Offers heuristic arguments showing that a simple closed curve of specified length that encloses a maximum area must be a circle. Develops the problem by demonstrating that such an n-gon must be convex, that such a convex n-gon must be regular, and that such a simple closed curve must be a circle. (MDH)

Presents an activity in which students develop their own theorem involving the relationship between the triangles determined by the squares constructed on the sides of any triangle. Provides a set of four reproducible worksheets, directions on their use, worksheet answers, and suggestions for follow-up activities. (MDH)

Describes the process of problem identification, data collection, and generalization in a mathematical experiment to find the speed at which a bug travels at the end of a fan blade. Presents the learning outcomes of the experiment and possible implications of using this teaching method. (MDH)

Presents three stories from mathematics history that can be integrated into classroom teaching: (1) the account of how Eratosthenes measured the circumference of the earth to discuss the concept of units in measurement, (2) ideas from Archimedes, Vite, and Descartes to introduce pi, and (3) the discovery of the Cardanic formula as an example of…

Presents two activities that utilize problem solving to promote concept development. The first uses a treasure hunt to teach locus of points. The second uses a tug-of-war model to teach mixture problems involving ratios. (MDH)

Described is an alternative first year algebra program developed to bridge the gap between the NCTM's Curriculum and Evaluation Standards and institutional demands of schools. Increased attention is given to graphing as a context for algebra, calculator use, solving "memorable problems," and incorporating geometry concepts, while…