While progress is real in public schools, look to charters as laboratories of learning.

Mayor de Blasio and Schools Chancellor Carmen Fariña were beaming Tuesday as they got the news that six in 10 New York City students are unable to do math and English at grade level. Believe it or not, that’s real progress. Scores on state tests went up for a fourth straight year: The percentage of third- through eighth-graders proficient in math was up 2.6 points to 40.6%; English proficiency went up 1.4 points, to 37.8%.

New York City’s gains in both English and math exceeded the rest of the state’s.

For this, kids and teachers and principals, de Blasio and Fariña, get real credit. Slow but steady gains are preferable to flatlining or backsliding.

But dare not lose sight of that first fact: Even after years of modest gains, most students fell below the math and English thresholds — meaning, to the best of the school system’s knowledge, they’re not on track to succeed in college or careers in an increasingly knowledge-based economy.

Meanwhile, in a parallel public educational universe, excellence is now routine. Yes, we speak of the city’s best public charter schools, among them the single largest network: Success Academy, de Blasio’s bête noire.

With 15,500 students, it would be the state’s seventh largest district. And among its students — 88% black and Hispanic, with an average household income of $32,191 — 95% were proficient in math, and 84% in English, tops in the state.

Not everything Success does is replicable. Though it accepts kids by random lottery, it likely attracts more motivated families. And when kids wash out for whatever reason, it’s the regular district schools’ responsibility to teach them.

But the mayor and chancellor must learn everything possible from these laboratories of learning. Something very right is happening there.