It’s been a bumpy couple of years for the Broward school district — corruption arrests rocked both the school board and teachers union, while deep budget cuts prompted mass teacher layoffs.

This year’s proposed $1.6 billion budget won’t fix all of the district’s issues, but it largely aims to steady the ship by focusing attention, and resources, on classroom instruction.

To that end, Broward is adding more than 650 teacher positions in its 2012-13 budget, a stark departure from last year’s spending plan that eliminated well over 1,000 teachers.

“This budget reflects a clear priority of directing our dollars to the schools,” School Board member Laurie Rich Levinson said. “Parents should see that we are clearly on the right track in terms of being fiscally responsible.”

The school district will be holding an upcoming job fair for the teacher positions, but applicants must register online by Tuesday to participate. The registration form can be found at www.browardschools.com.

As a result of these new hires, Broward will be able to reinstate music, art and physical education to its elementary schools. Those positions were cut last year — sparking complaints from parents.

For homeowners, though, there will be a slight bump upward in their property tax bill. The school district portion of property tax bills will rise by about 1.5 percent, or $3.80 for a $125,000 home that claims a standard homestead exemption.

Broward’s added teachers will be key to the district’s goal of complying, as best it can, with the state’s class-size requirements. Last year’s widespread teacher layoffs led to more than half of Broward’s classes being in violation of class-size rules. The state slapped Broward with a $66 million fine as punishment, though the fine was reduced to $8.5 million after Broward adopted strategies to tackle the issue.

Broward Superintendent of Schools Robert Runcie predicted the district will do “significantly better” when it comes to managing class sizes, though he cautioned that it is nearly impossible to score perfectly under the state’s formula. Two years ago, before that massive round of teacher layoffs, Broward boasted a 97 percent compliance rate.

Though the district received a modest $22 million increase in state funding for the upcoming year, much of its ability to deploy more teachers came from internal restructuring. The school system’s long-troubled transportation department, which had been plagued by absenteeism and other issues, was overhauled for a projected savings of $14 million. School bus routes were reconfigured to save fuel costs, the allowable amount of overtime was reduced, and school bus tires will be now leased because it’s cheaper (Broward already does the same with its public transit buses).

Not all of Runcie’s efforts to squeeze productivity out of district employees have been well-received, however. A proposed switch to a centralized bookkeeping system, announced earlier this year, has been scaled back to a trial pilot program. Many Broward schools have long had their own in-house bookkeeper, and those employees reacted with alarm at the suggestion that such services were no longer needed.

“It was kind of delayed, rightly so,” said School Board member Nora Rupert, who added that phasing in such a dramatic change “at least gives these people time to plan their future.”