A Utah student group was called “Black and Proud.” The principal had it renamed. A New Hampshire history teacher used to discuss current events in a unit about race and economics. No more. And Florida school officials canceled a lecture for teachers on the history of the civil rights movement while they considered whether it would violate state rules.

In 13 states, new laws or directives govern how race can be taught in schools, in some cases creating reporting systems for complaints. The result, teachers and principals say, is a climate of fear around how to comply with rules they often do not understand.

The new measures typically bar teachers from suggesting the United States is a racist country, from elevating one race or gender over another or implying that one race is superior. So far, they have not triggered wholesale rewrites of the curriculum, and few educators have faced prosecution or punishment. Some teachers say they see no changes at all.

But many teachers nonetheless describe a chilling effect. They say they now err on the side of caution for fear that a student or parent might complain, resulting in a public battle — or even, in extreme cases, that they might lose their jobs. In New Hampshire and Oklahoma, which allow anyone unhappy with a teacher to complain to the state, there is an extra layer of fear. Teachers found to be out of compliance can lose their teaching licenses.