This article discusses an activity designed to encourage writing to learn in mathematics. There were three stages of data collection. An assessment, requiring basic algebra only, was completed by 118 undergraduates from statistics and calculus courses. Students were given summaries of all participant responses, along with the correct answers.…

In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…

Seven articles present: 1) a solution to a force equilibrium problem, 2) a magic square, 3) a characteristic of right triangles, 4) a family tree of Pythagorean triples, 5) a misunderstanding which may be cleared through modern mathematics, 6) a technique for solving conversion problems, and 7) a special permatation problem. (RS)

Examples of the presentation and solution of variations on a common projectile trajectory problem are presented. (BB)

The focus is on how line graphs can be used to approximate solutions to rate problems and to suggest equations that offer exact algebraic solutions to the problem. Four problems requiring progressively greater graphing sophistication are presented plus four exercises. (MNS)

This workbook is designed to be used as a review at the end of a college level course in algebra and trigonometry. Four review sheets containing 117 problems provide hints and detailed solutions for each problem. (YP)

A computer program generates sets of simultaneous linear equations for students to solve; the program also solves the systems and provides teachers with solutions. (SD)

This article describes a procedure for presenting routine practice problems on a programable calculator with attached teletype. The program uses a random number generator to write problems, gives feedback and assigns grades according to the procedures outlined (and flow-charted) by the author. (SD)

The goal of this study was to find a way to quantify three criteria of representational quality, described by Greeno, so that it would be possible to examine statistically the relationship between representational quality and other variables related to problem solution. The sample consisted of 18 college students, 84 percent of whom had…

Determines which chessboards contain a chromatic rectangle having all four corners the same color for any black-white coloring. Expands the problem to a three color problem. (YP)

In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…

This book contains about 200 problems. It is suggested that it be used by students, teachers or anyone interested in exploring mathematics. In addition to a general discussion on problem solving, there are problems concerned with number theory, algebra, geometry, and combinatorics. (PK)

P-adic or g-adic sets are sets of elements formed by linear combinations of powers of p, a prime number, or g, a counting number, where the coefficients are whole numbers less than p or g. Discusses exercises illustrating basic numerical operations for p-adic and g-adic sets. Provides BASIC computer programs to verify the solutions. (MDH)

College algebra is currently being taught using graphing calculators such as the TI-81. This document presents exploratory and problem solving activities that have resulted from classroom experiences with the TI-81. The activities have been designed to enhance the learning of some standard college algebra topics through the easy access to…

This document contains the course syllabus and 12 independent practice modules for an introductory college algebra course that requires some previous knowledge of algebra and the ability to work at a rapid pace. Topics include the basic operations with signed integers; fractions; decimals; literal expressions; algebraic fractions; radicals;…