To build on prior knowledge and mathematical understanding, middle school students need to be given the opportunity to make connections among a variety of representations. Graphs, tables, algebraic formulas, and models are just a few examples of representations that can help students explore quantitative relationships. As a mathematics educator,…

This study investigates measurement decision theory (MDT) as an underlying model for computer adaptive testing when the goal is to classify examinees into one of a finite number of groups. The first analysis compares MDT with a popular item response theory model and finds little difference in terms of the percentage of correct classifications. The…

The beginning of modern science is marked by efforts of pioneers to understand the natural world using a quantitative approach. As Galileo wrote, "the book of nature is written in the language of mathematics". The traditional undergraduate course curriculum is heavily focused on individual disciplines like biology, physics, chemistry,…

The purpose of this study was to examine technical and instructional features of a kindergarten curriculum-based measurement (CBM) tool designed to track students' mathematics progress in terms of computational concepts, procedures, and counting strategies. Students in 10 kindergarten classrooms in three elementary schools completed alternate…

Cognitive and conceptual uncertainties are critical elements in geology from the earliest data collection stage to concluding interpretations. How a geologist conceptually weighs the importance of various data greatly influences final interpretations. In order for the process of data selection and interpretation to be transparent and repeatable,…

An extensive review of the research literature and a study comparing over 36,000 survey responses with archival true scores indicated that one should expect a minimum of at least three percent random error for the least ambiguous of self-report measures. The Gulliver Effect occurs when a small proportion of error in a sizable subpopulation exerts…

This paper proposes a novel method for recommending books to pupils based on a framework called Edu-mining. One of the properties of the proposed method is that it uses only loan histories (pupil ID, book ID, date of loan) whereas the conventional methods require additional information such as taste information from a great number of users which…

The local average treatment effect (LATE) may differ from the average treatment effect (ATE) when those influenced by the instrument are not representative of the overall population. Heterogeneity in treatment effects may imply that parameter estimates from 2SLS are uninformative regarding the average treatment effect, motivating a search for…

Humans are adept at inferring the mental states underlying other agents' actions, such as goals, beliefs, desires, emotions and other thoughts. We propose a computational framework based on Bayesian inverse planning for modeling human action understanding. The framework represents an intuitive theory of intentional agents' behavior based on the…

We illustrate and discuss the method, called CORDIC, which many hand calculators use to calculate the trigonometric and other functions.

The purpose of this study was to compare the effects of cover-copy-compare alone and combined with two forms of goal setting to a control condition on the mathematics fluency of 173 third-grade students. Treatment sessions occurred twice weekly for a total of 6 weeks, and multilevel modeling was used to examine progress across intervention…

The Statistics Online Computational Resource (http://www.SOCR.ucla.edu) provides one of the largest collections of free Internet-based resources for probability and statistics education. SOCR develops, validates and disseminates two core types of materials--instructional resources and computational libraries. (Contains 2 figures.)

The aim of this paper was to estimate how suicide rates in the United States are affected by changes in per capita consumption during the postwar period. The analysis included Annual suicide rates and per capita alcohol consumption data (total and beverage specific) for the period 1950-2002. Gender- and age-specific models were estimated using the…

This article presents a method for assessing the internal consistency of scales that works equally well with short and long scales, namely, the average proportional distance. The method provides information on the average distance between item scores for a particular scale. In this article, we sought to demonstrate how this relatively simple…

Davidian-curve item response theory (DC-IRT) is introduced, evaluated with simulations, and illustrated using data from the Schedule for Nonadaptive and Adaptive Personality Entitlement scale. DC-IRT is a method for fitting unidimensional IRT models with maximum marginal likelihood estimation, in which the latent density is estimated,…