It is surprising to students to learn that a natural combination of simple functions, the function sin(1/x), exhibits behaviour that is a great challenge to visualize. When x is large the function is relatively easy to draw; as x gets smaller the function begins to behave in an increasingly wild manner. The sin(1/x) function can serve as one of…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Emphasizes the commonalities among classes of polynomial functions. Provides exploratory activities for students as well as a teacher's guide. (KHR)

A variety of applications of logarithms are presented along with suggestions about how this topic might be made more interesting and relevant in a secondary classroom. In most cases, the treatment is multi-modal using numerical, graphical and algebraic approaches.

Graphs are viewed as extremely useful tools in communication, which enable readers to see at a glance facts that might take several paragraphs to describe adequately. An ability to read graphs critically is seen to be an important objective for any elementary curriculum, and ways to introduce them are presented. (Author/MP)

A collection of brief articles on mathematics and teaching mathematics. (FL)

Discusses how grocery shopping activities can help primary and intermediate grade students develop mathematics skills useful in real life. (BB)

Differing treatments of graphs in mathematics and science are discussed. A teaching sequence to develop contrasts between real and ideal data is suggested. (MP)

Uses the process of normalization in the Cartesian coordinate system which entails radial projection onto a transect to compare different compositions of minerals. Warns that the ternary diagram should not be used as a framework for calculations. (MVL)

The focus of these four activities is on gathering, using and interpreting data about bicycles as a basis for integrating mathematics. Measurement, ratios, and other relationships are explored through making graphs, finding bicycling speeds and a parent-involvement activity sheet. (CW)

Discusses a classroom presentation using a Tonka toy truck's forward and backward motion that (1) develops a graphical representation of the truck's one-dimensional motion; (2) creates graphs representing constant velocity; (3) leads students to a definition of average velocity; and (4) introduces the concept of instantaneous velocity. (MDH)

Several studies have shown the difficulties students encounter in making sense of situations involving rate of change. This study concerns how students discover errors and refine their knowledge when working with rate of change. The part of the study reported here concerns the responses of four precalculus students to a task which asked them to…