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Nearly a year after determining the system Texas uses to finance public education is unconstitutional, a state judge is set to hear new testimony beginning Tuesday on whether more money and fewer standardized tests have adequately improved the balance for students in rich and poor areas.

During the second round of the state's much-watched school finance trial, Judge John Dietz is weighing whether actions the Texas Legislature took this past summer will alter his February 2013 decision. Testimony is expected to last at least three weeks.

Lawmakers increased funding for schools by $3.4 billion, a rate far lower than the increase Dietz had suggested, while cutting the number of standardized tests students must pass to graduate high school from a nation-leading 15 to five.

The original case was built on the Legislature's 2011 cuts of $5.4 billion in classroom funding. That prompted more than 600 school districts responsible for educating two-thirds of the state's 5 million-plus public school students to sue, claiming the funding reductions violated the Texas Constitution's guarantees to an adequate education.

They also argued that the "Robin Hood" finance system — where school districts in wealthy areas share their local property-tax revenue with those in poorer parts — meant funding was distributed unfairly.

Dietz's initial ruling sided with them, but was only made verbally. He has yet to submit a full, written opinion. Arguing on behalf of the state is Texas Attorney General Greg Abbott's office, which is expected to appeal the written decision to the state Supreme Court.

Abbott, who is running for governor, is not handling the case. But the new arguments should streamline the appeals process since they will be part of the record the Supreme Court gets, rather than its justices having to remand the case back to a lower court to consider the effect of the funding increase and testing roll-back.

The school districts argued that the 2011 cuts, coupled with public school enrollment growth of nearly 80,000 students per year thanks to Texas' booming population, left them with inadequate resources to prepare youngsters for sky-high graduation standards.

David Thompson, an attorney representing school districts that educate about 2 million students around the state, said the additional funding and less strenuous curriculum standards approved last year don't go far enough.

"Putting some of the money back, we appreciate that, but it didn't correct underlying problems," Thompson said. "Nothing changed that changes the structural problems that the judge noted in his original decision."

Lauren Bean, a spokeswoman for Abbott's office, declined to comment ahead of the trail's reopening.

The additional funding means school districts get about $5,810 per pupil this school year — about 2 percent above 2010-2011 school year funding levels. In his verbal ruling, Dietz suggested that truly fixing the system would require an additional $2,000 per pupil — or between $10 billion and $11 billion extra in every two-year state budget.

Meanwhile, the Legislature made no changes to "Robin Hood," which districts in rich and poor parts of the state are united in opposing. Those in economically disadvantaged areas say it still leaves them underfunded, while wealthy-area districts argue they too are starved of funding since local voters who would otherwise support property tax increases for their schools refuse to do so — knowing much of the money will go elsewhere.

And a strong feeling of deja vu is lost on none of the case's parties. The school finance legal battle now in its second chapter is the sixth of its kind in Texas since 1984.

In announcing the case was heading back to court, Dietz recalled a soap opera that aired from 1956 until 2010.

"There were 13,858 episodes of As the World Turns," he joked. "We're getting pretty close."

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