(CNN) -- Striking Chicago public school teachers amassed outside the school system's headquarters for a second day Tuesday, September 11th as their union announced little progress on reaching a new contract deal.
"It is not accurate to say both sides are extremely close -- this is misinformation on behalf of the Board and Mayor (Rahm) Emanuel," Chicago Teachers Union spokeswoman Stephanie Gadlin said in a news release.
"We have a considerable way to go. This is a fact they cannot deny," she said.
Of 49 points in the contract offer, the union has signed off on only six, she said.
"We are fighting for our students; we are fighting for education justice," she said.
But Emanuel cast the strike in very different terms.
"This was a strike of choice. And it's the wrong choice for the children," he told reporters Tuesday.
"We're down to two issues," after months of negotiations, he said.
The talks could have continued without a strike, which was "totally avoidable, totally unnecessary," Emanuel said.
After no final deal was reached Monday, talks resumed Tuesday morning.
School board President David Vitale said Monday night that a deal could come soon that would help get the city's 350,000 students back into classrooms.
"This is hard work. We want to get this resolved. We want our kids back in school," he said.
Chicago's first teachers strike in 25 years has pushed parents to scramble for alternatives for their children.
"If the kids are not in school, they're out getting into some kind of trouble ... when they should be in school, learning," said Shatara Scaggs, a mother of two children in kindergarten and first grade who opposes the teachers' decision to strike. "I think they should be in school getting an education."
Police, expecting an uptick in trouble with more kids on the streets, pulled officers from desk duty to increase patrols due to the strike. Dozens of churches and civic organizations stepped in to provide activities for thousands of suddenly idle students, while the school district opened 144 of its 578 schools for part of the day to provide a safe environment and meals to children in need.
Many children going to these in-school programs had to pass picket lines, as their teachers chanted, held signs and otherwise made their opinions heard. Ola Esho, the father of a student at Ray Elementary School, told CNN affiliate WBBM he "was not happy" about the commotion and tension, 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, another father of children at the same school in the city's Hyde Park neighborhood.
The union that represents nearly 30,000 teachers and support staff in the nation's third-largest school district called the strike after negotiators reached an impasse. The union said the two sides were close Sunday night to a deal on pay, but far apart on teacher evaluations, benefits and other issues.
Emanuel said the sticking points are teacher evaluations and provisions dealing with jobs for laid-off teachers.
Teachers are concerned about job security in the wake of a new program that evaluates them based on students' standardized test scores. Chicago Teachers Union board member Jay Rehak called the idea "data-driven madness."
As many as 6,000 teachers could lose their jobs under the evaluation system, according to Lewis, who called the system "unacceptable." The mayor's office, the city of Chicago, 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 ensure that over time, the quality of teachers will improve. The testing was "designed by teachers for teachers to take," he said, and the first year results won't count against teachers while the system is improved.
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.
Pay another issue. However, the union said the two sides are close to a pay agreement after school officials offered to increase salaries 16% over four years on average for most teachers.
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 existing proposal would cost $400 million over four years, Vitale said.
CNN's Josh Levs, Michael Pearson, Casey Wian, Greg Botelho, Ted Rowlands and Greg Morrison contributed to this report.