We’ve all seen the infamous video by now: The Upper West Side mother objecting to a proposal to set aside 25 percent of seats in New York City’s District 3 middle schools for students who score either a 2 (below proficient) or a 1 (well below proficient) on their NY state standardized tests.

The conceit is that since the students performing below grade level will (naturally) be minority and low-income, this will be an easy way to integrate the neighborhood’s majority white and middle-class high-performing schools.

But while Chancellor Richard Carranza cried racism and Mayor Bill de Blasio, remembering that the loudly and proudly liberal Upper West Side was his primary voting base, walked the charge back, no one was talking about the most insidious part of the infuriated mom’s rant.

She said she’d paid $5,000 to get her child tutored for the state tests so that they could get into a good middle school.

Hold on… Wait a minute… She had her child tutored for the state tests? Why would she do that? Didn’t her child already go to a “good” Upper West Side elementary school?

And aren’t those “good” labels reserved for schools with high test scores?

Let’s look at a couple of them:

• PS 9 has 86 percent of students performing at or above grade level in math, and 81 percent in English.
• PS 199 has 84 percent of students performing at or above grade level in math, and 80 percent in English.
• PS 87 has 78 percent of students performing at or above grade level in math, and 81 percent in English.

Wow! Those schools must have amazing teachers and administrators for their results to be twice the city’s passing averages! No wonder families are clamoring to get in! The Chancellor is right: If schools with numbers like that start admitting low-performing students, those kids will instantly become high-achievers!

Except that, even in those high-performing schools, aren’t an average 15 percent of pupils not performing at grade level?

How is that possible? What happened to those amazing teachers and superior administrators?

Could it be that the children racking up those top scores are those who are getting outside tutoring (to the tune of $5,000 or more), and the ones who aren’t… aren’t?

Let’s say we do what the Community Education Council is proposing and assign 25 percent of seats in the highest-achieving middle schools to tweens scoring in the lowest percentages. Then what?

No one is talking about what will happen after. Will those kids be put in remedial classes? If so, then is it really integration, or is it just segregation within one building, something Gifted & Talented programs already do?

And if students are placed in mixed-ability classrooms, what will be done to help those who are already behind catch and keep up?

So far, the answer seems to be… nothing. Just sitting poor minority kids next to middle-class white ones will magically increase test scores – or so the theory goes.

The irony is that it will… in a way.

Because if a fraction of low-achievers is mixed in with a majority of high-achievers, the school’s test scores will likely dip a little but still remain well above the city’s average (which, by the way is 42 percent proficiency in math, 43 percent proficiency in reading; although some schools, like PS 123, clock a dismal 9 percent in math).

The Department of Education will then be able to crow about how they not only kept test scores high, but also fully integrated these schools. Meanwhile, at low-performing schools where some high-performers will be redirected under the new plan, the DOE will cheer their rising test scores, too.

Everybody wins!

Except for the same kids who, no matter what schools they’re in, are still not performing at grade level if they can’t afford the test prep.

But now they’re a lot harder to see. And, as a result, a lot easier to ignore.

The DOE can say they did their jobs. They made sure the schools reflected NYC’s (rather warped) definition of diversity, and test scores remained above average.

That must mean that, like in Lake Wobegon, all the children in them are also above average!

With those kinds of quantitative reasoning skills, no wonder over 50 percent of NYC teens are graduating high school not college ready.

Unless they can afford $5,000 worth of tutoring outside of their “good” schools….