This article proposes an innovative approach to estimating the counterfactual without the necessity of generating information from either a control group or a before-measure. Building on the idea that program participants are capable of estimating the hypothetical state they would be in had they not participated, the basics of the Roy-Rubin model…

From 1982-1997, 35 states adopted legislation, referred to as homeschool rights, that explicitly granted families the right to educate their children at home. Using data from the National Household Education Survey, this article examines the impact that this legislation has had on the decision to homeschool a child versus the alternatives of…

We study the properties of two specification tests that have been applied to a variety of estimators in the context of value-added measures (VAMs) of teacher and school quality: the Hausman test for choosing between random and fixed effects and a test for feedback (sometimes called a "falsification test"). We discuss theoretical…

This document provides an overview of the critical role of fiscal data in state Part C systems. This information is intended to help state Part C lead agency staff better understand strategic fiscal policy questions, the fiscal data elements needed to address those questions, and the benefits of using these data. Fiscal data provide powerful…

Marlene Chesney describes a piece of research where the participants were asked to complete a calculation, 16 + 8, and then asked to describe how they solved it. The diversity of invented strategies will be of interest to teachers along with the recommendations that are made. So "how do 'you' solve 16 + 8?"

In school-based randomized control trials (RCTs), a common design is to follow student cohorts over time. For such designs, education researchers usually focus on the place-based (PB) impact parameter, which is estimated using data collected on all students enrolled in the study schools at each data collection point. A potential problem with this…

The standard for measuring fuel efficiency in the U.S. has been miles per gallon (mpg). However, the Environmental Protection Agency's (EPA) switch in rating fuel efficiency from miles per gallon to gallons per hundred miles with the 2013 model-year cars leads to interesting and relevant mathematics with real-world connections. By modeling…

The order of problems presented to students is an important variable that affects learning effectiveness. Previous studies have shown that solving problems in a blocked order, in which all problems of one type are completed before the student is switched to the next problem type, results in less effective performance than does solving the problems…

The need to endow marketing graduates with skills relevant to employability grows ever more important. Marketing math and elementary financial understanding are essential employability skills, particularly given the contemporary emphasis on marketing metrics, but the evidence is that marketing graduates are often relatively weak in such skills.…

Many problems of electric field strength on a boundary between two media require college-level mathematical analysis. However, when the boundary between media is represented by a sphere or a flat plane, these types of problems can be solved algebraically, placing them within reach of high school students. This article presents a solution analysis…

Generalizability theory and analysis of variance methods are employed, together with the concept of objective time pressure, to estimate response time distributions and the degree of time pressure in timed tests. By estimating response time variance components due to person, item, and their interaction, and fixed effects due to item types and…

The Madelung constants for binary ionic nanoparticles are determined. The computational method described here sums the Coulombic interactions of each ion in the particle without the use of partial charges commonly used for bulk materials. The results show size-dependent lattice energies. This is a useful concept in teaching how properties such as…

In this study, the accuracies of four strategies were compared for estimating conditional differential item functioning (DIF), including raw data, logistic regression, log-linear models, and kernel smoothing. Real data simulations were used to evaluate the estimation strategies across six items, DIF and No DIF situations, and four sample size…

This article provides a way to determine adequate sample size for the confidence interval of covariate-adjusted mean difference in randomized experiments. The standard error of adjusted mean difference depends on covariate variance and balance, which are two unknown quantities at the stage of planning sample size. If covariate observations are…

A latent variable modeling method is outlined for constructing a confidence interval (CI) of a popular multivariate effect size measure. The procedure uses the conventional multivariate analysis of variance (MANOVA) setup and is applicable with large samples. The approach provides a population range of plausible values for the proportion of…