There are two different visions for school construction in Suffolk during the next few years — that of the School Board and that of the City Council.

With a gap of at least $24.7 million separating the two visions, a special joint meeting on Wednesday had, in part, been intended for the two groups to compare their ideas and look for a consensus on the issue.

Ideas were shared, but the two groups seemed no closer to an accord at the end of the meeting than they were before the got together.

The two entities are at odds over two elements in the Suffolk Public School’s 10-year capital improvements plan: funding for a new elementary school and a new middle school.

“We have different numbers and methodologies, but we’re working together on this and will come up with the best final numbers to build a quality school,” School Superintendent Milton Liverman said.

The School Board seeks $20.5 million for a new facility to replace Southwestern and Robertson elementary schools, along with $51.4 million for a middle school.

City Council, on the other hand, has proposed to spend $16 million for the elementary school, not including $1.5 million in prior funding, and $32.4 million for the middle school.

The City Council plan also recommends either upgrading John Yeates Middle School or building a new middle school on that site to save site costs. The council plan includes $20.4 million in 2012 to accomplish that task.

Liverman said the council’s recommendation would be something for the board to consider.

The $5.5-million difference between the School Board’s and City Council’s estimates for the new elementary school was attributed to sources used and factors taken into account when formulating their estimates.

Anne Seward, budget director for the city administration, said the city used the state education department’s website, which publishes costs of for school construction, to calculate costs. Liverman said the School Board took those same costs into account, in addition to local information that would impact the building phase.

Jim Thorsen, director of facilities and planning for the schools, said the board’s costs also included other necessary items, such as furnishings, technology and fire protection, which he said were not included in the state’s numbers that the city used.

The School Board’s estimates also included enhancements such as terrazzo floors and pitched roofs. Such upgrades may cost more up front but will save the schools money in the future, Liverman said.

Both sides agreed they must work together with available resources and wait until bids are in until the next step can be made.