NEW YORK >> Sixty children in a first-grade class can get loud — sometimes too loud for a teacher to explain a lesson.

So while waiting for her teacher to come by, one little girl arranged the pennies she had been given to practice subtraction into a smiley face. Another shook her pennies in a plastic bag. A high-pitched argument broke out over someone’s missing quarter.

“We don’t know what we are supposed to be doing, but we are learning about math,” Thea Burnett, 6, said.

Across the room, a second teacher, Jennifer McSorley, successfully led the class’ weakest students in a counting rhyme. But when she leaned forward out of her chair to write a word on an easel, a 6-year-old boy moved it, and she fell when she tried to sit back down.

“Jahmeer, sit down,” McSorley demanded, unharmed but flustered. “I could have hurt myself very badly.” Then another boy ran off to hide under an easel. Someone grabbed someone else’s pennies. The noise snowballed.

All this was the early stages of an audacious public education experiment taking place in the Crown Heights section of Brooklyn, one that its founder hopes will revolutionize both how students learn and how teachers are trained. Instead of assigning one teacher to roughly 25 children, the New American Academy began the school year with four teachers in large, open classrooms of 60 students.

The school stresses student-led lessons over teacher-led ones, scientific inquiry over rote memorization and freedom and self-expression over strict structure and discipline. The founder, Shimon Waronker, developed the idea with several other graduate students at Harvard. It draws its inspiration, he said, from Phillips Exeter Academy, an elite boarding high school in New Hampshire where students in small classes work collaboratively and hold discussions around tables.

But Waronker decided to try out the model in one of the nation’s toughest learning environments, an elementary school in a high-poverty area where 20 percent of the children have been found to have emotional, physical or learning disabilities. The idea, he said, was to prove that his method could help any child, and should be widely used elsewhere. “I didn’t want to create an environment that wasn’t real for everyone else and then say, look at my success,” he said.

The challenges have been considerable. Faced with out-of-control classroom situations, Waronker, 42, had to rethink his idea that his model could work for even the most disturbed children. By January, three children who were violent had been moved to more-structured environments; seven other first-graders moved away or withdrew, reducing the class size to 50.

The school was founded with the strong backing of Joel I. Klein, the former schools chancellor, who frequently lauded Waronker for his efforts as the principal of a tough middle school in the South Bronx. They found a space in an elementary school three blocks from Waronker’s home in the Crown Heights, and in a special deal with the teachers’ union, he won the right to pay teachers on a scale that considered performance.

While the model flies against efforts to keep class sizes low, 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 re-creates 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.”

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.”

The first grade was tougher, with less-experienced teachers and more children who were violent. In the first two months of school, a student pulled a chunk of an adult’s hair out, and an ambulance crew was called twice to calm a child. Eight weeks into the year, the only student work visible on the blue-painted walls was a poster with finger-painted hand prints and the words “Hands Are Not for Hitting.”

“Many of the children have already had a year in what I would call a state of nature, when Rousseau spoke about people who live under no civilization,” Waronker said, referring to the children’s experience in a regular public school kindergarten. Fifteen children still could not recognize letters, and only one-third were at grade level. “This is messy work — this is the front lines.”

In the front of the room, Kathleen Kearns, a first-year teacher, strained to get her 20 students to understand how to use a chart to classify similarities and differences between two characters in a book. About half a dozen students refused to sit in their places.

“I need you here; your job is here,” she said to one, trying to be heard. After class, she said, “I am exhausted at the end of the day.”

It is the same struggle that first-year teachers across the city face, but the difference, Waronker said, is that in his school, it is out in the open. Other teachers can offer advice and pitch in, and they have 90 minutes of joint planning time each morning. The intensive collaboration, he believes, is what will cause his model, while admittedly still in a “trial-and-error” phase, to ultimately surpass others.

Indeed, by this month, there were significant improvements. Children appeared more focused during lessons. Jahmeer decided to play with pencils rather than do his counting work sheet, but he stayed in his seat, and another child asked if he needed help. One boy started crying, but not because someone pushed him; he wanted to have a turn writing his answer on the board.

“It’s tough on them, it’s tough on all of us,” Keema Flourney, the first-grade master teacher, said of her teachers, “but they are pulling through.”

Next year, Waronker said, he will hire more-experienced teachers, because expecting that novices could learn quickly enough from the master teachers was wrong. “I put added stressors that shouldn’t have been there,” he said.

Most of the teachers said they felt the school’s model would show good results over time. Several parents praised the school’s inclusiveness and its effort to offer something different. But one father, who withdrew his daughter, said the school was not for her because of her behavior problems.

The first-year teacher who had been leading the penny lesson in November for Thea and 19 other children, Daniella Schonbuch, while the master teacher was away, said she calmed herself after tough days by remembering that she would have years to build progress with her students. By January, she was leading a regular morning French lesson.

“It’s small moments, it really is,” said McSorley, the first-grade teacher whose chair had been pulled out from under her. “We are still in the process of figuring out what works for the kids, and what works today does not always work tomorrow.”

© 2011 The New York Times Company