The notation for vector analysis has a contentious nineteenth century history, with many different notations describing the same or similar concepts competing for use. While the twentieth century has seen a great deal of unification in vector analysis notation, variation still remains. In this paper, the two primary notations used for expressing…

American Educational Research Association (AERA) standards stipulate that researchers show evidence of the internal structure of instruments. Confirmatory factor analysis (CFA) is one structural equation modeling procedure designed to assess construct validity of assessments that has broad applicability for counselors interested in instrument…

Getting students adopt the habits of mind specific to many disciplines can be seen as an anchor that will support them to solve the problems in their daily lives. Starting from this premise, a new subject, featuring the habits of mind and how to use and improve them in educational environments seems to worth thinking on. This article describes an…

The increasing availability of massive administrative datasets linking postsecondary enrollees with post-college earnings records has stimulated a wealth of new research on the returns to college, and has accelerated state and federal efforts to hold institutions accountable for students' labor market outcomes. Many of these new research and…

Novel computational representations, such as simulation models of complex systems and video games for scientific discovery (Foldit, EteRNA etc.), are dramatically changing the way discoveries emerge in science and engineering. The cognitive roles played by such computational representations in discovery are not well understood. We present a…

Student growth percentiles (SGPs, Betebenner, 2009) are used to locate a student's current score in a conditional distribution based on the student's past scores. Currently, following Betebenner (2009), quantile regression (QR) is most often used operationally to estimate the SGPs. Alternatively, multidimensional item response theory (MIRT) may…

Classification consistency and accuracy are viewed as important indicators for evaluating the reliability and validity of classification results in cognitive diagnostic assessment (CDA). Pattern-level classification consistency and accuracy indices were introduced by Cui, Gierl, and Chang. However, the indices at the attribute level have not yet…

Quantitative information about test score reliability can be presented in terms of the distribution of equated scores on an alternate form of the test for test takers with a given score on the form taken. In this paper, we describe a procedure for estimating that distribution, for any specified score on the test form taken, by estimating the joint…

Learning to compute integrals via the various techniques of integration (e.g., integration by parts, partial fractions, etc.) is difficult for many students. Here, we look at how students in a college level Calculus II course develop the ability to categorize integrals and the difficulties they encounter using a card sort-resort activity. Analysis…

The purpose of this paper is to introduce students of science and engineering to the orbital lifetimes of satellites in circular low Earth orbits. It is only necessary to know about classical mechanics for this calculation. The orbital decay of satellites is due to the interaction of the satellite with the surrounding gas, atmospheric drag.…

This article introduces a fun, hands-on activity for comparing hand water displacements.

A few years ago it was suggested that the distance to celestial bodies could be computed by tracking their position over about 24 hours and then solving a regression problem. One only needed to use inexpensive telescopes, cameras, and astrometry tools, and the experiment could be done from one's backyard. However, it is not obvious to an amateur…

We walk through a module intended for undergraduates in mathematics, with the focus of finding the best strategies for competing in the Showcase Showdown on the game show "The Price Is Right." Students should have completed one semester of calculus, as well as some probability. We also give numerous suggestions for further questions that…

A multilevel logistic model for estimating a nonlinear trajectory in a multiple-baseline design is introduced. The model is applied to data from a real multiple-baseline design study to demonstrate interpretation of relevant parameters. A simple change-in-levels (?"Levels") model and a model involving a quadratic function…

To further understand the properties of data-generation algorithms for multivariate, nonnormal data, two Monte Carlo simulation studies comparing the Vale and Maurelli method and the Headrick fifth-order polynomial method were implemented. Combinations of skewness and kurtosis found in four published articles were run and attention was…