After observing secondary school students having great difficulty learning geometry in their classes, Dutch educators Pierre van Hiele and Dina van Hiele-Geldof developed a theoretical model involving five levels of thought development in geometry. It is the purpose of this monograph to present English translations of some significant works of the…

The focus is on the formulation and solution of mathematical models with the idea of a population employed mainly as a pedogogical tool. If the biological setting is stripped away, the material can be interpreted as topics or the qualitative behavior of differential and difference equations. The first group of models investigate the dynamics of a…

The first four units cover aspects of medical applications of calculus: 71-Measuring Cardiac Output; 72-Prescribing Safe and Effective Dosage; 73-Epidemics; and 74-Tracer Methods in Permiability. All units include a set of exercises and answers to at least some of the problems. Unit 72 also contains a model exam and answers to this exam. The fifth…

Employers and school admissions officials must consider several factors when making choices among applicants, particularly when faced with a need to increase selection of minority group members. Should different standards be applied to different groups? Will acceptance of less qualified applicants from one group affect the overall quality of the…

A study was conducted to compare tailored testing procedures based on a Bayesian ability estimation technique and on a maximum likelihood ability estimation technique. The Bayesian tailored testing procedure selected items so as to minimize the posterior variance of the ability estimate distribution, while the maximum likelihood tailored testing…

The efficacy of employing subsets of items from a calibrated item pool to estimate the Rasch model person parameters was investigated. Specifically, the degree of invariance of Rasch model ability-parameter estimates was examined across differing collections of simulated items. The ability-parameter estimates were obtained from a simulation of…

Three test-analysis models were used to analyze three types of simulated test score data plus the results of eight achievement tests. Chi-square goodness-of-fit statistics were used to evaluate the appropriateness of the models to the four kinds of data. Data were generated to simulate the responses of 1,000 students to 36 pseudo-items by…

Alternative mathematical models for scoring and decision making with criterion referenced tests are described, especially as they concern appropriate test length and methods of establishing statistically valid cutting scores. Several of these approaches are reviewed and compared on formal-analytic and empirical grounds: (1) Block's approach to…

A study was conducted at Thomas Nelson Community College (TNCC) to assess the college's economic impact on its service area in fiscal year 1979. Models, based on linear cash flow formulas, were used to determine impacts on local businesses, governments, and individuals. Students' expenditures and spending for construction were omitted from the…

Three methods of item selection were used to select sets of 38 items from a 50-item verbal analogies test and the resulting item sets were compared for internal consistency, standard errors of measurement, item difficulty, biserial item-test correlations, and relative efficiency. Three groups of 1,500 cases each were used for item selection. First…

Six approaches to assessing test item bias were examined: transformed item difficulty, point biserial correlations, chi-square, factor analysis, one parameter item characteristic curve, and three parameter item characteristic curve. Data sets for analysis were generated by a Monte Carlo technique based on the three parameter model; thus, four…

The purpose of this paper is to introduce a model of the psychological processes that take place when a persuader decides to use or not to use a given persuasive message. The assumption is made that if the perceived emotional impact of a message is more positive than an ethical threshold (which varies from person to person), the persuader will use…

The costs of providing access to serial literature in four university research libraries were examined in this study, and a methodology was developed for comparing borrowing costs with the costs of acquisition, cataloging, maintenance, and circulation. Mathematical models are provided by which any library can determine at what frequency of use of…

Unlike the past models guiding cross-cultural psychological research, a new paradigm facilitates multiple level investigations by incorporating both culture-specific (nested) and culture-general (crossed) independent variables within its partially-hierarchical framework. Based upon the generalizability analysis, this model generates sequential…

The Design of Training Systems (DOTS) project was initiated by the Department of Defense to develop tools for the effective management of military training organizations. Phase 2 of the project, from which this report emanates, involved the design and development of three computer-based mathematical models and their validation. Volume 1 presents…