Nonlinear Gompertz curve models of achievement gaps in mathematics and reading

This study examined achievement trajectories in mathematics and reading from school entry through the end of middle school with linear and nonlinear growth curves in 2 large longitudinal data sets (National Longitudinal Study of Youth-Children and Young Adults and Early Childhood Longitudinal Study- Kindergarten Cohort [ECLS-K]). The S-shaped Gompertz model showed best fit in both data sets and decomposed individual changes in terms of 3 interindividual difference parameters that represented total growth, rate of approach (instantaneous approach to total growth), and timing of accelerated growth. The fastest rates of approach were observed for both mathematics and reading before 3rd grade. In ECLS-K, demographic predictors of the 3 parameters of change were consistent with prior work showing socioeconomic status and race/ethnic gaps that widen over time in both subjects and a female advantage in reading and a male advantage in mathematics. Results indicate a new shape of development for both domains, with implications for research, policy, and practice to understand and support students especially in the early years of schooling.