Testing giant Pearson would continue providing the Specialized High School Admissions Test under a New York City Department of Education recommendation for a six-year, $13.4 million contract.

The contract calls for Pearson to continue its work aligning the entrance exam to Common Core standards. A new provision would also allow seven high-needs middle schools to administer the test during  the school day in October, rather than on the weekend — a pilot project that education officials hope will result in a more diverse mix of students taking the exam.

A passing score on the SHSAT is the only requirement to get into the city’s elite high schools, which have long been criticized for enrolling few students of color.

While 68 percent of New York City students are black and Hispanic, they make up only 11 percent of students at specialized schools, according to the Department of Education.

Critics have called for multiple measures to be considered for admissions, something Mayor Bill de Blasio has echoed while also blaming state law for tying the city’s hands.

“This is a matter of fairness,” de Blasio said at a press conference on the first day of school. “These are some of the very best high schools in America. They have to be representative of this city’s population.”

The testing contract, which was put out to bid in 2014, was temporarily put on hold as the city explored ways to make specialized high schools more inclusive. In June, the DOE announced a six-point plan to do that, including free test prep, expanding acceptance programs for students who just missed the cutoff scores, and student outreach.

At the middle schools that will pilot giving the test during the school day, all eighth-graders will be signed up to take the exam — but they can choose to opt-out, according to a DOE spokesman.

Lazar Treschan, director of youth policy at the Community Service Society of New York, said such moves usually increase the volume of test-takers without really addressing diversity issues. Treschan said the ultimate goal should be changing the single-test requirement.

“It’s up to the city to decide whether they want to take a stand and do something about that in a big way,” he said.

In October, the Community Service Society was among several advocacy organizations and local officials who sent a letter to schools Chancellor Carmen Fariña on how the city could make schools, including specialized high schools, more diverse. The department already has the authority to make admissions changes at a majority of specialized high schools, they wrote.

Among their suggestions: offering guaranteed admission for top-performing middle school students. A New York University study found that was the only admissions rule change that would substantially alter student demographics at specialized high schools.

A DOE spokesman said in an email that entering into a new contract with Pearson doesn’t preclude the city from moving towards multiple measures for admissions “in the event state law changes.”

The DOE recommended Pearson over competitor Questar, even though the company’s bid came in $1.7 million higher. Still, Pearson showed a “stronger” understanding of the test and presented a “clearer” proposal, according to contract documents.

Pearson has come under criticism for some high-profile test errors, and a nonsensical passage about a pineapple. New York State recently dropped Pearson as its vendor for its English and Math exams.

In an email, a spokesman for the company wrote: “Pearson maintains the highest industry standards for fairness and quality, and we have a proud history of serving students in New York.”

The Panel for Educational Policy will vote on the contract Sept. 21.