It’s been well established that the pay of San Francisco’s public school teachers is lower than most school districts around California, not nearly enough to pay for decent housing in this ridiculously priced city.

But, as the new school year starts Monday, there’s a persistent and so far unanswered question: If the district’s money isn’t going to teacher salaries, where is it going?

A group of about 30 principals and assistant principals has been meeting privately for more than a year to try to figure out the answer. They’re tired of seeing so many teachers leave because of poor pay, and constantly having to hire and train new ones.

When the administrators returned to work in early August, they were notified by district officials that just 88 percent of vacancies were filled after a rash of departures over the summer. Ninety-five teachers resigned after July 1, even though many of them had signed pledges to return this school year.

The school district has threatened to report them to the California Commission on Teacher Credentialing for the possible suspension of their teaching credentials. But, frankly, considering their low pay and miserable housing options, who can blame them for spending their summers looking for a way out?

A Chronicle investigation last year found the city’s cost of living was by far the highest among 821 school districts in the state, but its average teacher pay ranked No. 528 alongside the likes of Dixon, Susanville (Lassen County) and Chowchilla (Madera County). Mayor Ed Lee committed $44 million in May to fund up to 150 units of teacher housing, an important project but one that needs to be accompanied by raises.

As of Tuesday, after a mad hiring scramble, the district had found teachers for 96 percent of its vacancies. Still, that meant 23 classrooms lacked teachers six days before the students’ return.

Having bodies in as many classrooms as possible is a good baseline, but having a well-paid, consistent and experienced teaching staff in which students see the same faces year after year would be far better. In this extremely wealthy city, it’s embarrassing we are settling for anything less.

I have a 7-year-old son in a San Francisco public school that my family loves. But in a district with such a constant churn, the summer always brings fretting over just which staff will return.

“As school leaders, we spend an enormous amount of time and energy and effort training people and getting them up to speed. Then, after a few years, they move,” said Matt Alexander, assistant principal at June Jordan School for Equity, a high school in the Excelsior.

“No matter how much potential they have, a first-year teacher is never as good as a fourth- or fifth-year teacher,” Alexander continued. “It raises the question, ‘Are we getting a dollar’s worth of learning for every dollar we spend?’”

Alexander and the dozens of other administrators he’s been meeting with are pretty sure the answer is no.

They point to a website called Education Data Partnership, which shows that San Francisco Unified School District spent $704 million in 2015-16, the most recent year available, but spent only 41 percent of that on instruction, which means teacher pay. Statewide, the average is 61 percent.

“Forty-one percent is ridiculously low,” Alexander said. “Where’s the rest of the money going?”

He and the other administrators say a bloated central office seems to be a key problem. He said that 10 years ago, there were two layers of management between principals and the superintendent, and now there are four. An increasing number of teachers are being reassigned as coaches to mentor new ones. The superintendent makes $310,000 a year, whereas new teachers earn about $54,000 in salary.

District spokeswoman Gentle Blythe said comparing San Francisco Unified School District’s percentage spent on teacher salaries with that of other school districts isn’t fair because San Francisco also operates as its own county office of education.

Most school districts receive support from county offices in areas such as human resources, business operations and technology, but San Francisco must shoulder that cost itself. While the district receives extra money from the state because of its odd setup, Blythe said it’s not enough.

County offices of education also provide assistance to districts for their special education students. Blythe explained that if the money for special education were lumped in with the rest of the teacher salary pot, the percentage spent paying teachers would be 55 percent. Still, that’s lower than the state average of 61 percent.

Blythe said the district has made other financial commitments that directly benefit students, including small class sizes, subsidizing a preschool program and a healthy food program, and giving teachers of Advanced Placement high school courses an extra hour per day of prep time. She said the district also maintains more small schools than other districts, all of which require their own administrative staff.

Ron Bennett is the CEO of School Services of California, a Sacramento consulting firm that advises school districts around the state. He said districts can provide high salaries, good benefits or small class sizes, but never all three.

San Francisco extends lifetime health benefits for teachers, which fewer than 5 percent of the state’s school districts offer, Bennett said. In addition, the district has emphasized hiring not only teachers, but social workers, nurses, reading specialists, classroom aides and other school staff, he said. All told, there are 16.4 students per educator in San Francisco, whereas the state average is 21.5.

“It’s a choice that every community and every district really gets to make,” Bennett said. “Admittedly, when you see the salaries for San Francisco, they have trouble even staying around the midpoint.”

It would be great to fund all those things and more — like preschool, reading specialists, healthy food and lifetime health benefits — if the district had enough money to also pay its teachers living wages. But it doesn’t, and many teachers commute from the far reaches of the Bay Area, work second and third jobs, rent in-law units without kitchens, or squeeze into studio apartments with their spouses and kids. And these are professionals with credentials and, in many cases, master’s degrees.

In fact, San Francisco teachers are starting the new year on the exact same salary schedule as last year because the district and teachers union are still far apart in agreeing to a new contract. The old one expired June 30. The district is offering an 11 percent raise over three years, while the union wants 16 percent.

The school district has already approved its budget for the new year, but hasn’t set aside any money for teacher raises, meaning there could be big cuts elsewhere once there is agreement on a contract.

The school board needs to start making some tough decisions. One near-certain move will be placing a parcel tax on the ballot in November 2018 to pay for teacher raises. Mark Sanchez, a school board member, said he also plans to call for an independent audit of the school district compared with other districts because its funding is so opaque.

“We need to have some independent eyes looking at our budget and making some recommendations,” he said. “I wouldn’t call it a shell game, but it’s really hard to track.”

And if somebody charged with approving the budget every year thinks that, how are we parents and taxpayers supposed to get a handle on it?

Luckily for Danielle Battee, these frustrating questions are behind her. The high school English teacher excitedly arrived in San Francisco two years ago for a job at Wallenberg High in the Western Addition, lured by the beautiful city and the school district’s emphasis on social justice.

Last month, she just as excitedly left, driven out by the district’s low pay and the city’s insane housing prices. She’s one of those 95 teachers who left midsummer.

Battee, 38, took a job at Crenshaw Arts-Technology Charter High School in Los Angeles. She’ll make more than $10,000 a year more than she did in San Francisco.

She has already put an offer down on a $450,000, three-bedroom house 3 miles from her new school. Sure beats her housing in San Francisco: couch surfing followed by a $2,000-per-month apartment that had black mold on its walls and smelled like urine, followed by a decent room in a larger unit for $1,400 a month. Making about $58,000, she lived paycheck to paycheck the entire time.

“San Francisco is such a beautiful city, and I’m going to miss my students a lot,” Battee said. “But it’s just been so much easier here. A teacher can live like a normal human being here.”

The San Francisco public schools need to figure out how their teachers, too, can live like normal human beings. Our children are counting on it.

San Francisco Chronicle columnist Heather Knight appears Sundays and Tuesdays. Email: hknight@sfchronicle.com Twitter: @hknightsf

Teacher pay in California