CHICAGO (CNN) -- A second day of negotiations between Chicago's school board and its striking public school teachers ended Tuesday, September 11th with neither side expressing optimism that an agreement was near.
"This was silly season," board President David Vitale told reporters after emerging from more than 10 hours of talks. "It is time for us to get serious."
Vitale said the board had presented the union with a "comprehensive proposal" and would resume negotiating only after "we receive a written response or a comprehensive proposal of their own."
But Barbara Byrd Bennett, interim chief education officer, said the negotiating would continue Wednesday, whatever happens. "Our team will be back here tomorrow," she said.
Chicago Teachers Union Vice President Jesse Sharkey said the day's discussions had centered on teacher evaluation and that "some substantial movement" had been made, but not enough.
"I don't want to get in the weeds, but I'd say we moved more than they did today," he said.
The board proposal would leave some 28% of teachers in danger of dismissal within a two years, he said, calling that "an insult to our profession."
"They basically dug in their heels and said if we didn't give them a comprehensive proposal, we didn't have anything to talk about," Sharkey said.
The negotiations ended after thousands of striking teachers had spent much of the day massed outside the Chicago public school system's headquarters.
Carrying signs, they chanted and marched through the streets in an expression of solidarity in their fight against the school board.
"We have a considerable way to go," union spokeswoman Stephanie Gadlin said in a news release. "This is a fact they cannot deny."
Of 49 points in the contract offer, the union has agreed to just six, she said.
"We are fighting for our students; we are fighting for education justice," she said.
Mayor Rahm Emanuel cast the strike in different terms.
"This was a strike of choice. And it's the wrong choice for the children," he told reporters.
After five months of negotiations, "we're down to two issues," he said. The sticking points are teacher evaluations and provisions dealing with jobs for laid-off teachers, said Emanuel.
The talks could have continued without a strike, which was "totally avoidable, totally unnecessary," Emanuel said.
After no deal was reached Monday, talks resumed Tuesday morning.
Late in the afternoon, U.S. Education Secretary Arne Duncan issued a statement expressing confidence "that both sides have the best interests of the students at heart, and that they can collaborate at the bargaining table -- as teachers and school districts have done all over the country -- to reach a solution that puts kids first."
Chicago's first teachers' strike in 25 years has left many parents scrambling to find alternatives for their children.
"If the kids are not in school, they're out getting into some kind of trouble," said Shatara Scaggs, a mother of a kindergartner and first grader. "They should be in school getting an education."
To prevent a possible uptick in trouble from kids on the streets, police pulled officers from desk duty to increase patrols. Dozens of churches and civic organizations have stepped in to provide activities for idle students, and the school district has opened 144 of its 578 schools for part of the day to provide a safe environment and meals to children.
Many children going to these in-school programs saw their teachers chanting, holding signs and otherwise voicing their opinions. Ola Esho, whose child attends Ray Elementary School, told CNN affiliate WBBM he "was not happy" about the commotion, which he said unnerved his children.
"I would not want to keep my children here unnecessarily, so I'm taking them back home," said Yahu Vinayaraj, whose children attend the same school in the city's Hyde Park neighborhood.
The union, which represents nearly 30,000 teachers and support staff in the nation's third-largest school district, called the strike Sunday night. The union said the two sides had been close to a deal on pay, but far apart on teacher evaluations, benefits and other issues.
Teachers are concerned about job security in the wake of a new program that evaluates them based on their students' standardized test scores. Chicago Teachers Union board member Jay Rehak called the program "data-driven madness."
As many as 6,000 teachers could lose their jobs under the evaluation system, said union President Karen Lewis, who called the system "unacceptable." The mayor's office, the city and school officials have questioned that job-loss figure.
Randi Weingarten, president of the American Federation of Teachers, said the situation in Chicago speaks to national concerns.
"Between the need to actually help kids really learn how to apply knowledge, not rote memorization skills, combined with the poverty that is increasing in this country, combined with all of the budget cuts, it has made situations all across the country really difficult for both parents and teachers," Weingarten told CNN. "And a lot of that is playing itself out in Chicago."
Teachers want to "make sure that the time that we have with kids is about teaching and learning, not about test prep," she said.
Emanuel said the goal is to improve teaching. The testing was "designed by teachers for teachers to take," he said.
The union supports a "recall" policy that would put laid-off teachers in line for job openings at other schools within the district. Emanuel said such a policy would take hiring decisions away from school principals and put them in the hands of central administrators and union leaders.
"Direction and dictation should not come out of downtown," the mayor said.
Teachers also want to block changes to their health benefits and win concessions on classroom conditions.
However, the union said the two sides are close to a pay agreement after school officials offered to increase salaries by an average of 16% over four years.
The median base salary for Chicago public schools teachers in 2011 was $67,974, according to the system's annual financial report.
In addition to a pay raise, the school system's offer includes paid maternity leave and short-term disability coverage. It would also freeze health care cost increases for two-thirds of the union's membership.
The high school day would be shortened slightly, and teachers would be limited to teaching five classes, the district said.
The district's proposal would cost $400 million over four years, Vitale said.
CNN's Amanda Watts, Josh Levs, Michael Pearson, Casey Wian, Greg Botelho, Ted Rowlands and Greg Morrison contributed to this report.