Using a simple trigonometric limit, we provide an intuitive geometric proof of the Singular Value Decomposition of an arbitrary matrix.

Maximal ideals in the ring of continuous functions on the closed interval [0, 1] are not finitely generated. This is well-known. What is not as well-known, but perhaps should be, is the fact that these ideals are not countably generated although the proof is not harder! We prove this here and use the result to produce some non-prime ideals in the…

Klingner and Boardman (this issue) offer a cogent and compelling argument for opening the door for the acceptance and use of mixed methods in special education research. Self-identifying as pragmatists, they embody this paradigmatic view by focusing on the utility, efficacy, and accuracy of mixed methods, an argument that should appeal to the…

The purpose of this study was to demonstrate the bias in the Bland-Altman (BA) limits of agreement method when it is used to validate regression models. Data from 1,158 men were used to develop three regression equations to estimate maximum oxygen uptake (R[superscript 2] = 0.40, 0.61, and 0.82, respectively). The equations were evaluated in a…

The authors describe the development and initial validation of a home-based version of the Laboratory Temperament Assessment Battery (Lab-TAB), which was designed to assess childhood temperament with a comprehensive series of emotion-eliciting behavioral episodes. This article provides researchers with general guidelines for assessing specific…

The current study was the 1st to examine the psychometric properties of the Positive and Negative Affect Schedule for Children-Parent Version (PANAS-C-P) using a large school-based sample of children and adolescents ages 8 to 18 (N = 606). Confirmatory factor analysis supported a 2-factor (correlated) model of positive affect (PA) and negative…

This study aims to identify and review tools used to evaluate consumer-oriented written medicine (WMI) and health (WHI) information from a document and user perspective. Articles that met the following inclusion criteria were reviewed: studies evaluating readability, presentation, suitability, quality of WMI/WHI. A total of 152 articles were…

The purposes of this paper are to highlight the foundations of multilevel construct validation, describe two methodological approaches and associated analytic techniques, and then apply these approaches and techniques to the multilevel construct validation of a widely-used school readiness measure called the Early Development Instrument (EDI;…

In recent years, there has been a growth in the use of rater cognitive data to inform test development and validity arguments. In this study, we examined differences in feature attention and categorisation between experienced and inexperienced raters for a college-level assessment of oral communication. The focus was two-fold: (a) rater cognition…

Students often have difficulty understanding algebraic proofs of statistics theorems. However, it sometimes is possible to prove statistical theorems with pictures in which case students can gain understanding more easily. I provide examples for two versions of Bayes' theorem.

We present a model to analyze the students' activities of argumentation and proof in the graphical context of Elementary Calculus. The theoretical background is provided by the integration of Toulmin's structural description of arguments, Peirce's notions of sign, diagrammatic reasoning and abduction, and Habermas' model for rational behavior.…

The first-order equation relating object and image location for a mirror of arbitrary conic-sectional shape is derived. It is also shown that the parabolic reflecting surface is the only one free of aberration and only in the limiting case of distant sources. (Contains 3 figures.)

The well-known Stolz-Cesaro lemma is due to the mathematicians Ernesto Cesaro (1859-1906) and Otto Stolz (1842-1905). The aim of this article is to give new forms of Stolz-Cesaro lemma involving the limit [image omitted].

Objective: The objective of this study was to test the factor structure of the parent version of the Columbia Impairment Scale (CIS) in a sample of mothers who brought their children for community mental health (CMH) services (n = 280). Method: Confirmatory factor analysis (CFA) was used to test the fit of the hypothesized four-factor structure…

The purpose of this study was to provide additional validity evidence for a model of person-environment fit based on polychronicity, stimulus load, and information processing capacities. In this line of research the confluence of polychronicity and information processing (e.g., the ability of individuals to process stimuli from the environment…