#### WBEZ (NPR in Chicago) and the Better Government Association have determined that thousands of dropouts in Chicago Public Schools were incorrectly classified as transfers, which inflated the city’s official high school graduation rate and allowed Mayor Rahm Emanuel to boast about the improvements during his first term in office.

The city has since revised the number to reflect the accurate classification of those students who dropped out, a move that comes conveniently after the election for mayor in Chicago. About 2,200 students across 25 district high schools were reclassified, WBEZ reports.

The Chicago Public Schools acknowledged the error in the spring, and the revision is expected to be on the order of a few percentage points. The official graduation rate for 2014 was actually 66.3 percent, not 69.4 percent, school officials said on October 1. Going back to 2011, when Mr Emanuel became mayor, all the official graduation rates have been adjusted downward by about the same amount.

## The difficulty in computing the graduation rate

Last month, Voxitatis reported that US graduation rates were higher for the Class of 2013 than they have ever been, according to ASCD, citing data from the National Center for Education Statistics. But only since the 2010-11 school year has the method of determining the graduation rate been consistent from state to state.

$latex C_{2013} = \frac{D_{2013}}{s + t_{i4} – t_{o4} – e_4 – d_4}&s=4$

C is the adjusted cohort graduation rate, and D represents the number of cohort members who earned a regular high school diploma by the end of the 2012-13 school year.

The “cohort” is found in the denominator, defined as the number of first-time ninth graders in the 2009-10 school year, adjusted for any additions or subtractions of students from that cohort over the four academic years prior to 2013: add students who transfer into the cohort after ninth grade (ti4) and subtract any students who transfer out (to4), emigrate to another country (e4), or die (d4) during the 2009-10, 2010-11, 2011-12, or 2012-13 school year.

That’s how it’s supposed to be counted, but that’s on a national level. It can also be applied to the state level, even though it’s a little trickier to identify with certainty transfers to other states, since those state departments of education have no official reporting requirements to the student’s original state.

When it comes to the graduation rate in a single system—or school, as the video from WBEZ explains—it can be nearly impossible to decide which students to count in either the numerator or the denominator. It can be like playing a game of musical chairs.

The school that gets credit for a graduate is usually the school where the student started ninth grade, but that school may be in a different part of the city, state, or country. The normal practice, if a student’s graduation status can’t be determined, is to subtract the student from the denominator. CPS was subtracting too many students—dropouts as well as transfers—from the denominator, WBEZ found, and that made the graduation rate artificially high.

To illustrate with an example, suppose you’re the principal at Homewood-Flossmoor High School in suburban Chicago. You know 630 students enrolled as freshmen four years ago, with the 2010-11 school year, and that 590 graduated last year. I’m not sure on those numbers, but for example purposes, they work. Simply dividing 590 by 630 would yield a four-year graduation rate of about 94 percent, which is what it is for H-F.

But what happened to those 40 students? If one of them died, for example, that student would be subtracted from the 630 to give a denominator of 629. If one of them transferred to another school system and is not being counted in the numerator for H-F, the student should also be subtracted from the denominator.

However, if the student dropped out, he or she should be kept in the denominator and not counted in the numerator. This is the mistake CPS made: they did subtract students from the denominator who dropped out. When those students were added back into the denominator, the graduation rate went down, as would be expected.