Kansas lawmakers based funding in the new school finance plan on data similar to this, showing how well districts performed on a certain measure compared to how they would be expected to perform, given their demographic makeup and other risk factors. Source: Kansas State Department of Education.

After six and a half years of litigation and four previous trips to the Kansas Supreme Court, the long-running school finance case Gannon v. Kansas will come to another climax on Tuesday. That’s when lawyers for the state and the plaintiff school districts go back to the Supreme Court to argue whether the school funding bill lawmakers passed in June is constitutional.

There is a lot riding on this hearing. In March, the court said that the funding in place at the time, a little more than $3 billion a year, was inadequate and therefore unconstitutional, primarily because it left roughly 25 percent of all public school students — including half of all African-American students and one-third of all Hispanic students — scoring below grade level on state reading and math tests.

It gave the Legislature until June 30 to come up with a funding scheme that is “reasonably calculated” to make sure all students receive an adequate education. And the court warned that it would not allow the state to operate schools under an unconstitutional funding system beyond June 30.

That threat to close schools and force lawmakers back into a special session is why a lot of people will be sitting on the edge of their seats during Tuesday’s oral arguments, which will be live-streamed on the court’s website, listening to the justices’ comments and questions for any tell-tale hint about which direction they are leaning.

The justices, of course, know that’s what everyone is listening for, which is why they will likely do everything they can to not tip their hand too much so as not to be accused of having prejudged the case.

With that in mind, here are three things viewers at home, or at the office, can watch and listen for as the lawyers are making their cases.

• “What evidence do you have … ?” At this stage of the lawsuit, the burden of proof is on the state to show that the Legislature has met its duty to adequately fund public schools and that the amount of funding lawmakers provided is “reasonably calculated to have all Kansas public school students meet or exceed” a set of educational outcome standards known as the Rose standards.

Those standards basically say that by the time a student graduates from high school, he or she ought to have a basic set of knowledge and skills to compete in the job market and to be able to fully participate in community and civic life. So, any question that starts with the words “what evidence do you have” especially when directed at the state’s attorney, Stephen McAllister, might indicate that a justice hasn’t yet been convinced that the state has met its burden.

• Challenging the “successful schools” model: The state, for its part, is going to rely heavily on something called the “successful schools” analysis that the Legislature’s nonpartisan Research Department put together, based on previous research done by the Kansas State Department of Education and others. It goes like this:

There are certain risk factors that affect how well students within a district will perform at school. Those include such things as poverty status, chronic absenteeism, suspensions and expulsions, non-English speaking population, mobility and the number of new teachers in a district.

Using those factors, researchers developed a model to predict how many students within a district would be expected to perform at grade level. Then they identified the “outliers,” the ones that are performing significantly better than would be expected. They show up on a chart like this:

Lawmakers then identified 41 outlier districts shown in the blue shaded area, looked at how much they were spending per-student and used that as the basis for a formula that gradually raises base per-pupil aid to $4,128 over the next two years.

The plaintiffs are challenging that analysis, arguing that it leads to a select group of large districts whose demographics do not match those of the rest of the state. The extent to which the justices challenge the successful schools model could indicate how much they’re buying into it.

• Equity questions: Tuesday’s hearing won’t be all about the amount of money going to public schools, but also about how fairly it’s spread among the state’s 286 school districts. And this is where some of the arguments could get highly technical and hard to follow because it involves things like capital outlay budgets and equalization formulas.

Capital outlay budgets are special funds school districts set up to pay for big-ticket purchases like computers, furniture, building repairs and the like. And districts are allowed to levy a separate property tax for those funds.

One of the things lawmakers did in this year’s school finance bill was to expand the number of allowable uses of that money to include things like utility costs and insurance premiums.

Plaintiffs in the case say that’s unfair because those are really operational costs, not capital outlay costs, and therefore it gives wealthier districts access to more money for basic school operations.

The hearing begins at 9 a.m., and each side has been given 60 minutes to make its case. If the past is any indication, though, the hearing will probably last longer because the justices themselves will have more than an hour’s worth of questions.