First amendment in public schools

In the context of public schools, the U.S. Supreme Court has expressly recognized, in Tinker v. Des Moines School District, that neither "students nor teachers shed their constitutional rights to freedom of speech or expression at the schoolhouse gate." On the other hand, the Court has also recognized that, in light of "the special characteristics of the school environment," public school officials may restrict expression that would "materially and substantially interfere" with the core activities of the school. Thus, in Bethel School District v. Fraser, the Court upheld a public high school's decision to discipline a student for using "vulgar and lewd speech" in a public assembly because such expression "would undermine the school's basic educational mission." Similarly, although a public school may not generally deny a student's right to speak or to access information on school grounds or through school facilities, it may restrict expression or access to information that "would undermine the school's basic educational mission," so long as school officials do not attempt to deny access to ideas because they disagree with them.

Source
National Research Council, Computer Science and Telecommunications Board, "Youth, Pornography, and the Internet" §4.1.7 (Dick Thornburgh & Herbert S. Lin eds. 2002).