New York City residents won’t be appointing Mayor Bloomberg as students’ chief lobbyist any time soon.

Nearly twice as many New Yorkers trust the teachers union to protect students’ interests than they do Bloomberg, according to a new poll out of Quinnipiac University. Bloomberg’s approval rating on schools has hovered around 25 percent since early 2011, according to the poll.

The poll, conducted Jan. 30-Feb. 5, found that 56 percent of registered voters in New York City say they trust the union more to go to bat for students. Less than a third, 31 percent, said they trust Bloomberg more. (The poll of 1,222 registered voters had a margin of error of 2.8 percent.)

Among households containing public school students, the split was even more pronounced. Just 21 percent of those voters picked Bloomberg, and 69 percent chose the teachers union. Parents’ backed the union more often than even households with union members.

The news comes in an education-packed poll conducted after a month in which in a showdown over new teacher evaluations led Bloomberg and Gov. Andrew Cuomo each to ratchet up rhetoric against teachers and their unions. The poll found that the percentage of New Yorkers with favorable opinions of teachers had fallen, from 54 percent last March to 47 percent now.

But while a different poll earlier this week found high approval for Cuomo’s school policies, a set of questions designed to assess New Yorkers’ feelings about a slate of policy initiatives Bloomberg proposed during his State of the City address last month elicited mixed results.

In that speech, Bloomberg proposed increasing the salaries of teachers who receive high ratings on new evaluations and offering loan forgiveness to top college students who become city teachers.

The poll asked New Yorkers for their opinions on those ideas and others. Here’s what they said:

  • Eighty-four percent of poll respondents said they approved of Bloomberg’s loan forgiveness proposal. The proposal was the only one in Bloomberg’s speech to win immediate support from the United Federation of Teachers.
  • But just 54 percent said they thought it made sense to offer a $20,000 pay raise to teachers with high ratings on new evaluations. Thirty-nine percent said the raises sounded like a bad idea.
  • The broad idea that “public school teachers who do an outstanding job should be rewarded with additional pay, so called merit pay” got support from 72 percent of respondents. Twenty-four percent said the idea sounded bad. Support for merit pay was up eight points since last March.
  • Fifty-four percent of respondents said they thought making it easier to fire teachers sounds like a good idea. Thirty-eight percent said it was a bad idea. Those numbers were the same as a year ago, the first time the poll asked about the topic.
  • Just 11 percent of New Yorkers said they thought teacher layoffs should take place according to seniority, as they would under current rules. Just over 80 percent said they thought layoffs should go in order of performance. A year ago, when Bloomberg was actually threatening layoffs and calling for an end to “last in, first out” seniority layoff rules, support for seniority layoffs was higher, at 16 percent.
  • Just over half of New Yorkers said they thought charter schools should expand in the city, and 38 percent said the publicly funded but privately managed schools should not expand. In 2009, the first time this question was asked, two-thirds of New Yorkers said charter schools should expand and just 26 percent said there should be no expansion. At the time, the city was approaching a state-set charter school limit that was raised in 2010.
  • Just a third of New Yorkers support the Bloomberg administration’s recent decision to bar churches from using school space to hold services. Nearly 60 percent said the ban is a bad idea.

Overall, according to the poll, just 26 percent of New Yorkers approve of how Bloomberg has handled the schools. That figure is statistically identical to the 25 percent low Bloomberg received last spring, during the waning days of Cathie Black’s brief tenure as chancellor. Fifty-seven percent of poll respondents said Bloomberg’s takeover of the schools had been a failure, the same as last year.

Black New Yorkers and those living in the Bronx gave Bloomberg his lowest approval ratings on schools, 21 percent and 19 percent respectively. He did best among New Yorkers making more than $100,000 a year: A full third of them said they supported his schools management.

The news for Chancellor Dennis Walcott was also not good. His approval numbers stayed the same since December, at 34 percent, but his disapproval rate has continued to inch upward and now stands at 37 percent.

Overall, just 13 percent of New Yorkers said the mayor should retain sole control of the city schools after Bloomberg leaves office in 2013. Two-thirds said a new mayor should share control with an independent school board. The law authorizing mayoral control of the city schools is set to expire in 2016.

Half of respondents say they want their next mayor to be someone with government, rather than business, experience. But they gave only mixed reviews to the job performance of three city officials who are plotting mayoral runs: City Council Speaker Christine Quinn, Public Advocate Bill de Blasio, and Comptroller John Liu.