The cognitive structure of an algebra test was defined and validated using the linear test model (LLTM) and quadratic assignment (QA) techniques. The LLTM is an extension of the Rasch model with a linear constraint that describes item difficulty in terms of the cognitive operations required to solve the item. The model permits the specification of…

The focus of this report is children's construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in their strategies for dealing with isomorphic combinatorial problems presented in "hands-on" and written form. Case studies of 9-year-olds, one low and one high achieving in school…

The impact of test item multidimensionality was examined as it affected fitting items on a teacher licensure test to an item response theory (IRT) model. Test item data from the 1990 study of G. W. Guiton and G. Delandshere are used. The Connecticut Elementary Certification Test (CONNECT) is a licensure examination designed to assess the subject…

The logic and methodological concepts behind the application of a quantitative methodology to the problem of effective resource utilization in the New York State suburban schools is detailed. The goal of the study was to determine the best composition of available "factors of production," measured in dollar amounts by function, that…

Modeling and data collection efforts needed to develop a test of the effectiveness of adult literacy and language training programs in increasing the earnings of trainees are reviewed. After reviewing the framework developed for the Manpower Development and Training Act and the Comprehensive Employment and Training Act (CETA) evaluations and the…

The internal/external (I/E) frame of reference model describes relations among Verbal self-concept (VSC), Math self-concept (MSC), and corresponding achievement scores (VACH, MACH). In support of the model Marsh (1986) found that: (1) VSC and MSC were nearly uncorrelated; (2) the effect of VACH on VSC, and of MACH on MSC, were positive; but (3)…

This paper discussed methods currently under study for use with multiple-response data. Besides using Bonferroni inequality methods to control type one error rate over a set of inferences involving multiple response data, a recently proposed methodology of plotting the p-values resulting from multiple significance tests was explored. Proficiency…

A necessary prerequisite to the operational use of item response theory (IRT) in any testing program is the investigation of the feasibility of such an approach. This report presents the results of such research for the Graduate Management Admission Test (GMAT). Despite the fact that GMAT data appear to violate a basic assumption of the…

One of the most appropriate quasiexperimental approaches to compensatory education is the regression-discontinuity design. However, it remains underutilized, in part because of the need to clarify the link between the mathematical model and administrative decision-making. This paper explains the derivation of a program efficiency index congruent…

The feasibility of pre-equating, or establishing conversions from raw to scaled scores through the use of pretest data before operationally administering a test, was investigated for the Scholastic Aptitude Test (SAT). Item-response theory based equating methods were used to estimate item parameters on SAT pretest data, instead of using final form…

Results of a three-year study to estimate the future supply and requirements for physicians, which was conducted by the Graduate Medical Education National Advisory Committee (GMENAC), are summarized. The research methodology, which consisted of three mathematical models to project physician supply and requirements, is described, and 40…

In order to compose equivalent certification tests in the basic skills in reading, mathematics calculations and applications, and writing for high school graduation requirements, the San Jose Unified School District, California, used the Rasch computer program to arrive at the scaled difficulty level of test items. The procedure for achieving a…

The Consortium on Methodology for Aggregating Data in Educational Research was designed as a collaborative effort by research methodologists from economics, education and sociology. Consortium goals were to delineate what was known about the problems associated with the analysis of data from the multiple levels (pupil, teacher/classroom, school)…

This conference focuses upon various aspects of testing within a society, and upon technical advances in measurement. Philip H. DuBois's paper deals with China, a society dominated by tests, from 1115 BC--1905 AD. Donald W. Fiske discusses the effect of testing on the individual in modern America in his paper, "The Subject Looks at…

The development of computer-directed instruction in which the learning protocol is tailored to each student on the basis of his learning history requires a means by which the many different trajectories open to a student can be resolved. Such an optimization procedure can be constructed to reduce the long and costly calculations associated with…