Trivia: Although in real life Principal Joe Clark improved the discipline problems at Eastside High School, he did not, contrary to what the film has you believe, improve the academics in any meaningful way. Although test scores improved very slightly his first couple of years as principal (partly due to the fact that he expelled so many bad students) from 1986 to 1988, during his time as principal, Eastside High School had the lowest state exam passage rates in all of New Jersey. One of these years in particular, under Clark's tenure, Eastside High's passage rate was as low as 24.1%.
Trivia: Regina Taylor plays Mrs Carter, mother of Kaneesha Carter (Karen Malina White). In real life, Taylor is only five years older than White.
Chosen answer: They are discussing some of the things that Mr. Clark has done that has "embarassed" the school. They are debating what to do about him. And by "posturing," they mean his insistance on wearing African dress and espousing his political beliefs.