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A chart from the latest CREDO study about city charter schools shows that students at many charter schools make outsized gains in math. But in reading, charter school students tend fall behind more often, researchers found.

City students benefit from attending city charter schools, according to a new study — but the advantages are not universal.

The study, by Stanford University’s Center for Research on Education Outcomes, which analyzes charter school performance, concluded that city charter school students, on average, learn five more months of math each year than similar students in neighboring schools. In Harlem, where the charter school enrollment share is highest, the math gain was seven months, the researchers found.

And in reading, charter school students averaged one month’s additional learning each year, the researchers found. All of the gains were measured by students’ state test scores.

Yet within the sector, some schools did far better than the average — and others far worse. The study found that nearly two thirds of charter schools moved their students forward in math significantly farther than other schools in the area. But a full quarter of charter schools moved their students forward significantly less in reading.

In 2010, CREDO found that students at New York City charter schools advanced in math and reading faster than students at schools operated by the city Department of Education. The new study looks at a larger number of schools and also uses a methodology that CREDO has applied elsewhere. The methodology compares actual charter school students’ performance to that of “virtual twins” in district schools — students who are demographically identical and start with similar academic skills.

In almost all cases where students in charter and district schools had statistically significant differences, students’ test scores increased faster in charter schools than in district schools. All of the exceptions were for reading scores — for black and Hispanic students, where students on average did slightly worse; students in schools that spanned many grades; students in their first year at a charter school; and students in schools that do not belong to charter management organizations.

The study draws special attention to the 46 percent of charter schools whose student achievement on state reading tests was lower than the city average — and whose students made less progress than average, too.

“The number that demands attention is the nearly 46 percent of New York City charter schools that have both low growth and low achievement in reading,” Devora Davis, the lead author of the CREDO report said in a statement. “If things continue as they are students in these schools may be at risk of falling further behind their peers in the state over time.”

Charter school advocates said the 46 percent number was misleading because it was based on a calculation with a larger margin of error than most of those in the report. But they said low-performing and high-performing schools should both get a closer look. Nationally, the charter sector is lobbying charter school authorizers to close more low-performing charter schools.

“These results should finally ignite a conversation around what is working in these schools, and how successful practices can be spread so that many more students in both traditional and charter public schools can benefit,” said James Merriman, CEO of the New York City Charter School Center, in a statement.

And Bill Phillips, president of the Northeast Charter Schools Network, said the findings helped make the case for charter schools to be able to secure state funding for pre-kindergarten, an issue that is at the top of the charter sector’s agenda for the year.

And a spokesman for the city Department of Education said the report’s findings proved that school choice is benefiting students.

“This report further validates our strategy to offer families high quality school options,” said the spokesman, Devon Puglia. “We’re continuing to stay focused on building a system of great schools, and on improving outcomes in all of them — district and charter.”

Because so many Harlem students attend charter schools — 25 percent during the period analyzed in the study — the researchers could take a closer look at the impact of schools there on different kinds of students. They found that poor students, low-scoring students, and students who have repeated grades all make gains faster in charter schools. English language learners and students with special needs did not post significantly different growth in the two kids of schools.

The full CREDO report is below: