This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…

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…

Two approaches are discussed for calculating the work necessary to pump water from a conical or parabolic container. The direct method derived from the definition of work is easy to misuse, as illustrated by a student's incorrect solution. (JP)

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)

Nine examples of this principle show what a powerful tool it is. Several map coloring theorems are proven and some exercises are listed. (MP)

Math anxiety is an affliction that causes several intelligent students to believe, mistakenly, that they lack the ability to master the subject. Professors are starting to question their teaching tactics in hopes of tackling math anxiety, with some educators looking at ways to make their classes more interactive, while others are considering…

The goal of this pamphlet is to provide instructors of various scientific disciplines with mathematically accurate graphs of elementary polynomial functions. The figures in this pamphlet are intended to provide suitable material for the preparation of classroom handouts and overhead transparencies. In addition, sample sets of exercises are…

Demonstrated is how the concept of equivalence classes modulo n can provide a basis for solving a wide range of problems. Five problems are presented and described to illustrate the power and usefulness of modular arithmetic in problem solving. (MNS)

Over the past two decades, calculus reformers have called for the use of alternative pedagogical techniques to promote student learning. Some mathematics instructors have responded by developing a set of student projects intended to hone thinking skills and improve the mathematical writing skills of calculus students. Drawbacks to this strategy…

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

A sequence of numbers from combinatorial theory called the Bell numbers is discussed, along with several problems and examples that demonstrate their usefulness. (MN)

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)

Considered are the main elements of computational chemistry problems and how these elements can be used to formulate the problems mathematically. Techniques that are useful in devising an appropriate solution are also considered. (Author/TG)

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)