This module applies linear algebraic methods to solve the following problem: If an object in a three-dimensional coordinate system is first rotated about a given axis through the origin by a given angle, and then rotated about another axis through the origin by another angle, there is a straightforward way to calculate the combined result of the…

It is noted that with the prominence of computers in today's technological society, digital communication systems have become widely used in a variety of applications. Some of the problems that arise in digital communications systems are described. This unit presents the problem of correcting errors in such systems. Error correcting codes are…

Applied mathematics is seen often to involve the solution of single equations or systems of equations. A particular technique for solving equations in the context of functions on the real line is examined. This technique includes an iterative process, which is viewed as an algorithm that can be implemented readily on inexpensive and widely…

This module is designed to apply mathematical models to nuclear deterrent problems, and to aid users in developing enlightened skepticism about the use of linear models in stability analyses and long-term predictions. An attempt is made at avoiding overwhelming complexities through concentration on land-based missile forces. It is noted that after…

Two units make up this material. They focus on applications of second-order difference equations to American politics. The goals of the first module include helping the user understand: 1) the difference between a theoretical construct and an observable; 2) the nature of choices which exist in modeling any particular empirical phenomenon; and 3)…

This document consists of two major sections. The first of these is actually three units that look at applications of arithmetic to business. Basic pre-algebra mathematics is an assumed prerequisite. These units are titled: 367-The Real Numbers; 368-Fractions and Their Uses: Ratio and Proportion; and 369-Exponents: Powers and Roots. Each module…

This material contains two units which view applications of computer science. The first of these examines Horner's scheme; and is designed to instruct the user on how to apply both this scheme and related algorithms. The second unit aims for student understanding of standard bisection, secant, and Newton methods of root finding and appreciation of…

Presented is a graphical approach to teaching higher degree, rational function, and absolute value inequalities that simplifies the solution of these inequalities and thereby reduces the amount of classroom time that has to be devoted to this topic. Applications are also given for signum functions, maximum-minimum, and points of inflection…

Reframing, (redirecting or changing the perceptual experience of a situation by placing it in another frame that fits the facts equally well or better) is a relatively unique approach to interpersonal problem solving. A study was conducted to determine whether reframing could be taught as a self-help interpersonal problem-solving skill and to…

This study explored the variance in mathematical problem-solving achievement accounted for by sex and ethnicity. Each of 316 adolescents in a rural school district in southeast Texas was administered the California Achievement Test and a set of five affective scales. Reading scores accounted for 49.5% of the variance; computation, 14.6%; affective…

This paper describes the application of a systems approach model to assessing families with a labeled noncompliant child. The first section describes and comments on the applied methodology for the model. The second section describes the classification of 61 families containing a child labeled by the family as noncompliant. An analysis of data…

This study addressed: (1) what difference, if any, would calculators make on a typical mathematics assessment instrument; (2) what might occur if students were allowed to use, but were not furnished with, calculators for testing; and (3) what implications do answers to these questions have for future statewide assessment. Eighth-grade students…

This collection of material is designed to illustrate the nature and variety of the idea of proof in mathematics. It is intended to be a "background book" for the use of teachers, particularly those in initial training courses. Individual chapter titles are: (1) The Role of Proof in Mathematics; (2) Logical Reasoning: The Idea of Implication; (3)…

Improving the quality of education is difficult today when many schools are experiencing a steady decline in student enrollment and financial resources. In such a climate it is increasingly important to stretch resources and adjust programs to provide for the diverse needs of all students. The National Association of Secondary School Principals…

A description is given of the organization and operation of a network of persons who work together to accomplish the following six educational goals: (1) diagnose problems that impair student performance in the basic skills and other areas; (2) link schools with the best available educational programs to meet their needs; (3) link schools with…