The advent of powerful, affordable output devices offers the potential for a vastly expanded landscape of computationally-enriched mathematical craft activities in education. Craft activities have both intellectual and emotional affordances that are relatively lacking in "traditional" computer-based education. Describes three software applications…

Investigates what the role of arguments from physics within mathematical proof is, and how this role should be reflected in the classroom. Presents examples showing the fruitfulness of center of gravity arguments in terms of geometrical configuration and the laws of the lever. Discusses educational advantages of the use of arguments from physics…

Presented is an example of a typical geometry theorem which can be used to create geometry test questions and geometry contest questions. Thirteen problems are suggested. (CW)

Four algebra problems and their solutions are presented to illustrate the use of a mathematical theorem. (CW)

Presents some examples from geometry: area of a circle; centroid of a sector; Buffon's needle problem; and expression for pi. Describes several roles of the trigonometric function in mathematics and applications, including Fourier analysis, spectral theory, approximation theory, and numerical analysis. (YP)

Discusses the need for a geometry course in a two-year college mathematics program. Provided are guidelines for developing the geometry course separately or integrally with current curricular pattern. (25 references) (YP)

A problem concerning circles and points from a comic strip is presented. Its solution, using coordinate geometry, is then presented. The problem demonstrates how much one can learn by looking beyond the simple or partial solutions to a problem. (MNS)

An easier-to-understand alternative to the usual proofs of inequalities in triangles is presented. (MNS)

Presents a model for teaching reasoning using technology in the contexts of algebra and geometry. (MKR)

Includes two activities: (1) a skit to review variations of the trigonometric functions, and (2) a geometry problem about maximizing costs that exposes students to a variety of different solution strategies and makes the material more meaningful. (MKR)

Describes two problem-solving videodisc adventure stories related to geometry and reports reactions of (n=25) teachers and their students who used the adventures. Results found teachers and students had increased knowledge of ways to apply geometry. (12 references) (MKR)

Examines research relevant to the debate about the relative emphasis that formal proof should play in high school geometry. Discussion includes establishing truth in geometry, research in students' learning of proof, developing the notion of proof, alternatives to axiomatic approaches, computer construction programs, and classroom recommendations.…

Examines how ancient Chinese mathematicians attempted to correct an error concerning the volume of a sphere in the Nine Chapters on the Mathematical Art, a compendium of the mathematics known and used in China in ancient times. (MKR)

Introduces a strategy for writing equations of graphs to help students and teachers build strong conceptual connections between the symbolic representations of algebra and the spatial representations of geometry. (Author/MKR)

A series of spatial tasks involving conceptualization and manipulation of unfamiliar plane shapes administered to (n=20) children aged 4 to 12 revealed that both initial perception of a shape and approach to task solution strongly influenced children's success at shape recognition. (20 references) (Author/MKR)