Previous work has identified four areas of difficulty that students seem to have with the topic of similarity: (1) understanding the definition of similarity; (2) proportional reasoning; (3) dimensional growth relationships; and (4) correspondences in right triangle similarity. This paper reports the results of an investigation into high school…

Describes the solution to a geometric problem by two ninth-grade mathematicians using The Geometer's Sketchpad computer software program. The problem was to divide any line segment into a regular partition of any number of parts, a variation on a problem by Euclid. The solution yielded two constructions, one a GLaD construction and the other using…

Describes the stages of a process of reflective thinking. Investigates how geometrical models can be used in learning and teaching mathematics in connection with the process. Identifies two models for children of age four to eight: constant path in the space of shapes and continuous path of varied polygonal shapes. (Author/YP)

Described is a computer algorithm for obtaining the coordinates of vertices, chord factors, and dihedral angles for plotting orthographic and axonometric projections, and for tabulating chord lengths and dihedral angles. (Author)

Graphical representations of geometrical objects from high school textbooks are categorized according to the implicit conventions underlying their display. The fact that specific illustrations can lead to students' misconceptions about geometric objects is analyzed in relationship to the principle of parallel projection with implications for the…

The production and application of images based on fractal geometry are described. Discussed are fractal language groups, fractal image coding, and fractal dialects. Implications for these applications of geometry to mathematics education are suggested. (CW)

Identified are three obstacles which students must overcome when examining and interpreting diagrams. The resources of the Geometric Supposer, a set of microcomputer tools designed to aid students, are outlined. The advantages of the use of this software are emphasized. (CW)

After observing secondary school students having great difficulty learning geometry in their classes, Dutch educators Pierre van Hiele and Dina van Hiele-Geldof developed a theoretical model involving five levels of thought development in geometry. It is the purpose of this monograph to present English translations of some significant works of the…