Statistical description of the learning process. Consideration of pairwise interactions

The present paper is initiated by the necessity of improving the procedure of statistical processing of sociological data on the dynamics of mastering new material in the process of learning physics at secondary schools. A statistical model is constructed in which the dynamics of learning is described by the Fokker-Planck-Kolmogorov (FPK) equation. The initial problem is reduced to a description of an averaged "ideal" student. Under assumption of weak interactions among students, the problem is reduced to a one-dimensional special FPK equation. The parameters of this equation are determined from the available experimental data by the least squares method. Consideration of pairwise interactions between "ideal" students leads to the FPK equation with nonlocal nonlinearity. The quantitative characteristics of the learning process are analyzed for the examined model. ©2002 Plenum Publishing Corporation.