EAST GREENWICH — More than a month after the opening of schools — delayed three days by a teachers walkout — the School Committee and the 235-member East Greenwich Education Association appear to be no closer to a contract settlement.

The second mediated bargaining session since the teachers’ court-ordered return to work was scheduled for 6:30 last night in the Cranston offices of National Education Association Rhode Island, the East Greenwich union’s parent organization.

Neither NEARI representative Jane Argentieri nor School Committee Chairwoman Suzanne McGee Cienki saw any reason for optimism about the session, although Argentieri added, “I still have a Polyanna approach to this.”

The school board’s latest proposal calls for a three-year agreement to replace the one that expired Aug. 31. It provides raises of 2.5 percent in the first year and 2 percent in each of the remaining years; and an increase in the members’ contribution toward the cost of their health coverage — which currently ranges from 5 to 10 percent, depending on length of service — to 12 percent in the first year, 15 percent in the second and 18 percent in the third.

The union has countered that offer, but it has not made public the terms of its proposal.

“I don’t think we are any closer,” Cienki said yesterday. “As the process continues . . . our budget outlook is going to get bleaker and bleaker. Everything [pensions, insurance] is spiking up higher than we even anticipated.”

Cienki said the district is anticipating a 15 percent increase in its pension contributions and that the schools’ premium for property liability insurance rose 16 percent.

“Those are the things you look at. As your numbers come in you set your budget,” she said. “The pot of money that you have starts to shrink. As the numbers projections come in, we have less and less flexibility.”

Argentieri said the the union is “convinced that the management is inflating the increases.”