Measuring continuous change or growth in individual students' academic abilities over time currently uses several statistical models or transformations to move from data representing a student's correct or incorrect responses on individual test items to inferences about the form and quantity of changes in the student's underlying ability. This study proposed and investigated a single integrated model of underlying growth within an Item Response Theory framework as a potential alternative to this approach. A Monte Carlo investigation explored parameter recovery for marginal maximum likelihood estimates via the Expectation-Maximization algorithm under variations of several conditions, including the form of the underlying growth trajectory, the amount of inter-individual variation in the rate(s) of growth, the sample size, the number of items at each time point, and the selection of items administered across time points. A real data illustration with mathematics assessment data from the Early Childhood Longitudinal Study showed the practical use of this integrated model for measuring gains in academic achievement. Overall, this exploration of an integrated model approach contributed to a better understanding of the appropriate use of growth models to draw valid inferences about students' academic growth over time.