This document consists of five units which all view applications of mathematics to American politics. The first three view calculus applications, the last two deal with applications of algebra. The first module is geared to teach a student how to: 1) compute estimates of the value of the parameters in negative exponential models; and draw…

This publication is a study guide prepared for use in a National Science Foundation (NSF) Chautaugua-Type Short Course for College Teachers. The purpose of the guide is to provide college teachers with a variety of modeling methods that can be used with problem solving. Mathematical applications and illustrations are included, along with listings…

This report is concerned with the observation that many teenagers and adults are unable to apply arithmetic even when they know how to perform the operations. It is speculated that this is probably due to not having been taught when to use the fundamental operations. Examples of types of "real" problems which require the various…

The use of games and gaming, which are simulated decision making, is examined in a paper addressed to the manager and administrator in higher education. Focus is on the use of games in situations of resource allocation for budgeting and long-range planning. Basic definitions and concepts are presented, followed by a discussion of the scope and…

The mathematical exercise of the the Prisoner's Dilemma is used to explore the issue of whether present models or paradigms of policy analysis cover the complete range of rational decision making. A review of the competing paradigms of the cybernetic concept, the analytic probability concept, and the cognitive categorization concept reveals…

With the rapid increase in number and size of junior colleges, administrators must take advantage of the decision-making tools already used in business and industry. This study investigated how these quantitative techniques could be applied to junior college problems. A survey of 195 California junior college administrators found that the problems…

Several models for problem solving are discussed, and the idea of a heuristic frame is developed. This concept provides a description of the evolution of problem-solving skills in terms of the growth of the number of algorithms available and increased sophistication in their use. The heuristic frame model is applied to two sets of physical…

Strategy games are used to expose teachers and their students to the techniques and strategies involved in true problem solving. (JT)

A model of qualities of mathematical activity was developed within a framework of learning goals. A clinical application of the model is described, in which ninth-grade students were given assignment projects. A hierarchy of effective guidance was established, permitting diagnostic evaluation and progressive development of mathematical activity.…

A variety of tips about problem solving are included, with the focus on helping students recall an image. Manipulative materials and models using grids are included in most of the activities. (MNS)

Activities are given for solving verbal subtraction problems. Take-away and comparison situations are described, and three levels of activities to model the situations are given: one involving concrete materials and verbal descriptions; the second with these plus written symbols; and the third encouraging mental images. (MNS)

This paper addresses the first year of a three-year, longitudinal study which introduces mathematical modeling to young children and provides professional development for their teachers. Four classes of third-graders (8 years of age) and their teachers participated in the first year of the program, which involved several preliminary modeling…

A mathematical model, using the vector maximization technique, is developed to study the underlying structure of a set of cost/benefit alternatives. (Author)

Details of a course on mathematical modeling for graduate teachers of mathematics are presented. The rationale, objectives, course content, assessment methods are discussed along with several illustrative examples and difficulties encountered in finding appropriate problems. (MP)

Student weaknesses on problem-solving portions of the NAEP mathematics assessment are discussed using Polya's heuristics as a framework. Recommendations for classroom instruction are discussed. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).