Many generalization studies in education are typically based on a sample of 30-70 schools while the inference population is at least twenty times larger. This small sample to population size ratio limits the precision of design-based estimators of the population average treatment effect. Prior work has shown the potential of small area estimation…

In this paper is proposed a straightforward model selection approach that indicates the most suitable count regression model based on relevant data characteristics. The proposed selection approach includes four of the most popular count regression models (i.e. Poisson, negative binomial, and respective zero-inflated frameworks). Moreover, it…

In causal matching designs, some control subjects are often left unmatched, and some covariates are often left unmodeled. This article introduces "rebar," a method using high-dimensional modeling to incorporate these commonly discarded data without sacrificing the integrity of the matching design. After constructing a match, a researcher…

The sudden perception of a connection between ideas is exhilarating. We might call these moments 'Aha!' moments. The purpose of this paper is to demonstrate how several different ideas can come together in Year 12 mathematics. The subject Further Mathematics in the Victorian Certificate of Education (VCE) is the Victorian adaptation of General…

Many students' knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's integrated magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process…

Two objectives guided this research. First, this study examined how well teachers' tracking decisions contribute to the homogenization of their students' achievements. Second, the study explored whether teachers' tracking decisions would be outperformed in homogenizing the students' achievements by statistical models of tracking decisions. These…

Large-scale assessment programs such as the National Assessment of Educational Progress (NAEP), Trends in International Mathematics and Science Study (TIMSS), and Programme for International Student Assessment (PISA) use a sophisticated assessment administration design called matrix sampling that minimizes the testing burden on individual…

Regression, weighting and related approaches to estimating a population mean from a sample with nonrandom missing data often rely on the assumption that conditional on covariates, observed samples can be treated as random. Standard methods using this assumption generally will fail to yield consistent estimators when covariates are measured with…

In large-scale educational surveys, a latent regression model is used to compensate for the shortage of cognitive information. Conventionally, the covariates in the latent regression model are principal components extracted from background data. This operational method has several important disadvantages, such as the handling of missing data and…

School suspension rates have been rising since the early 1970s, especially for children of color. One body of research has demonstrated that suspension from school is harmful to students, as it increases the risk of retention and school dropout. Another has demonstrated that school dropouts impose huge social costs on their states and localities,…

We analyze class-size effects on academic achievement in secondary school in Denmark exploiting an institutional setting where pupils cannot predict class size prior to enrollment, and where post-enrollment responses aimed at affecting realized class size are unlikely. We identify class-size effects combining a regression discontinuity design with…

The purpose of the current study was to evaluate the importance of growth in math fact skills within the context of overall math proficiency. Data for 1,493 elementary and middle school students were included for analysis. Regression models were fit to examine the relative value of math fact fluency growth, prior state test performance, and a fall…

Numerical understanding and arithmetic skills are easier to acquire for whole numbers than fractions. The "integrated theory of numerical development" posits that, in addition to these differences, whole numbers and fractions also have important commonalities. In both, students need to learn how to interpret number symbols in terms of…

The School Composition and the Black-White Achievement Gap study was undertaken by the National Center for Education Statistics to present both descriptive and associative information on the relationships among the percentage of students in a school who were Black (referred to as "Black student density" or "density"), the…

The purpose of this study is two-fold; the first aim being to show the effect of outliers on the widely used least squares regression estimator in social sciences. The second aim is to compare the classical method of least squares with the robust M-estimator using the "determination of coefficient" (R[superscript 2]). For this purpose,…