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A high school’s size and its concentration of low-achieving and overage students strongly predicts its graduation rate, according to an internal Department of Education study obtained by GothamSchools today.

The 20-page report, prepared for the city by the consultant firm Parthenon Group in 2008, gives fodder for both supporters and critics of the city’s strategy of closing low-performing large high schools and replacing them with new small schools.

The presentation shows that large schools struggle to serve large concentrations of challenging students. But it also suggests that the Department of Education knew about this problem years ago but continued to allow many large schools to be flooded with low-performing students.

Leonie Haimson, the executive director of Class Size Matters and an outspoken critic of the city’s school closure efforts, provided the report to GothamSchools.

The report examines how a students’ chance of graduation varies widely depending on the type of high school he or she attends.

For example, a hypothetical black or Hispanic girl with the median city test scores and middle school attendance and no special needs would have an 83 percent chance of graduating from a small school with a low concentration of challenging students. The same student would have just a 55 percent chance of graduating from a large high school with much higher percentage of students with special needs.

Those predictions were born of a model the Parthenon Group drew up to predict high schools’ graduation rates using their size and concentrations of challenging students. The consultants then compared their predictions to city schools’ actual graduation rates, and found that they were spot on 77 percent of the time. Just a fifth of schools posted rates 10 percentage points above or below their predictions.

Just one large high school with a high concentration of students who enter ninth-grade low-performing, overage or with low attendance rates — Harry Truman High School — posted higher graduation rates than the consultants’ model predicted.

The model’s success suggests that as large high schools currently slated for closure began to enroll higher numbers of challenging students — as a report released today showed they did — it would seem likely that their graduation rates would decline. Critics of the city’s practice of closing schools frequently argue that the city flooded previously well-functioning large neighborhood high schools with low-achieving students and then punished the schools with closure as they began to flounder academically.

The report also shows a wide gap in graduation rates between the new small schools opened under the Bloomberg administration and other city high schools. But most of that gap is accounted for by local diplomas awarded by the schools.

Other studies have shown that small schools relied heavily on the local diploma to power their higher graduation rates. The Parthenon report adds a comparison to large high schools — and finds that the large and older high schools are not much further behind.

For example, for students entering high school with a low level 2 on their eighth grade state tests, new small schools post graduation rates that are 26 percentage points higher than other schools. But the gap between those students who eventually earn Regents diplomas is much smaller — just 7 percent.

That distinction is important because the state is in the process of phasing out the local diplomas, arguing that they are not rigorous enough to prepare students for college. Observers have warned that small schools’ reliance on local diplomas mean graduation rates could plummet when the new tougher requirements go into effect, though city officials have said they are making changes at the middle school level to prepare for the change.

The report also questioned small schools’ ability to sustain their high performance, a criticism that has been made by other studies, including a 2009 report from the New York City Center for Public Affairs.

But the report also showed that a disproportionately high number of the schools outperforming their predicted graduation rates are small schools with relatively high rates of overage and low-performing students. Of the schools that the report says “beat the odds,” 34 percent are small schools with medium to high rates of students entering ninth grade overage.

City officials said today that the report helped inform and validate their small school approach and described the reports’ findings as precursors to more recent studies that found small schools boost graduation rates.

“This was an internal study, but it confirms what we’ve seen time and again: our new small schools have been enormously successful in educating students and helping them graduate,” said DOE spokesman Jack Zarin-Rosenfeld.

In its concluding slide, the presentation asks several questions raised by the reports’ findings. One of those questions suggests that the city could have prevented some large high school’s academic slide by changing admissions policies to prevent them from enrolling much larger numbers of struggling students:

Should we consider constraints on the [high school] admissions process that take into consideration the predicted graduation rate of the school? (e.g. “don’t allow any school to have a predicted rate less than 45%”)