When charter school teachers push to unionize, charter leaders often fight back.

That’s happened in Chicago, New Orleans, Los Angeles, Philadelphia, and Washington DC. Unionizing, they argue, would limit the schools’ ability to innovate, ultimately hurting kids.

But a new study of California schools finds that, far from harming student achievement, unionization of charter schools actually boosts test scores.

“In contrast to the predominant public opinion about school unionizations, we find that unionization has a positive … impact on student math performance,” write researchers Jordan Matsudaira of Cornell and Richard Patterson of the U.S. Military Academy.

The analysis is hardly the last word on the question, but it highlights the limited evidence for the idea that not having unionized teachers helps charter schools succeed — even though that is a major aspect of the charter-school movement, as most charters are not unionized.

“Contrary to the anti-worker and anti-union ideologues, the teacher unions in charter schools don’t impede teaching and learning or hurt kids,” said Randi Weingarten, the president of the American Federation of Teachers, which represents teachers in more than 240 charter schools. “And the findings — that schools with teachers who have an independent voice through its unions have a positive effects on student performance — are consistent with common sense and other studies.”

The study, just published in the peer-reviewed Economics of Education Review, finds that about a quarter of all charters in California — 277 of 1,127 — were unionized as of 2013. Together, they taught nearly a third of the state’s students in charter schools.

Forty-four of those schools unionized between 2003 and 2013. To understand the effects of that change, the researchers compared trends in test scores of schools after they unionized to similar schools that didn’t unionize during that time.

The researchers find that unionization increased students’ annual math test scores, and those gains persisted for at least three years. The students who started at the lowest achievement levels seemed to benefit the most.

Those gains were fairly substantial: In math, they were about three times the size of the total advantage conferred by urban charter schools nationwide, according to research frequently cited by charter school advocates.

The estimated impact on English scores was positive, but small and not statistically significant.

The paper was not able to explain why unionization seemed to improve student learning, though the authors say it could relate to improved teacher morale or better relationships between teachers and school leadership. Oddly, unionization seemed to lead to a decline in teachers’ years of experience; it did not have any effect on class size.

The study comes with some significant caveats. Although the researchers make extensive efforts to make apples-to-apples comparisons among schools, it’s difficult to be sure that unionization is what caused the test-score gains. If schools that were already more likely to improve were also more likely to unionize, that could explain the results.

David Griffith, a senior research and policy associate at the Fordham Institute, a conservative think tank, said the study was well done but noted its inability to explain the results.

Griffith, who released an analysis last week showing that unionized charter schools have relatively high rates of teacher absenteeism, also pointed out that many charters without unions are successful.

“Even if this study is true for these particular schools, we have examples of really high-performing non-unionized charter schools,” he said. “It’s difficult to leap from this study to say that [for example] KIPP, which gets these fantastic results, should unionize.”

Previous research has shown middling performance for one of the most high-profile unionized charters in the state, Green Dot, while other non-unionized schools, like the Alliance charter network in Los Angeles, posted better scores.

In contrast to the latest research, a previous study of California’s charter schools found that unionization had no significant effect on test scores.

Since the findings are focused on just a fraction of California’s unionized charter schools, they might not apply to other charter schools in the state or country — or say anything about the effects of unions in traditional public schools.