Presents a lesson designed to give teachers the know-how to offer secondary school students opportunities to model real-world phenomena through a variety of functions and construct and draw inferences from tables and graphs summarizing data from these situations. Investigates the roller-coaster questions in a graduate class on methods of teaching…

Addresses the observed actions of prospective Swedish mathematics teachers as they worked with a modeling situation. Explores prospective teachers' preparation to teach in grades 4-12 during a course of mathematical modeling. Focuses on preservice teachers' understanding of modeling and how they relate mathematical models to the real world.…

Discusses certain transferable skills and a strategy for developing them via an intensive short course on mathematical modeling. Includes student reactions and comments on the course. Suggests that this course developed modeling as well as generic skills through teaching, learning, and assessment style. (Author/KHR)

Uses a foundation-equalizing model to develop a number of indicators measuring the extent to which states utilize the full range of equalization tools at its disposal. Illustrates the utility of these indicators through an evaluation of the school finance reform instituted by Rhode Island between 1992 and 1996. (Contains 25 references.)…

The effectiveness of two iterative methods of item response theory (IRT) item bias detection was examined in a simulation study. A modified form of the iterative item parameter linking method of F. Drasgow and an adaptation of the test purification procedure of F. M. Lord were compared. (SLD)

The linear logistic model with relaxed assumption is extended to designs with any number of time points or with different sets of items presented on different occasions, provided that one unidimensional subscale is available per latent trait. A sample application is presented. (SLD)

Under certain conditions it may be possible to determine the difficulty of previously untested test items. Although no recipe can be provided, reflections on this topic are presented, drawing on concepts of item banking. A functional constructive method is suggested as having the most potential. (SLD)

A model based on latent trait theory, with maximum likelihood parameter estimates and associated asymptotic tests, is presented. Latent curve analysis is a method for representing development and is an alternative to repeated measures analysis of variance and first-order auto-regressive models. (SLD)

Discusses the use of mathematical modeling. Describes types, examples, and importance of mathematical models. (YP)

A modification index is presented to aid in reformulating hypothetical models rejected after analysis of empirical data. This index is an improvement over the one in the LISREL V computer program in that it takes into account changes in all parameters of the model when one parameter is freed. (SLD)

Four measurement designs are presented for use with correlation coefficients corrected, in one variable, for attenuation due to unreliability (partially disattenuated). Associated asymptotic variance/covariance expressions are presented. Empirical simulation results illustrate the satisfactory Type I error control and statistical power of the…

A polychotomous nominal response model-based computerized adaptive test (CAT) was simulated using data from 1,093 University of Texas students. The ability estimation of this model and its overall performance were compared with those of a dichotomous three-parameter logistic model-based CAT. Advantages and drawbacks of nominal response CAT are…

False positive and false negative error rates were studied for competency testing when failing examinees are permitted to retake the test. Formulas are provided for the beta-binomial and Rasch models. Estimates based on these models are compared for six data sets from the South Carolina Basic Skills Assessment Program. (SLD)

For anchor test equating, 3 linear observed score methods are derived for populations differing in ability. Each version requires that the correlations of the tests with the selection variable be known. Five sets of assumptions are made for each model--yielding 15 methods--which are then related to existing methods. (SLD)

Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)