Unfortunately, you are wrong. A lot of twists and turns in following laws regarding educational instituions. First was "Gun Free Schools" law #1 passed by Congress. This was thrown out by the courts as being unconstitutional. Then, Congress passed "Gun Free Schools" law #2 which allowed the states to exempt certain classes of individuals from the law. So, if a state licenses an individual to carry a pistol, and does not explicitly declare schools to be off limits, then it is legal for that person to carry. However, most states with concealed licensing laws explicitly forbid individuals from carrying in schools. The only exceptions I know about are Oregon and Utah.
And just how, pray tell, does your comment show me up as "wrong?" Did you have something else in mind that you forgot to post? I suggest that it should be policy that teachers be trained and allowed to carry. How does that conflict with your observations? Or is that your all-occasion preface to a reply?
In Pennsylvania, the law prohibits carrying in a school 'except for lawful purposes'. Different jurisdictions interpret it in different ways. Some people have been prosecuted, but some DAs have said publicly that they will not prosecute someone with a permit if they are behaving properly. Most permits are issued for 'self defense' and since that is a 'lawful purpose' should exempt you from prosecution.