The equating methods and sampling designs used in the empirical studies in this special issue on the use of matched samples for test equating are described. Four requisites for equating are listed, and the invariance of equating functions requisite is identified as the focus of this issue. (SLD)

Illustrates how heuristics can provide a psychological narrative of Hippocrates' and Archytas' thinking on the duplication of the cube. Four general heuristic techniques were used. (YP)

The neuronal model shown to code sound-source azimuth in the barn owl by H. Wagner et al. in 1987 is used as the basis for a speculative brain-based human model, which can establish contrastive phonetic categories to solve the problem of perception "non-invariance." (SLD)

A method is proposed for equating different sets of items administered to different groups using the Rasch model. The Rasch equating model formulated describes one common Rasch scale in different groups with different but overlapping item sets. The model, based on the quasi-loglinear Rasch model, can be tested globally. (SLD)

Explores the use of computers for teaching mathematical models of transposition ciphers. Illustrates the ideas, includes activities and extensions, provides a mathematical model and includes computer programs to implement these topics. (MVL)

A stochastic version of a knowledge space is developed in which knowledge states are considered as possible epochs in a subject's learning history. It specifies how a subject is channeled through and progresses along a "gradation." The model's application to artificial data is described, based on maximum likelihood methods. (TJH)

Presents a model for electronic books based on the paper book metaphor. Discussion includes how the book evolves under the effects of its functional components; the use and impact of the model for organizing and presenting electronic documents in the context of electronic publishing; and the possible applications of a system based on the model.…

Investigates the relationships between the parameters of the Simon-Yule model and the shapes of three bibliometric distributions: Lotka's Law of Scientific Productivity; Bradford's Law of Bibliometric Scattering; and Zipf's Law of Word Frequency. The results indicate that the probability of a new entry determines the characteristics of all three…

Argues that Vygotsky's "zone of proximal development" (ZPD) can be redefined as a nonlinear dynamic model. Presents a mathematical reformulation that generates a variety of developmental patterns and has the capacity to show under which conditions unwanted or unsuccessful developmental paths may occur. Illustrates how this reformulation…

By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

Suggests that the ability to process narrative information is fundamental to understanding human psychological development. Notes that a culture's system of understanding and interpreting the world is carried mostly by stories and texts. Explores how narrative understanding can be modeled in Fuzzy Trace Theory by using the principles of this…

Discusses the hydrodynamic reasons why a riverbed meanders through a plain. Describes how water movement at a bend in a river causes erosion and changes in the riverbed. Provides a mathematical model to explain the periodic shape of meanders of a river in a plain. (MDH)

Asymptotic distributions of the estimators of communalities are derived for the maximum likelihood method in factor analysis. It is shown that equating the asymptotic standard error of the communality estimate to the unique variance estimate is not correct for the unstandardized case. Monte Carlo simulations illustrate the study. (SLD)

Effects of violating the independence assumption when combining correlation coefficients in a meta-analysis were studied. This Monte-Carlo simulation varied sample size, predictor number, population intercorrelation among predictors, and population correlation between predictors and criterion. Combining statistics from nonindependent data in a…

Implications of metanalytic results from Monte Carlo studies of the robustness of the F test in the one- and two-factor fixed effects analysis of variance (ANOVA) models and Monte Carlo results for the B. L. Welch (1947) and Kruskal-Wallis (1952) tests are discussed. (SLD)