A lawsuit by a group called New Yorkers for Students’ Educational Rights estimates that, despite increases in recent years, the state is still about $5.6 billion a year short of its commitment under that formula.

A second lawsuit was filed on behalf of students in several small cities in the state, including Jamestown, Port Jervis, Mount Vernon and Newburgh. It says that per pupil funding in the cities, which have an average 72 percent student poverty rate, is $2,500 to $6,300 less than called for in the 2007 formula, making it impossible to provide the instruction other services needed to meet the State Constitution’s definition of a “sound basic education.”

These communities and others like them are further disadvantaged by having low property values and by a statewide cap enacted in 2011 that limits what money they are able to raise through property taxes. And last year the New York State United Teachers union said that the cap had been particularly harmful to poorer districts.

These inequalities are compounded by the fact that New York State, which regards itself as a bastion of liberalism, has the most racially and economically segregated schools in the nation. A scathing 2014 study of this problem by the Civil Rights Project at the University of California, Los Angeles, charged that New York had essentially given up on this problem. It said, “The children who most depend on the public schools for any chance in life are concentrated in schools struggling with all the dimensions of family and neighborhood poverty and isolation.”

The Cuomo administration seemed not to acknowledge these issues in a letter last month to the chancellor of the New York State Board of Regents and the commissioner of education in which it promised “an aggressive legislative package” to improve education in the state. Among the dozen issues it said it wanted to address were strengthening the teacher evaluation system, improving the process for removing low-performing teachers and improving teacher training.