Which case recognized that public schools are limited in how they can address free speech?

The case that recognized public schools are limited in how they can address free speech is Tinker v. Des Moines. This landmark Supreme Court decision, decided in 1969, established that students do not lose their First Amendment rights to freedom of speech when they enter school grounds. The ruling emphasized that student expression is protected as long as it does not cause substantial disruption to the educational process.

In this case, the court upheld the right of students to wear black armbands to protest the Vietnam War, reinforcing the idea that schools must respect and facilitate student speech while also being able to regulate activities that could lead to disruption. Tinker v. Des Moines set a significant precedent in balancing students' rights and schools' authority, laying the groundwork for how free expression in educational settings is understood.

The other options, while relevant in their own contexts, do not specifically address the limitations on student speech in public schools in the same way that Tinker v. Des Moines does. Hazelwood v. Kuhlmeier addressed the rights of school officials to control student publications; Engel v. Vitale dealt with school-sponsored prayer and its constitutionality; and New York Times Co. v. Sullivan focused on press freedoms regarding public figures, illustrating different aspects of free speech