Recently, Lima lamented on the 'time-consuming and tiresome' pedagogical nature of repeated integration by parts, throwing down the challenge of providing a pencil-and-paper solution to a related problem in a few seconds. Lima put forth a simple formula as an alternative. In this work, I offer a response to Lima's challenge and his formula.…

This article presents the author's response to Yan Ping Xin and Dake Zhang's recent critical evaluation of her and colleagues' work in "Exploring a Conceptual Model-Based Approach to Teaching Situated Word Problems," published in "The Journal of Educational Research" in 2009 (Vol. 102, No. 6). Most critiques of prior research are written in a fair…

This article presents the authors' response to Asha K. Jitendra's Response to Xin and Zhang ("The Journal of Educational Research," 2009, Vol. 102, No. 6). The claim of "factual errors, including inappropriate quotes, misrepresentation of information, and inadequate scholarship in Xin and Zhang's text" are not justified. In this rejoinder, the…

The reactions by Ridley and Shaw-Ridley (EJ832451) and Lichtenberg (EJ832452) to the authors' meta-analysis on the effects of experience on judgment accuracy add positively to what is hoped will become an ever more focused discourse on this most basic question: How can mental health clinical decision making be improved? In this rejoinder, the…

A generalization of a well-known result for the arctangent function poses a number of interesting questions concerning the existence of integer solutions of related problems.

In this paper, the author recommends that every teacher of mathematics should undertake an analysis using their own data. She further recommends that they reflect on the outcomes of their analysis and share it with colleagues. Teachers can look at an individual student's results, variations in results between student sub-groups in their classes,…

The author drew the 2008 Easter conference to a close. During the final address, the author chose to focus on the domain of perimeter and area both because it is a topic accessible to teachers of all ages and because learners display considerable confusion between them. The core difficulty seems to lie in the necessity to attend either to the…

Discusses the measurement of the growth and obsolescence of literature and shows that growth and obsolescence can be studied by the same mathematical techniques. A combined growth-obsolescence theory is presented that can be measured with continuous rates, and three earlier papers are reconsidered and results are reproven. (Contains 18…

Discussion of authorship distributions focuses on the results of a numerical study for fractional authorship attribution. Highlights include coauthors; multinomial coefficients; Lotka functions; probability distributions of articles per author; and probability distributions of authors per article. (LRW)

Discusses structural differences between author-publication systems and journal-article systems, i.e., articles can have more than one author. Frequency functions are examined; and a new conceptual explanation of Lotka's Law, based on convolution theory, is proposed. (Contains eight references.) (LRW)

Discussion of information retrieval focuses on an Interaction Information Retrieval model in which documents are interconnected; queries and documents are treated in the same way; and retrieval is the result of the interconnection between query and documents. A theoretical mathematical formulation of this type of retrieval is given. (Contains 31…

Discussion of probabilistic information retrieval (IR) systems challenges the probability ranking principle in IR from the perspective of (1) signal detection-decision theory and (2) utility theory. Calibration, certainty, and independent assessment are discussed in terms of the relevance of documents, and standard retrieval policies are analyzed.…

Discussion of the interpolation methodology expounded by Goosen and Kusel to model business functions for simulation design criticizes the approach's simplicity because interactive effects between variables in the functional relationships are not considered. (six references) (EA)

Proposes and explains a new mechanism for controlling the access requests in information protection systems that is based on Newton's interpolating polynomial. Access control matrices are discussed; single-key-lock systems are described; relevant algorithms are explained; and an example of the new mechanism is included. (10 references) (LRW)

Addresses objections to the validity of assuming a Poisson loglinear model as the generating process for citations from one journal into another. Fluctuations in citation rate, serial dependence on citations, impossibility of distinguishing between rate changes and serial dependence, evidence for changes in Poisson rate, and transitivity…