Plaintiffs in the Kansas school finance lawsuit say the district court did not order a big enough increase in education funding, and they’re asking the state Supreme Court to order much more.

In a cross-appeal filed with the Kansas Supreme Court this week, the plaintiffs — a coalition of school districts and individuals — argue that the trial court should have ordered about $1.3 billion a year in additional spending, far more than the estimated $515 million the trial court ordered in January.

In its order last month, a three-judge panel ruled the Legislature needs to increase base per-pupil funding to $4,492, the amount currently required by statute. That’s also the amount that the Supreme Court accepted as constitutional when it reviewed the last school finance case, Montoy vs. Kansas, in 2006.

Since 2009, however, the state has cut school funding in response to declining revenues brought on by the recession. Base per-pupil funding this year is set at $3,838.

Increasing the base funding amount to $4,492 would cost about $442 million, according to Kansas Department of Education estimates. The trial court also ordered increases in special education funding. It also ordered the legislature to restore “equalization aid” for the capital outlay budgets of lower-wealth districts.

The state is appealing that ruling. Kansas Attorney General Derek Schmidt has also filed motions to stay the trial court’s order pending appeal and for the Supreme Court to appoint a mediator to resolve the dispute.

But in documents filed with the Supreme Court on Wednesday, the plaintiffs said they are also appealing the ruling, arguing that the trial court’s award was too small. They argue that base funding should be set somewhere between $5,723 and $6,365 per pupil.

The plaintiffs cite three sources that were used in the trial to support those estimates: an update of a cost study commissioned by the Kansas Legislature by the consulting firm Augenblick and Myers; an update of another cost study performed by the Legislative Post Audit Division; and applying an inflation adjustment to the Supreme Court’s order in the Montoy case.

John Robb, lead attorney for the plaintiffs, said that a funding formula of $6,000 per-pupil would cost the state about $1.3 billion a year.

The plaintiffs also want the High Court to rule that education is a “fundamental right” and that by under-funding public schools, the state has denied students their rights to due process and equal protection — two claims that the trial court rejected.

The Supreme Court has not yet set a schedule for the appeal. But attorneys say that under a normal schedule, the Court would schedule oral arguments for the fall, with a decision expected around the first of next year.