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At one of New York City’s most chronically troubled schools, Automotive High School, 56% of teachers didn’t get a good rating last year, according to state data released Thursday.

At another, Boys & Girls High School, 39% weren’t effective.

These low ratings, which stand in contrast to the high marks given to the vast majority of teachers statewide, highlight the difficulty of turning around schools that have long had poor test scores and graduation rates.

Mayor Bill de Blasio ’s administration says it is up to the challenge of fixing them and wants time to see its vision take hold, including having all staff at those two high schools reapply for their jobs this year.

The schools are part of the mayor’s $150 million plan to overhaul 94 struggling schools by adding social services, teacher training and other remedies.

ENLARGE

At Boys & Girls High School in Brooklyn, 39% of teachers didn’t get a good rating last year.PHOTO: KEVIN HAGEN FOR THE WALL STREET JOURNAL

But Gov. Andrew Cuomowants more state power to take over persistently failing schools and districts, and released a report Thursday detailing per-pupil costs in 178 of the most troubled schools statewide.

At Boys & Girls, for example, taxpayers spent $20,226 per student in 2012-13, almost double the national average. Cuomo administration officials said throwing more money at ailing schools isn’t working.

The report said on average, only 6% of third- through eighth-graders at these schools are proficient in math and language arts.

The report also listed lawmakers representing the schools’ neighborhoods to encourage voters to demand change.

The governor’s salvo drew immediate fire from New York State United Teachers, which argued that the real problem plaguing these schools is lack of resources to help students facing severe poverty, disabilities and language barriers.

“Inequality in how public schools are funded has reached record levels since this governor took office,’ Andrew Pallotta, NYSUT’s executive vice president, said in a news release.

Mr. Cuomo wants schools deemed failing for three years to be eligible for state receivership, in which the state education department would appoint a turnaround expert, a nonprofit such as a charter school or another district to take over. He points to Lawrence, Mass., as a model.

Officials in Lawrence say test scores have improved and graduation rates have risen to 67% from 52% since that district was put under receivership three years ago.

In an interview, Jeffrey Riley, the state-appointed superintendent, said that “having the authority to make rapid change is important.”

Mr. Riley said he replaced half the principals and dismissed 10% of the teachers in the 33 schools. Outside experts took over four of the lowest performing schools and the local teachers union took charge of one school.

The superintendent said the model is transferable if everyone “adopts the mind-set that things need to change and that people will work together.”

In New York City, education officials said they have already seen progress at Automotive and Boys & Girls, where they appointed a new principal, Michael Wiltshire, last fall.

Dr. Wiltshire said many of the teachers deemed ineffective last year have left, and he has added professional development, student mentoring and longer school hours. Attendance has risen and students fared better on Regents exams in January than in the past.

Mr. Cuomo is also in conflict with teacher unions and many educators over his call for tougher teacher evaluations, with outside observers giving 35% of a teacher’s score.

The governor says for teachers in tested grades and subjects, 50% of ratings should be tied to student growth on state tests. Many educators argue such reviews aren’t fair or accurate, and principals should have more say in evaluating their staff.

At PS 321 in Brooklyn, where state data said 4% of teachers were effective last year and 96% highly effective, teachers have sent letters to families asking them to lobby against the governor’s plan.

They said if it becomes law, teachers will be forced to do more test preparation.

“Realistically, many of us could be fired,” the letter said. “And many more of us would be pushed away from the profession we love.”

Write to Leslie Brody at leslie.brody@wsj.com