Ares, N., Stroup, W. M., & Schademan, A. R. (2009). Cognition and Instruction, 27(1), 1–24. A new generation of networked classroom technology immerses students and teachers in the group-level construction of powerful mathematical and scientific concepts. We examine these networks from a sociocultural point of view as a new form of mediating artifact. We present a mixed-method, microgenetic analysis to characterize students’ appropriation of mathematical content and practice as mediated by the Participatory Simulations system. Central findings of the study are that networked activities provided the opportunity for students and the teacher to: (a) act on multiple representations, (b) create collectively a linked set of mathematical objects that they could examine and discuss together, and (c) exercise agency in the production of mathematical discourse and practice. These opportunities fostered the development of powerful mathematical discourse.

Marder, M., & Bansal, D. (2009). Flow and diffusion of high-stakes test scores. Proceedings of the National Academies of Science, 106, 17267–17270. 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.