The board is considering a resolution calling for her resignation.
Drucker has served for five years and posted to Facebook that she has no plans to step down.
" I am fully committed to continuing to advocate for my District 9 community," she said. "I extend my genuine apology for any discordant feelings that my misdemeanor matter has created within our community and the St. Tammany Parish School Board."
The board can not force her to resign.