Two well-known theorems from geometry are shown to be essentially the same using the principle of duality of lines and points. (MP)

Six conjectures are established concerning a rectangular solid with the lengths of all its face diagonals and the lengths of all its edges being positive integers. (MP)

The simultaneous solution of equations in polar form does not always yield the points of intersection of their graphs. An explanation is given. (MP)

The effect of four variables (number of steps, superfluous information, verbal cue, and question) on problem solving performance was investigated. A total of 800 junior high students from five schools responded to four different types of questions. Three variables were found to be significant: questions, steps, and superfluous information. (DT)

Conditions for congruency of triangles are investigated. (DT)

The organization of several mathematics competitions within the United States is described. Sample contest problems are included. (DT)

The geometric notions of tangent, secant, and sine are explored. (DT)

Presents activities for teaching the logistic growth model using calculators and spreadsheets. (ASK)

Provides information on knot theory and its properties. Presents an activity for grades 9-12 on the applications of knot theory and some unsolved questions in the theory. (ASK)

Describes the need for standards based reform to improve student achievement, examining the Mathematics Achievement Partnership (MAP), which brings together a consortium of states to jointly develop key components of standards-based reform focused on middle school mathematics and culminating with an end-of-eighth-grade assessment. Components…

Provides activities that support students as they develop their intuitive notions of graphs. Activities help students describe the relationships expressed in the graphs and make generalizations about inferences on the basis of the visual image. (ASK)

Demonstrates a way to develop the concept of the logarithmic function that builds on students' knowledge of the definition of a function and its inverse. (ASK)

Describes an activity involving six investigations. Introduces students to fractals, allows them to study the properties of some famous fractals, and encourages them to create their own fractal artwork. Contains 14 references. (ASK)

Discusses cooperative learning and describes a method of implementing a cooperative-learning setting called Exchange of Knowledge. Contains 28 references. (ASK)

Derives lessons from the human process of constructing the proof of Fermat's last theorem such as serious mathematical thinking takes time as well as intellectual courage and skills. (ASK)