This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

This study focuses on the role of multiple solution tasks (MST) incorporating multiple learning tools and representation systems (MTRS) in encouraging each student to develop multiple perspectives on the learning concepts under study and creativity of thought. Specifically, two types of MST were used, namely tasks that allowed and demanded…

This article describes a geometrical solution to a problem that is usually solved geometrically as an example of how alternative solutions may enrich the teaching and learning of mathematics. (Contains 11 figures.)

A formula for the ratio of the variance of the pooled transformed data under departure from the binomial assumption to the variance of the pooled transformed data when the binomial assumption holds is given. (Authors)

Four types of metric scales are distinguished: absolute, ratio, difference, and interval. A general coefficient of association for two variables of the same scale type is developed which reduces to specific coefficients of association for each scale type. (NSF)

Formulas for transforming scores and statistics on a rating scale having any number of categories to a scale having a different number of categories are described. To illustrate the use of one of the formulas, the means and variances of items on six forms of a course evaluation questionnaire were compared. (Author/LMO)

Reviews the bibliometric laws of Bradford, Leimkuhler, Mandelbrot, Lotka, Brookes, and Zipf, and classifies them in two groups, based on the use of mathematical logic and equivalency. (8 references) (CLB)

A procedure is outlined showing how the axiom of local independence for latent structure models can be weakened. (CK)

The distance approach to nonlinear multivariate analysis proposed by J. J. Meulman (1986) is reviewed. Several generalizations are discussed by combining features from the conventional multivariate analysis approach, which seeks weighted sums of variables, with the alternative approach, which seeks to fit distances. (SLD)

This method of generating multivariate data differs from previous techniques in that it uses Crout factorization to develop the desired variance-covariance matrix. (Author/CK)

Three factors that increase score variability yet can be associated with an increase, a decrease, or no change in Pearson's correlation coefficient (r) are discussed (restriction of range, errors of measurement, and linear transformations of data). The connection between changes in variability and r depends on how changes occur. (SLD)

The DEcomposition into DIrectional COMponents (DEDICOM) method for analysis of asymmetric data gives representations that are identified only up to a non-singular transformation. To identify solutions, it is proposed that subspace constraints be imposed on the stimulus coefficients. Procedures are discussed for several cases. (SLD)

To study the applicability of simple structure logic for factorial data from scientific disciplines outside psychology, four correlation matrices from each of six scientific areas were factor analyzed by five factoring methods. Resulting factor matrices were compared on two objective criteria of simple structure before and after rotation.…

A method requiring minimal computational effort is presented for transforming ordered residuals for purposes of testing the correctness of a regression model. The method maintains the same logical ordering in the transformed residuals as that of the original residuals and is suitable for either correlated or uncorrelated data. (Author/BS)