Presents an activity using similar rectangles to help children conceptualize ratio relationships in several different ways. Develops proportional reasoning without introducing the process of cross- multiplication. (YDS)

Discusses ways in which teachers can use the appealing study of quilts as a tool for teaching mathematics concepts and connecting multicultural history, literacy, and art. (Author/NB)

Describes how Thales, one of the Seven Sages of ancient times, used shadows and similar triangles to measure the heights of the pyramids. Includes activities on surveying. (YDS)

Investigates problems called "cranium crackers" and focuses on number sense, logical reasoning, data analysis, geometry, measurement, and algebraic thinking. (Author/NB)

Presents a discovery lesson in which students investigate the limit of angle measures formed by repeatedly folding a strip of paper. (KHR)

Describes the idea of teaching as active learning and defines direction in mathematics teaching as action and perception. Presents an example of a mathematics classroom activity in which students are centered. (KHR)

The exploration, discovery, and generation of attractive two-dimensional designs as an approach to informal geometry and spatial learning is discussed. Six activities with brief instructions are presented. (CW)

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…