Eva Moskowitz, Success Academy’s founder, now runs forty-six schools. Illustration by Ben Wiseman Audio: Listen to this story. To hear more feature stories, download the Audm app for your iPhone.

One of the most celebrated educational experiments in history was performed by James Mill, the British historian, on his eldest son, John Stuart Mill, who was born outside London in 1806. John began learning Greek when he was three, and read Herodotus and other historians and philosophers before commencing Latin, at the age of seven. By the time he was twelve, he was widely read in history and had studied experimental science, mathematics, philosophy, and economics. James Mill’s pedagogical approach reflected the influence of Jeremy Bentham, the founder of utilitarian philosophy, and was intended to discover whether a child of unexceptional intellectual capacities could, through rigorous exposure, learn material that was typically acquired in adulthood, if at all. The answer, according to the research subject, was yes. “I started, I may fairly say, with a quarter of a century over my contemporaries,” J. S. Mill wrote in his 1873 “Autobiography.”

Mill’s remarkable upbringing is cited by Eva Moskowitz, the founder of the Success Academy Charter School network, in her own autobiography, “The Education of Eva Moskowitz,” which was published in September. The book recounts Moskowitz’s learning curve, from her youth in the Morningside Heights area of Manhattan—where she was brought up by leftist intellectuals and attended public school—to her time on the New York City Council, where she developed a reputation for courting controversy while chairing the Education Committee, to her founding of the Success Academy, the city’s largest charter-school network. She is now the reliable scourge of the public-education establishment in New York City and, outside its borders, a favorite of the national education-reform movement.

Success Academy began in 2006, with a single elementary school in Harlem, and now has forty-six schools, in every borough except Staten Island. The overwhelming majority of the students are black or Latino, and in most of the schools at least two-thirds of them come from poor families. More than fifteen thousand children are enrolled, from kindergarten to twelfth grade. Students hardly follow Mill’s curriculum—there is no Greek or Latin in kindergarten, or even in later grades. But the schools do well by the favored metric of twenty-first-century public education: they get consistently high scores on standardized tests administered by the State of New York. In the most recent available results, ninety-five per cent of Success Academy students achieved proficiency in math, and eighty-four per cent in English Language Arts; citywide, the respective rates were thirty-six and thirty-eight per cent. This spring, Success Academy was awarded the Broad Prize, a quarter-million-dollar grant given to charter-school organizations, particularly those serving low-income student populations, that have delivered consistently high performances on standardized tests. Moskowitz has said that, within a decade, she hopes to be running a hundred schools. This year, a Success high school, on Thirty-third Street, will produce the network’s first graduating class: seventeen students. This pioneering class originated with a cohort of seventy-three first graders.

As a charter school, Success Academy is required to admit children by lottery. But prominent critics, such as Diane Ravitch, the historian and public-education advocate, have alleged that Success Academy essentially weeds out students, by maintaining unreasonably high expectations of behavior and academic achievement. Similarly, critics claim that the program reduces class size by not accepting new students beyond fourth grade, whereas zoned public schools must accept all comers. To Moskowitz’s detractors, Success’s celebration of standardized test-taking—students attend “Slam the Exam” rallies—is a cynical capitulation to a bureaucratic mode of learning. Success Academy has attracted large donations—in the past two years, the hedge-fund manager Julian Robertson has given forty-five million dollars to the group—and Moskowitz’s opponents say that such gifts erode the principle that a quality education should be provided by the government. Last fall, Donald Trump summoned Moskowitz, who is a Democrat, shortly after he was elected President. Although she declined to be considered as his Education Secretary, she was widely criticized for agreeing to the meeting, including by members of her own staff, who noted that Trump’s racist and anti-immigrant rhetoric on the campaign trail had stoked fear in the kind of families served by Success Academy schools.

For all the controversy, one question has, surprisingly, been overlooked: What are the distinguishing characteristics of a Success Academy education? Moskowitz’s memoir, which recounts her battles with union leaders, journalists, and bureaucrats, does not focus on her pedagogical preferences; she directs readers interested in curricular details to Success Academy’s Web site. Her book portrays the school network as an evolving experiment that regularly incorporates new teaching methods in the hope of nudging student achievement ever higher. At one point, she cites the inspiring example of John Stuart Mill. “Can children learn as much today?” Moskowitz writes. “And if so, how much can they learn? I don’t know, but I do know that what we’re achieving at Success today is far short of what is possible, and that people will someday look at the education Success offers today much as we now look at travel by horse and buggy.”

Parents have flocked to Success Academy schools, in part, because Moskowitz has convinced them that their children can tackle more than the local public school demands. But Moskowitz’s book glosses over the fact that James Mill’s experiment on his son was not entirely positive in its impact. At the age of twenty, J. S. Mill sank into what we would now call a severe depression. He ascribed his mental breakdown to his education, which had been entirely directed toward developing his rational and analytic powers; as he later wrote, his curriculum lacked any cultivation of feeling, and any valuation of poetry, “and of Imagination generally, as an element in human nature.” He described himself as “stranded at the commencement of my voyage, with a well-equipped ship and a rudder, but no sail.” Mill recovered—reading Wordsworth helped—and went on to become one of the leading philosophers and political theorists of the Victorian era. His example is a triumphant one, but it also offers a warning: that grand educational experiments can have unintended consequences.

Success Academy Springfield Gardens, in Queens, opened in the fall of 2014. The neighborhood, close to J.F.K. Airport, has many Caribbean immigrants, as well as a large African-American population. The school is on an upper floor of a building that it shares with a zoned middle school, I.S. 59; both schools principally serve students of color whose families qualify for public assistance. The floor tiles of Springfield Gardens’ freshly painted hallways are labelled with spelling words, so that children can absorb information even as they file, in silence, from one room to another. The classrooms are carpeted, muffling the baseline din that usually accompanies students at work—the scraping of chairs, the dropping of pencils—and imbuing even a space occupied by more than two dozen second graders with the hush of a corporate conference room.

One morning earlier this year, the second graders were engaged in a group reading lesson. (Over several weeks, I was permitted to observe classes at eight Success Academies around the city, from the elementary to the high-school level.) The teacher sat on a chair at the front of the classroom. Her students—or “scholars,” as they are known at Success—sat at her feet on a deep-blue rug patterned with a grid. They wore uniforms: plaid dresses or navy pants for the girls, pants and polo shirts for the boys. Everyone wore black slip-on shoes, as prescribed in the Success Academy parents’ manual; Moskowitz does not want teachers to waste instructional time tying errant laces.