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…

Technological and pedagogical advances in distance education have accentuated the necessity for higher education to keep pace regarding institutional infrastructures. Each infrastructure--driven by a common mission to provide quality learning--interprets quality according to standards established by various governmental and accrediting entities.…

A simulation study compared the performance of robust normal theory maximum likelihood (ML) and robust categorical least squares (cat-LS) methodology for estimating confirmatory factor analysis models with ordinal variables. Data were generated from 2 models with 2-7 categories, 4 sample sizes, 2 latent distributions, and 5 patterns of category…

With increased accountability attached to students' results on national testing in Australia, teachers feel under pressure to prepare students for the tests. However, this can lead to shallow teaching of a narrowed curriculum. An alternative approach involves using data to identify common errors and misconceptions, discussing strategies aimed at…

Within a response to intervention model, educators increasingly use progress monitoring (PM) to support medium- to high-stakes decisions for individual students. For PM to serve these more demanding decisions requires more careful consideration of measurement error. That error should be calculated within a fixed linear regression model rather than…

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…