Flow and diffusion of high-stakes test scores.

We apply visualization and modeling methods for convective and diffusive flows to public school mathematics test scores from Texas. We obtain plots that show the most likely future and past scores of students, the effects of random processes such as guessing, and the rate at which students appear in and disappear from schools. We show that student outcomes depend strongly upon economic class, and identify the grade levels where flows of different groups diverge most strongly. Changing the effectiveness of instruction in one grade naturally leads to strongly nonlinear effects on student outcomes in subsequent grades.