From Aesop to Sun Tzu, the importance of working together has long been acknowledged. Yet as long as cooperation has existed, so have the difficulties associated with it. Pooling two fields might mean twice the power, but this union also brings twice the jargon, twice the competing theories, and twice the head butting. Nonetheless, in this…

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…

Web enjoyment has been regarded as a component of system experience. However, there has been little targeted research considering the role of web enjoyment alone in student learning using web-based systems. To address this gap, this study aims to examine the influence of web enjoyment on learning performance and perceptions by controlling system…

Following a pretest, 11 participants who were naive with regard to various algebraic and trigonometric transformations received an introductory lecture regarding the fundamentals of the rectangular coordinate system. Following the lecture, they took part in a computer-interactive matching-to-sample procedure in which they received training on…

This article presents a teaching experiment on the relationship between informal out-of-school and formal in-school mathematics, and the ways each can inform the other in the development of abstract mathematical knowledge. This study concerns the understanding of some aspects of the multiplicative structure of decimal numbers. It involved a series…

Statistical methodology for handling omitted variables is presented in a multilevel modeling framework. In many nonexperimental studies, the analyst may not have access to all requisite variables, and this omission may lead to biased estimates of model parameters. By exploiting the hierarchical nature of multilevel data, a battery of statistical…

Mathematics educators frequently recommend that students use strategies for measurement estimation, such as the reference point or benchmark strategy; however, little is known about the effects of using this strategy on estimation accuracy or representations of standard measurement units. One reason for the paucity of research in this area is that…

This article describes four hands-on activities that can be used to develop probabilistic and statistical thinking in the middle grades. (Contains 3 figures and 1 table.)

Hoping to develop in her students an understanding of mathematics as a way of thinking more than a way of doing, the author of this article describes how her students worked on a spatial reasoning problem stemming from an iteratively constructed sequence of cylinders. She presents an activity of making cylinders out of paper models, and for every…

This paper uses data from the National Education Longitudinal Study to estimate the association between high school alcohol use and educational attainment measured around age 26. Initially, the effect of alcohol use on educational attainment is estimated using baseline probit models, which ignore the possibility that unmeasured determinants of…

To complement recent articles in this journal on structural equation modeling (SEM) practice and principles by Martens and by Quintana and Maxwell, respectively, the authors offer a consumer's guide to SEM. Using an example derived from theory and research on vocational psychology, the authors outline six steps in SEM: model specification,…

The effects of five ability estimators, that is, maximum likelihood estimator, weighted likelihood estimator, maximum a posteriori, expected a posteriori, and Owen's sequential estimator, on the performances of the item response theory-based adaptive classification procedure on multiple categories were studied via simulations. The following…

This study contributes to understanding sources of gender differential item functioning (DIF) on mathematics tests. This study focused on identifying sources of DIF and differential bundle functioning for boys and girls on the British Columbia Principles of Mathematics Exam (Grade 12) using a confirmatory SIBTEST approach based on a…

We examine whether abortion removes from the population those infants most at risk of homicide. As part of our identification strategy, we find that abortion reduces the number of unwanted births, estimating that 1 percent increase in the abortion ratio reduces unwanted births by approximately 0.35 percent. Using cross-sectional time-series data…

This paper details the challenges encountered by authors summarizing evidence from a primary study to describe a treatment's effectiveness using an effect size (ES) estimate. Dilemmas that are encountered, including how to calculate and interpret the pertinent standardized mean difference ES for results from studies of various research designs,…