The article develops the structure and estimates the parameters of a nonlinear learning model applicable to research designs in which students are tested at the beginning and end of a course of study. A student's precourse score is an error-ridden proxy for his precourse aptitude. As a remedy for this problem, the article combines a probit model of test score outcomes, a learning function, and a linear equation relating aptitude to demographic characteristics to deduce the exact test score distribution. An empirical example of maximum likelihood estimation of the model's parameters is presented.