Quantitative methods to determine the student workload: II. Statistical models for the microcurricular performance indicators

Previously, we observed that the student workload follows an inverse relation with the learning rate (an application of the kinematic notion of speed contextualized to the learning process). Motivated by this finding, we propose a quantitative estimation of the learning rate using a different source of information: the historical records of final grades of a given course. According to empirical data analyzed in other similar studies, the distribution functions of final grades exhibit a regular pattern: a Gaussian behavior for the approval region and a homogeneous distribution for the failed one. This fact is combined with the incidence of student elimination-desertion rules for introducing two simple agent-based models. Our analysis is complemented by revisiting the performance indicators typically employed to characterize the student promotion and progression. We discuss some other performance indicators to characterize the learning advancement of students: the group learning rate and the learning curve. We compare the results of Monte Carlo simulations with empirical data, observing a good agreement in the behavior of performance indicators derived from these sources. This analysis suggests an adaptive method for the readjustment of the student workload (the number of academic credits) considering the group learning rates during a follow-up period, which resembles the readjustment of prices of goods (and services) in correspondence with the evolution of supply and demand.