CHICAGO – Chicago Mayor Rahm Emanuel wants contract negotiations with teachers to continue with students in class.

He spoke to reporters Wednesday as teachers in the nation's third-largest school district picketed for the third day. A number of issues remain, including teacher evaluations. But the Chicago Teachers Union says they're far from an agreement.

The strike has left more than 350,000 students out of class.

Meanwhile, Chicago Public Schools has increased the hours it's keeping schools open where children can go during the day. Those schools don't offer instruction, but allow students to get meals and be supervised.

Emanuel says those 140 some schools will also be increasing their availability with computers. He says that's so students can get in some learning.

Emanuel reiterated his message that the strike was avoidable.

Union leaders said they were meeting Wednesday to review a new, comprehensive proposal from school board negotiators that addresses all the issues still on the table. The board has requested either a written response or a comprehensive counterproposal from the union.

But the teachers were lowering expectations for an agreement, buoyed by energetic rallies in which even parents inconvenienced by the strike waved placards in support. Other unions were joining in, with school custodian representatives saying their members will walk off the job this week as well.

Board President David Vitale, the lead schools negotiator, said that a deal could be reached, but union President Karen Lewis and her colleagues emerged from the talks accusing the board of having dug in its heels with its new proposal. Among the biggest remaining issues are a new teacher evaluation system and a process for deciding which laid-off teachers can be rehired.