The application of visualization methods to educational data sets with inspiration from statistical and fluid mechanics
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This dissertation focuses on the development of visualization methods that enable us to examine longitudinal data in a unique way. We take inspiration from statistical and fluid mechanics to represent our data as a "flow" through time. Our visualizations represent vector fields (or flow plots), streamlines, and trajectories, and they are constructed in a similar manner to how one might analyze the aggregate motion of particles in a fluid. However, the subject of our research extends beyond ordinary fluid mechanics. We will use our visualizations to examine statewide standardized test scores in Texas from 2003 to 2011. The nature of the data makes it a perfect match for our methodology, since students' test scores tend to change over time in a semi-deterministic but nonlinear manner. Furthermore, our methods represent a departure from the standard ways of analyzing educational data. By visualizing the changes in students' test scores over a nine-year period, we discovered that our flow plots were changing with the eventual graduating class of 2012. The change in our visualizations was caused by an educational policy known as the Student Success Initiative, or SSI. The policy forced students to pass their standardized tests in 5th and 8th grade, or risk being held back a grade. To help with this process, students who initially failed were given extra instruction and additional opportunities to take the test. SSI was implemented in such a way that it would affect the class of 2012 and beyond, although we did not know of the program's existence until our plots had been developed. SSI had a successful impact on the educational career of Texas students; a far greater percentage of students were able to pass the 5th and 8th grade standardized tests after SSI was implemented. The striking feature of SSI, however, is that it also significantly improved test scores in 6th, 7th, 9th, and 10th grade. Despite its success at improving test scores over many years and grades, the program was eventually defunded. This was partially due to an inability to construct a lengthy longitudinal analysis of the program's influence. Our methodology would have conclusively shown the effectiveness of the SSI policy. Despite the defunding of the SSI, I am confident our methodology can be extended to illustrate changes in other data systems. These systems may or may not be related to education; our code and techniques are designed to be as universal as possible. We will explore several extensions to other data sets at the end of this dissertation.