Recent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the…

The lesson plans in this book engage students by using a tool they enjoy--the Internet--to explore key concepts in algebra. Working either individually or in groups, students learn to approach algebra from a problem solving perspective. Each lesson shows learners how to use the Internet as a resource for gathering facts, data, and other…

Presents a method for solving linear equations involving the use of inverses instead of memorizing rules. (MKR)

A possible method of derivation of prescriptions for solving problems, found in Babylonian cuneiform texts, is presented. It is a kind of "geometric algebra" based mainly on one figure and the manipulation of or within various areas and segments. (MNS)

Four unusual mathematics problems with interesting routes to solution are presented. A general method of solution to problems of this type is proposed. (MP)

Using sequential chains of regular n-gons in a row with one side touching, as for example, one triangle, two triangles, three triangles, and so on, students graph the length of the perimeter versus the number of n-gons and determine the functional relationship for different values of n. (MKR)

Two mathematical topics are interpreted from the viewpoints of traditional (performing algorithms) and contemporary (creating algorithms and thinking in terms of them for solving problems and developing theory) algorithmic mathematics. The two topics are Horner's method for evaluating polynomials and Gauss's method for solving systems of linear…

This paper consists of a learning unit for college algebra in which the problem presents three different payment plans for a tuition plan to pay for college expenses. The details of each payment plan are presented, each followed by several exercises so that comparisons of the results can be made across payment plans. (MM)

Procedures to help algebra students solve problems more efficiently are discussed, using linear programing graphs. (MNS)

A computer program that uses determinants to solve simultaneous systems of equations is presented. The purpose is to show teachers how to use topics from algebra, geometry, and programing to lead pupils to appreciate the beauty and unity of mathematics. (MP)

This booklet contains mathematics unit plans for Algebra 1, Geometry, Math for Technology, Mathematical Problem Solving, and Pre-Algebra developed by PACE (Promoting Academic Excellence In Mathematics, Science & Technology for Workers of the 21st Century). Each unit plan contains suggested timing, objectives, skills to be acquired, workplace…

Algebra word problems were analyzed in terms of the information integration tasks that are required to solve the problems. These tasks were classified into three levels: value assignment, value derivation, and equation construction. Novices (35 first year algebra students) and experts (13 analytic geometry students) were compared on the proportion…

By translating inequalities into equations (e.g., x greater than 0 can be written x- absolute value of x = 0) and forming equations for unions and intersections of solution sets, students can develop equations for polygons. The method can be generalized to yield equations in three dimensions. (SD)

The method of finite differences is discussed with some applications. The method is described in detail, with illustrative sequences, and several problems are presented. (MNS)

A problem on speed of travel is stated in general terms to provide practice in algebraic manipulation while maintaining a sense of real-world usefulness. A computer program is listed. (MNS)