In a decision that could fundamentally reshape public education in Connecticut, the state was ordered on Wednesday to make changes in everything from how schools are financed to which students are eligible to graduate from high school to how teachers are paid and evaluated.

Reading his ruling from the bench for more than two hours, Judge Thomas Moukawsher of State Superior Court in Hartford said that “Connecticut is defaulting on its constitutional duty” to give all children an adequate education.

Judge Moukawsher’s decision was a response to a lawsuit filed more than a decade ago that claimed the state was shortchanging the poorest districts when it came to school funding. What separates the decision from those in dozens of similar suits around the country is that rather than addressing money only, it requires the state to rethink nearly every major aspect of its system.

“This is a game changer,” said Joseph P. Ganim, the mayor of Bridgeport, Conn., one of the state’s poorest and lowest-performing school districts. “It’s an indictment of the application of the system, and of the system itself.”