Even a stopped clock is right twice a day.

That seems to be the reaction of education experts to Mayor de Blasio’s announcement last week that New York City would be offering all public-school students the opportunity to take the SATs for free.

It might mark the first time de Blasio has united education watchers on both sides of the aisle in support of one of his administration’s ideas. And they’re right.

The program, which will cost $1.8 million, is being hailed by the mayor’s office as the latest plan to address inequality in New York. “The opportunity to go to college should never be decided by students’ backgrounds or ZIP codes,” said Schools Chancellor Carmen Fariña.

While offering free SATs during a school day (making many students more likely to take them) may seem like the latest sideshow in an education policy circus, this one may actually achieve something.

“The de Blasio administration’s approach to K-12 education has often seemed to me to be evidence-free and misguided,” Russ Whitehurst of the Brookings Institution tells me. But “the policy of offering students the chance to take the SAT for free during school hours is a notable exception. I’m strongly in favor of it and expect that it will have a meaningful impact on the percentage of low-income students in the NYC schools that makes a college application and shows up at the door.”

Whitehurst cites a Harvard study in which students who were able to submit ACT scores to more institutions free of charge ended up applying to more schools and attending more selective ones. This was true “even though the cost of submitting an extra application was only $6.” Whitehurst suggests that “since the cost and trouble of taking an SAT exam is far greater than the cost of simply submitting the results of an exam to another college . . . the impact of the de Blasio policy [will] be greater.”

Indeed, if the administration wanted to improve on the policy further, it might also pay for sending the scores to more schools and providing college guidance to students who do score well.

The reason this matters so much is that there are “diamonds in the rough,” as University of Arkansas education professor Gary Ritter argues. These are smart, capable kids who might now get a shot they otherwise wouldn’t. That, in turn, could change the preparedness and socioeconomic distribution of college students from New York City.

Ritter argues schools should “mandate” that students take exams “that have the potential to have real-life consequences.” He says, “I would rather schools give priority to exams which have an effect on the students’ post-secondary opportunities than to end-of-course exams that only matter for school accountability ratings.”

“On the margins, it’s a positive move,” says Chester Finn, former federal assistant secretary of education.

Finn also suggests that this new policy would be good for data collection. One of the criticisms of the SATs is that not enough lower-income kids actually take it, and so we don’t have a full statistical picture of American kids’ performance.

On the whole, of course, the SATs are hardly the most complicated part of the college process. Students who are faced with writing essays or filling out financial-aid forms longer than most people’s tax returns will find plenty of reason to be deterred.

But those who might not otherwise see themselves as college material (or selective- college material) could think again after receiving their SAT scores. And colleges that receive a disadvantaged student’s decent or high SAT scores may encourage them to apply.

For all the criticism of testing in general — and the SATs in particular — as a needless stress on students and a means for exhibiting white male privilege, it turns out tests do serve a purpose. Colleges care about the likelihood students will actually be able to complete coursework and graduate. And the SATs turn out to be a pretty good measure of that. If you want more colleges to take more low-income students, you have to help them find the diamonds in the rough.

Ultimately, the reason for the vast inequality in college admissions — the reason that so few poor children get a decent higher education — has little to do with who takes the SATs. It’s because poor kids are cheated out of a decent K-12 education. In this, de Blasio is hardly free of blame, thanks to his opposition to school choice.

In the meantime, though, says Whitehurst, “We have a strong body of rigorous research demonstrating that small things can make a big difference when it comes to college application and admission.”

A good thing — because small things are all we’re likely to get from this mayor.

Naomi Schaefer Riley is a senior fellow at the Independent Women’s Forum.