In this extension to a classic physical chemistry experiment, students record the proton nuclear magnetic resonance spectra of the [beta]-diketones 2,4-pentanedione, 3-methyl-2,4-pentanedione, and 3-chloro-2,4-pentanedione to investigate the effect of substituents on keto-enol tautomerization equilibria. From the integrated intensities of keto and…

This study examined how much improvement was attainable with respect to accuracy of differential item functioning (DIF) measures and DIF detection rates in the Mantel-Haenszel procedure when employing focal and reference groups with notably unbalanced sample sizes where the focal group has a fixed small sample which does not satisfy the minimum…

Estimation is more than a skill or an isolated topic. It is a thinking tool that needs to be emphasized during instruction so that students will learn to develop algorithmic procedures and meaning for fraction operations. For students to realize when fractions should be added, subtracted, multiplied, or divided, they need to develop a sense of…

The purpose of this simulation study was to assess the performance of latent variable models that take into account the complex sampling mechanism that often underlies data used in educational, psychological, and other social science research. Analyses were conducted using the multiple indicator multiple cause (MIMIC) model, which is a flexible…

Very often, we understand differences in literacy performance exclusively in terms of the skills that individuals bring to the literacy tasks they face. Drawing on a new, highly integrative theory of functional literacy--the text-task-respondent (TTR) theory--this article presents a set of seven literacy skills that are required for everyday…

This paper proposes a structural analysis for generalized linear models when some explanatory variables are measured with error and the measurement error variance is a function of the true variables. The focus is on latent variables investigated on the basis of questionnaires and estimated using item response theory models. Latent variable…

A branch of mathematics commonly used in cryptography is Galois Fields GF(p[superscript n]). Two basic operations performed in GF(p[superscript n]) are the addition and the multiplication. While the addition is generally easy to compute, the multiplication requires a special treatment. A well-known method to compute the multiplication is based on…

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.…

Using multitrait, multimethod data, and confirmatory factor analysis, the current study examined the effects of arithmetic item formatting and the possibility that across formats, abilities other than arithmetic may contribute to children's answers. Measurement hypotheses were guided by several leading theories of arithmetic cognition. With a…

Incorporating new methods and approaches in learning environments is imperative to the development of education systems. By enhancing learning processes, education becomes more attainable at all levels. "The Handbook of Research on Instructional Systems and Educational Technology" is an essential reference source for the latest scholarly…

Mode estimation, the visual determination of the proportions of the components of a rock, is a valuable tool in geology, providing one of the most efficient means of describing rock mineralogy and chemistry. However, current methods of teaching mode estimation suffer from the often-mediocre mode-estimation skills of the instructors. Fifty-nine…