The October 13th Edition of the Proceedings of the National Academy of Science features a very interesting article by Michael Marder and Dhruv Bansal from the University of Texas.
From the article … “Texas began testing almost every student in almost every public school in grades 3-11 in 2003 with the Texas Assessment of Knowledge and Skills (TAKS). Every other state in the United States administers similar tests and gathers similar data, either because of its own testing history, or because of the Elementary and Secondary Education Act of 2001 (No Child Left Behind, or NCLB). Texas mathematics scores for the years 2003 through 2007 comprise a data set involving more than 17 million examinations of over 4.6 million distinct students. Here we borrow techniques from statistical mechanics developed to describe particle ﬂows with convection and diffusion and apply them to these mathematics scores. The methods we use to display data are motivated by the desire to let the numbers speak for themselves with minimal ﬁltering by expectations or theories.
The most similar previous work describes schools using Markov models. “Demographic accounting” predicts changes in the distribution of a population over time using Markov models and has been used to try to predict student enrollment year to year, likely graduation times for students, and the production of and demand for teachers. We obtain a more detailed description of students based on large quantities of testing data that are just starting to become available. Working in a space of score and time we pursue approximations that lead from general Markov models to Fokker–Planck equations, and obtain the advantages in physical interpretation that follow from the ideas of convection and diffusion.”