TOPEKA ? Kansas Gov. Sam Brownback says work on a new formula for funding the state’s public schools should focus on how local districts spend their money, create incentives to shift dollars into classroom instruction and encourage merit pay for teachers.

The Republican governor said during an Associated Press interview that he’d like the GOP-dominated Legislature to draft a new formula next year, a goal shared by some prominent Republican lawmakers. Such a formula would determine how the state distributes the bulk of its aid to the 286 districts, now more than $4 billion.

Brownback rejected arguments from many superintendents and school board members — and four districts suing the state — that the state isn’t providing enough aid to provide a suitable education for every child. He said a key issue is making sure that a greater percentage of state funding goes into the classroom, rather than toward administrative overhead.

The governor also said a new formula should include early childhood education so programs are better coordinated across the state. And a new formula should encourage districts to use merit pay to reward their best teachers, he said.

“I want more money going to teachers. I’m for merit pay,” he said during a 30-minute session last week. “So you really try to incent paying really good teachers, pay them more. Let’s incent the classroom.”

Brownback said his administration is in an early, information-gathering stage of discussing potential school funding proposals. Pressed to provide details about his ideas, he said, “We’re not that far along.”

But the governor’s call for merit pay is likely to rile many teachers and their largest union, the Kansas National Education Association. Mark Desetti, a KNEA lobbyist, said such proposals represent a way of avoiding boosting aid to districts enough to ensure that teachers across the state are adequately paid.

“We don’t have to put in as much because we’re going to pay only a few people well,” he said.

Legislative leaders created a committee to study school funding issues this fall, before the full Legislature reconvenes in January.

Earlier this year, a law enacted by top Republicans with Brownback’s support replaced the state’s per-pupil formula for distributing aid to districts with stable “block grants” based on what districts received in 2013-14. The law provides for grants only through June 2017, and its backers anticipated from the beginning that legislators would draft a replacement formula.

Brownback and other Republicans argued that the old formula didn’t put enough money into classrooms and created the wrong incentives, such as encouraging districts to pursue big construction projects. The old formula’s defenders note that it automatically adjusted a district’s aid to reflect changing conditions, such as an increase in student numbers.

A lawsuit pursued by the Dodge City, Hutchinson, Wichita and Kansas City, Kansas, districts contends the state is falling far short of adequately funding schools. A three-judge Shawnee County District Court panel ruled aid must increase by at least $548 million annually, and the state appealed to the Kansas Supreme Court.

John Robb, an attorney for the four school districts, said Brownback and many GOP legislators are trying to work backward from the amount of money they want to spend, rather than providing an adequate amount. Robb said Brownback and his allies could have provided aid “at a constitutional level” had they not enacted massive personal income tax cuts in 2012 and 2013 to stimulate the economy.

“They’re trying to fit the product they want — which is competent children — into an inadequate budget number,” Robb said.

Brownback called the criticism unfair. While Brownback’s opponents say increases in aid aren’t keeping pace with rising costs and point out that higher spending on teacher pensions will fuel most of the increases this school year, the governor notes that total aid is at record levels.

“What you need is more money in the classroom,” he said.

Desetti acknowledged that Brownback’s call for more money into classrooms is “a great talking point” because, “people nod.” But he said it’s not clear exactly where spending would drop.

“Shall we take the fuel out of the buses?” he said.