This decision comes as battles over the way teachers are hired, fired and evaluated swirl through courtrooms and statehouses across the country. In January, Gov. Andrew M. Cuomo began a battle of his own with teachers’ unions, proposing a change to evaluations that would tie teacher performance ratings more closely with state tests.

The tenure lawsuit, filed in State Supreme Court on Staten Island, was brought against the state last year on behalf of about a dozen families. The suit — originally two lawsuits, which have been combined — contends that teacher tenure and discipline policies deprive children of their right to a “sound basic education,” essentially by making it too difficult to fire bad teachers.

On Thursday, Justice Philip G. Minardo denied a motion to dismiss that case, filed by New York state, city and union officials, allowing the suit to continue.

“This ruling is a major victory for New Yorkers, especially for parents and students,” said Campbell Brown, founder of the Partnership for Educational Justice, a group involved in bringing the lawsuit. “New Yorkers are one step closer to having access to the data that shows the degree to which quality teaching impacts a student’s ability to succeed and…