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…

Causal inference involves determining whether a treatment (e.g., an education program) causes a change in outcomes (e.g., academic achievement). It is well-known that causal effects are more challenging to estimate than associations. Over the past 50 years, the potential outcomes framework has become one of the most widely used approaches for…

The finite population correction (FPC) factor is often used to adjust variance estimators for survey data sampled from a finite population without replacement. As a replicated resampling approach, the jackknife approach is usually implemented without the FPC factor incorporated in its variance estimates. A paradigm is proposed to compare the…

The purpose of this study was to analyze the problem-solving techniques that students in a fifth-grade classroom applied while solving mathematical word problems. Fifth-grade students in a private school with Ministry of Education curricula in Al Ain, Abu Dhabi, were given a set of 15-word problems to solve with detailed justifications. The…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

When nonrandom treatments occur across sites, within-site matching (WM) is often desirable. This approach, however, can significantly reduce treatment group sample size and exclude substantively important subgroups. To limit these drawbacks, we extend a matching approach developed by Stuart and Rubin to a multisite study. We demonstrate the…

In the author's experience with this activity, students struggle with the idea of representativeness in probability. Therefore, this student misconception is part of the classroom discussion about the activities in this lesson. Representativeness is related to the (incorrect) idea that outcomes that seem more random are more likely to happen. This…

One of the best-known methods for setting a benchmark standard on a test is that of Angoff and its modifications. When scored dichotomously, judges estimate the probability that a benchmark student has of answering each item correctly. As in most methods of standard setting, it is assumed implicitly that the unit of the latent scale of the…

In Maori medium schools, research that investigates children's mathematical computation with number and connections they might make to mathematical ideas in other strands is limited. This paper seeks to share ideas elicited in a task-based observation and interview with one child about the number ideas she utilises to solve a problem requiring…

When competence tests are administered, subjects frequently omit items. These missing responses pose a threat to correctly estimating the proficiency level. Newer model-based approaches aim to take nonignorable missing data processes into account by incorporating a latent missing propensity into the measurement model. Two assumptions are typically…

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…

We investigate factors influencing student sign-ups for Washington State's College Bound Scholarship (CBS) program. We find a substantial share of eligible middle school students fail to sign the CBS, forgoing college financial aid. Student characteristics associated with signing the scholarship parallel characteristics of low-income students who…

As a result of the use of random assignment to treatment, randomized experiments typically have high internal validity. However, units are very rarely randomly selected from a well-defined population of interest into an experiment; this results in low external validity. Under nonrandom sampling, this means that the estimate of the sample average…

A core component of informal statistical inference is the recognition that judgments based on sample data are inherently uncertain. This implies that instruction aimed at developing informal inference needs to foster basic probabilistic reasoning. In this article, we analyze and critique the now-common practice of introducing students to both…

This article describes the development of early warning indicators for high school and beyond in the Milwaukee Public Schools (MPS) by the Value-Added Research Center (VARC) at the University of Wisconsin-Madison, working in conjunction with staff from the Division of Research and Evaluation at MPS. Our work in MPS builds on prior early warning…