Item response theory (IRT) refers to a family of mathematical models which describe the relationship between latent continuous variables (attributes or characteristics) and their manifestations (dichotomous/polytomous observed outcomes or responses) with regard to a set of item characteristics. Researchers typically use parametric IRT (PIRT)…

This book seeks to illustrate the research on mathematics competencies and disposition in China according to the conceptual development and empirical investigation perspective. Mathematics education in China has a distinguishing feature a focus of attention to mathematical competency. Paradoxically, there has not been an explicit, refined, and…

The relevance of research: The relevance of the problem studied is caused by the acceleration of transition of the Russian economy on an innovative way of development, which depends on the vector of innovative sphere of services and, to a large extent, information and communication services, as well as it is caused by the poor drafting of…

Educational strategies have evolved over the years, due to research breakthroughs and the application of technology. By using the latest learning innovations, curriculum and instructional design can be enhanced and strengthened. The "Handbook of Research on Driving STEM Learning with Educational Technologies" is an authoritative…

The beginning of modern science is marked by efforts of pioneers to understand the natural world using a quantitative approach. As Galileo wrote, "the book of nature is written in the language of mathematics". The traditional undergraduate course curriculum is heavily focused on individual disciplines like biology, physics, chemistry,…

Although the "K"-means algorithm for minimizing the within-cluster sums of squared deviations from cluster centroids is perhaps the most common method for applied cluster analyses, a variety of other criteria are available. The "p"-median model is an especially well-studied clustering problem that requires the selection of "p" objects to serve as…

Recent advances in data recording technology have given researchers new ways of collecting on-line and continuous data for analyzing input-output systems. For example, continuous response digital interfaces are increasingly used in psychophysics. The statistical problem related to these input-output systems reduces to linking time-varying…

Most researchers using analysis of variance (ANOVA) use a fixed-effects model. However, a random- or mixed-effects model may be a more appropriate fit for many research designs. One benefit of the random- and mixed-effects models is that they yield more generalizable results. This paper focuses on the similarities and differences between the…

This analysis of Zipf's law uses an index for the sequence of observed values of the variables in a Zipf-type relationship. Three important properties relating rank, count, and frequency are identified, shapes of Zipf-type curves are described, and parameters of the Mandelbrot-Zipf law are discussed. (Author/LRW)

Description of management games continues a previous article's discussion of how mathematical modeling and microeconomic concepts can be used by players. Highlights include an initial condition simulating a profit-maximizing monopoly; simulating the transition from monopoly to oligopoly; and how mathematical properties of the model affect final…

Compares and expands upon two approaches to dealing with fuzzy relational databases. The proposed similarity measure is based on a fuzzy Hausdorff distance and estimates the mismatch between two possibility distributions using a reduction process. The consequences of the reduction process on query evaluation are studied. (Author/EM)

Relations on a finite set V are viewed as weighted graphs. Using the language of graph theory, two methods of partitioning V are examined: selecting threshold values and applying them to a maximal weighted spanning forest, and using a parametric linear program to obtain a most adhesive partition. (Author/EM)

Proposes a probabilistic mechanism to describe various forms of the Bradford phenomenon reported in bibliographic research. The inclusion of a time parameter in the model to allow predictions of dynamic systems is explained. (58 references) (CLB)

Presents a mathematical model of a decision maker subject to goal uncertainty which shows that a dominant course of action will always emerge. The theory of multivalued functions is used to express goal uncertainty, and a specific example is described to provide insight into how the procedure works in practice. (Author/EM)

Presents notations and definitions necessary to identify the concepts and relationships that are important in modelling information retrieval objects and processes in the context of vector spaces. Earlier work on the use of vector models is evaluated in terms of the concepts introduced and certain problems are identified. (Author/EM)