So much for the First Amendment.
The First Amendment doesn't protect your right to make death threats....
Whether or not this girl's story qualifies as such is a different question -- I'd have to see the story first, and understand the context in which it was written. (For example, did she have an actual antipathy toward her 6th period math teacher?)
I NEVER trust media articles on topics like this. They're invariably written from a viewpoint that is sympathetic to one side ... usually the student's.
This case has absolutely nothing to do with the First Amendment.
A student in my fifth grade class was suspended from school for a week because he called the teacher a "****ing b****."
Were his First Amendment rights violated? After all, he was just expressing an opinion.