Topeka ? Plaintiffs in the ongoing school finance lawsuit are telling the Kansas Supreme Court that student test scores in reading and math prove Kansas is failing to fund its public schools adequately and that schools need roughly half a billion dollars a year in additional funding.

But attorneys for the state counter that funding is at record levels and all schools are meeting state accreditation standards, and they say a court order for additional funding would be “a flagrant violation of the separation of powers.”

Those are some of the central arguments that both parties made in briefs filed with the court on Friday.

To bolster its case, the four plaintiff school districts point to recent scores on the National Assessment of Educational Progress, or NAEP scores, that show minority students, particularly black students, and students from lower-income households consistently score lower than white and upper-income students, and that in many cases the disadvantaged groups are falling further behind.

The NAEP exams in reading and math are administered every other year to a random sample of fourth- and eighth-grade students in each state. Their scores are ranked into three achievement levels: “proficient,” defined as “solid academic performance;” “basic,” meaning “partial mastery” of the knowledge and skills needed at each grade level; and “below basic.”

Among Kansas fourth-graders, the plaintiffs argue, the number of students scoring “below basic” on the national reading test grew substantially from 2009 to 2015, from 28 percent to 32 percent. But the biggest increases were among black and Hispanic students and students from lower-income households.

Attorney Alan Rupe, representing four Kansas school districts, makes a point during oral arguments in Gannon v. State of Kansas at the Kansas Supreme Court Friday, Nov. 6, 2015, in Topeka, Kan.

More than half (56 percent) of black fourth-graders scored “below basic” on the reading test in 2015, along with 46 percent of Hispanic students and 46 percent of students who qualify for free or reduced price meals.

All of those percentages were sharply higher than they were in 2009, the year Kansas began cutting school funding in the wake of the Great Recession, the plaintiffs argued. Furthermore, the number of fourth-grade minority students scoring below basic grew in Kansas even as similar minority students nationwide were improving.

Among all students nationally, however, only 32 percent scored “below basic” on the fourth-grade reading test, which was virtually unchanged from 2009.

On the fourth-grade math test, there was a similar decline in performance among Kansas students. The number scoring “below basic” grew from 11 percent to 17 percent over six years, while nationally the number held steady at 19 percent.

Representing the State of Kansas, attorney Stephen McAllister argues his case in Gannon v. State of Kansas at the Kansas Supreme Court Friday, Nov. 6, 2015, in Topeka, Kan.

But among minority and poor students, the numbers grew even more sharply, to 43 percent among blacks, 29 percent for Hispanics and 26 percent for lower-income students.

Eighth-grade reading and math scores were relatively stable over that period. But still, minority and lower-income students in Kansas were much more likely than students overall, both nationally and in Kansas, to score “below basic.”

The plaintiffs also point to the state’s own reading and math assessments, which were administered for the first time in 2015 in line with the state’s new College and Career Ready academic standards.

Based on those first-year results, nearly a quarter of all students in Kansas were performing below grade level in math, and two-thirds of them were not considered on track for college readiness.

In English language arts, more than one-fifth of Kansas students were performing below grade level, and more than half (58 percent) were not on track for college readiness.

“The failures reflected in the assessments are directly attributable to the State’s inadequate funding of education,” Alan Rupe, lead attorney for the plaintiffs, stated in his brief.

Attorneys for the state, however, state repeatedly in their brief that current public school funding is at “record” levels and that all schools are currently accredited, which means they must be providing all of the required services.

“The Plaintiff Districts have not met their heavy burden of proving that current funding is constitutionally inadequate,” Kansas Solicitor General Stephen McAllister wrote in the state’s brief.

Kansas will spend just over $4.5 billion from all funding sources, including $3.1 billion from the state general fund, for public schools this year. That makes K-12 education the single largest category of state spending, accounting for half of all general fund spending.

In January 2013, a three-judge panel in Topeka ruled that funding levels at that time were inadequate and ordered the state to restore the cuts that had been made since 2009, roughly $450 million at the time.

A year later, though, the Kansas Supreme Court reversed that ruling and sent the case back, telling the panel to reconsider using a different legal standard for judging adequacy, one based on student outcomes rather than the cost of providing services.

After a new set of hearings, though, the panel reaffirmed its earlier ruling, using test scores available at the time to show a large number of students, especially lower-income and minority students, were failing to meet the state’s standards on reading and math tests.

In 2015, however, Kansas lawmakers abolished the school funding formula that had been in place more than 20 years, replacing it for two years with a block grant funding system that effectively froze funding for each school district in place, regardless of changes in their enrollment.

That has already become a major issue in the 2016 elections for the Kansas House and Senate. Next year, after the elections, lawmakers are expected to craft a new funding formula.

But the Supreme Court could have a lot to say about what that new formula looks like and how much money needs to go into it when it weighs the two sides’ arguments and rules on the lawsuit later this year.

Oral arguments before the court are set for Sept. 21. A decision could come at any time after that.