Long Islanders on Tuesday began voting on billions of dollars in school spending proposed by 124 districts across the region, including five districts where the stakes include potential losses to taxpayers of state rebate checks.

Projected tax hikes in most districts are at their lowest point in more than 40 years -- a point cited by many school administrators in predicting high passage rates for budgets.

But four districts -- Bridgehampton, East Hampton, Sayville and West Babylon -- have proposed budgets that would override a state tax cap and thus disqualify residents from receiving tax rebates. In Patchogue-Medford, a ballot proposition sponsored by a parent group to expand busing for students in nonpublic schools would push that district over its cap as well.

Overriding tax-levy limits requires voter majorities of at least 60 percent.

The attempted cap-bustings have sparked controversy in several communities, including West Babylon.

Outside the polls at Santapogue Elementary School in West Babylon, several residents stood on the sidewalk this morning debating the district's plan to raise next year's tax collections by 3.61 percent. West Babylon's capped limit is 1.36 percent.

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One voter, Nancy Meyer, 72, a retired billing clerk, told a Newsday reporter outside the polling site at Santapogue that she had not really wanted to support the district's proposed $100.5 million spending plan.

"But I have a grandson in the district, so I voted 'yes,' " Meyer added. "He deserves the services."

Vincenza D'Accordo, 79, who also voted at Santapogue, said she disagreed with the district's rationale for raising taxes, especially its contention that some of the extra money would help preserve junior-high sports.

"There's a lot of waste," said D'Accordo, who voted together with her husband, Vincent, 80. "And the sports -- they're always talking about cutting sports. But that's not the most important thing in the world."

A trickle of voters were turning out shortly after noon, some using their lunch hour to vote, at the Pine Park Elementary School in Brentwood.

Most said they were aware that the district was proposing a budget with an increase that was equal to the state's tax-cap limit of 1.53 percent.

Carlos Cintron, a retired police officer, said he was concerned about taxes but found the proposed tax increase "manageable."

"The taxes keep going up and that's not good for anyone but I think our teachers should be paid a good salary," said Cintron, 55, who voted with his wife and daughter, a district graduate. "That was great that the district stayed under the cap. We didn't get killed with the budget numbers this year . . . and if I want good schools for my granddaughter here I have to support it."

Islandwide, property-tax collections, known as levies, would rise an average of just 1.57 percent in the 2014-15 school year.

State tax officials have said qualified homeowners should face no dollar increases at all because of tax-rebate checks scheduled to be mailed out shortly before November's state elections.

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School taxes make up more than 60 percent of homeowners' property-tax bills on average and are the only type of taxation generally subject to a direct vote.

To qualify for the tax rebate, however, homeowners must live in districts that keep within state-imposed caps.

The state's basic cap this year is pegged at an inflation rate of 1.46 percent. Adjusted caps vary widely from district to district, however, because certain revenue and expenses, such as costs of voter-approved school construction, are excluded from state calculations.

Patchogue-Medford faces an unusual situation, with potential statewide ramifications.

The district's proposed $171.4 million budget would stay within the local cap, with a slight reduction in taxes of 0.07 percent. However, a separate $330,948 proposition, placed on the ballot by residents' petition, would result in a 0.26 percent tax increase and pierce the cap.

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Some voters in Hempstead went to the polls seeking a change in leadership, citing poor graduation rates and a lack of activities for students among their biggest gripes.

Also on the mind of voters was a state audit that found the Hempstead Union Free School District routinely and improperly boosted students' grades from failing to passing.

Voter Valeria Batchelor, 47, said she was casting her vote against the incumbent, saying "I'm sure she did a good job back then. But today is a new day."

Across the Island, school leaders predicted high passage rates for budgets, citing a combination of low tax increases and frugality. District spending is projected to rise next year by an average 2.4 percent in Nassau and 2.15 percent in Suffolk -- well below regional averages in recent years.

Over the past six years, more than 90 percent of districts' spending plans have consistently won voter approval during the first round of balloting in May. Any districts where budgets fail can hold June revotes.

Local educators cautioned against complacency, noting that fewer than 15 percent of voters normally turn out for school elections.

"I would say there's genuinely a feeling of optimism about the outcome of budget votes," said David Feller, the North Merrick school chief and president of the Nassau County Council of School Superintendents.

"But you don't want to take this for granted," Feller added. "It's important to come out and vote. It's people's constitutional right, and it's a good example for their kids."

The number of districts on Long Island with proposed overrides has dropped steadily over the three years that caps have been enforced -- from 17 in 2012, to seven last year, to five this year.

A total of 371 school board candidates are running Islandwide, many of them unopposed. Sixty-five districts have 251 candidates in contested elections.

A growing parents' movement against standardized state tests based on new Common Core academic standards has injected that issue into dozens of district contests.

Leaders of Long Island Opt-Out, a grassroots parent organization, had endorsed 36 candidates in 24 districts as of noon Monday and were continuing to review other candidates. The group supports changes in state law that would allow parents to legally pull children out of state tests.

Jeanette Deutermann, of North Bellmore, a founder of the opt-out movement on the Island, said she was urging parents to vote "yes" on school budgets, because "no" votes would not alter state testing.

"Unfortunately, some people feel that turning down a budget is a way to stop the expense of testing and curriculum associated with Common Core," Deutermann said. "What they don't understand is that those will be the only things left, because testing is mandated in law. So they'll take away music instead."

With Victor Manuel Ramos and Jo Napolitano