Superintendent Jane Pryne, in an emailed statement while attending a conference out of town, said the district already has a policy in place regarding politics in the classroom and that the issue has been addressed.
Port Angeles parent Cynthia Deford, whose daughter attends Steven Middle School, said she wants more to be done.
She said last week that she wants an apology and sensitivity training for teachers.
Neither Pryne nor Deford would identify the teacher after requests from the Peninsula Daily News.
Deford, in her online petition discussion, indicates that the teacher in question is male and teaches mathematics.
Deford launched an online petition at tinyurl.com/cjcgw99 on Nov. 10, saying the teacher wore the political button urging a no vote on Referendum 74, which legalized same-sex marriage in the state in class during the days before the Nov. 6 general election.
The button's message was "No on 74: one man + one woman = marriage," Deford said.
Referendum 74 won 53 percent approval statewide.
Clallam County voters rejected the measure by 53 percent. Jefferson County approved it by 64 percent.
Deford, who has a same-sex partner, said that her child, who she does not want to identify, came home after school and told her about the button worn by the teacher.
The button surprised and offended her daughter, Deford said.
Deford said she thought the teacher should have known better than to wear a political button of any kind while teaching class.
"It just shocked me that it happened here," Deford said.
Stevens Middle School is a very good, award-winning school, she said, and her child likes it.
Her petition says: "Urge the Port Angeles School District to prohibit politicking by teachers in the K-12 classrooms. This would not affect balanced discussion of political issues in civics, history, social sciences, etc."
Deford also writes: "My daughter lives with myself and my lesbian partner. My daughter loves me very much and we have a good family relationship.
"But [until this incident] she also thought highly of this teacher. Now she is uncomfortable with him and does not want to go back to his class.
"Now she has to worry about discrimination where she didn't before."
As of Saturday afternoon, 159 people had signed the petition, which says it is to be delivered to Pryne and Deford, as well as Stevens Middle School Principal Chuck Lisk and President Barack Obama.
Most of those signing the petition are from communities on the North Olympic Peninsula, but signatures also appear from California, Oregon, Arizona, Texas, Massachusetts, New York and Hawaii.
Pryne, in her email message, said she cannot comment except to say that a policy is already in place and that the district has dealt with the issue.
"I very much appreciate the concerns and input by these citizens," Pryne wrote.
"The Port Angeles School District has both a policy and procedure that provides that employees may not campaign for a political candidate or for a political issue during school hours on school property.
"Of course, teachers have the right to engage in political activity off campus and on their own time.
"The petition here arises from an incident that has been addressed by the district," Pryne wrote.
"Of course, I cannot comment on the specifics of this confidential matter involving employees and students."
The district's Procedure 5252P, Part C, directly addresses the issue:
"An employee may not campaign for a political candidate or for a political issue during school hours on school property."
In her petition, Deford says that she is aware of the school policy but that "we are proposing that they amend their antidiscrimination policy to make it (specifically) inappropriate for teachers K-12 to politic while in class.
Deford said she hasn't decided if she will bring the issue to the School Board.
She emphasized that she doesn't want the teacher fired or to sue the district.
"I am asking the teacher to apologize to all of the students in his class, and for additional sensitivity training for teachers," she said.
Peninsula Daily News Managing Editor for News Leah Leach contributed to this report.
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