DOVER — Budget-writing lawmakers broached the possibility of consolidating some of the state’s 19 school districts Wednesday, but top education officials said it wouldn’t save much money.

Department of Education officials appeared before the Joint Finance Committee for the second day in the monthlong series of budget hearings. But, despite meeting for six hours, the committee didn’t finish covering the agency and its $1.38 billion budget.

About one-third of the state’s current budget goes to the department and the schools.

Several lawmakers questioned the notion that fewer school districts would largely result in the same expenses, a conclusion reached in a past study.

Committee members asked what the state can do to better attract and keep educators. JFC co-chair Sen. Harris McDowell, D-Wilmington, noted “we are a net exporter of well-educated teachers.”

Appoquinimink School District Superintendent Matthew Burrows, appearing alongside the state’s new education secretary Susan Bunting, told the committee Delaware does well in terms of keeping teachers — the problem is getting them to settle in Delaware in the first place.

According to the National Education Association — the teachers’ union — for the 2012-13 school year a teacher starting his or her career in Delaware was paid $39,338.

That’s above the national average but more than $2,500 below Pennsylvania, $4,000 below Maryland and $9,000 below New Jersey.

“Once they get into our system we retain a lot of those great teachers because they buy into what we’re doing,” Mr. Burrows, the head of the statewide superintendents’ association, said.

Appoquinimink is taking part in a pilot program designed to keep teachers in the classroom, giving them opportunities to move up the ladder there rather than by jumping into administration.

Gov. John Carney, who took office in January, plans to shift the department from a regulatory agency to one more geared toward supporting individual schools and districts.

His predecessor, Gov. Jack Markell, had been criticized for what some critics saw as a heavy-handed approach and over-centralized education department.

Delaware has seen a large increase in special-needs children in recent years — a result, Dr. Bunting said, of the state working to identify students at a younger age.

Dr. Bunting told JFC the department will give students Individualized Education Programs even if students have not been conclusively diagnosed. The concern, she said, is that not doing so could eventually lead to litigation.

“Special needs can run the gambit from a reading disability to an emotional disturbance,” she said.

People also move into the state specifically for its highly touted special education programs, according to department officials.

Education department officials will again appear before JFC again today, with the hearing for the state’s universities being shifted to next week