Issues surrounding a recent voting rights case in Los Angeles (California) are discussed and evaluated in this introduction to the remainder of this special issue. The most important issues are geographical compactness, political cohesiveness, and racial voting blocs. (SLD)

Type I error rates of four multivariate tests (Pilai-Bartlett trace, Johansen's test, James' first-order test, and James' second-order test) were compared for heterogeneous covariance matrices in 360 simulated experiments. The superior performance of Johansen's test and James' second-order test is discussed. (SLD)

The ability of 3-way INDSCAL and ALSCAL models to recover true structure in proximity data based on 2-dimensional configurations varying in number of subjects (15 and 20) and stimuli, amount of error, and monotonic transformation is examined. INDSCAL outperformed metric and nonmetric ALSCAL in all conditions. (SLD)

This article describes a collaboration between a university professor and a sixth-grade teacher who teamed to introduce algebra using a visual approach. The project began with a study of qualitative graphs, moved on to quantitative graphs, then introduced tables of values and finally concentrated on equations. (Contains 12 figures.)

Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

The following article presents a proposal for the redesign of a traditional course in Differential Equations at Middle Georgia College. The redesign of the course involves a new approach to teaching traditional concepts: one where the understanding of the physical aspects of each problem takes precedence over the actual mechanics of solving the…

The quality of knowledge underlying students' algebraic thinking is a major concern of K-12 mathematics teaching and reform-driven curriculum documents. In this paper the author examines this issue by characterizing a group of high school students' algebraic knowledge and patterns of use of that knowledge during the solution of selected problems.…

This document proves that the F statistic can be obtained by squaring t-test values, or that equivalent t-test values may be obtained by extracting the positive square roots of F values. Proof to varying degrees of completeness and accessibility has been given by other scholars, but generally these prior statements, particularly those available to…

"University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and…

The construct validity of algebra word problems for measuring quantitative reasoning was examined, focusing on an analysis of problem attributes and on the analysis of constructed-response solutions. Constructed-response solutions to 20 problems from the Graduate Record Examinations (GRE) General Test were collected from 51 undergraduates.…

A multidimensional item response theory (IRT) model for polytomously scored items, based on the graded response model and using the normal ogive, is developed; and an EM algorithm that may be used to estimate the parameters of the model is also discussed. The model is illustrated through a simulation study in which the polytomous item responses of…

This document presents Core Course Proficiencies for the State of New Jersey whose purpose is to ensure that all students have equal access to the fundamental knowledge and skills critical to achieving success in mathematics. After an introduction providing rationale and background, the Core Course Proficiencies are presented in three sections.…

Procedures used to map the achievement levels, expressed as total expected scores on the full set of items presented to a grade, onto the Mathematics Composite of the 1990 National Assessment of Educational Progress (NAEP) are described. The Composite, defined as a weighted average of subdomain scores, provides a global measure of mathematics…

Methods are proposed for the construction of weakly parallel tests, that is, tests with the same test information function. A mathematical programing model for constructing tests with a prespecified test information function and a heuristic for assigning items to tests such that their information functions are equal play an important role in the…

This manual outlines an advanced mathematics course for secondary school students in Manitoba (Canada). Included are eight different topics for a total of ten modules, with each module accounting for 18 40-minute periods. Teachers, or teachers and students cooperatively, should select the equivalent of five modules from the eight topics covered.…