To demonstrate concepts or rapidly create quizzes, teachers commonly encounter the need to quickly create mathematical examples. Unfortunately, by producing undesirable or overly complex solutions, extemporaneously created examples can become problematic, create tense learning environments and become more confusing than they are worth. Experience…

Much of modern mathematical research requires a serious level of commitment and ability on the part of the researcher and, as a natural consequence, precludes any real involvement by undergraduate mathematicians. However, to put it crudely, Computer Algebra Systems, can make experts of us all. With the use of such systems even the average…

This article describes an activity that involves the use of simulation for decision-making. It is useful for demonstrating concepts in probability and statistics. (Contains 4 figures and 2 tables.)

The intent of this project was to develop a course for mathematics graduate students at Iowa State University. They would design and write computer programs for use by undergraduate mathematics students, and then offer the course and actually produce the software. Phase plane graphics for ordinary differential equations was selected as the topic.…

Peer-tutoring programs have been found to produce positive effects on student achievement. There has been relatively little research on the effects of tutor characteristics on the achievement of college students who receive tutoring. The purpose of this study was to investigate the relationship between the sex of tutors and students' sex on…

One way in which a computer simulation can convince students of the validity of formulas for the density and distributive functions of the sum of two variables is described. Four computer program listings are included. (MNS)

Timing stoplights and trying to determine the best way to allocate cycle time to the two directions is discussed. The simple case and improving the model are both considered. (MNS)

Described is the development and implementation of a course on the history of irrational numbers for inservice mathematics teachers in Israel. Some of the materials included in the course are discussed. (RH)

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)

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)