This book introduces concepts of geometry that students use throughout middle-grade and higher-level mathematics courses. These concepts, presented through the study of transformations, provide a framework for other important topics such as number, measurement, proportional reasoning, and graphing on the coordinate plane. The book is designed for…

An enrichment activity used in sixth and seventh grade mathematics classes to develop geometric concepts is presented. (JG)

An activity unit is described that helps children recognize the inside and outside of closed curves. (MP)

Illustrates how mathematicians work and do mathematical research through the use of a puzzle. Demonstrates how general rules, then theorems develop from special cases. This approach may be used as a research project in high school classrooms or math club settings with the teacher helping to formulate questions, set goals, and avoid becoming…

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)

An exercise which relates particle scattering and the calculation of cross-sections to answer the following question--"Do you get wetter by walking or running through the rain?"--is described. The calculations used to answer the question are provided. (KR)

Considers teaching strategies to help children overcome misconceptions and difficulties with the mathematical concept of angles. (ASK)

With both "Cabri" and "Autograph" now venturing into 3D, the dimension that previously was only demonstrated in the classroom with a lot of arm waving and crude wire cages can now be explored dynamically on screen. "Cabri 3D" concentrates on constructions, using the principles of Euclidian geometry, whereas "Autograph" creates objects using a…

Several examples proved Van Hiele theory to be a useful ingredient in teaching of a summer course for high school students who had failed geometry during the school year are discussed. The theory provided a framework to help organize and reflect upon instruction for some key concepts in geometry.

This paper gives a broad descriptive account of some activities that the author has designed using Sketchpad to develop teachers' understanding of other functions of proof than just the traditional function of 'verification'. These other functions of proof illustrated here are those of explanation, discovery and systematization (in the context of…

This article details an exploration of Baravelle spirals as visual representations of infinite geometric series, focusing on a variety of strategies used by preservice teachers in discovering patterns and investigating relationships of variables.

In this paper, we will focus on an innovative way to teach some of the engineering fundamentals at the freshman level in an introductory engineering class. Unfortunately, today many students graduate without a good grasp of these fundamental concepts--concepts that every engineer, regardless of his or her area of specialization, should know. In…