The union team spent more than an hour and a half reviewing the district’s proposal, which officials said would invest more money into teacher pay over the next three years. Ultimately, Henry Roman, the union president, said it seemed to him the district “deliberately constructed a proposal” that seemed to significantly change things, when it did not.

Cordova said she was extremely disappointed that the union wasn’t willing to continue negotiating.

“This is the most important thing we can be doing right now,” Cordova said. She added that this dispute will end in an agreement sooner than later, and questioned why there was a need to wait.

Union officials asked Cordova to agree to the concepts they wanted to change: offering a salary schedule with more opportunities for teachers to earn raises by changing “lanes” on the schedule, and allowing teachers to use in-district training to do that. If she could not agree to those concepts, union officials said it was a waste of time to stay.

Cordova pleaded with the union negotiators to stay as long as it took to reach an agreement, and said she would need time to consider the union’s counterproposal, but she refused to agree to anything specific in the moment. She also criticized what appeared to her like several million dollars in new costs in the union counterproposal.

“We brought millions of dollars to the table today,” Cordova said. “What you’ve effectively done is you’ve increased the cost to make us further apart.”

Saturday’s negotiations repeated a pattern that has occurred several times during bargaining, with district leaders making what they see as significant concessions, only for members of the bargaining team to dismiss them as too little — or as not as good for teachers as they might appear on the surface.

The district’s last offer on Saturday night would put an additional $23.5 million into teacher salaries next year. The union’s last counterproposal did not have a price tag associated with it, but previous union proposals have not come lower than $28 million.

In the end, Rob Gould, the union’s lead negotiator said if the district really needed more time, “they can have until Tuesday.”

Teachers clapped and cried, and emptied the room within minutes. The union is now preparing to start a strike on Monday morning. Union leaders said they would consider returning to bargain on Tuesday.

The district and the union are not negotiating their master contract this year, but rather how to revamp ProComp, Denver Public Schools’ system of bonuses and incentives that teachers receive on top of their base pay. The union wants to shrink the number and size of incentives, and significantly boost teachers’ base salaries.

The district wants to keep certain incentives more robust. Cordova has said she thinks extra pay is key to attracting and retaining good teachers at high-poverty schools. But the data on teacher retention at schools where teachers currently get a “highest-priority” incentive is mixed. Increasing the size of this incentive

In explaining the district’s proposal Saturday, Cordova said she had completed her evaluation of each department in the district and now said the district would cut 150 positions to save the district about $20 million. She promised the cuts would not be made to employees such as janitors or teacher’s aides, but said the central office employees that would be cut are still some who interact regularly with schools. She said the impact will be noticeable.

That new money would go into slightly higher base salaries for teachers than previously proposed.

Union leaders characterized their time as wasted. Friday’s bargaining session and the first three hours Saturday had been spent discussing details of how teachers might get salary increases with credits from the district’s teacher training, or “professional development units,” but the big district proposal Saturday overlooked the details from those discussions, they said.

District officials say one of their concerns is that if they allow teachers to get raises too easily by accumulating credits from district training, too many teachers would be getting salary increases each year and costs would balloon.

Union negotiators don’t think that concern is realistic. Gould, the union’s lead negotiator, estimated that under the district’s plan it would take teachers 300 hours of training outside of the work week to get a raise in one year.

“Your concern is that everyone is going to run right out and do five PDUs per year,” Gould said. “Teachers are already stretched to the max. There’s no possible way.”