City councillor Marjorie Decker is asking that the schools budget be referred to the full council for a vote and facing questions over a canceled May 16 meeting on the topic.

The $151 million schools budget – frozen in the Finance Committee May 9 despite the expectation that the full City Council would adopt the city’s full, $507 million proposed budget today – are sure to be a big part of the 5:30 p.m. meeting of the City Council.

While the mayor and councillor Marjorie Decker, who leads the Finance Committee, are asking that the schools budget be discharged from committee and referred to the full council for a vote, three councillors are holding firm for further budget hearings.

Councillors Leland Cheung, Craig Kelley and Denise Simmons say there is time for more hearings before a June 3 adoption, with June 5 being the deadline for adopting a city budget.

“The city councillors that voted against moving this proposed school budget out of committee did so with the understanding that another Finance Committee meeting was tentatively scheduled for May 16 … to allow for any further budget discussions that might be needed,” they wrote in policy order to be heard tonight. “For reasons that remain unclear, the Finance Committee subsequently canceled the hearing that was to take place on May 16.”

Mayor Henrietta Davis, who also leads the School Committee that approved the budget for a vote by the council, has another idea: A June 10 roundtable of the two boards to serve as a follow-up meeting to discuss issues raised in the budget hearing.

Whatever happens Monday, Superintendent Jeffrey Young and councillors agree their concerns won’t be addressed further in the coming fiscal year’s budget, and in a Thursday letter four councillors – Cheung, Kelley, Simmons and Ken Reeves – agreed as well that there should be more roundtables with the School Committee and district administrators.

But they also laid out their seven primary concerns, including a lack of universal early childhood education; teacher training on classroom management and school discipline and climate; family liaisons and family engagement; the loss of students from the district, including to charter schools; the lack of a comprehensive long-term picture to make informed decisions about expenditures; the need for a five-year projection for the Innovation Agenda; and “demographically disparate” events, activities, programs and awards in a system that is supposed to be multicultural.

“Many citizens throughout the city share this concern. In each of the last three Citizen Satisfaction Surveys, the quality of our public schools has been the top-ranking concern amongst all Cambridge residents,” they wrote.

Minka vanBeuzekom was the fourth councillor to vote to hold the budget in committee; Reeves left before a vote, and Tim Toomey voted “present.”

The council meets at 5:30 p.m. Monday at City Hall, 795 Massachusetts Ave., Central Square.