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Michael Casserly, executive director of the Council of the Great City Schools, said that the circumstances leading to Mrs. Black’s resignation were specific to her case, and send no messages about whether choosing a newcomer to the education field is always a bad idea.

But since it was becoming obvious Mrs. Black was not working out, Mr. Casserly said he was “delighted” Mr. Bloomberg and his advisers decided to “cut bait quickly” and move forward.

“They deserve some credit for that,” Mr. Casserly said.