Traditional and innovative uses of the Rasch model in the development and validation of both small- and large-scale psychological instruments are illustrated and discussed. Advantages of the model in maximizing scale interpretability and validity are presented. Both mathematical and conceptual explanations are provided using counseling psychology…

Provides a general mathematical framework is provided that can be specialized to four different reliability coefficients. Consideration of this general framework makes it easier to convey to students the individual character of the formulations of reliability and the extent of their underlying similarity. (SLD)

Hazard rate models are described, and selected techniques are used to analyze paired hazard rates when event times are right censored. The techniques are illustrated by looking at mortality patterns in husbands and wives. Recently developed measures and models are introduced. The advantages and disadvantages of the measures are discussed.…

Describes the Rasch measurement partial credit model, what it is, how it differs from other Rasch models, and when and how to use it. Also describes the calibration of instruments with increasingly complex items. Explains pivot anchoring and illustrates its use and describes the effect of pivot anchoring on step calibrations, item hierarchy, and…

This book is a compendium of recent item response theory (IRT) research that reviews 27 IRT models. The book contains a historical overview of IRT followed by six sections that deal with the application of a particular IRT model or set of models. (SLD)

Using higher order factor models, this article illustrates latent curve analysis for the purpose of modeling longitudinal change directly in a latent construct. Provides examples with simultaneous estimation of covariance and mean structures for a single-group and two-group structure. (SLD)

This article analyses mathematical modelling from several different perspectives and contrasts modelling with problem solving. Then it describes the ways in which modelling, applications, and problem solving are approached in several Latin American countries. It further describes workshops for secondary schools and for university teachers in which…

Hidden Markov models (HMMs) are widely used in bioinformatics, speech recognition and many other areas. This note presents HMMs via the framework of classical Markov chain models. A simple example is given to illustrate the model. An estimation method for the transition probabilities of the hidden states is also discussed.

The author of this paper submits the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method in a Probability and Mathematical Statistics (PAMS) course sequence to teach students PAMS. Furthermore, the author of this paper opines that set theory…

The purpose of this study is selecting type of university that can create its competitive advantages in a changing world. The study analyzes 25 related experiential professors. The VIKOR-based methodology is used to tackle the ranking of four types of universities. The study found that the rank of the university types is: Research-Intensive,…

The first part of this two-part paper [see EJ787497] described the development of a new freshman business mathematics (FBM) course at our college. In this paper, we discuss our assessment tool, the business memo, as a venue for students to apply mathematical skills, via mathematical modelling, to realistic business problems. These memos have…

This article presents a study of Web 2.0 articles intended to (a) analyze the content of what is written and (b) develop a statistical model to predict whether authors' write about the need for new instructional design strategies and models. Eighty-eight technology articles were subjected to lexical analysis and a logistic regression model was…

We present mathematical learning models--predictions of student's knowledge vs amount of instruction--that are based on assumptions motivated by various theories of learning: tabula rasa, constructivist, and tutoring. These models predict the improvement (on the post-test) as a function of the pretest score due to intervening instruction and also…

Purpose: The present study was a methodological study designed to reveal the dynamic mechanisms of phonation instability pressure (PIP) using bifurcation analysis. Phonation pressure range (PPR) was also proposed for assessing the pressure range of normal vocal fold vibrations. Method: The authors first introduced the concept of bifurcation on the…

This article describes an alternate way to utilize a circular model to represent thirds by incorporating areas of circular segments, trigonometric functions, and geometric transformations. This method is appropriate for students studying geometry and trigonometry at the high shool level. This task provides valuable learning experiences that…