TOPEKA — Most of a proposed $600 million in additional K-12 spending would go to resources for school personnel, boosting funding for at-risk children and lowering class sizes, school districts told legislators Monday ahead of a school finance debate expected to dominate the legislative session.

Kansas legislators must come up with a new school finance plan by April 30 after the Kansas Supreme Court ruled the state’s formula unconstitutional in October. Former Gov. Sam Brownback proposed another $600 million in school spending in his January budget, but did not account for how the state would pay for it in the coming years, drawing frustration from Republican legislators.

Gov. Jeff Colyer seemingly backed off that proposal last week.

School districts reported nearly 34 percent of those funds would go toward teacher salaries, with another 9 percent for other school personnel. They argued Kansas’ low teacher wages make it difficult for districts to compete with other industries for talent. Schools along the state’s borders also struggle to compete with districts across the state line.

John Allison, superintendent of Olathe Public Schools, said competition for teacher candidates in the Kansas City area has changed.

“Typically, in the Johnson County area, Shawnee Mission, Blue Valley, Olathe — your Johnson County schools, would have a waiting list to be able to talk to candidates,” Allison said. “That wasn’t how it occurred this last time. The waiting lists were Lee’s Summit, Blue Springs, Park Hill.”

Sue Givens, superintendent of El Dorado Public Schools, said her district struggled to compete with other industries to hire nonlicensed staff, like maintenance and cafeteria workers.

Superintendents said they would also aim funds at hiring more counselors and social workers to address rising prevalence of mental health needs among their students. Givens said the all-day kindergarten funding included in the existing school finance formula freed up money the district used to hire its first social worker.

Garden City Public Schools expects to spend 60 percent to 70 percent of any additional funds to support employees and have a high-quality staff, said superintendent Steven Karlin. That would include paying competitive salaries and benefits, lowering class sizes, offering professional development and hiring sufficient support staff.

Rep. Melissa Rooker, a Fairway Republican who has consistently advocated for more money for schools, said she thought the briefing from school districts would help inform the school finance debate, and she said she hoped legislators’ minds would be open. She said improving schools meant recruiting and retaining quality teachers and wrapping services around children.

“To align the work going on in our schools to the goals we all say we want for our kids — we want the outcomes to improve — this is how you get there,” Rooker said.

Rep. Fred Patton, a Topeka Republican and chair of the House K-12 Budget Committee, said he thought it was important to know where schools would spend additional money as legislators work toward a school finance plan.

“Obviously as there’s competition … it’s important that we pay salaries that are competitive so we can get good teachers, and actually (not) just in metro Kansas City or Wichita, but Western Kansas where it’s hard to get people to live out there, and so you’ve got to pay decent salaries to recruit people,” Patton said.