Student growth percentiles (SGPs) are currently used by several states and school districts to provide information about individual students as well as to evaluate teachers, schools, and school districts. For SGPs to be defensible for these purposes, they should be reliable. In this study, we examine the amount of systematic and random error in…

In this paper, we present a third-grade ecology learning environment that integrates two forms of modeling--embodied modeling and agent-based modeling (ABMs)--through the generation of mathematical representations that are common to both forms of modeling. The term "agent" in the context of ABMs indicates individual computational objects…

Sources of longitudinal achievement data are increasing thanks partially to the expansion of available interim assessments. These tests are often used to monitor the progress of students, classrooms, and schools within and across school years. Yet, few statistical models equipped to approximate the distinctly seasonal patterns in the data exist,…

This article explains the process behind estimating a National Education Cost Model (NECM) and generating from that model projections of per-pupil costs to achieve 2016 national average outcomes (reading and math grades 3 to 8) across all districts in the United States, from 2019-20 to 2020-21. This article is a follow-up to a preliminary report…

Effect sizes in the Cohen's d family are often used in education to compare estimates across studies, measures, and sample sizes. For example, effect sizes are used to compare gains in achievement students make over time, either in pre- and post-treatment studies or in the absence of intervention, such as when estimating achievement gaps. However,…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…

Houston's experience with the Educational Value-Added Assessment System (R) (EVAAS) raises questions that other districts should consider before buying the software and using it for high-stakes decisions. Researchers found that teachers in Houston, all of whom were under the EVAAS gun, but who taught relatively more racial minority students,…

This article proposes a latent variable regression four-level hierarchical model (LVR-HM4) that uses a fully Bayesian approach. Using multisite multiple-cohort longitudinal data, for example, annual assessment scores over grades for students who are nested within cohorts within schools, the LVR-HM4 attempts to simultaneously model two types of…

The purpose of this study is to evaluate the relationship of mathematics calculation rate (curriculum-based measurement of mathematics; CBM-M), reading rate (curriculum-based measurement of reading; CBM-R), and mathematics application and problem solving skills (mathematics screener) among students at four levels of proficiency on a statewide…

Public schools with impressive records of serving lower-performing students are often overlooked because their average test scores, even when students are growing quickly, are lower than scores in schools that serve higher-performing students. Schools may appear to be doing poorly either because baseline achievement is not easily accounted for or…

In recent years the use of the latent curve model (LCM) among researchers in social sciences has increased noticeably, probably thanks to contemporary software developments and the availability of specialized literature. Extensions of the LCM, like the the latent change score model (LCSM), have also increased in popularity. At the same time, the R…

In this article we propose several modeling choices to extend propensity score analysis to clustered data. We describe different possible model specifications for estimation of the propensity score: single-level model, fixed effects model, and two random effects models. We also consider both conditioning within clusters and conditioning across…

Value-added approaches for attributing student growth to teachers often use weighted estimates of building-level factors based on "typical" schools to represent a range of community, school, and other variables related to teacher and student work that are not easily measured directly. This study examines whether such estimates are likely…

This study investigated the sensitivity of fit indices to model misspecification in within-individual covariance structure, between-individual covariance structure, and marginal mean structure in growth curve models. Five commonly used fit indices were examined, including the likelihood ratio test statistic, root mean square error of…

The purpose of this study was to determine whether patterns of strategy use in second, third and fourth grade children's arithmetic supported Steffe's model of numerical development. In addition to student-generated strategies, we looked at commonly taught algorithms not considered in Steffe's model to determine whether these algorithms reflected…