Negotiators for the Chicago Teachers Union and the nation's third-largest school district resume talks on Thursday with fresh optimism about an agreement to end a four-day strike over education reforms sought by Mayor Rahm Emanuel.

"We are definitely coming much closer together than we were," a smiling Karen Lewis, the teachers union president, said after talks went late into the night on Wednesday. "Both sides making movement, coming together."

The strike by 29,000 public school teachers and support staff began on Monday and has affected 350,000 elementary and high school students in the biggest strike in the United States this year.

"The conversation was productive," Barbara Byrd-Bennett, chief education adviser for Chicago Public Schools, said on Thursday. "There was steady and substantial movement on key issues around teacher evaluation and layoffs and recall.

"As these conversations proceed this morning there is little doubt in my mind that if the union wants to we can wrap this as an agreement and our children can be in school tomorrow."

The walkout has spotlighted contentious education reforms backed by the Obama administration and tested union backing for Obama and Democrats heading into the November elections.

"The statements were very positive last night and we can hope for more progress," said Terry Mazany, former CEO of Chicago Public Schools. "The strike has opened up a Pandora's box. The challenge for leaders of both sides is to get the members back in the box, the public back in the box."

For the first time in days, Emanuel's chief negotiator, School Board President David Vitale, agreed with Lewis' summary of the talks on Wednesday night. Only 24 hours earlier, Vitale had threatened not to come back to the negotiating table until the union put forward a better offer.

"We had a very productive evening," Vitale said. "We all go away hopeful that we can go come together on this."

TEACHERS, PARENTS TESTED

Patience of parents was strained as hopes of a quick resolution to the biggest U.S. labor strike in a year faded earlier on Wednesday. About 150 Chicago schools have been staffed by principals and volunteers to provide meals and half-day care this week but only a fraction of idle students have shown up. Parents have stayed home from work, tapped relatives, and used community centers, churches, park district facilities and other resources to supervise children during the strike.

Lewis acknowledged progress on the two most vexing issues - using student test scores to evaluate teachers and giving more authority to local principals to hire teachers.

The union is concerned that more than a quarter of its membership could be fired because the teachers work in poor neighborhoods where students perform poorly on standardized tests, which Emanuel wants to use to evaluate teachers.

"This is really not a 'gotcha' evaluation system," Byrd-Bennett said. "It's to make sure we have a very high standard ... that will keep the very best teachers in front of our students every day."

Lewis said the union fears Emanuel plans to close scores of schools, putting unionized teachers out of work. In recent years about 100 public schools have been closed, with officials usually citing low enrollments. At the same time, a similar number of public-funded, non-union charter schools have opened.

About 52,000 students enrolled at those schools have not been affected by the strike this week.

The strike in Barack Obama's home city also has put the U.S. president in a tough spot between Emanuel, formerly a top aide to Obama, and the labor unions that Obama is counting on to work for his re-election on November 6.

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.

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. Chicago schools already have a projected $665 million budget gap for the year that began in July, a key factor driving Emanuel's reforms.

More than 80 percent of Chicago public school students qualify for free school lunches because they come from low-income households.