County Executive Isiah Leggett calls the high-achieving Montgomery public school system “the crown jewel,” the heart of the county’s appeal to families and companies looking to relocate.

That has meant the royal treatment for K-12 education at budget time, especially when the economy was strong. Schools claim about half of the county’s $4 billion operating budget.

“The money was so readily available, the question wasn’t ‘if,’ it was ‘how much,’ ” said council member Valerie Ervin (D-Eastern County), a former member of the Montgomery Board of Education.

But the Great Recession has squeezed Montgomery’s finances and frayed relations between the Board of Education and the County Council. As the 2014 budget season begins with a $135 million budget gap, council members are asking increasingly pointed questions about their heavy investment.

Some of their displeasure comes from a report released Tuesday on the achievement gap separating Montgomery’s white and minority children. It frames this year’s $2.23 billion budget request from the board and Superintendent Joshua P. Starr in a different and perhaps harsher light.

The study, by the council’s Office of Legislative Oversight, shows a widening academic gulf separating white and Asian students from black and Hispanic students in certain measures. Although the system improved in some categories, such as graduation rates, disparities have deepened on state math exams in grades three, five and eight, where whites and Asians are far more likely to score at advanced levels.

“I’m disappointed in the results,” said council Vice President Craig Rice (D-Upcounty), a member of the council’s education committee and a public school parent. “With the amount of money we’ve invested over the years, I would have expected to see more.”

The board’s proposed budget, for the fiscal year that begins July 1 is nearly $10 million above the level mandated by the state’s “maintenance of effort” law, which requires that schools receive, at a minimum, the same rate of per-pupil funding as in the previous year.

Given the overall size of the budget, $10 million is a modest amount. Yet it has taken on a symbolic significance as council members, frustrated that most county employees had to forgo raises last year while teachers saw increases, call the system to account.

Rice, like other council members, said he wants assurances that any extra funding will go directly toward addressing the achievement gap.

Starr said his budget meets that objective. The additional money sought for fiscal 2014 addresses achievement gaps — particularly in middle schools, where disparities are the widest, he said.

His proposal includes nearly $2 million to hire 30 middle school math and reading teachers. About $1.5 million would upgrade training and support for middle school teachers. Funds for about 160 new positions would be aimed at improving special education and instruction for students who speak English as a second language.

“I did exactly what I said I was going to do,” Starr said. “I made sure the budget is aligned toward our strategic needs, and I think I’ve been pretty straightforward about it.”

But council members say some spending decisions by the school system reflect a tone-deafness, even arrogance, given the county’s fiscal straits in recent years.

While most county employees last year took furloughs and a $2,000 lump sum in lieu of an annual raise, teachers received two salary increases totaling about 7 percent, raising average pay from $74,700 to $80,000. County government employees saw an increase in their share of group insurance premiums and now pay 20 to 25 percent. Teachers pay 5 to 10 percent. Had the system raised the teacher share of the premiums, it might have prevented cuts to music teachers, media assistants and counselors, county officials say.

With a fragile economic recovery underway, Leggett (D) is proposing the first real raises for most county workers in three years as part of the 2014 budget he will unveil Friday. But Montgomery still faces the budget gap, and council members say that even if the economy continues to improve, a new normal is in place that makes a return to the free-spending days of the 1990s and early 2000s unlikely for the school system.

“Helping [school officials] understand the facts of the Montgomery tax base is a real challenge,” said council member Nancy Floreen (D-At-Large). “They just don’t seem to be interested.”

Starr said he stands by last year’s raises. His budget this year includes $18 million for increased pay, which he says is essential to meet more rigorous national education standards.

The school district is asking teachers “to do very different work than they did in the past, and they’ve embraced it,” Starr said.

Most Board of Education members said they are merely meeting their obligations to teachers and families by pressing for $10 million above what’s mandated by the maintenance-of-effort law.

“If you break it down, we’re talking about 36 cents per kid, per school day. That’s pretty reasonable,” Board of Education President Christopher S. Barclay said.

Board of Education Vice President Philip Kauffman said the board is trying to balance the country’s limited resources with a growing school system that is adding diverse students with more intense needs.

“They think we’re declaring war on them by asking for this increase,” Kauffman said. “If we wanted to declare war, we would have asked for a whole lot more.”

Kauffman said the maintenance-of-effort law wasn’t meant to establish a ceiling for education spending but a floor.

And that is what has also frustrated many members of the council. Under changes in the state law last year, engineered with heavy support of the teachers union, any spending above the maintenance-of-effort threshold automatically becomes part of the next year’s base. And, if the council fails to meet the legal minimum, county income tax revenue can be funneled directly to the public school system.

Leggett declined to say in an interview what he’ll recommend for school funding. But he said he does not begrudge the system’s aggressive pursuit of every possible dollar.

“I want a school board and a superintendent out there fighting for these kids,” he said.