* Two sides remain far apart on new teacher contract
* More than 350,000 public school students affected
* Union opposed to evaluations based on student test scores
By Greg McCune and Mary Wisniewski
CHICAGO, Sept 12 (Reuters) - Chicago teachers stayed away from public schools for a third day on Wednesday in a strike over Mayor Rahm Emanuel's demand for tough teacher evaluations that U.S. education reform advocates see as crucial to fixing urban schools.
With more than 350,000 children from kindergarten to high school age out of school, the patience of parents and labor negotiators began to fray as hopes of a quick resolution to the biggest U.S. labor strike in a year were dashed.
"There's frustration on both sides," Jesse Ruiz, vice president of the Chicago Board of Education, said on Wednesday. "There's got to be give and take."
Talks are scheduled to resume on Wednesday. Emanuel on Sunday called the strike "unnecessary" and said a deal was close. But fiery union president Karen Lewis, who has called Emanuel a "liar and a bully," on Tuesday said the two sides had agreed on only six of 49 provisions of a new contract.
An exasperated Chicago School Board President David Vitale said he would not go back to the negotiating table until the union made a comprehensive proposal to resolve the strike.
"I think the key is that the people making these decisions want to make them unilaterally," Lewis told reporters outside the site of talks at a Chicago hotel on Wednesday.
Lewis led the walkout on Monday of more than 29,000 teachers and support staff in the nation's third-largest school district, saying the union would not agree to school reforms it considers misguided and disrespectful.
The dispute jolted the United States, where a weakened labor movement seldom stages strikes and even less frequently wins them. Organized labor has lost several fights in the last year including Wisconsin stripping public sector unions of most of their bargaining power, Indiana making union dues voluntary and two California cities voting to pare pensions for union workers.
The strike in Barack Obama's home city has also put the U.S. president in a tough spot between his ally and former top White House aide Emanuel and labor unions Obama is counting on to win re-election on Nov. 6.
Obama has said nothing in public about the dispute, allowing administration surrogates to urge the two sides to settle.
"The president has said what is appropriate to be said, which is that it is a local issue," said Randi Weingarten, national president of the union that represents Chicago teachers. "It has to be settled at the bargaining table."
Obama's own Education Department has championed some of the reforms Emanuel is seeking, and a win for the ambitious Chicago mayor would add momentum to the national school reform movement.
"Being on the sidelines at the moment is fine. As long as it gets settled in a reasonable time period, no one's going to blame the president," Dick Simpson, a professor at the University of Illinois at Chicago, said of Obama and the 2012 election.
"He needs to get the full support of the unions and the Democratic Party but he also has to appeal to the independent voter to win the margin in the key states," Simpson said.
Emanuel, who was scheduled to speak to a group of bankers in New York on Friday, has canceled the trip, his office said.
NO COMMON GROUND?
The first poll of Chicago voters since the strike showed 47 percent supporting the teachers union, 39 percent against the strike and the rest uncommitted, according to the Chicago Sun-Times newspaper.
The city is operating 147 schools with non-union staff to offer meals and "keep children safe and engaged," but only a fraction of parents have been using that option, officials say.
At Disney elementary school on the city's northwest said, several dozen strikers with homemade signs targeting Emanuel and school policies picketed in cool, sunny weather on Wednesday.
Kent Barnhart, a music teacher for the past 25 years, said neighborhood parents had been supportive, offering water and opening their homes and even joining picket lines to march. But he said teachers were frustrated with the slow talks.
"It's difficult for us to understand why they have not truly discussed over the last 11 months things that have been very important," he said of school officials. "It didn't seem like they took it seriously - really important things like evaluations, health benefits and pay."
Both sides agree Chicago schools need fixing. Chicago students consistently perform poorly on standardized math and reading tests. About 60 percent of high school students graduate, compared with 75 percent nationwide and more than 90 percent in some affluent Chicago suburban schools.
The fight does not appear to center on wages, with the school district offering an average 16 percent rise over four years and some benefit improvements.
The union is fiercely opposed to Emanuel's demand that teacher performance be evaluated in part on the results of their students on standardized tests because it says teachers have no control over the conditions in which students live such as crime-ridden neighborhoods, poverty and disengaged parents.
More than 80 percent of Chicago public school students qualify for free lunches at school because they come from low-income households.