One of Gov. Andrew Cuomo’s priorities this year, he said recently, is to make sure that needy schools get their fair share of funding.

“Right now we have no idea where the money is going,” Cuomo said earlier this month. “We have a formula. We direct it to the poorer districts. But what did Buffalo do with it? What does New York City do with it?”

If he really wants to know what New York City does with its school aid, he could start by looking at the city’s “Fair Student Funding” formula.

The city adopted the school-budget system in 2007 as a way to send more money to schools with the neediest students. It replaced a system where funding was tied to teacher salaries, which had advantaged high-performing schools that ended up receiving more money because they attracted more experienced teachers with higher salaries.

But a decade later, the funding formula has not lived up to its promise. Most schools have never received the full amount the formula says they’re owed, while some actually get more than their fair share. And some principals say the formula has had the effect of making veteran teachers hard to afford.

One example: At the Metropolitan Expeditionary Learning School in Queens, a number of veteran staff members recently qualified for longevity-based raises that added roughly $340,000 to the school’s expenses. Because the formula does not give schools more money when teacher salaries rise, the co-principals had to start charging families for after-school programs and cut a planned teaching position to make ends meet.

“Eventually if all of our teachers keep staying with us,” said co-principal Damon McCord, “we won’t have any money.”

Now, as Cuomo shines a light on school-funding equity, here’s how the process works (or not) in New York City.

How does New York City divvy up school funding?

The funding formula that New York City adopted in 2007 sets school budgets based on the grades they serve, their type (for instance, whether they are vocational or selective), and their student populations.

Schools receive extra money for students who are poor, struggling academically, have a disability, or are learning English. The idea is that needier students require extra support — and their schools need additional resources — if they’re to catch up with their better-off peers.

The formula also rewards certain selective schools, under the premise that high-achieving students also need extra attention to reach their full potential.

New York City is one of about 30 districts across the country to use this type of weighted funding system, according to the Baltimore Sun. About $6 billion of the New York City education department’s $30.8 billion budget flows through the formula, which is designed to cover schools’ basic expenses — most importantly, teacher salaries.

In addition to allocating more money to educate the neediest schools, the formula was also designed to give principals more power. Under this system, principals can decide whether to devote more of their budgets to seasoned (and costly) teachers, or to hire more junior teachers and spend the savings on an after-school program, for example.

The formula was also meant to impose some order on what was an opaque, freewheeling budget process. In the past, principals haggled with their superintendents for more money, favoring those who could best work the system, according to Eric Nadelstern, a former principal under the old system who was an education department official when the formula was adopted.

“You had massive inequities,” said Nadelstern, now a professor at Teachers College. “The difference could amount to thousands of dollars per student, particularly for schools in middle-class neighborhoods and schools in poor neighborhoods.”

What’s wrong the city’s budgeting system?

The Fair Student Funding formula has never quite lived up to its ambitions.

When it was first adopted, city officials wanted to avoid taking money from wealthy schools, so instead they promised to raise poorer schools’ budgets. However, around the same time, the Great Recession hit, causing New York State to roll back planned increases in school aid to districts.

As a result, the formula has never been fully funded — and some poorer schools have never quite caught up to wealthier ones. Last year, only 23 percent of city schools received funding at or above the level to which the formula says they’re entitled, according to numbers provided by the city’s Independent Budget Office.

That creates situations like the one inside a school building in Lower Manhattan shared by New Design High School, which serves a very high-needs student population but does not see its full allocation, and the High School for Dual Language and Asian Studies, which enrolls a less needy population but gets more than its fair share.

The dual language school — where about 3 percent of students have a disability and 85 percent are poor — received 112 percent of what the Fair Student Funding formula said it was owed last year. By contrast, New Design — where nearly 28 percent of students have a disability and 100 percent are poor — got just 92 percent of its formula money.

“This whole system is just holding an old, antiquated, unfair system into place,” said Scott Conti, New Design’s principal.

Critics have also questioned the part of the formula that gives extra money to selective schools that enroll higher-achieving students — and which tend to enroll relatively small shares of black and Hispanic students. More than a dozen elite high schools get about $1,000 extra per student through the formula, which has added up to more than $100 million since 2012, according to WNYC.

Others have suggested that the city should spend less on district-wide initiatives, and instead give the money directly to schools to spend. Mayor Bill de Blasio’s “Equity and Excellence” agenda devotes millions of dollars to a slew of efforts, including more computer-science classes, advanced courses, and college counseling. Some principals say they would rather the city pour that money into their budgets.

“My preference would be for them to cancel all those programs and give it all to the Fair Student Funding formula,” said a Bronx principal who asked to remain anonymous.

City officials say they are working to increase funding for the formula, and added that Equity and Excellence and other initiatives directly support schools. But they also said the city needs help from the state in order to fully fund the formula.

“By raising the Fair Student Funding floor citywide and making targeted investments through our Equity and Excellence for All agenda, this administration is investing more than ever in all our schools,” said education department spokesman Douglas Cohen in a statement. “To fully support Fair Student Funding, we need the state to meet its obligation to provide Campaign for Fiscal Equity funding.”