The debate over school funding dates to the 1960s, when lawmakers amended the Constitution, adding an article that laid out provisions for education aid. It read, in part that “the Legislature shall make suitable provision for finance” of public education.

Several court cases in the ensuing years wrestled with education funding. The current case, Gannon v. Kansas, grew out of one that started a decade ago, Montoy v. Kansas. In Montoy, a coalition of students and school districts argued that the Legislature failed to finance schools at a level in accordance with the state’s Constitution.

Montoy resulted in a 2005 ruling in which lawmakers raised the base state funding to $4,492 per student (from about $3,900), and the court approved it.

The state began phasing in increases each year and got up to $4,400 per pupil by the 2008-9 school year. But amid a financial crisis, the Legislature and the governor, Mark V. Parkinson, a Democrat, began scaling back the amount of aid in 2009. The decreases have continued under Mr. Brownback and the per student figure is now at $3,838.

In response to the cuts, a new coalition of students and school districts sued the state in what has become the current case, Gannon v. Kansas. A district court in January ruled in favor of the Gannon plaintiffs and the case is now before the Supreme Court on an appeal by the state.

The judges seemed to question whether the state could be trusted, given that it agreed in the Montoy case to funding increases and then stopped. “Clearly, the promise you and others were espousing six years ago has never been kept,” Justice Eric S. Rosen said to Mr. McAllister.