The purpose of the present study was to explore the 3rd-grade cognitive predictors of 5th-grade computational skill with rational numbers and how those are similar to and different from the cognitive predictors of whole-number computational skill. Students (n=688) were assessed on incoming whole-number calculation skill, language, nonverbal…

This article presents the Variable Match Index (VM-Index), a new statistic for detecting answer copying. The power of the VM-Index relies on two-dimensional conditioning as well as the structure of the test. The asymptotic distribution of the VM-Index is analyzed by reduction to Poisson trials. A computational study comparing the VM-Index with the…

The author shows how a quick approximation of the Lorenz curve's Gini coefficient can be calculated empirically using numerical data presented in cumulative income quintiles. When the technique here was used to estimate 621 income quintile/Gini coefficient observations from the Deninger and Squire/World Bank data set, this approach performed…

Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of…

When developing online classrooms it is necessary to ensure that all learners will be successful in the course regardless of the topic or discipline that is being discussed. This becomes especially important when the class involves numerical data. This paper outlines the difficulty of delivering online classes such as algebra, accounting, and…

Despite broad concern about the mathematics knowledge of elementary teachers and evidence that textbooks influence the mathematics they are taught, little is known about the content of books used in their mathematics courses. Research efforts have been limited by the lack of shared guidelines about what the texts should convey and the lack of…

This thesis aims to define and extend a line of computational models for text comprehension that are humanly plausible. Since natural language is human by nature, computational models of human language will always be just that--models. To the degree that they miss out on information that humans would tap into, they may be improved by considering…

Biology has been revolutionized in recent years by an explosion in the availability of data. Transforming this new wealth of data into meaningful biological insights and clinical breakthroughs requires a complete overhaul both in the questions being asked and the methodologies used to answer them. A major challenge in organizing and understanding…

The 3PL model is a flexible and widely used tool in assessment. However, it suffers from limitations due to its need for large sample sizes. This study introduces and evaluates the efficacy of a new sample size augmentation technique called Duplicate, Erase, and Replace (DupER) Augmentation through a simulation study. Data are augmented using…

This research investigated how the accuracy of person ability and item difficulty parameter estimation varied across five IRT models with respect to the presence of guessing, targeting, and varied combinations of sample sizes and test lengths. The data were simulated with 50 replications under each of the 18 combined conditions. Five IRT models…

In France, as in many other countries, there is an ongoing debate on how residence-based assignment to schools affects both educational and residential segregation. Theoretical models (including Benabou, 1993; Fernandez and Rogerson, 1996; Epple and Romano, 2003; Rothstein, 2006) have shown that the existence of peer effects in education yields…

Heuristics embodying limited information search and noncompensatory processing of information can yield robust performance relative to computationally more complex models. One criticism raised against heuristics is the argument that complexity is hidden in the calculation of the cue order used to make predictions. We discuss ways to order cues…

Using readily available computational applications and resources, students can construct a high-level ab initio potential energy surface (PES) for the argon dimer. From this information, they can obtain detailed molecular constants of the dimer, including its dissociation energy, which compare well with experimental determinations. Using both…

Dividing by fractions is considered by many to be one of the most complicated procedures in elementary mathematics. The computations are not only complicated but also challenging to explain in the context of a word problem. In this article, the author discusses the role of the divisor in the concept of division by fractions. She examines three…

Metal oxalate synthesis and pyrolysis provides an opportunity for students to (i) learn stoichiometry, (ii) experience the consequences of proper stoichiometric calculations and experimental techniques, and (iii) be introduced to the relevance of chemistry by highlighting oxalates in context, for example, usages and health effects. At our…