Mr. Broeren said he could not discuss specific students or complaints, but added that the district took any reported bullying seriously and was willing to try any measure that could help tackle the complex issue. Doing so requires parents to be aware of their children’s behavior and to be active in changing it, he said.

“By its very nature, bullying is not overt,” Mr. Broeren said. “Someone doesn’t holler down the hall in earshot of adults.”

Wisconsin Rapids, in the central part of the state, is not alone in looking to parents to solve the vexing problem of bullying, which 20 percent of students ages 12 to 18 experience at school each year, according to the Department of Education. Several other municipalities, and at least one state legislature, have considered fining — or even jailing — parents whose children bully.

Where such legislation has passed, though, the penalties are rarely imposed. Local officials compared the ordinances to truancy laws, acting as deterrents rather than punishments. Still, some critics say the bills could backfire and unfairly punish parents for their children’s actions.

Dr. Amanda Nickerson, who directs the Alberti Center for Bullying Abuse Prevention at the University at Buffalo, said she was skeptical that being fined would suddenly motivate parents to become involved in changing their child’s behavior. She said the key to engaging parents was to set up meetings between them and teachers to discuss how to encourage good behavior, before seeking any kind of penalty.