(Reuters) - Kansas sought on Wednesday to avoid a court ruling that could force the cash-strapped state to increase school funding by more than $1 billion. Lawyers for the state and for public school districts faced off before the Kansas Supreme Court in the latest chapter of a decades-long battle over equitable and adequate funding. Stephen McAllister, the state’s solicitor general, argued that while Kansas may be spending less on education than some other states, student achievement is improving. “Kansas is making excellent use of resources to do pretty well compared to the nation,” he told the justices. The state spends about $4 billion on schools, but lawyers for the four districts suing the state claim another $430 million to $1.4 billion would be required to meet the state constitution’s requirement for adequate funding.  “We’re falling short and we’re leaving massive numbers of kids behind,” said Alan Rupe, an attorney for the districts. He asked the court to declare the system unconstitutional and give the state legislature some direction on achieving constitutionality and a full legislative session to come up with a new system. The justices did not indicate when they might rule. The adequacy question comes after the court ruled in June that Kansas had complied with its order to resolve inequities in educating students. Kansas’ budget is feeling the effects of actions taken by Republican Governor Sam Brownback and the legislature in recent years to cut corporate and other income taxes in hopes of helping the state compete with bordering Missouri and other states for business development and jobs. The state’s fiscal woes led Standard & Poor’s to downgrade Kansas’ credit rating by one notch to AA-minus in July. 