This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem soving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses…

This book shows how to increase one's power to analyze and comprehend problems. First, it outlines and illustrates the methods that good problem solvers use in attacking complex ideas. Then it gives some practice in applying these methods to a variety of questions in comprehension and reasoning. Chapters include: (1) "Test Your Mind--See How…

This teaching guide accompanies the film series "Challenge of the Unknown," which focuses on problem solving in the real world. The guide is designed to bridge the gap between the concepts presented in the films and their classroom applications, by answering teachers' questions and needs and providing a variety of possible activities.…

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…

This student textbook is designed to incorporate programable calculators in grade 12 mathematics. The seven chapters contained in this document are: (1) Using Calculators in Mathematics; (2) Sequences, Series, and Limits; (3) Iteration, Mathematical Induction, and the Binomial Theorem; (4) Applications of the Fundamental Counting Principle; (5)…

A number of space science resource materials and activities are developed into a useful format for classroom presentation. The application of mathematical properties in making scientific discoveries is the major emphasis. Each section has a discussion centered on the men and history behind the discovery of physical laws and phenomena relevant to…

Presents three traditional problems from discrete mathematics with alternative solutions and discussion of those solutions. (PK)

Discusses the development of problem-oriented mathematics materials for a wide variety of students. Materials include teaching guides, student materials, case studies in mathematical modeling, and project activities. Examples of these materials (including a sports-related activity for students who have not had success in mathematics) are provided.…

This publication features articles that illustrate how several Northwest teachers are using problem solving to achieve rigorous and imaginative learning in their classrooms. Articles include: (1) "Open-Ended Problem Solving: Weaving a Web of Ideas" (Denise Jarrett); (2) "Teenager or Tyke, Students Learn Best by Tackling Challenging Math" (Suzie…