This is the 1st Amendment:
"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances."
I'd say that if you ban prayer from public schools, or anywhere for that matter, that is in violation of the First Amendment, not in recognition of it ("or prohibiting the free exercise thereof). The "separation of church and state" has been incredibly misinterpreted.