Final answer:
Prayer in public schools violates the Establishment Clause of the First Amendment, as the government cannot endorse or establish religion, and school-led prayers would result in such an endorsement.
Step-by-step explanation:
According to the Supreme Court, prayer in public schools violates the Establishment Clause of the First Amendment. The Establishment Clause prohibits the government from endorsing a state-sponsored religion and from favoring some religious beliefs over others or religion over non-religion. This clause has been interpreted to prevent public schools from organizing or facilitating school prayer as it constitutes an establishment of religion, which the government is not allowed to do.
Several landmark Supreme Court decisions reinforce this interpretation. For instance, in Santa Fe Independent School District v. Doe, the court found that student-led prayer at school events violates the Establishment Clause. Moreover, the Court has established three tests in Lemon v. Kurtzman to determine whether a law or act is constitutional under this clause: it must have a secular purpose, not advance or inhibit religion, and not excessively entangle the government with religion.
While the Free Exercise Clause protects individuals' rights to practice their religion, it does not permit the government to become involved in religious activities, which would be the case with school-led prayers. Therefore, while students are free to pray voluntarily and non-disruptively, official endorsement or organization of prayer in public schools is unconstitutional.