Los Angeles school district officials Tuesday will hear from all sides about how much money they have for next year and how it should be spent.

The specially called budget session, which begins at 9 a.m. at the district's downtown headquarters, first will feature experts from L.A. Unified and from outside. A key point of debate is how much more money than last year will be available to the nation's second-largest school system.

Things are looking up because of an improved economy and because voters passed a tax increase last fall. But revenues remain in flux and so does the fate of a proposal to reshape education spending by California Gov. Jerry Brown. If Brown gets his way, more money will flow to low-income, urban school systems such as L.A. Unified. If his plan fails to pass the Legislature, sharp cuts could be necessary, said L.A. schools Supt. John Deasy.

The second portion of the meeting begins at 5 p.m. -- an opportunity for parents, labor groups and others to discuss their spending priorities. The teachers union, United Teachers Los Angeles, has been vocal about wanting money spent to restore school positions lost during the peak of the recession. Thousands of teachers and other employees lost their jobs, leading to reduced services and larger class sizes. The adult education program was especially hard hit because school districts could transfer that funding to the program for children.

Three board members have coauthored a resolution that appears closely in line with the union's goals. That measure is scheduled for introduction Tuesday and could return for a vote later in June. Four votes would be needed for passage on the seven-member Board of Education. Critics worry that the proposal could limit Deasy's flexiblity to spend money where it delivers the most dividends or chain the district to expenses it cannot afford.

The sponsors of the resolution are Bennett Kayser, Steve Zimmer and Richard Vladovic. Kayser and Zimmer enjoy strong support from the teachers union. Vladovic was elected with backing from L.A. Mayor Antonio Villaraigosa, an ally of Deasy. In recent months, Vladovic has taken an increasingly independent course. It was Kayser who proposed the special meeting. The new budget year begins July 1.

Another resolution is being introduced by board member Tamar Galatzan, who represents the west San Fernando Valley. Her measure supports the governor's proposal, but also asks for safeguards to make sure that all schools receive reasonable basic funding. Schools in Galatzan's area tend to have more middle-class students and have lost dollars that were redirected to schools in lower-income neighborhoods.

At this point, Deasy has not put forward a specific budget to argue over. Nor have jousting board members offered many specifics.

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Twitter: @howardblume | howard.blume@latimes.com