Presented are solutions to variations of a combinatorics problem from a recent International Mathematics Olympiad. In particular, the matrix algebra solution illustrates an interaction among the undergraduate areas of geometry, combinatorics, linear algebra, and group theory. (JJK)

This column solicits mistakes, fallacies, anomalies, et cetera, that raise interesting mathematical issues and may prove useful to teachers. Included in this issue are yet another proof that zero equals one and a differentiation that yields three equals two. (Author/JJK)

The number theory concepts of perfect, deficient, and abundant numbers are subdivided and then utilized to discuss propositions concerning semiperfect, weird, and integer-perfect numbers. Conjectures about relationships among these latter numbers are suggested as avenues for further investigation. (JJK)

Presents a murder mystery in the form of five Calculus I worksheets in which students must apply mathematics to determine which of the suspects committed the murder. Concludes that effort was made to create scenarios that realistically lend themselves to the use of mathematics. (Author/ASK)

Provides information on how to develop a humanistic academic environment for learning undergraduate mathematics. Recommends writing invitation letters to students for participating in honors calculus courses or having no placement tests for assigning students to mathematics courses. (ASK)

Discusses the necessary characteristics of an introductory college-mathematics curriculum for improving mathematics education at the college level. (ASK)

Although data is often used to estimate parameters for models in calculus and differential equations, the models themselves are seldom justified. Uses the data itself to motivate mathematical models in introductory mathematics courses. Illustrates various regression and optimization techniques. (Author/ASK)

Discusses some questions connected with Cauchy's theorem which states that two convex closed polyhedral surfaces whose corresponding faces are congruent and whose faces adjoin each other in the same way are congruent. Describes how to construct a flexible polyhedron. (ASK)

Examines why a flexible polyhedron must be convex. Discusses the theorems of Cauchy and Euler. (ASK)

Using MAPLE enables students to consider many examples which would be very tedious to work out by hand. This applies to graph plotting as well as to algebraic manipulation. The challenge is to use these observations to develop the students' understanding of mathematical concepts. In this note an interesting relationship arising from inverse…

This report complements the Mathematical Association of America's curriculum recommendations about the undergraduate program in mathematics with a case studies approach that describes effective practices in undergraduate mathematics programs. The primary focus of this case studies project is not course content, but more general issues in the…

A project is described that provides explicit instruction on the skills necessary for solving word problems. An informal inventory of such skills is being developed, intended for diagnostic use. It contains six sections, each keyed to the problem-solving skills of understanding the problem, representing the unknown, writing the equation, and…

Many kinds of individual differences among learners have been studied by psychologists and educators in an attempt to improve the educational process. Some emphasis has been placed on the notion of cognitive style in an effort to understand more of the cognitive processes which underlie academic performance. The purpose of the present study was to…

Two questions are dealt with: (1) Can those strategies or behaviors which enable experts to solve problems well be characterized, and (2) Can students be trained to use such strategies? A problem-solving course for college students is described and the model on which the course is based is outlined in an attempt to answer these questions. The…