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Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study — Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this study was to examine the average treatment effect of preschool special education services on children''s kindergarten academic skills. Using data from a nationally representative sample of United States children who participated in the Early Childhood Longitudinal Study—Birth Cohort, we examined the effectiveness of preschool special education services by comparing reading and math outcomes for children who received special education services at preschool-age to a propensity-score-weighted sample of children who did not receive these services. Results indicated that the receipt of these special education services had a statistically significant moderate negative effect on children''s kindergarten skills in both reading (d =−0.21) and mathematics (d =−0.29). These findings have implications for the implementation and evaluation of services for young children experiencing developmental delays or disabilities. [Copyright &y& Elsevier]