A second day of negotiations between Chicago's school board and its striking public school teachers ended Tuesday 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.