Students in New York City charter schools make larger learning gains, on average, in both reading and mathematics, according to a new report from Stanford University researchers. But the gains are much more pronounced in math.

The report by Stanford’s Center for Research on Education Outcomes (CREDO) looked at nearly 20,000 students’ records from 79 schools. It relied on state data for six years of schooling, beginning with the 2005-2006 school year and concluding in 2010-2011, It compared students in grades 3 through 8 who transfer to charter schools to similar students who remained in the regular schools. The authors say they controlled for prior test scores and made sure the comparison group was similar in terms of gender, race, disabilities, family income and English language learner status.

Test scores were compared for students, and for whole schools. On average, charter students gained an additional one month of learning in reading over the course of a school year compared to their counterparts in district schools. Their advantage in math was much stronger: they gained an additional five months of learning over the course of a school year.

At the school level, 22 percent of the charter schools have significantly more positive learning gains than traditional public schools in reading, while 25 percent of charters have significantly lower learning gains. In math, nearly 63 percent of the charter schools studied outperformed their local public schools. About 14 percent perform worse.

Charters that are part of networks tended to score higher than those that are independently managed. The report also looked at Harlem charters, in particular, where the privately managed schools are highly concentrated.

Report authors found: “In reading, charter schools in Harlem have a smaller impact on learning gains than overall or other neighborhoods in New York City. The reverse is true in math; students in Harlem charter schools have larger learning gains than students at charters elsewhere in the city.”

The students in Harlem gained about seven months in math compared to less than a full additional month in reading.

When comparing students in poverty, the report found low-income students at charters performed better than their peers who pay the full-price for lunch. But the report did not break down low-income students into those who receive free meals and those whose families make a little more money, and therefore receive a reduced-price lunch. Several critics have noted that charters tend to take fewer of the lowest income students (those getting free lunch) than their local public schools.

The report also found English Language Learners make about the same learning gains in math and reading regardless of whether they attend a charter or a regular public school.

Charter schools often hold more students back a grade than traditional public schools. The report looked into this and saw that students who were retained a grade performed worse than their peers regardless of whether they attended charters or regular schools. But charter students who are retained a grade showed more learning gains than their counterparts at district schools.

This new report is CREDO’s second study of charters in New York City; the previous one, in 2010, also found learning gains, and it was widely debated with critics suggesting charters were merely doing a better job at test prep.

The new report acknowledged that overall, charter schools have different populations than those of regular public schools because they tend to have more black students, and fewer white and Asians pupils. They also tend to have fewer children with special needs and fewer students who are still learning English.