Discusses the compass and the straightedge in terms of Euclidean geometry. Includes a worksheet in the text. (KHR)

Provides an historical account of how proving evolved in school geometry. Explains how the two-column proof format brought stability to the course of studies in geometry. Uncovers what the nature of school geometry came to be as a result of the emphasis on student learning. Draws connections between that century-old reform and current reform…

Analyzes different solution strategies to find the area of an octagon. Describes four different generalizations of the original problem and illustrates solutions. (KHR)

Describes using children's and adults' natural curiosity when it comes to bubbles as a perfect vehicle for investigating geometry, data analysis, and measurement. (KHR)

Uses the book "Spaghetti and Meatballs for All! A Mathematical Story" to help children differentiate between the mathematical concepts of perimeter and area. (KHR)

Presents a measurement problem that can be explored by students of varying ability. Discusses aspects that make it accessible in a heterogeneous class. (YDS)

Explains the basics of spherical geometry and describes a series of activities developed for grade 6 middle school students. (YDS)

Describes using clusters of high-quality literature to support the teaching of key geometry and measurement ideas. (Contains 29 references.) (YDS)

Shows how students explored geometric properties of the South Korean flag using proportional reasoning. (YDS)

Examines activities and children's thinking in four main areas of the Geometry Standard in the National Council of Teachers of Mathematics' (NCTM) "Principles and Standards for School Mathematics": (1) properties of shapes; (2) locations and spatial relationships; (3) transformations and symmetry; and (4) visualization. (Author)

Illustrated is the use of isometric graph paper in the discovery of nonstandard area formulas. The use of definitions, geometric construction, record keeping, and conjectures about triangles, rhombuses, hexagons, parallelograms, isosceles trapezoids, rectangles, and trapezoids are described. (YP)

Challenges abstract mathematics requirements in U.S. high schools. Refutes various philosophical and psychological assumptions underlying math instruction, particularly the correlation between simple numbers and the physical world, the math/logical thinking connection, and frequency of use arguments. Suggests that high schools require only one…

Presents an activity in which students use geometric figures, rep-tiles, to design a tile floor. Rep-tiles are geometric figures of which copies can fit together to form a larger similar figure. Includes reproducible student worksheet. (MKR)

Presents an activity, involving pentagons and using a figure manipulator such as The Geometer's Sketchpad, that requires students to reason geometrically without making unsubstantiated assumptions based on diagrams. (MKR)

Archimedes' method for estimating the value of pi is developed and compared with the Gregory-Machin infinite series method. Programs for the TI-81 calculator for finding the upper and lower bounds using the classical method and estimating pi using infinite series are provided.(Author/MKR)