With a little more than a week remaining in the school year, public school teachers will begin voting today on a proposed contract offer they overwhelmingly rejected in January and that Gov. Neil Abercrombie says has no legal standing.

Voting online and by phone will run through Tuesday.

If teachers reject the proposal again, their "no" votes will give the Hawaii State Teachers Association authorization to strike.

Given the state’s position that it no longer recognizes the contract offer, it’s unclear what would happen if teachers approve it.

In a statement Wednesday, HSTA President Wil Okabe said, "We continue to believe, as the governor did in January, that the tentative agreement we reached with him is in the best interest of teachers, students and the state of Hawaii."

Under the proposal, teachers would continue to take 5 percent wage reductions through June 30, 2013, before moving to a new salary schedule that recognizes years of service.

The state Department of Education also would move to a revised teacher evaluation system that takes into account student academic growth. Teachers rated "effective" or "highly effective" would be eligible for 1 percent "step" raises annually.

The union has said there is precedence nationally for a second vote on a rejected contract, and officials are hoping the state will reconsider its position.

The state, meanwhile, has questioned why the union moved forward with a vote on a deal that has already been voted down rather than continue with negotiations.

In recent weeks, the union canceled three bargaining sessions with the state.

Donalyn Dela Cruz, Abercrombie’s spokeswoman, said the union also declined an offer last week to return to the table.

In a bulletin distributed to teachers, the union said the second vote was called in part because "bargaining at the table with the employer has not been productive."

HSTA also said "a strike vote is our only legal option should the January agreement not be approved."

Since July, teachers have been working under a "last, best and final" contract offer the state imposed when talks reached an impasse.

Paul Daugherty, a member of HSTA’s negotiating committee and a math teacher at Konawaena High School, said a number of teachers who rejected the contract in January have changed their minds and now support the offer.

But, he said, "I think teachers are concerned about what happens if they do approve it. My response: Let’s approve it and put it on the governor."

Daugherty added that if a strike is authorized, "it doesn’t mean it’s going to happen. But it does give a different flavor to the negotiations process when you basically tell the employer we’re willing to do it."

Still, some teachers remain staunchly against the proposal and have expressed anger about the union’s decision to hold another vote.

Kalani High art teacher John Nippolt said he won’t vote again.

"This is a waste of time and money," he said. "The governor has already said there’s nothing on the table."