This study investigated the understanding of and reasoning about geometry of 120 mathematically talented students in the sixth through eight grades prior to taking a course in geometry. Results found that, although the students were able to deduce meaning from context, they lacked understanding of basic definitions, concepts, and properties.…

Presents new proofs of the Pythagorean theorem while exploring examination questions. Briefly reviews the work of Elisha Scott Loomis, a mathematician who amassed 320 different proofs of the theorem. (DDR)

Shows how an empirical approach to geometry using computer-based dynamic geometry software can create didactic situations in which students require proofs. Reports classroom experiences that show where students felt the need for proof in order to explain phenomena or to convince themselves of counterintuitive results. (Author/MKR)

Describes three activities in discrete mathematics that involve coloring geometric objects: counting colored regions of overlapping simple closed curves, counting colored triangulations of polygons, and determining the number of colors required to paint the plane so that no two points one inch apart are the same color. (MKR)

Includes lesson plans and worksheets that deal with transformational geometry, specifically reflections. The lesson for grades three to four focuses on angles of incidence and reflection and that for grades five to six involves mirror images. (MKR)

Presents an inexpensive laboratory experiment that combines the recommended techniques for teaching fractal geometry in the classroom with the standard procedures for studying electrochemical deposition of ramified patterns in the regime of low solution concentration and low applied constant driving force. Introduces students to fractal growth…

Presents a perspective on the nature of the use of proofs in high school geometry. Compares three currently used approaches to the geometry curriculum: (1) traditional geometry with no explanation of the axiomatic system; (2) hands-on geometry with no proofs until the end of the course; and (3) experimental geometry with no proofs. (DDR)

Provides suggestions for implementing the geometry standards in an elementary curriculum by including all aspects of geometry. (KHR)

Analyzes one student's thinking using the Van Hiele levels of geometric thinking. (KHR)

Describes lessons with year 7 and year 9 classes that used the ATM Active Geometry package. Presents the main activities and how to use prepared files in the geometry package for mathematics instruction. (KHR)

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)