During oral arguments Monday, the Supreme Court’s two newest justices seemed to be on opposite sides of a major free-speech case, forecasting possible sharp divisions among justices on the power of public-school officials to censor students.

The case Morse v. Frederick began in 2002 when Joseph Frederick, then a Juneau, Alaska, high school student, unfurled a banner bearing what even he says was a nonsensical message: “BONG HITS 4 JESUS.” Principal Deborah Morse, interpreting it as a pro-drug message, told him to take it down and suspended him when he didn’t.