Superintendent Billy Lee identified the board member as Ted Bonner according to KARK.
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Lee said there is no law to recall the board member and he has since apologized.
But parents like Faye Smith want him removed.
"Number one, it's appalling," said Smith. "Number two, it's inappropriate for a school board member to disrespect students that he's over, who are black."
People familiar with the picture said it was taken Bonner at a Halloween party, a couple of weeks ago.
"Why is that every time you make a joke, it's blackface?" said Smith. "Why is blackface funny? We have a whole race of people who don't think looking in the mirror is a joke."
In front of Bonner is a sign that reads 'Blak Lives Matters,' but the international activist movement is titled 'Black Lives Matter."
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"I don't appreciate the fact that you're mocking the thing that I'm teaching my boys is something to be proud of," said Smith. "Being a black man, and then you do this to make them feel like 'well you're a joke' " said Smith.
Smith has two sons at Blevins High School.
"It's a little bit hurtful in the way to think my children are being supervised by a person who feels like that is all they're worth," said Smith.
Superintendent Lee released the following statement:
"This district is deeply committed to creating and maintaining a strong and healthy school culture free of bullying, and any form of discrimination. I have no personal knowledge of any actions by district staff or elected officials. Please rest assured that if it comes to my attention that any staff member has behaved in a way inconsistent with this district's values and policy of anti-discrimination, a swift investigation and response would be forthcoming." -- Superintendent Billy Lee.
Superintendent Lee said Bonner apologized at a school board meeting Monday night.
"If you blacken my eye and come back and tell me 'I'm sorry' the black eye is still there," said Smith. "It's always a reminder of what you did."
Superintendent Lee said Bonner can step down on his own or he can be removed when his term on the board is up, which is in 2018.