As teachers working with students in entry-level algebra classes, authors Amy Nebesniak and A. Aaron Burgoa realized that their instruction was a major factor in how their students viewed mathematics. They often presented students with abstract formulas that seemed to appear out of thin air. One instance occurred while they were teaching students…

In mathematics, as in baseball, the conventional wisdom is to avoid errors at all costs. That advice might be on target in baseball, but in mathematics, avoiding errors is not always a good idea. Sometimes an analysis of errors provides much deeper insights into mathematical ideas. Certain types of errors, rather than something to be eschewed, can…

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…

This article provides for a fast extremely accurate approach to graphing functions that is based on learning function reference graphs and then applying algebraic transformations to these reference graphs.

This article describes an activity for developing the notion of association between two quantitative variables. By exploring a collection of scatter plots, the authors propose a nonstandard "intuitive" measure of association; and by examining properties of this measure, they develop the more standard measure, Pearson's Correlation Coefficient. The…

Describes a five-step graphing method for various trigonometric periodic functions. Emphases is on teaching constants and functions. (YP)

Discusses solving inequality problems involving linear programing. Describes the usual and alternative approaches. Presents an intuitive approach for finding a feasible solution by maximizing the objective function. (YP)

Describes a way of using multiple representations to help students learn data analysis and make sense out of a large amount of data. Includes an activity for a group-learning environment. (KHR)

Discusses when to use the computer, paper-and-pencil, or mental-computation procedures. Provides examples of solving problems dealing with roots of polynomial using computer graphing and other strategies. Suggests implications for curricular planning. (YP)

Discusses the use of graphing calculators for polar and parametric equations. Presents eight lines of the program for the graph of a parametric equation and 11 lines of the program for a graph of a polar equation. Illustrates the application of the programs for planetary motion and free-fall motion. (YP)

Describes four laboratory activities in algebra and precalculus classes that provide hands-on experiences related to functions: slowing down the acceleration of gravity; calculating the acceleration of gravity; generating a parabola using a steel ball and a tilted board; and photographing projectile motion. (YP)

The formula used by the telephone company to determine long distance charges is presented and several sample problems are included. (MP)

Suggests that in the mathematics classroom the federal income tax may serve as a familiar example to illustrate several aspects of the mathematical concept of function. (PK)

This section provides mathematical activities in reproducible formats appropriate for students in grades 8-10. The activity is designed to provide an experience in model building while developing the concept of slope. (PK)