While the model flies against efforts to keep class sizes low, Mr. Waronker notes that the teacher-student ratio is lower than in most schools. At its heart is the idea that the teachers, not to mention the students, will collaborate and learn from one another, rather than being isolated in separate classrooms. He hired one $120,000-per-year master teacher per class. Most of the others are novice early childhood teachers, which recreates the staff composition in typical high-poverty schools.

New American Academy opened with 126 kindergartners and first graders and at least eight adults per classroom, including intern principals and paraprofessionals assigned to disabled children. It will expand by one grade per year until it reaches the fifth grade, and the teachers will stay with the same children every year, to build accountability for their learning. There is no assistant principal, dean or art teacher, saving money for classroom salaries.

Lessons are a series of complex choreographies. In the 2,000-square-foot kindergarten, for example, each child is assigned a “university” a grouping by skill level  and another group by color: blue, red or green. Every 40 minutes or so, the children regroup in a different part of the room. During a visit in November, an observer noticed that each move led to the children’s standing up, running, talking, and then having to quiet down again.

“This is the hardest moment of the day,” said Lorraine Scorsone, the master teacher in the kindergarten, as eight adults tried to wrangle the children into a semicircle for group reading time. “In early childhood, disengaging is very difficult, and moving to another activity is very difficult.”

Ms. Scorsone, with 23 years of experience, had what appeared to be a magical touch, and the children listened raptly one day in November as she explained how a banana travels from foreign lands to local stores. But the other teachers, who do the bulk of the teaching, had more trouble gaining the attention of the children, who lay on carpets looking at the ceiling or fiddled with belts and shoelaces on the outskirts of lessons.

“Ewww,” squealed a boy named Ethan when he was told that the class would plant a banana tree later that day. Other children began mimicking the sound, which they had been making earlier. “Ethan, stop it,” said his teacher, Pepe Gutierrez. “I don’t know why you are screaming.”