Calculus has frequently been called one the greatest intellectual achievements of humankind. As a key transitional course to college mathematics, it combines such elementary ideas as rate with new abstract ideas--such as infinity, instantaneous change, and limit--to formulate the derivative and the integral. Most calculus texts begin with the…

Calculus instruction is an important topic for high school and college teachers alike. A prime target for attention is integration, which, unfortunately, students too often treat as a rote procedure. Understanding the integral better will support students' application of their mathematical knowledge to science, technology, and engineering…

Much of what is taught, especially in college, is designed to support other disciplines. To determine the current mathematical needs of twenty-three partner disciplines, the Mathematical Association of America (MAA) conducted the Curriculum Foundations Project (Ganter and Barker 2004; Ganter and Haver 2011), as discussed in the appendix…

Under the backdrop of the investigation of rational functions and their respective curved asymptotes, the reader is invited to experience the mathematical process alongside the authors and observe the application of the NCTM Process Standards and the use of multiple representations in the investigation and solution of a problem. (Contains 9…

A nontraditional approach of graphing equations using parallel axes produces some dual concepts when compared to graphing equations with the traditional perpendicular axes. (JT)

A system similar to the slope method of graphing a linear equation is described for graphing parabolas. (JT)

Methods for getting a computer-linked plotter to do a total plot of a relation are discussed. (DT)

By changing the Euclidean metric definition, a new geometry is developed. Properties of figures are analyzed and theorems are proven in this new system. (DT)

Graphs of exotic functions which can be defined using algebraic operations are discussed. (SD)

A transformation technique for graphing is described. (DT)

Curve stitching activities can be used to motivate calculus students. The problem described here involves showing that a given envelope of a curve is parabolic. (SD)