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.