“I think it’s all good and well that these people are finally stepping up to support education,” said Michael Mulgrew, president of the United Federation of Teachers, referring to wealthy hedge funders. “But I would wish they would do it in a more foundational way, a way that would help all the children instead of just a small group.”

Charter schools often have a longer school year, Saturday classes, uniforms and a passion for measuring results. Most of them are in the city’s poorest neighborhoods and admit children by lottery. Approximately 30,000, or 2.5 percent of the city’s public school students, attend charters, although in Harlem and parts of Brooklyn the figure is closer to 20 percent.

The schools present the kind of opportunity that “electrifies” hedge fund managers, said Mr. Tilson, 43, who is on the board of the Knowledge Is Power Program, which manages charter schools around the country. A founding member of Teach for America in the late 1980s (before earning an M.B.A.), Mr. Tilson also blogs about charters at edreform.blogspot.com. “It’s the most important cause in the nation, obviously, and with the state providing so much of the money, outside contributions are insanely well leveraged,” he said.

Charter schools’ reliance on metrics and tests to measure progress is another attraction for hedge funders. Mr. Petry, who cultivates a schlumpy aura that is more headmaster than Master of the Universe  he carries an eight-year-old Blackberry the size of a Stephen King paperback stuffed in a nylon backpack and favors fleece pullovers  said he reads spreadsheets of education statistics as much as those for new investments he’s chasing. “I can’t understand how anyone could look at the raw numbers and not see what’s at stake,” he said during an interview in a restaurant near the Upper West Side apartment where he lives with his wife, a former teacher, and three young children.

Image CHARITABLEJohn Sabat, center, and Doug Snyder, right, at a Success Charter Network event. Credit... Nicholas Roberts for The New York Times

Whether charters do a better job of educating children, even with the extra help from private donors, is much debated. A study released in September by researchers headed by Caroline M. Hoxby, an economist at Stanford who is a fellow at the Hoover Institution, concluded that on average New York City charters outperform local schools. But another study by a different group of Stanford researchers last summer suggested that nationally the numbers are muddier.