A slight rewording can often transform a routine exercise into a nonroutine one. Three problems (with solutions) from first-year college calculus are presented to illustrate how the technique can be used and how it is applicable to any course. (JN)

The rational plane, consisting of the points in the Cartesian plane having two rational coordinates, is a model in which certain properties do not hold. Nine theorems are discussed. (MNS)

A program for drawing a line segment is developed. (MNS)

Women from five Canadian universities overestimated their final grades less often and underestimated them more often than men did. No sex-related difference was found in level of confidence to complete the bachelor's program, but women expressed less confidence in their ability to obtain the doctorate. (MNS)

The author arranges 26 current states of mathematical knowledge (in relation to solving a problem) in an informal taxonomy and comments on them. (MNS)

An exercise simulating the tossing of N dice is described. Calculation of expected gain and extension to a two-person game are each discussed. (MNS)

A one-semester course at the third-year level at York University is described. It tries to legitimize in students' eyes that it makes sense to talk about mathematics as well as do mathematics. Seven course themes are discussed, followed by nine problems used in the course. (MNS)

Examples of diversions with cards that may be used to illustrate the concept of a cyclic group and structural properties of the integers modulo a prime are presented. (MNS)

Explores whether there is a component of mathematics anxiety distinct from numerical anxiety and mathematics test anxiety. A 30-item instrument was administered to 365 community college students. A factor involving anxiety associated with specific mathematics topics, labeled "abstraction anxiety," was found. (MNS)

A construction of an ellipse, given its foci and major-axis length 2a and using a compass and straightedge, is illustrated. It is based on Dandelin's elegant proofs that the sections formed by the intersections of a cone with a plane are an ellipse, parabola, or hyperbola. (MNS)

Shows a direct solution for factoring trinomials, without trial and error, using a calculator. When a calculator is not available, the mathematical chore is eased somewhat using reference tables, as shown in two noncalculator methods (determining nonfactorability and factorability). (JN)

Roberts discusses his perception that the college introductory curriculum in mathematics is outdated. Reactions are then presented from Lucas, Hamming, Tall, David, Ellis, Thompson, Mason, and Guy, with a response by Roberts. The need to change instructional methods as well as curriculum is noted by most. (MNS)

An efficient division algorithm is developed, using a computer program, to convert any positive fraction to its decimal representation. The computer program listing is included. (MNS)

The Monte Carlo method and its logic are reviewed, then three experiments that tested the value of the method in a variety of class settings are described. (DT)

This paper discusses a pedagogical technique called the discovery approach in teaching remedial and college algebra. Examples of how to introduce and enhance some algebra topics using this approach in mathematics classrooms are illustrated. It is argued that student performance would improve if more topics were presented in a discovery fashion.…