Describes three activities in discrete mathematics that involve coloring geometric objects: counting colored regions of overlapping simple closed curves, counting colored triangulations of polygons, and determining the number of colors required to paint the plane so that no two points one inch apart are the same color. (MKR)

Discusses the value of student self-assessment in promoting students' confidence in their ability to do mathematics and allowing them to become more independent in their learning of mathematics. The article describes various methods by which a student may self-evaluate and how the teacher might respond in fairly detailed examples. (AIM)

Discusses the value of journal assignments for diagnosing and trouble-shooting misconceptions and for helping with lesson plans. Examples of assignments are included as well as student responses. (AIM)

Presents five guided activities that use a graphing calculator to help students discover the fundamental theorem of algebra. Includes student worksheets and illustrates solutions. (KHR)

Presents a classification of factorable cubics and shows how the associated factor graphs determine domains of disconnected branches and furnish a skeletal framework for the number and shape of the branches. Illustrates three dimensional visualization and examines level curves and spikes of surfaces. (KHR)

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

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

Discusses what a good model of student assessment is, recommends the National Council of Teachers of Mathematics' (NCTM) Assessment Standards for School Mathematics (1995), and describes how it works. Suggests criteria for relevant assessment items with examples. (KHR)

Presents a recounting of the work of Kepler and Wiles, great minds who made a tangible impact on the field of mathematics but who had to overcome seemingly insurmountable roadblocks. (KHR)

Analyzes different solution strategies to find the area of an octagon. Describes four different generalizations of the original problem and illustrates solutions. (KHR)

Presents activities designed to engage students in an experiential and theoretical application of problems in precalculus and to study geometry, coordinate systems, rates, linear applications, and the concept of function. Illustrates problem situations and includes student worksheets and a teacher's guide. (KHR)

Introduces RSA, one of the most popular public-key cryptosystems that is used to protect the privacy of computer users. Describes the mathematical foundation of public key cryptography. (KHR)

Presents problems designed to focus student attention on the visual representations that accompany the verbal statements of problem situations involving motion over a period of time. Shows that as a result of engaging in these activities, students gain a better understanding of a given problem situation before they apply procedures to answer…

Investigates the idea of the center of mass of a polygon and illustrates centroids of polygons. Connects physics, mathematics, and technology to produces results that serve to generalize the notion of centroid to polygons other than triangles. (KHR)

Provides classroom suggestions for combining numerical, algebraic, and geometric techniques with the understanding of a simple method for computing square roots. Historical origins of the method illustrate the debt owed to ancient minds living in what are now India, Pakistan, Iraq, and Egypt. (Author/NB)