In New York City’s breakneck effort to offer free preschool to all 4-year olds, officials have banked on teacher training as a key way to ensure that quality keeps up with access.

About three years into Mayor Bill de Blasio’s signature education policy achievement, the education department and New York University are partnering to study whether that teacher training is doing the trick. One of the first studies of its kind of New York City’s high-profile program, the results could be used to fine-tune the city’s training programs to increase their impact on student achievement.

“The question for us is, ‘How do we make pre-K better, as fast as we can?’” said Josh Wallack, a deputy chancellor for the education department and a principal investigator for the study. “This study will point us in the right direction, we believe.”

Pre-K for All now enrolls about 70,000 students — providing free public preschool to any family who wants it, according to the city. When launching its program, the city homed in on research from pre-K initiatives in Boston and Tulsa that showed teacher training and coaching had an outsize impact on student performance.

“The mayor and chancellor believe that the evidence is in: We know that high-quality pre-K leads to improved student outcomes,” Wallack said. “So our research agenda really focuses on the methods we use to help programs improve quality, and one of the ways we do that is through teacher training.”

The NYU study will use measures of student behavior such as self-regulation, third-grade test scores, and how often students are held back to track the impact of the city’s different teacher training programs. The city assigns its pre-K providers to four training tracks, each with a different focus.

Those tracks are: Pre-K Explore, which focuses on math; Pre-K Thrive, which emphasizes child behavior and working with families; and Pre-K Create, which is arts-driven. A fourth track, Pre-K Inspire, gives schools more flexibility to choose what type of training they receive from the city.

The study will compare outcomes of students who attended schools in the Explore, Thrive and Create tracks to those who attended schools that choose the Inspire track. About half of all pre-K sites participate in the Inspire track, according to figures provided by the education department.

“Our expectation is that some of the models may support teacher development and kids’ learning more effectively than other models,” said Pamela Morris, a principal investigator for the grant, and vice dean for research and faculty affairs at NYU Steinhardt. “Understanding that process will be important.”

One common pitfall of teacher training is that educators often struggle to put it into practice in their classrooms. The NYU study will also measure how well pre-K teachers use the skills they learn.

Funded by a $5 million grant from Institute of Education Sciences — the research and data arm of the U.S. Education Department — the five-year study is designed to be a partnership between the city and NYU. School district-university partnerships are common, with the goal being to produce research that helps districts improve their practices.

“It really infuses the system with a huge amount of research to build this quality infrastructure,” Morris said.

Russ Whitehurst, former director of the Institute, said there is often another reason why such partnerships are necessary: to gain access to data that can otherwise be difficult to get. The need for data can create pressure on researchers to work collaboratively with districts, he said.

“It’s the nature of how these things work,” said Whitehurst, who is now a senior fellow in economic studies at the Brookings Institution. “You sort of have to play nice to get someone to want to partner with you.”

Wallack said the city has experts who can help crunch data for the study, but the bulk of that job will be in the hands of NYU researchers, who Wallack said would retain their independence.

“It’s just important to emphasize that, in the end, NYU will really be running the analysis here — and the analysis will be based on objective measures,” he said.

NYU and the education department have partnered in the past, and Morris said the city has proven itself to be committed to transparency. She said a “very strong” advisory board would help “ensure the research integrity.”

“I would not be engaging in the partnership if I didn’t think the city would be open,” she said. “They’ve been really terrific about seeing where the data leads them.”