Mayor Bill de Blasio and Chancellor Richard Carranza have put school integration on the table once again in New York, approving changes to middle-school admissions in two of the city’s 32 school districts, and promising to review those policies in the rest of the city. The current effort appears to be no more than a diversion of attention from the very real needs of black and Hispanic students.

Fact is, there are simply not enough white students in Department of Education schools to make the well-being of black and Hispanic youngsters dependent on the presence of whites in their schools: Only 15 percent of kids in city schools are white, while 66 percent are either black or Hispanic.

Black and Hispanic students have long been ill-served by DOE schools. Their parents have had to seek alternatives: Well over 100,000 now attend public charter schools, and another 60,000 have opted for private and parochial schools.

For good reason: In schools under the mayor’s control, only 35 percent of black and Hispanic students scored “proficient” on the state’s English Language Arts exam last spring; in math, fewer than 28 percent did, and fully 43 percent scored at the lowest level.

The advantage provided by charters is most pronounced in math, where over 8,100 black students scored at the highest level, compared to 7,300 black students in DOE schools — even though 60,000 more black kids took the test in DOE schools than in charters.

Yet, rather than support charters and provide them the space they need to grow, the mayor and chancellor have set up roadblocks, such as opposing an increase in the state cap on the number of charters and denying them space in underused DOE buildings.

To their thinking, it’s more promising to play around with admissions policies at a small number of middle schools that have white or Asian majorities and that screen students based on academic achievement. It’s worth noting that under the law charters are not allowed to screen students and must admit them based on a lottery. Apparently, the mayor’s sense of fairness only goes so far.

The zeal the mayor and chancellor are showing for their integration efforts also highlights their refusal to look critically within their own system. They should identify both schools that are failing to provide quality educations to black and Hispanic students and those that are succeeding and deserve greater investment.

The failure of the mayor’s $700 million Renewal schools program is well-known; these are schools that his predecessor would have likely closed. This mayor promised he would improve them, but time and test scores have proven him wrong.

My recent report identifies 34 selective, majority-black and -Hispanic DOE middle schools, where the percentages of the black and Hispanic students scoring at proficiency level in ELA are much higher than those groups show in the citywide statistics. These schools serve over 7,700 black and Hispanic students in grades 6-8. Most — 21 out of 34 — are fully screened; seven are unscreened or geographically zoned, and the remaining three screen for some of their seats.

Thus, in these schools, the screening mechanism does not seem to disadvantage black and Hispanic students. A true commitment to increasing educational opportunity for black and Hispanic students would include greater investment in these effective schools rather than continued spending on those Renewal schools that continue to fail year in and year out.

Given the demographics of the city’s schools, efforts to improve educational opportunities for black and Hispanic students need to move beyond racial-integration efforts.

The impact of the newly announced changes to middle schools in Districts 3 and 15 will be seen over time. Even if they benefit some number of black and Hispanic students at no detriment to Asian or white students, these middle schools represent only a small handful of seats that can be made available to black or Hispanic kids.

Meanwhile, there are numerous schools run by either DOE or charter groups that are succeeding with predominately black and Hispanic students. New York City needs more of these schools. Simply moving students around among a limited number of high-performing schools is not going to be enough to help kids.

Ray Domanico is director of education policy at the Manhattan Institute and author of the new report “Closing the Racial Achievement Gap in NYC Schools — Integration Is Not Enough.”