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.