Cuts, meanwhile, had slashed so deeply at some schools that principals reported taking on the duties of a secretary, a social worker or a janitor.

Although a major goal of the lawsuit by the Campaign for Fiscal Equity was to limit class sizes, they remain high, the report said. All the New York City middle and high schools in the survey reported classes of 30 or more students.

According to statistics from the city’s Education Department, class sizes have been steadily increasing; the average class size in elementary schools rose to 24.4 in 2011-12 from 23.7 in 2010-11, and in middle schools to 27 from 26.8 over the same periods. In high schools, they remained at 26.3.

According to the report, teachers said the minimum standards, hard as they were to follow, were still too low to ensure a meaningful education, which the court defined in its ruling as preparing students to become competitive workers and productive citizens.

Even if the schools had the resources to meet the minimum standards, teachers said, students were unlikely to meet Regents standards or the state’s new Common Core learning standards, which are more stringent.

But between the recession and Hurricane Sandy, Gov. Andrew M. Cuomo faces a difficult fiscal situation. The governor’s office has repeatedly fretted over the fact that New York leads the nation in education spending yet apparently has little to show for it.

“The facts on the governor’s priorities for education are clear,” Matt Wing, a spokesman for the governor, said in a statement. “Last year, he invested an additional $800 million in our schools, despite a multibillion deficit, and prioritized low-income districts with a spending formula that gives them a higher percentage of state aid.”