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…

Examples and solutions to these problems are presented. Figures for which different equations are necessary are presented. The use of the geoboard for this exploration is emphasized. (CW)

The experiences of elementary teachers who invited their students to verify geometric theorems prior to the introduction of protractors form the basis of a pedagogical strategy for a sequence of learning activities offered here. Discussion focuses on the students learning strategies about angle concepts utilizing the dynamic interpretation of a…

This book offers ideas to enrich instruction and help teachers explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, the symmetries, patterns, processes, paradoxes, and surprises that have facilitated generations of great thinkers are revealed. Activities include: (1) The Beauty in…

This guidebook is designed to assist teachers and other local school district personnel in the planning and the teaching of the high school geometry course, with essential elements as mandated by the Texas State Board of Education in 1989. Research on student learning in geometry provides the logical rationale for the instructional sequencing and…

Described is a two-week summer residential program designed for students who have been identified through one of several middle school talent searches. Discussed are the assumptions and goals, course content and pedagogy, evaluation, and materials of the program. (CW)

Properties of information most likely to attract student attention and how students use information they generate are clarified. Students' expectations of empirical information in geometry and the design of a new version of the Geometric Supposer are discussed. (CW)

A method for helping students to find formulas involving symmetry under various conditions is explained. Necklace symmetries, orbit counting, tetrahedra and cubes, relationship patterns, and finding patterns are discussed. (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)

Described is a short program for teaching and learning about geometric transformations. The integration of geometry problem solving and BASIC programing is discussed. Applications of computer graphics are illustrated. (CW)

Mathematical fiction writing as a learning tool is discussed utilizing an actual example of a student's fictional text related to the field of geometry. Commentary about this example and how it relates to other areas of mathematics can provide teachers with insight into students' schema for organization and internalization of mathematical…

Described are ways in which some teachers have used a software package called "The Geometric Supposer." The development of inquiry skills is stressed. Recommendations for students using the Supposer are provided. (CW)

Described and evaluated are microcomputers as a tool for construction in geometry education and heuristic theorem finding through interactive continuous variation of geometric configurations. Numerous examples of theorem finding processes are provided using the prototype graphics system CABRI-Geometer. (MDH)

Describes an intermediate level, college geometry course that is designated as both writing and speaking intensive. Suggests methods that utilize writing and speaking activities to enhance student learning, and discusses student reactions to the course. (nine references) (JJK)

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)