The split announced Tuesday affirms a federal appeals court ruling that lets teachers' and other public employee unions continue collecting service fees from non-union members.
The justices appeared sharply divided over whether religious schools must take action if they want to opt out of providing contraceptive services under the Affordable Care Act.
The justices unanimously upheld the right of a tribe in Nebraska to impose a liquor tax, in a case watched by school districts on or near American Indian reservations.
Merrick Garland, a federal appeals court judge, has also been a lawyer in private practice, a federal prosecutor, and a U.S. Justice Department official.
James E. Ryan, dean of the Harvard Graduate School of Education, aims in his blog to ask the right questions about school policy.
The justices refuse to take up cases on off-campus student speech, outsourcing of education to a private religious school, and teacher pension contributions.
Cases involving student off-campus speech, state support of religious schools, and the outsourcing of education have been appealed to the justices.
Justice Antonin Scalia, found dead Saturday at age 79, brought his conservative outlook to many education cases in nearly three decades on the Supreme Court.
The state's highest court has revived a lawsuit brought by cheerleaders who were barred, for a time, from displaying banners with religious messages at school football games.
The justices made retroactive their decision of four years ago barring life-without-parole sentences for murders by all but the most incorrigible juvenile offenders.