In a historic final day of the Supreme Court term Thursday, the justices by a 5-4 vote struck down plans in Seattle and Louisville, Ky., that used race as a factor in making public school assignments.

With both sides invoking the landmark case Brown v. Board of Education — either to attack consideration of race by public schools or to support it — the decision in Parents Involved in Community Schools v. Seattle School District No. 1 and Meredith v. Jefferson County Board of Education represented a major doctrinal shift that can be traced to the Court’s new members, Chief Justice John Roberts Jr. and Justice Samuel Alito Jr.