In the context of a generic harmonic oscillator, we investigated students' accuracy in determining the period, frequency, and angular frequency from mathematical and graphical representations. In a series of studies including interviews, free response tests, and multiple-choice tests developed in an iterative process, we assessed students in both…

The purpose of this article is to introduce and review the capability and performance of the Stata item response theory (IRT) package that is available from Stata v.14, 2015. Using a simulated data set and a publicly available item response data set extracted from Programme of International Student Assessment, we review the IRT package from…

This research suggests that structural accommodation can be implemented during the construction phase of standardized mathematics examinations. Data from a racially diverse district in the United States are used to compare student performance on questions with and without graphical aids. Findings suggest that mathematics questions possessing…

There are numerous statistical procedures for detecting items that function differently across subgroups of examinees that take a test or survey. However, in endeavouring to detect items that may function differentially, selection of the statistical method is only one of many important decisions. In this article, we discuss the important decisions…

Research on the graphical facilitation of probabilistic reasoning has been characterised by the effort expended to identify valid assessment tools. The authors developed an assessment instrument to compare reasoning performances when problems were presented in verbal-numerical and graphical-pictorial formats. A sample of undergraduate psychology…

This paper illustrates a method of item analysis used to identify discriminating multiple-choice items in placement data. The data come from two rounds of pilots given to both SHL students and Spanish as a Second Language (SSL) students. In the first round, 104 items were administered to 507 students. After discarding poor items, the second round…

This paper describes an approach to item analysis that is based on the estimation of a set of response curves for each item. The response curves show, at a glance, the difficulty and the discriminating power of the item and the popularity of each distractor, at any level of the criterion variable (e.g., total score). The curves are estimated by…

Problems of scale typically arise when comparing test score trends, gaps, and gap trends across different tests. To overcome some of these difficulties, we can express the difference between the observed test performance of two groups with graphs or statistics that are metric-free (i.e., invariant under positive monotonic transformations of the…