Computes rates of return to education in Singapore for 1980-1994, using the cost-benefit approach. Rates of return varied with education level. Although remaining higher than return rates for secondary education, those for tertiary education were declining. Polytechnic education enjoys the highest social/private return rates. (Contains 40…

Some aspects of biology, for example the Hardy-Weinberg simulation of population genetics or modelling heat flow in lizards, have an undeniable mathematical basis. Students can find the level of mathematical skill required to deal with such concepts to be an insurmountable hurdle to understanding. If not used effectively, spreadsheet models…

This article discusses issues in measuring lexical diversity, before outlining an approach based on mathematical modelling that produces a measure, D, designed to address these problems. The procedure for obtaining values for D directly from transcripts using software (vocd) is introduced, and then applied to thirty-two children from the Bristol…

The mechanisms of perceptual learning are analyzed theoretically, probed in an orientation-discrimination experiment involving a novel nonstationary context manipulation, and instantiated in a detailed computational model. Two hypotheses are examined: modification of early cortical representations versus task-specific selective reweighting.…

We present a project for a differential equations class: an analysis of an H. G. Wells story in which is given a submersible's descent time, its ascent time, and its eruption from the surface before splashdown. (Contains 5 figures.)

This study investigated the dimensionality of mathematics subscale scores from the National Assessment of Educational Progress for the assessment's Technical Review Panel, specifically for the data from the 1990 and 1992 main assessment in relation to students' instructional and noninstructional background variables. Discriminant analysis was…

The concept of a user-specified validity sector is discussed. The idea of the validity sector combines the work of M. D. Reckase (1986) and R. Shealy and W. Stout (1991). Reckase developed a methodology to represent an item in a multidimensional latent space as a vector. Item vectors are computed using multidimensional item response theory item…

Large sample standard errors of linear equating for the single-group design are derived without making the normality assumption. Two general methods based on the delta method of M. Kendall and A. Stuart (1977) are described. One method uses the exact partial derivatives, and the other uses numerical derivatives. Simulation using the beta-binomial…

Equating tests from different calibrations under item response theory (IRT) requires calculation of the slope and intercept of the appropriate linear transformation. Two methods have been proposed recently for equating graded response items under IRT, a test characteristic curve method and a minimum chi-square method. These two methods are…

A detailed investigation of the statistical procedure of W. Stout (the computer program DIMTEST) for testing the hypothesis that an essentially unidimensional latent trait model fits observed binary response data from a psychological test is presented. One finding is that DIMTEST may fail to perform as desired in the presence of guessing when…

The graded response model for two-stage testing was applied to an attitudes toward science scale using real-data simulation. The 48-item scale was administered to 920 students at a grade-8 equivalent in Singapore. A two-stage 16-item computerized adaptive test was developed. In two-stage testing an initial, or routing, test is followed by a…

The existence of differential prediction of two-year grade point average is reported for gender groups within programs of study at the University of Iowa. Academic records of all freshmen entering the University in 1978 in the fields of Business, Liberal Arts, Pre-Medicine, and those undecided as to major were analyzed with respect to American…

An interview protocol was devised to determine whether demands on working memory are reduced by the use of drawn or telegraphic formats. Students were chosen because some aspect of their group testing on presentation formats was provocative (e.g. high spatial score, but low reading comprehension score; high drawn score and low verbal score, etc.).…

This paper describes a quantitative model that can be used to evaluate faculty performance for promotion decisions. Through the use of an evaluation form, the system (1) informs faculty members how they will be evaluated at the end of each academic year; (2) allows faculty growth to be documented in teaching, research, and other activities which…

Activities and teaching methods for developing an understanding of fractions are presented. The activities, which use mathematical models (visual representations of fractions), are divided into three sections: (1) equivalent fraction circles; (2) fraction bars; and (3) multiplication of fractional numbers using squares. Each section includes the…