Describes the mathematics of cycloidal curves. Illustrates how a Spirograph can be used to produce them. Discusses some modifications and applications of the Spirograph. (YP)

Describes seven spatial abilities related to mathematics including eye-motor coordination, figure-ground perception, perceptual constancy, position-in-space perception, perception of spatial relationships, visual discrimination, and visual memory. Discusses the relationship of the spatial abilities to the study of geometry. Lists 19 references.…

Illustrates how heuristics can provide a psychological narrative of Hippocrates' and Archytas' thinking on the duplication of the cube. Four general heuristic techniques were used. (YP)

Describes the algorithm used to select a simple random sample of certain size without having to list all possible samples and a justification based on Pascal's triangle. Provides testing results by various computers. (YP)

Discusses the notions and language of spatial relations of various cultures, particularly those of deaf students. (MKR)

Discusses classroom activities that involve applications of fractal geometry. Includes an activity sheet that explores Pascal's triangle, Sierpinsky's gasket, and modular arithmetic in two and three dimensions. (Author/MKR)

Discusses important mathematical ideas taken from combinatorics, arithmetic, and geometry which are considered in the context of their development in various societies around the globe, including Hebrew, Islamic, Italian, Mayan, German, and Anasazi work. (11 references) (MKR)

The question "What shape will have the largest area for a given perimeter?" identifies an important relationship between area and perimeter that has long been intuitively realized in many cultures. Historically, numerous cultures have made use of this relationship between area and perimeter when struggling to build dwellings with shapes…

Shows various methods of folding and cutting 4-, 5-, 6-, 7-, 9-, and 11-pointed stars. Discusses the geometry underlying each method. (MKR/SW)

Describes a variety of methods for creating star patterns using overlapping rectangles of thin colored paper. (MKR)

Results of 6 experiments involving 200 Australian elementary and secondary school students support the hypothesis that negative consequences of the split attention effect in geometry may be ameliorated by presenting geometry statements in auditory rather than visual form. (SLD)

Presents 10 creative, informal, intuitive geometry activities that stress higher-order thinking. (MKR)

Describes the use of formal writing and speaking in upper level geometry and analysis courses. Includes student journals, students reviewing written proofs with a student writing associate, and simulated conferences. Includes a 16-item list of possible topics. (Author/MKR)

Proposes that the writing of proofs in geometry class can be a vehicle for attaining the goals of problem solving, reasoning, and communication in the mathematics classroom. Presents a student-teacher dialogue illustrating this process. (11 references) (MKR)

A preservice teacher education course involving the applications for a computer within the mathematics classroom is described in terms of its evolution from a workshop to a regular curricular offering. Included are samples of computer experiments which suggest computer teaching activities for the prospective teacher lacking in field experience.…