The Catch-22 of educating students who don’t show up when school is open and don’t sign on when it’s not is bad enough. Apologists offer the usual excuses, most of which have some element of truth in them but leave out the fact that if students and their parents wanted them to be educated, they would do everything in their power to make that happen. Yet, they don’t.

While the complaint/excuse cycle persists in New York City schools. the mayor has come up with a solution to address the “achievement gap.”

Some 700,000 of the city’s one million public school students are learning from home. The city is still working to convince teachers and parents that the schools are safe, a process that will continue well into next year — until vaccination is widespread. Many students, including homeless children, are still fighting just to gain reliable access to broadband internet service.

When 70% of students are not going to school, facing a loss of education (mediocre at best though it may be), that’s going to have a deleterious impact no matter how you twist it. Is the answer to “convince” students or to provide open schools, particularly for those who lack “reliable” internet access?

It’s unclear how many “many students, including homeless children,” there are, covered by adjectives rather than numbers, and it’s unclear whether the problem could be solved by putting broadband into homeless shelters, even though that would raise the next levels of problems, computers, space and quiet for students to learn from home. There are many stumbling blocks and excuses. Fix one and the next renders the fix worthless. The only thing certain is that more money is needed, though how that will make the problems go away remains a mystery.

But there are two ways to reduce the achievement gap. Raise the failing students up or push the succeeding students down.

Against the backdrop of such inequality, it was welcome news Friday when Mayor Bill de Blasio said the city would make long overdue changes to middle and high school admissions processes. For at least one year, the city will eliminate the use of grades and other screens in the middle school admissions process, and will instead use a lottery system. The city will also end a practice that allowed some high schools to give preference in admissions to students who live near a school. Both measures could racially integrate some of the city’s most selective schools, which are largely white and Asian, and are an important step toward a fairer city.

Where it was once hard to get into the top feeder middle schools, requiring testing to demonstrate that students were smart enough, equipped to learn at a level of above that of their peers, so the schools could provide an excellent education to students who would make use of it and excel, it will now be a matter of lottery to get into Harrison Bergeron Middle School.

Then there is a concomitant shift for neighborhood schools, so students weren’t required to travel for an hour on the subway each way to reach the school to which they were assigned even though they had a public school a block away from their home. Some parents chose to live close to a school so their children wouldn’t spend their day commuting. These tended to be parents who cared about education, and instilled that value in their children. Their schools tended to be better because the children who attended the schools wanted to learn. This, too, was unfair, as they also tended to be white and Asian.

Both measures could racially integrate some of the city’s most selective schools, which are largely white and Asian, and are an important step toward a fairer city.

It may well be true that these changes “could” racially integrate schools. The problem is that they will no longer be “selective schools” because they no longer select their students, which was what made them selective.

Unfortunately, the measures won’t change the high-stakes admissions exams used by its most sought-after public high schools. In the coming months, it looks likely that New York will plow ahead with those tests, which have left all but a handful of Black and Latino students shut out of the city’s most competitive schools. This year, the exams will work like accelerant in a giant conflagration of inequality.

The shift will be in the middle schools, not the high schools that are renowned for their excellence, or as they’re called in the New York Times, a “giant conflagration of inequality.” But the ability to score well enough to get into the big name high schools comes from attending a selective middle school. If your math abilities end at 2+2=5, you’re going to struggle with the entrance exam.

If the seats in feeder middle schools are at least partially filled with butts of students with neither the ability nor interest in being educated, that’s going to hold back the class. There will be disruption and worse. What there will not be is a classroom filled with students dedicated to doing the best they can to get into Bronx Science, and then Yale after that.

The schools, the city and society are facing a catastrophe with the students who are losing this year of their education. You can’t give children back a lost year of their lives and education, and no excuse will substitute for an education. In the very near future, this will produce a great many young people lacking some portion of the basic knowledge that would help them function in society, higher education and the workforce.

But for those who would find a way to learn, who are willing to do whatever it takes not to lose a year of their education, their opportunity will be blunted, perhaps eliminated, to prevent them from getting too far ahead of the students who just won’t show up. This might well have the desired impact on the achievement gap, but it will be achieved by pushing the top down rather than lifting the bottom up. But hey, a gap’s a gap, and as long as it’s reduced, isn’t that equity?