Archimedes viewed the method of centroids as a valuable tool for intuitive discoveries. This article presents several uses of this technique and discusses how the method of centroids could be used in secondary schools. (Author/MK)

Contains an analysis of the activities of 12-year-old students solving problems of polygonal tilings and presents two categories of the thinking processes of these students: instantaneous thinking resulting in perceptions of simple structures and discursive thinking appearing in drawing activities and arguments of proofs. (13 references)…

Presents five worksheets that contain hands-on geometry activities dealing with the ideas of quadrilateral, trapezoid, parallelogram, isosceles, kite, axis of symmetry, and rhombus. (MKR)

Criteria for a reasonable axiomatic system are discussed. A discussion of the historical attempts to prove the independence of Euclids parallel postulate introduces non-Euclidean geometries. Poincare's model for a non-Euclidean geometry is defined and analyzed. (LS)

These exercises explore both square and nonsquare rhombi constructed on dot-paper grids. The materials are designed to provide reinforcement of geometric concepts, construction of figures from their symmetric properties, and discovery of figures related to each other by transformations. Student access to geoboards is encouraged as helpful. (MP)

A system of area measurement developed for the isometric geoboard is used to justify some relationships that are often proved using square units of area. (Author/MK)

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)

Describes some student explorations of angle rotations and of reasonable and unreasonable conjectures using the Geometer's Sketchpad. (MKR)

Discusses partitioning and hierarchical types of classification, a theoretical analysis of the role and function of hierarchical classification in mathematics, and the teaching of a hierarchical classification of quadrilaterals. (Contains 21 references.) (MKR)

Outlined are the minimum requirements for a quinmester course of introduction to high school geometry. After a description of the course content and overall goals, further details are presented in nine sections. Each section gives performance objectives, textbook references, content (including lists of vocabulary and associated properties), and…

A method is given for the analysis of geodesic domes involving plane geometry. The method shows how to calculate all necessary angles and chords, given the length of one side. (MP)

In response to low achievement in mathematics at a middle school, an ethnomathematic approach was used to teach coordinate planes. Whether there were achievement differences between students taught by the culturally sensitive approach and those taught by a traditional method was studied. Data were collected from the coordinate planes unit…