Updated

Texas pumping more than $3 billion back into public education helped but still left classrooms desperately underfunded, while doing nothing to fix fundamental flaws in the balance for students in rich and poor parts of the state, attorneys representing 600-plus school districts argued Tuesday.

The state countered that school funding is even more adequate and fairly distributed than ever.

The arguments began the second chapter of a pivotal case affecting more than 5 million public school students across Texas. In February, state District Judge John Dietz ruled that the way Texas finances public education was so inadequate and unevenly distributed that it violated state constitutional guarantees to provide young people an adequate education.

Three months later, however, the state Legislature increased funding for schools by at least $3.4 billion, while cutting the number of standardized tests students must pass to graduate high school from a nation-leading 15 to five.

Richard Gray, an attorney who represents more than 400 school districts, told Dietz that the additional funding "was a step in the right direction but an exceedingly small step," adding that the new money was "woefully inadequate."

"The court found the system unconstitutional a year ago and we believe that, after the evidence presented here, the court will continue to find the system unconstitutional," Gray said.

The original case was built on lawmakers' 2011 cuts of $5.4 billion in classroom funding. That prompted about two-thirds of school districts statewide to sue, claiming they no longer had sufficient resources to educate students — especially given public school enrollment growth of nearly 80,000 students per year thanks to Texas' booming population and the tough and getting-tough, state-mandated standardized testing and curriculum requirements to graduate high school.

Dietz's initial decision sided with the districts, but was only made verbally. He has yet to submit a full, written opinion, and will only do so after hearing new evidence on the Legislature's actions. The case's second phase is expected to last at least three weeks. Once his final ruling is ready, it will almost certainly be appealed to the Texas Supreme Court.

The new arguments should streamline the appeals process, though, 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 rollback. Still, during a sideline meeting with attorneys, Dietz said "there are over 1 million pages" already in the case record and noted that no Supreme Court justice will want to read through even that much material, not to mention supporting documents on the new evidence.

Texas Assistant Attorney General Shelly Dahlberg said Tuesday that lawmakers added funding and injected much-needed flexibility into high school curriculum standards at the urging of students, parents and school administrators. She said the change "impacts, if not moots, many of the plaintiffs' claims."

"We believe the system remains constitutional," Dahlberg said. "And the plaintiffs will not be able to introduce evidence in these proceedings to prove otherwise."

The school finance case is the sixth of its kind since 1984 in Texas, where school districts say legal challenges are the only way to ensure adequate funding from the Legislature. "To quote Yogi Berra: It's like deja vu all over again," Dietz joked.

Meanwhile, lawmakers in 2013 made no major changes to Texas' "Robin Hood" system, under which school districts in wealthy areas share part of their local property tax revenue with poorer-area schools. Most districts statewide are united in opposing the system.

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.

Gray said the state's 15 percent poorest school districts have to levy property taxes at levels 8.6 percent higher than the state's 15 percent wealthiest districts, yet have a per-student return of about $2,100 less. He said the additional 2013 school funding will reduce that gap by only $210 by fiscal year 2015.

David Thompson, a lawyer representing school districts in both rich and poor parts of Texas, noted that one-time appropriations to educational grant programs means that actually closer to $3.7 billion in additional funding will flow to schools over the life of the two-year state budget. But he said even that is only about 68 percent of the funding schools lost after 2011.

About 60 percent of Texas students receive free or reduced-price lunches at school, while nearly 20 percent require additional instruction in English language skills — two populations that cost more for schools to educate. David Hinojosa, who represents theb Mexican American Legal Defense and Educational Fund, said curriculum standards are still too high given rising classroom costs.

"The state can't dumb down its constitutional obligation and say: Perhaps students aren't held to the same college-readiness standard that they were previously," Hinojosa said.