Cumulative advantage in early elementary mathematics: An autoregressive latent trajectory analysis

Abstract

Early mathematics proficiency lays the foundation for long-term academic success, as it influences high school achievement and career aspirations, which in turn leads to college enrollment and opens pathways into high-prestige careers. The present study utilized 267,861 i-Ready Diagnostic for Mathematics academic screening assessment records from 36,894 public school students in Hawai’i who enrolled in Grade 1 between the 2016–2017 to 2020–2021 school years. Each cohort was tracked through Grade 3 from 2018–2019 to 2022. Data were collected by the Hawaii State Department of Education as part of the Multi-Tiered systems of Support process. This study aimed to (a) examine mathematics growth trajectories from Grade 1 through Grade 3; (b) identify possible differential patterns across initial mathematics skill level, student demographic subgroups, and cohorts impacted by the COVID-19; and (c) assess how early elementary growth rates relate to third-grade state assessment performance.Growth trajectories were examined using the autoregressive latent trajectory (ALT) model which augments the latent growth curve (LGC) model by explicitly incorporating the influence of prior scores on subsequent mathematics achievement. Although the ALT model is not commonly used in education research, explicitly modeling these autoregressive effects provided a superior fit to the data over traditional LGC model, allowing for more precise identification of development patterns in mathematics proficiency over time. Several findings were notable. First, growth rates varied across the five cohorts, showing both cumulative advantage (high initial starters growing faster) and compensatory (lower starters catching up) patterns. Second, demographic differences in initial achievement and growth rates were observed overall and within initial mathematics tier. Students who were female, Native Hawaiian or Pacific Islander, economically disadvantaged, or who attended a rural school tended to have lower growth rates. Third, average mathematics screening scores were lower in post-COVID assessment periods, and potential measurement error during the fall 2020 assessment period may have contributed to inconsistent growth patterns across cohorts. Fourth, performance on the third-grade state assessment was positively related to initial achievement and growth rates on the mathematics screening assessments. Students who were Native Hawaiian or Pacific Islander, economically disadvantaged, and reading at below grade level at the start of Grade 1 had significantly lower third-grade state assessment scores. These results suggest that standard interventions may not fully address the needs of students and disparities in early mathematics development. More tailored supports may be needed to address differences in starting skill levels and growth rates even within initial mathematics tier. Limitations and future research are also discussed.