The use of basis matrix methods to rotate axes is detailed. It is felt that persons who have need to rotate axes often will find that the matrix method saves considerable work. One drawback is that most students first learning to rotate axes will not yet have studied linear algebra. (MP)

In a multiple regression analysis with three or more predictors, every set of alternate weights belongs to an infinite class of "fungible weights" (Waller, Psychometrica, "in press") that yields identical "SSE" (sum of squared errors) and R[superscript 2] values. When the R[superscript 2] using the alternate weights is a fixed value, fungible…

This curriculum for mathematics is designed as a teachable curriculum directed toward workplace needs. It is intended to be workplace specific and to move the learner toward a full 12th-grade level attainment. The two modules in this curriculum are further divided into modules dealing with specific topics. The first module, Basic Mathematics,…

Graphing bivariate data in a scatter plot and drawing an approximate line of best fit for the data have become commonly recommended activities for middle school and high school students. The graphing calculator has provided a mechanism for students both to approximate a best-fit line and to calculate the best-fit line using a built-in option. Two…

Nearly 48 percent of the students in Developmental Studies Mathematics courses at a major southern university during the fall of 1983 had taken college preparatory mathematics courses in high school. Some had even taken trigonometry, pre-calculus, or calculus. Yet, they were placed in university developmental studies mathematics courses because…

A point "E" inside a triangle "ABC" can be coordinatized by the areas of the triangles "EBC," "ECA," and "EAB." These are called the barycentric coordinates of "E." It can also be coordinatized using the six segments into which the cevians through "E" divide the sides of "ABC," or the six angles into which the cevians through "E" divide the angles…

The aim of this study is to identify the effects of formalism in teaching on primary and secondary school mathematics teacher trainees' algebraic and geometric interpretations of the notions of linear dependency/independency. Quantitative research methods are drawn in order to determine differences in success levels between algebraic and geometric…

Outlined are the minimum requirements for a quinmester course intended to strengthen a student's experience in a first algebra course, prior to entry to high school geometry and the second algebra course. After a brief description of overall goals and strategies, further details are presented in eight sections. Each section gives performance…

Behavioral objectives are specified for 82 topics in mathematics to be covered in grades 7 through 9. A general objective is given for each, followed by specific behavioral objectives with suggested activities. Topics include number properties and operations, geometry, number theory, algebra, set theory, ratio, proportion and percent, the metric…

According to the Merriam-Webster dictionary, a planimeter is "an instrument for measuring the area of a plane figure by tracing its boundary line". Even without knowing how a planimeter works, it is clear from the definition that the idea behind it is that one can compute the area of a figure just by "walking" on the boundary. For someone who has…

We propose a robust framework for clustering data. In practice, data obtained from real measurement devices can be incomplete, corrupted by gross errors, or not correspond to any assumed model. We show that, by properly harnessing the intrinsic low-dimensional structure of the data, these kinds of practical problems can be dealt with in a uniform…

This bulletin contains: (1) a summary and conclusions of a study of mathematics curricula in Europe and Japan, and (2) a description of beginning efforts to evaluate the Secondary School Mathematics Curriculum Improvement Study (SSMCIS) project. Some of the conclusions of the European and Japanese study are: (1) the study of Euclidean synthetic…

Because of the high incidence of failure in algebra I among ninth-grade students, the Louisiana State Board of Elementary and Secondary Education requested the development of this guide with the intention of providing a good pre-algebra foundation. The purposes of the guide are to recognize standards that involve the application of mathematical…

The primary aim of this guide is to aid teachers in planning and preparing a senior high school mathematics course for students preparing for college work. It is divided into separate one-semester courses of seven chapters each. The first-semester course consists of a traditional approach to the introduction of trigonometry and trigonometric…

The academic training needs of two-year college mathematics faculty are discussed in this paper and appropriate courses of study are proposed. After introductory comments on the diversity of two-year college students' needs for mathematics education, an undergraduate course of study appropriate for two-year college math faculty is proposed. This…