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.

In the early 1990s, the National Science Foundation funded many research projects for improving statistical education. Many of these stressed the need for classroom activities that illustrate important issues of designing experiments, generating quality data, fitting models, and performing statistical tests. Our paper describes such an activity on…

The mathematical models of intonation used in speech technology are often inaccessible to linguists. By the same token, phonological descriptions of intonation are rarely used by speech technologists, as they cannot be implemented directly in applications. Consequently, these research communities do not benefit much from each other's insights. In…

For a given orbital period and eccentricity, we determine the maximum time lapse between the winter solstice and the spring equinox on a planet. In addition, given an axial precession path, we determine the effects on the seasons. This material can be used at various levels to illustrate ideas such as periodicity, eccentricity, polar coordinates,…

The factor structure of the "KeyMath--Revised Normative Update" (KMR-NU) "Form A" was analyzed using data from a sample of 130 students. The KMR-NU is composed of 13 subtests that are purported to measure three important aspects of math ability: Basic Concepts, Operations, and Applications. A confirmatory factor analysis…

Algebraic reasoning skills can be enhanced by building connections among symbolic, tabular, and graphical representations. But how do classroom teachers change traditional teaching practices to foster the use of different representational forms? This article explores how I learned to incorporate representational fluency in teaching and assessment.…

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…