While teaching a methods class for preservice secondary school mathematics teachers, Christopher E. Smith found that although all students could draw a reasonably close approximation of a circle, not all could provide an entirely accurate definition of a circle. A discussion with students led him to think about ways of reintroducing students to…

Graphing bivariate data in a scatter plot and drawing an approximate line of best fit for the data have become commonly recommended activities for middle school and high school students. The graphing calculator has provided a mechanism for students both to approximate a best-fit line and to calculate the best-fit line using a built-in option. Two…

The inquiry-based approach to learning has gained popularity in recent times. Those who promote this approach maintain that mathematical investigation should be used to engage students. The National Council of Teachers of Mathematics (NCTM) recommends that problem solving be the center of mathematics teaching in promoting student learning through…

This article provides an overview of vertex-edge graphs as an essential topic in the high school mathematics curriculum, including rationale, recommendations, and sample applications. A classroom-ready activity with full teacher notes is also included. (Contains 1 table and 9 figures.)

This article describes two alternative coordinate systems and their use in graphing conic sections. This alternative graph paper helps students explore the idea of eccentricity using the definitions of the conic sections.

Topics covered are: a game to provide drill with linear equations; the relationship between area and perimeter in a triangle; a new form for factoring polynomials; and a technique for graphing inverse functions. (MP)

A geometric approach to the solution of quadratic equations and more general polynomials is based on finding points with minimum distance from the x-axis. The approach is useful in motivating the definition of complex numbers. (SD)

Some of the graphing capabilities of The Geometer's Sketchpad (GSP) in the "Technology Tips" are introduced. The new graphing features of GSP allow teachers to implement the software not only in geometry classrooms but also into their algebra, precalculus and calculus classes.

A mathematical derivation is given, developing the cardioid as an epicycloid locus. Curve-stitched designs are given for a family of epicycloids. (MP)

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)

Discusses the use of a dynamic geometry software package to improve teaching of graph theory in basic graph sketching and in isomorphic, bipartite, and planar graphs. (JRH)