Usually a student learns to solve a system of linear equations in two ways: "substitution" and "elimination." While the two methods will of course lead to the same answer they are considered different because the thinking process is different. In this paper the author solves a system in these two ways to demonstrate the…

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills,…

This article demonstrates how within an educational context, supported by the notion of hidden mathematics curriculum and enhanced by the use of technology, new mathematical knowledge can be discovered. More specifically, proceeding from the well-known representation of Fibonacci numbers through a second-order difference equation, this article…

A handout, developed for use with students at Arizona State University, describes Gaussian Elimination procedures to be used when working with matrices. (MK)

Discusses the theoretical and practical importance of linear algebra. Presents a brief history of linear algebra and matrix theory and describes the place of linear algebra in the undergraduate curriculum. (MDH)

Presents five recommendations of the Linear Algebra Curriculum Study Group: (1) The syllabus must respond to the client disciplines; (2) The first course should be matrix oriented; (3) Faculty should consider the needs and interests of students; (4) Faculty should use technology; and (5) At least one follow-up course should be required. Provides a…

This volume is an experimental edition for a high school course in the theory of matrices and vectors. One of the basic aims is to demonstrate the structure of mathematics. Another criterion is to provide some tools that will be useful in the student's transition from school to college. A last objective is that the intellectually vigorous students…

Discusses whether a map can be constructed using only the distances between 15 selected cities. Concepts used in the discussion come from geometry, matrix theory and trigonometry. (PK)

The author presents two examples of lattice multiplication followed by a computer algorithm to perform this multiplication. The algorithm is given in psuedocode but could easily be given in Pascal. (PK)

A 3-year core curriculum may be the fundamental change proposed for grades 9-12 in the "Standards." This article provides 2 examples for content differentiation for particular topics and problems. Some suggestions for adjusting the present curriculum to align with the core curriculum are provided. (YP)

This is the instructor's guide to a text designed for the contemporary business student who frequently questions the need for studying mathematics. The text material is presented in a "building-block" fashion, with skills learned in earlier chapters organized to provide a smooth transition into more difficult topics. This guide consists…

The article discusses the use of computers to teacher college level mathematics. In particular, the Gaussian elimination procedure for solving a system of n linear equations in n unknowns, using a computer, is examined. (PK)

Presents ideas that are intended to convey new insights on familiar topics and to enhance pedagogy. The mathematical topics addressed are applications of transformations to numerical integration, the golden ratio, Cramer's rule, a counting problem, and the general form of the arithmetic-geometric mean inequality. (PK)

This yearbook provides the mathematics education community with specific perceptions about discrete mathematics concerning its importance, its composition at various grade levels, and ideas about how to teach it. Many practical suggestions with respect to the implementation of a discrete mathematics school program are included. A unifying thread…

The National Council of Teachers of Mathematics (NCTM) has published three documents that propose standards related to mathematics education called "The Curriculum and Evaluation Standards for School Mathematics" (1989), "The Professional Standards for Teaching Mathematics" (1991), and "The Assessment Standards for School Mathematics" (1995). The…