Context is what makes mathematical modeling tasks different from more traditional textbook word problems. Math problems are sometimes stripped of context as they are worked on. For modeling problems, however, context is important for making sense of the mathematics. The task should be brought back to its real-world context as often as possible. In…

We present background and an activity meant to show both instructors and students that mere button pushing with technology is insufficient for success, but that additional thought and preparation will permit the technology to serve as an excellent tool in the understanding and learning of mathematics. (Contains 5 figures.)

In this article, the author describes the development and implementation of a measurement-based group activity designed to support students in understanding the connection between angle magnitude and the shape of the sine function. She explains that the benefit of this activity is that it allows students to build their trigonometric knowledge…

The kinematics teaching strategy is a teaching method that stimulates kinesthetic intelligence and thus offers students an unconventional approach for exploring mathematical ideas through movement. This article describes how to use the kinesthetic approach to introduce radian measure. The article includes detailed descriptions of easy-to-use…

Over the years the technology behind displaying the image of the unit circle has changed, but the defining features remain constant. The key question for the author as a teacher is this: are the relationships embodied in the image simple, memorable and rich enough to be grasped by any KS3 student at his school? It needs to be simple enough to…

A 2 m long wooden beam provides an ideal demonstration tool for exploring moments. A class set is cheap and can be used at introductory and advanced levels. This article explores how such beams can be used to support learning about moments, equilibrium, vectors, and simultaneous equations. (Contains 7 figures.)

This paper presents a derivation of all five Lagrange points by methods accessible to sixth-form students, and provides a further opportunity to match Newtonian gravity with centripetal force. The predictive powers of good scientific theories are also discussed with regard to the philosophy of science. Methods for calculating the positions of the…

In this pedagogical article, I explore a unified approach in obtaining the derivatives of functions and their inverses by adopting a guided self-discovery approach. I begin by finding the derivative of the exponential functions and the derivative of their inverses, the logarithmic functions. I extend this approach to generate formulae for the…

Two brief articles are included, one on a different method for solving percentage problems, and one on a trick for the calculator involving the sine to find one's age. (MNS)

The authors draw together a variety of facts concerning a nonlinear differential equation and compare the exact solution with approximate solutions. Then they provide an expository introduction to the elliptic sine function suitable for presentation in undergraduate courses on differential equations. (MNS)

An old way to determine asymptotes for curves described in polar coordinates is presented. Practice in solving trigonometric equations, in differentiation, and in calculating limits is involved. (MNS)

Some traditional and some less conventional approaches using the cotangent to solve the same problem are described. (MNS)

Uses a variation of Hansen's surveyor problem to illustrate how exploring students' assumptions can lead to interesting mathematical insights. Describes methods that utilize self-stick notes and overhead transparencies to adapt computer software to specific classroom needs. (MDH)

Argues that the derivation of the area of a circle using integral calculus is invalid. Describes the derivation of the area of a circle when the formula is not known by inscribing and circumscribing the circle with regular polygons whose areas converge to the same number. (MDH)

Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, and regular features that present book and software reviews and math problems. The first of two issues of volume 9…