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)

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…

Arguing that college mathematics education must be made more effective, especially for technology, engineering, mathematical sciences, and physical sciences students, this paper presents nine general principles to enhance math instruction for all students. Introductory material argues that changes in perception, attitudes, and role models are…

A description is given of a senior seminar in which each student reported on a topic centered around the works of David Hilbert. A brief description of each topic is given as well as a list of references. (MP)

Provides examples to show that parallel coverage of convergence theorems for both series and improper integrals will tend to strengthen each other. Indicates that such coverage should also help students to better understand the concept of asymptote. (JN)

Historical problems are presented which can readily be solved by students once some elementary probability concepts are developed. The Duke of Tuscany's Problem; the problem of points; and the question of proportions, divination, and Bertrand's Paradox are included. (MNS)

Provides an algorithm for determining the median and quartiles of discrete data sets. Describes the graphical equivalent of the numerical method. (JM)

A method for making divergent series converge is described. Proofs of the procedure are presented. (MNS)

Discusses the factoring of polynomials and Fibonacci numbers, offering several challenges teachers can give students. For example, they can give students a polynomial containing large numbers and challenge them to factor it. (JN)

Discusses insufficiency of the linear method and some informal practices (or heuristics) used by expositors in trying to alleviate it. Uses the Cantor-Bernstein theorem to illustrate the linear proof, structuring, and the structure proof. Argues that the informal practices considered be consistently applied to the presentation of pivots and…

This explanation of finding functions includes comments on how to help students move from finding specific solutions to determining generalized solutions. (MNS)

A method used in teaching abstract algebra is described; it could be applied to other classes. Students play a more active part in their own education by helping to select, prepare, and present material to the class. (MNS)

Computers can be used in elementary statistics courses not only to perform calculations, but also to perform simulations to clarify concepts and theorems. Computer programs for a sample distribution of the mean and for the central limit theorem are given and discussed. (MNS)

A traveling salesman problem is used to illustrate the key idea in a general proof of a reduction technique. It is reduced to a problem in propositional calculus. (MNS)