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The Buffalo Public Schools graduated 56 percent of their students last year, an increase of 8 percentage points that marked the biggest jump among the state’s Big 5 urban school systems.

In Erie and Niagara counties, two-thirds of high schools also saw their graduation rates improve. Overall, 81.1 percent of students in the two counties graduated last year, compared with 79.1 percent in 2012.

Buffalo’s gains appear to validate the projections of departing Superintendent Pamela C. Brown and are attributed in part to credit recovery programs that give extra help to students struggling to master specific skills within a course. Officials say the gains also reflect the impact of Say Yes Buffalo, which offers a free college education to qualified students.

Statewide, the graduation rate climbed to 77.8 percent in 2013, up from 76.7 percent in 2012, even as tougher standards were phased in.

But state officials caution that the percentages reflect the number of students meeting only minimum requirements. They say that only about a third of graduates are meeting advanced standards that would better prepare them for college and the workforce.

State officials also note significant gaps between racial groups in earning advanced degrees, with just 9 percent of black students who graduate with an advanced Regents diploma, compared with 43 percent of white students.

Regents Chancellor Merryl H. Tisch suggested that the disparity stems in part from an unequal distribution of resources and experienced teachers. She pointed to the need for a conversation on those issues.