Errors students typically generate while trying to translate problems into and out of algebraic notation are reviewed. Translation skills and pupil difficulties with them are seen as areas deserving further research. (MP)

Three Florida high schools used the computer-based PLATO Basic Skills Mathematics program for remedial mathematics lessons. Students showed a median gain of 1.5 grade equivalents and improved attitudes toward mathematics and school. A model of the project's cost effectiveness indicates the need to manage the program carefully. (Author/RW)

The problems involved in making reservations for airline flights is discussed in creating a mathematical model designed to maximize an airline's income. One issue not considered in the model is any public relations problem the airline may have. The model does take into account the issue of denied boarding compensation. (MP)

A simple teaching model, designed to show rapidly which are the principal factors in population growth and how they are related, is presented. The apparatus described allows students to play several different active roles. (MP)

A general discussion of prediction and the use of models as a means of understanding reality is provided, focusing on the application of mathematical models to various scientific disciplines and its role in experimentation. (DC)

Describes the basic philosophy, nomenclature, and techniques used in mathematical modelling to enable biologists, engineers, land managers, and others to understand the concepts and usefulness of models. Contrasts conceptual and empirical approaches, using ecosystem models as an example of the former. (DC)

The restrictions on item difficulties that must be met when binomial models are applied to domain-referenced testing are examined. Both a deterministic and a stochastic conception of item responses are discussed with respect to difficulty and Guttman-type items. (Author/BH)

A multitrait-multimethod (MTMM) analysis of alienation employed two personality constructs conceptually relevant to alienation: hostility and locus of control. MTMM analysis indicated that eight of 15 convergent validity coefficients were statistically significant; however, magnitude was small and Campbell-Fiske criteria were not satisfied…

Two methods of analyzing nonorthogonal (uneven cell sizes) cross-classified data sets are compared. The methods are direct standardization and the general linear model. The authors illustrate when direct standardization may be a desirable method of analysis. (JKS)

Mathematical modeling is defined. Examples are used to show that there are models available which illustrate both the traditional use of mathematics in the physical science and its newer use in nonphysical disciplines, and which are at a suitable level for teaching in schools. (Author/MK)

A newly developed input/output method for comparing the efficiency of urban elementary schools is presented. The method results in the identification of efficient and inefficient schools and provides management information relative to input and output measures. (Author/IRT)

Tesselations and n-dimensional geometry problems are reviewed. The author discusses possible models which could be used to approach and understand these special aspects of geometry. (MP)

Using reasonable values for the parameters in both null and alternative hypotheses about covariance matrices, an optimal and feasible combination of number of subjects, significance level, and power of the test were determined for an empirical study of the measurement of musical ability. (Author/BW)

An analysis is presented of pupil responses to several items on the second National Assessment of Educational Progress (NAEP) mathematics survey which focused on the concepts and models of the fundamental operations. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

The use of mathematical modelling as a systematic framework for solving word problems is presented. Applications for typical elementary algebra and calculus problems are featured. (MP)