Roughly two-thirds of New Yorkers are willing to pay more in taxes to avoid cuts or increase funding to programs that improve high school graduation rates or give kids who’ve dropped out a chance to get their diploma, a survey finds.

The latest installment of the Community Service Society’s “Unheard Third” survey –which aims to amplify the voices of low-income New Yorkers—also finds that more people believe public schools are succeeding than did in 2002.

CSS, which owns City Limits, found that 37 percent of those surveyed gave the schools a grade of A or B compared to 22 percent in 2002. Nine percent said the schools were failing, down from 14 percent nine years ago. Lower-income New Yorkers were more likely to give high grades than their more affluent neighbors. Impressions of public schools improved from 2002 to 2011 across boroughs and races (with the exception of Staten Island, whose sample was too small to offer comparisons, and Asians, whose view of schools did not change perceptibly.)

When it comes to paying more in taxes to avoid education cuts or fund new programs, New Yorkers were generally willing, with 67 percent indicating that they’d pay more to avoid cuts in programs that give school leavers a chance to get a diploma. Similar numbers registered when people were asked about paying more to avoid cuts in a second set of programs, to increase high-school graduation rates, or to increase funding for either policy goal.

But a substantially smaller number said they were “very willing” to pay more: For instance, only 32 percent were “very willing” to fork over more tax payments to allow more spending for programs to help school leavers.

This general willingness to pay more was true across income groups, political parties and races, but black New Yorkers were especially ready to face higher taxes. Eighty-percent of black respondents said they were willing to pay more taxes to increase spending on graduation rate improvement.

However, asked to rank their priorities for the 2013 mayoral election, respondents across race, party and income lines ranked “creating more jobs” ahead of “investing more in education,” often by healthy margins.

See the full survey results here.