Actually it is constitutional. The bill of rights was originally intended to apply ONLY to the federal government, not the states. After the 14th amendment was passed MOST of the rights guaranteed under the bill of rights were incorporated through it to apply to the states.
However, the Supreme Court held in Presser v. Illinois, 116 U.S. 252 (1886) that the Second Amendment limited only the power of Congress to control firearms, not the state. Thus, the Second Amendment wasn't incorporated in the 14th amendment. The state thus, due to the Tenth Amendment, could control firearms. School property is property of the district and the state, thus under the Tenth Amendment they can restrict gun possession.
If your position is correct, then why the need for a conceal and carry license? Isn't your state acting unconstitutionally by making you pay a fee, take a class, and get a license to conceal and carry? Why can't you walk into your governor's mansion brandishing a gun? Why can't you walk into Congress, or hell, the White House with a gun in your hand?
The point is you're just flat out wrong, Pro. Your interpretation of the Second Amendment couldn't be more misguided and incorrect. The federal and especially the state CAN tell you whether you can carry a gun onto public property. You can still carry a gun all you want, your right to keep and bears arms aren't being infringed, you just can't walk onto school property. Just like you can't walk into a courthouse with one. Just like you can't walk into Congress with one. Just like you can't walk into the White House with one.