Research has established that children's development of addition and subtraction skills progresses through a hierarchy of strategies that begin with counting-by-one methods through to flexible mental strategies using a combination of knowledge of basic facts and understanding of place value. An important transition point is the shift from the…

Many approaches to standard-setting use item calibration and student score estimation results to structure panelists' tasks. However, this requires collecting standard-setting judgments after the item analysis results are available. The Scoring Guide Alignment approach collects standard-setting judgments during the scoring sessions from teachers…

The authors investigated how 3- and 4-year-old children and adults use relative distance to judge nearbyness. Participants judged whether several blocks were by a landmark. The absolute and relative distance of the blocks from the landmark varied. In Experiment 1, judgments of nearbyness decreased as the distance from the landmark increased, …

Using time series data, this study shows that domestic students' academic performance is generally better than international students' performance, but the gap is significantly narrowing as international students' performance is improving over time. The study also shows that there is no strong correlation between the percentage of international…

This paper examines the estimation of two-stage clustered RCT designs in education research using the Neyman causal inference framework that underlies experiments. The key distinction between the considered causal models is whether potential treatment and control group outcomes are considered to be fixed for the study population (the…

A widely recognized concern in elementary school mathematics education is that teachers' understanding of the mathematical curricular content generally appears quite fragmented, sparsely connected, and procedurally oriented. This pilot study applies methods of educational neuroscience to investigate and improve preservice teachers' learning and…

As a group, children from disadvantaged, low-income families perform substantially worse in mathematics than their counterparts from higher-income families. Minority children are disproportionately represented in low-income populations, resulting in significant racial and social-class disparities in mathematics learning linked to diminished…

Recognizing the need to implement standards-based instructional materials with school-wide coherence led some Philadelphia schools to adopt whole-school reform (WSR) models during the late 1990s. The authors report on the relation between mathematics achievement growth for middle-grade students on the Pennsylvania System of School Assessments and…

We use exogenous variation in Social Security payments created by the Social Security benefits notch to estimate how retirees' use of prescription medications responds to changes in their incomes. Using data from the 1993 Wave of the AHEAD, we obtain instrumental variables estimates of the income elasticity of prescription drug use that are…

As the title says, this article considers the dog-on-the-beach problem from the perspective of the calculus of variations, making connections with the brachistochrone problem and Snell's law.

Neater representations for variance are given for small sample sizes, especially for 3 and 4. With these representations, variance can be calculated without a calculator if sample sizes are small and observations are integers, and an upper bound for the standard deviation is immediate. Accessible proofs of lower and upper bounds are presented for…

This article illustrates that not all statistical software packages are correctly calculating a "p"-value for the classical "F" test comparison of two independent Normal variances. This is illustrated with a simple example, and the reasons why are discussed. Eight different software packages are considered.

The notion of an impact factor was first posited by Eugene Garfield (1972) to study the use, prestige, and status of scientific journals. The Institute for Scientific Information created the impact factor as a means to measure the number of times an "average article" published in a journal was cited over a particular time period ("The impact…

This paper investigates a general identity which expresses an apparently complicated and intriguing sum of fractions as an elegant and straightforward sum of simple terms.

A method for the numerical evaluation of the error term in Gaussian quadrature rules is derived by means of Chebyshev polynomials of the first kind.