I think that the First Amendment's Establishment Clause does a fairly good job of delineating that school prayer in public schools cannot happen. The court has been fairly consistent in the last half century in its decisions about how secular ideas must be a part of the public school system. It is not seeking to eliminate religion as part of people's lives as much as ensuring that one specific set of religious principles are not advocated over others, not advocated by government over people, and/ or ensuring that the business of education in the school setting is not ensnared with the issue of religious worship. I think that the court rulings on these issues have suggested that the Establishment Clause along with the 14th Amendment ensuring that all public facilities be the benefactor of government action ensure that the school setting is not one in which prayer is evident. The recent trend towards "the moment of silence" is something that passes the "Lemon" test that the court developed in 1971 in that it does not "advance or inhibit religion" and does not increase the entanglement between government and religion. The secular nature of the "moment of silence" becomes part of what makes school prayer something that is not permitted by the Establishment Clause of the Constitution.