NJ.com reported that the Vineland School District teacher questioned why Dulce's mother wasn't more closely monitoring the girl.
"They're Mexican, it's their culture. They don't supervise their children like we do," the comment read.
On Wednesday, a subcommittee of the Board of Education met in a closed-door session to discuss the matter, but a decision has not been reached.
Our sister station WPVI-TV learned that on September 20, Vineland school officials were made aware of what they say was an "offense and unacceptable" social media post made by the teacher.
The president of the Vineland Education Association said the educator in question is a member of their organization and has been provided an attorney for representation. He also added that all members have been reminded to be mindful of what they share online.
Vineland Public Schools said an investigation is underway.
Dulce disappeared September 16 from a playground at Bridgeton City Park. The girl and her 3-year-old brother were playing while their mother sat in her car with an 8-year-old relative.
An Amber Alert was issued the following day. Authorities believe the girl was taken by a man who led her to a red van.
WATCH: Last images of Dulce Maria Alavez before she went missing
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