforce someone else's will (at least good ones aren't). They want to teach children, not just deliver government-approved information (the distinction is subtle, but I think the ability to see it is important for anyone interested in education/academia).
Again, this is tough. We don't want teachers to simply do whatever they want (although, a select few teachers would certainly put this freedom to great use), but at the same time, they shouldn't just be information spewing machines. I don't know where to strike the balance, but I definitely don't think Mayer should have been fired for simply responding to a question with her honest opinion.
So, anyway, the lower courts have so far sided with the school board, and now Mayer is appealing to the Supreme Court. It has not yet determined whether or not it will hear the case. Here's hoping it does, because while there are famous cases outlining students' speech rights in school, the area of teachers' rights is rather ambiguous.