Ms. Moskowitz repeatedly described the former assistant teacher as “unethical” for not sharing the video with the school’s principal, Kerri Nicholls, at the time she took it. Ms. Moskowitz said that the network had shown itself to be “very quick to investigate” when such matters were brought to its attention, as when a principal at one of its schools created a “Got to Go” list of difficult children whom he wanted to leave the school.

But the assistant teacher said that, because Ms. Nicholls had made it clear that Ms. Dial was a favorite of hers, she did not think raising her concerns would have any effect other than to possibly imperil her own job. Success teachers are not unionized and can be fired at will.

Around the same time that she took the video, the assistant teacher said, she saw Ms. Dial become frustrated with a girl who was playing with her hair. She said Ms. Dial proceeded to pull the girl’s hair into a ponytail in a manner that she perceived as rough. She shared her concerns with another staff member, who in turn told Ms. Nicholls. Ms. Nicholls called the assistant teacher in for a meeting, but seemed more annoyed at her than concerned about Ms. Dial’s behavior, the assistant teacher said.

Ms. Nicholls said in an interview that after investigating the incident she had found “nothing inappropriate aside from” the assistant teacher’s “lack of reporting her concerns.”

Dr. McDonald, the N.Y.U. professor, who also sits on the board of the Great Oaks Charter School on the Lower East Side, said that the behavior in the video violated an important principle of schooling.

“Because the child’s learning was still a little fragile — as learning always is initially — she made an error,” he said in his email. “Good classrooms (and schools) are places where error is regarded as a necessary byproduct of learning, and an opportunity for growth. But not here. Making an error here is a social offense. It confuses others — as if deliberately.”