**By Rebecca Goldin, Ph.D., December 30, 2013**

In the rush to get data about how students are doing on tests, we need a little lesson in how to use mathematics and, specifically, percentages. A case in point is a recent article by *The Washington Post*, “**In Fairfax, students score better on IB exams, while AP test results drop.” **The article is about a decrease in the number of students taking Advanced Placement (AP) exams, an increase in number of students taking International Baccalaureate (IB) exams, and the performance of students on these exams. Quite literally, the author notes increasing minority participation, and misinterprets data about the resulting scores to create an (incorrect) declining success rate in the face of significant achievement and improvement on minority scores.

How is that possible?** **All it takes is a slight of hand about which data you cite. First, remember each student may take several exams for different topics. With that in mind, consider the changes from 2010 to 2013.

The number of **students** participating in AP exams went up five percent over those 3 years, while the number of students participating in IB exams increased 20 percent. The increases were even more significant for minority students on IB exams. As *The Washington Post* noted, “Among black students, the number of those taking IB exams increased by 36 percent, and the number of Hispanic students taking IB tests increased by 54 percent.” The **number of exams** taken by these students also increased. “The number of IB tests taken by black students increased by 29 percent while the number of tests administered to Hispanic students jumped by 81 percent. Scores for both ethnic groups also improved slightly.” Yet, the *Post* added, “The increase in the number of tests, however, did not lead to better scores overall for black or Hispanics, as the scores for both ethnic groups dropped slightly during that time.”

So which is it, did the scores improve slightly or did they drop slightly? It turns out that *both *statements are misleading. **In fact, Fairfax County has seen phenomenal success. **

Here’s a closer look at the IB data. In 2010, 63 percent of IB tests taken by black students were passed (4 or better). In 2013, only 61 percent of IB tests taken by black students were passed. Presumably this is the slight drop the Washington Post was referring to. But this small drop in percentage came along with a *huge* increase in participation, which means that despite the drop, black students are seeing increased pass rates. In 2010, black students passed just 348 IB exams, while in 2013, they passed 431 exams. That constitutes a 24 percent increase, hardly a “slight” improvement. And in case anyone poses the question, no the black population did not increase 24 percent in those 3 years. Similarly, in 2010, 70 percent of IB exams taken by Hispanics were passed, while that number dropped to 66 percent in 2013. Yet in 2010, Hispanics passed 468 tests while in 2013, they passed 796 tests, an increase by 70 percent. Asians and Whites also improved their performance: Asians passed 1,077 exams in 2010 and 1,244 in 2013, an increase by 15.5 percent, and Whites went from 2,621 exams passed to 3,294 exams, an increase of 25.6 percent.

The moral of the story here is that the percentages (the pass rates) are only considering the students *as part of the group taking the tests. *But that group has changed from 2010 to 2013, including a significantly larger population with some weaker students. That’s the reason that it’s irrelevant to report the percentage of the population passing the exams, and to compare over the years – they are percentages of different groups. In contrast, the sheer number of exams passed indicates tremendous progress in minority success (and non-minority success) at passing IB exams.

Now one could argue that these successes may indicate a general shift from AP exams to IB exams. The data show that the number of White and Other students decreased participating in taking AP exams, while the number of Asians, Blacks, and Hispanics students participating in AP exams increased. The number of actual AP exams taken also went up, for all demographics except Other. In sum, the IB exams were not sucking up students from the AP tests – participation in both types of exams is going up, as are the success rates.

Finally, what can be made of the claims by the *Post* that the scores went slightly up, and also went slightly down? Presumably, the Post was looking at different time periods. From 2012 to 2013, the average (mean) score on the IB exam went up for all ethnic groups, but from 2010 to 2013, they went down slightly for Blacks and Hispanics. These comparisons are meaningless, however, because of the large changes in number of exams being taken. For the record and as a matter of comparison the average scores for AP tests went slightly up for all groups except Whites from 2010 to 2013, and the number of students taking the AP exams did not increase as much as they did for the IB exams.

Overall, Fairfax County should note its success at increasing minority and non-minority participation and success in these advanced exams. And the kids who studied so hard and succeeded in these college level exams should be congratulated.