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The United Federation of Teachers wants to stop the expansion of charter schools. As part of its longstanding campaign to drive charter operators out of New York City, the union has seized upon the so-called “enrollment gap.” Charters, they claim, get such great results because they find ways to avoid serving the most challenging students—namely, non-native English speakers and the disabled. The enrollment gap does exist, but as my research and new data from the New York City Independent Budget Office (IBO) confirms, the union’s explanation for it is highly misleading.

Charters aren’t systematically shutting out disadvantaged students. Enrollment is determined by lotteries, so when such students apply to attend charters, they are just as likely as other students to get in. But few English-language learner (ELL) students apply to attend charters, for perhaps understandable reasons. New immigrant families, for instance, may be less aware of schooling options beyond the neighborhood public school. Language barriers may also hinder parents of ELL students from researching schools and applying to them. In this respect, charters probably could do more to recruit ELL students—but that’s a far cry from suggesting a climate of active discrimination.

While the special-education charter enrollment gap is, admittedly, more complicated, the situation doesn’t warrant an indictment of New York City charters. Contrary to popular wisdom, the special-ed gap is not driven by charters’ failure to enroll students with “severe” disabilities. While such students are less likely to enroll in charters than in traditional public schools, their overall number in either sector is, in fact, so small that enrollment differences make little dent in the special-ed enrollment gap. Instead, the gap is a product of two disability-classification categories, which traditional public schools are more likely to use than charters.

My research following kids who entered kindergarten in 2008 reveals that 12.6 percent of Gotham kindergarteners in traditional public schools were classified as requiring special-ed services, compared with only 5.7 percent of students who applied to attend kindergarten in charters. More than half of the special-ed kindergarten enrollment gap is a product of this category of “speech and language disability.” As students advance through grades, the gap in this category actually declines sharply.

Specific learning disability (SLD) is the other classification driving the special-needs enrollment gap. Among entering kindergarten students in charter and traditional public schools, no difference exists in the percentage of SLD-classified students. Yet, as students progress through elementary school, a large SLD gap emerges, because traditional public schools classify a much larger share of students as SLD. These diagnoses are relatively subjective: empirical research demonstrates a tendency for over-diagnosis in traditional public schools.

All this suggests that fears sparked by charter schools having smaller ELL and special-education populations are overblown. Charters, of course, have room for improvement, particularly when it comes to recruiting ELL students. However, the popular anti-charter horror story—that charters systematically exclude difficult-to-educate students—is not rooted in empirical evidence. Indeed, New York charters’ “failure” to enroll higher percentages of students with disabilities is a poor reason to halt their growth—especially since, as my research and that of the Independent Budget Office show, once enrolled, ELL students and students with special needs are significantly less likely to leave a charter school than a traditional public school.