Updated 10/04/12 – 5:30 a.m.

EVERGREEN PARK, Ill. (CBS) — Talks to end the teachers’ strike in Evergreen Park broke down early Thursday morning, meaning kids will be kept out of class for a third day.

The talks ended after the school board rejected the latest offer from the union, spokesman Dave Comerford said. The union, according to Comerford, had made “significant movement” on the issue of health insurance.

Comerford said the union will now no longer meet face to face with the board after a “screaming outburst” by the board’s attorney. All communication will be conducted through a mediator, he said.

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School Board President Kathy Rohan says the school board lawyer may have been frustrated because the negotiators for the teachers continually interrupted him as he spoke.

Talks are expected to resume today at 4:30 p.m.

Both sides met Wednesday evening, to try to find some common ground across the bargaining table.

Contract talks resumed at about 4:30 p.m. and lasted late into the night.

Several people waited outside the Evergreen Park Village Hall for hours in the rain Wednesday evening, waiting to hear word of any progress.

Initially, talks were not set to resume until Friday, but sources said the two sides had their schedules come together, and heard angry words from parents, prompting Wednesday’s talks.

The teachers’ strike in Evergreen Park started on Tuesday, after negotiations ended late Monday night without a contract agreement.

The union said earlier contract talks ended when the school district threatened to not allow students to make up days lost to a school strike, or pay teachers for those lost days.

But the board has denied providing the union with a proposal denying students make-up dates for school days lost to the strike. The board said it did tell the union before the strike that teachers would not make up lost days, and would not be paid for them.

A statement from the board said, “the board does not intend to reward striking employees who harm the students, their parents, and the community.”

The district is seeking a four-year agreement, but teachers want a three-year deal.

The board has offered pay raises based on the consumer price index, with bonuses based on test scores. The teachers want raises of at least 3 percent a year, and oppose basing bonuses on test scores.

The board also wants to eliminate contributions to health reimbursement accounts, while teachers want the district’s contributions to increase slightly.