National Council of Teachers of Mathematics' (NCTM's) (2000) Connections Standard states that students should "recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect ...; [and] recognize and apply mathematics in contexts outside of mathematics" (p. 354). This article presents an in-depth…

Individual differences in general mental ability ("g") have important implications across multiple disciplines. Research suggests that the variance in "g" may be due to a general fitness factor. If this is the case, a relationship should exist between "g" and other reliable indicators of fitness. Some empirical results indicate a relationship…

The primary purpose of this study was to investigate the accuracy of the DF50 (ImpediMed Ltd, Eight Mile Plains, Queensland, Australia) bioelectrical impedance analysis device using dual-energy x-ray absorptiometry as the criterion in two groups: endurance athletes and power athletes. The secondary purpose was to develop accurate body fat…

Population models are often discussed in algebra, calculus, and differential equations courses. In this article we will use the human population of the world as our application. After quick looks at two common models we'll investigate more deeply a model which incorporates the negative effect that accumulated pollution may have on population.

Standardized parameter estimates are routinely used to summarize the results of multiple regression models of manifest variables and structural equation models of latent variables, because they facilitate interpretation. Although the typical standardization of interaction terms is not appropriate for multiple regression models, straightforward…

The air surrounding a projectile affects the projectile's motion in three very different ways: the drag force, the buoyant force, and the added mass. The added mass is an increase in the projectile's inertia from the motion of the air around it. Here we experimentally measure the added mass of a spherical projectile in air. The results agree well…

The Common Core State Standards for Mathematics will place more pressure on special education and math teachers to raise the skill levels of all students, especially those with disabilities in math (MD). The purpose of this study was to assess the effects of enhanced anchored instruction (EAI) on students with and without MD in co-taught general…

Recent research (Strunk and Reardon forthcoming) applies Partial Independence Item Response (PIIR) models to teacher bargaining agreements in California to calculate the latent restrictiveness of these contracts. Further research (Strunk and Grissom 2010; Strunk forthcoming) tests the external validity of these estimates. Given that much research…

Maximum likelihood (ML) estimation of generalized linear mixed models (GLMMs) is technically challenging because of the intractable likelihoods that involve high dimensional integrations over random effects. The problem is magnified when the random effects have a crossed design and thus the data cannot be reduced to small independent clusters. A…

The use of value-added modeling (VAM) in school accountability is expanding, but deciding how to embrace VAM is difficult. Various experts say it's too unreliable, causes more harm than good, and has a big margin for error. Others assert VAM is imperfect but useful, and provides valuable feedback. A closer look at the models, and their use,…

Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…

The need of after-school programs has become urgent for school-age children in many industrialized countries due to social structure changes. This research develops a hierarchical framework to evaluate after-school programs from two distinct aspects--service quality from parents' perspectives and marketing strategy from operators'…

Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging courses. In this method, the information from a word problem about percentages is presented in a two-way table. Such a table gives…

Audit studies testing for discrimination have been criticized because applicants from different groups may not appear identical to employers. Correspondence studies address this criticism by using fictitious paper applicants whose qualifications can be made identical across groups. However, Heckman and Siegelman (1993) show that group differences…

The reciprocal method of service department cost allocation requires linear equations to be solved simultaneously. These computations are often so complex as to cause the abandonment of the reciprocal method in favor of the less sophisticated direct or step-down methods. Here is a short example demonstrating how Excel's sometimes unknown matrix…