The developmental trend from overall-similarity to dimensional-identity classifications is explained by a quantitative model. The model provides good qualitative fits to the extant data. Three experiments examining classifications in 120 2- to 8-year-olds and in 20 undergraduates support specific new claims of the model. (TJH)

Covariance structures associated with linear structural equation models are discussed. Algorithms for computing maximum likelihood estimates (namely, the EM algorithm) are reviewed. An example of using likelihood ratio tests based on complete and incomplete data to improve the fit of a model is given. (SLD)

Summarizes the experimental evidence that indicates that text indexing systems based on the assignment of appropriately weighted single terms produce retrieval results superior to those obtained with more elaborate text representations, and provides baseline single term indexing models with which more elaborate content analysis procedures can be…

A fairly traditional precalculus problem is modified to address some common concerns with the teaching of problem solving. Areas of problem solving which are illustrated include: posing the problem; modeling the problem; transforming the data; and examining the solution. (PK)

Presents two proofs that only five regular polyhedra exist. The first is a geometric proof, and the second is based on graph theory, using the relationship between the vertices, edges, and regions of the graph model. (MDH)

Introduces the essential constructs involved in dynamic modeling, in relation to issues in psychological development. Presents several instances of how the principles of dynamic systems can be translated into mathematical formalism. Concludes that transition is a key invariance in development and that single subject, longitudinal designs are…

Proposes a new conceptual framework, embedded in a dynamic model, that accounts for children's failure to reason transitively. Examines five different models of transitive reasoning. Develops a model of how children initially represent and then use the ordered information available in the transitive inference model and how these processes change…

Implications of ignoring correlated error on parameter estimates in some simple structural equation models are examined. It is shown analytically and empirically through simulation that ignoring positive between-construct correlated error overestimates the structural parameter linking the two constructs. Effects become more pronounced with…

The PARallELogram Analysis (PARELLA) model is a probabilistic parallelogram model that can be used for the measurement of latent attitudes or latent preferences. A method is presented for testing for differential item functioning (DIF) for the PARELLA model using the approach of D. Thissen and others (1988). (SLD)

Provides a survey of models that use mathematics in a variety of fields of social science. Discusses specifically mathematical applications in demography, economics, management, political science, psychology, sociology, and other areas. Proposes four unsolved problems. (20 references) (MDH)

The use of statistical methods to combine the results of independent empirical research studies (metanalysis) has a long history, with work mainly divided into tests of the statistical significance of combined results and methods for combining estimates across studies. Methods of metanalysis and their applications are reviewed. (SLD)

A rationale is provided for the notion that mathematical games can be a valuable resource for the stimulation and support of student collaboration and cooperative classroom mathematical discussion. Included are examples of tangram games, people games, and board strategy games. (JJK)

Student research projects are open-ended questions or sets of questions intended to give undergraduate students experience doing introductory mathematical research. Proposed is an investigation of a Faro shuffle that is performed by cutting the deck exactly in half and then perfectly interleaving the cards of the two halves. (Author/JJK)

The National Assessment of Educational Progress (NAEP) makes possible comparison of groups of students and provides information about what these groups know and can do. The scale anchoring techniques described in this chapter address the latter purpose. The direct method and the smoothing method of scale anchoring are discussed. (SLD)

An extension is proposed for the network algorithm introduced by C.R. Mehta and N.R. Patel to construct exact tail probabilities for testing the general hypothesis that item responses are distributed according to the Rasch model. A simulation study indicates the efficiency of the algorithm. (SLD)