The answer is ... maybe.
Why a Minute of Silence May be Impermissible
During the 1980s, school prayer advocates were in search of new approaches that might prove constitutional. The so-called "minute of silence" has proven the most successful strategy, despite an early setback in which Alabama's requirement that school children observe a minute of silence each day was held unconstitutional by the Supreme Court in Wallace v. Jaffree (1985).
This law was struck down because the silent observance was described as a time when teachers would instruct willing students to pray, and the others to meditate silently. The suggestion by a state actor that students use the time for prayer amounted to a state endorsement of religion, which is impermissible under the First Amendment.
To proponents of prayer in schools, this may seem to be an overreach by a court dead set against allowing prayer in schools. However, a teacher's suggestion that students pray can have real consequences for students.
In Walter v. West Virginia Board of Education (1985), a Jewish student chose not to pray during a state mandated moment of silence and read a novel instead. That student's classmates later told him he should pray, otherwise he would "go to hell with the rest of the Jews." Baptist, Roman Catholic, Lutheran, and Muslim students also objected to the moment of silence. The trial court struck down the statute in that case, because it inhibited some students' abilities to practice their faith and had the effect of advancing religion during the school day.
Why a Minute of Silence May Be Permissible
However, states subsequently crafted laws that did survive constitutional review. One example is Virginia's minute of silence law, which requires children to begin the school day with a minute to "meditate, pray, or engage in silent activity." In July 2001, a panel of the 4th U. S. Circuit Court of Appeals upheld the constitutionality of the law, noting that it "introduced at most a minor and nonintrusive accommodation of religion" and, because it allowed any type of silent reflection, served both religious and secular interests. The U. S. Supreme Court declined to hear an appeal in the case, thus upholding Virginia's law. Legal observers predicted the law's success would lead to more such legislation in other states; as many as 18 states already permit a minute of silence under law.
The reason these "minute of silence" laws are upheld is because the state imposes absolutely no pressure on students to pray or engage in any kind of religious activity. Students may study, read, meditate, or contemplate anything they wish. Many schools have minutes of silence to recognize a great tragedy, such as the death of one of their fellow students. Once a teacher suggests that the moment should be used for prayer, the minute of silence is considered to advance religion and is constitutionally impermissible.
For more information, see FindLaw's sections on Student Speech and on the Types of Schools children may attend.