In Florida, the teachers’ union has lobbied to limit the use of standardized tests, and the governor last week signed a bill that limits the number of hours students can spend taking them.

The union in New Jersey financed an advertising campaign in which a grim-faced father talks about his son crying because of tests.

And in New York, where local unions have worked closely with parent groups that oppose testing, the president of the state union went so far as to urge parents to opt out of the annual tests, which began last week.

After several years in which teachers’ unions have been hammered on the issue of tenure, have lost collective bargaining rights in some states and have seen their evaluations increasingly tied to student scores, they have begun, with some success, to reassert themselves using a bread-and-butter issue: the annual tests given to elementary and middle school students in every state.