ABSTRACT

This volume reflects an appreciation of the interactive roles of subject matter, teacher, student, and technologies in designing classrooms that promote understanding of geometry and space. Although these elements of geometry education are mutually constituted, the book is organized to highlight, first, the editors' vision of a general geometry education; second, the development of student thinking in everyday and classroom contexts; and third, the role of technologies.

Rather than looking to high school geometry as the locus--and all too often, the apex--of geometric reasoning, the contributors to this volume suggest that reasoning about space can and should be successfully integrated with other forms of mathematics, starting at the elementary level and continuing through high school. Reintegrating spatial reasoning into the mathematical mainstream--indeed, placing it at the core of K-12 mathematics environments that promote learning with understanding--will mean increased attention to problems in modeling, structure, and design and reinvigoration of traditional topics such as measure, dimension, and form. Further, the editors' position is that the teaching of geometry and spatial visualization in school should not be compressed into a characterization of Greek geometry, but should include attention to contributions to the mathematics of space that developed subsequent to those of the Greeks.

This volume is essential reading for those involved in mathematics education at all levels, including university faculty, researchers, and graduate students.

part 1|104 pages

Why Teach Geometry?

chapter 2|22 pages

From a Different Perspective

Building on Students' Informal Knowledge

chapter 4|14 pages

Chaos in the Classroom

part 2|243 pages

Studies of Conceptual Development

chapter 5|27 pages

Interpreting Student Understanding in Geometry

A Synthesis of Two Models

chapter 9|22 pages

Students' Understanding of Three-Dimensional Cube Arrays

Findings from a Research and Curriculum Development Project

chapter 12|22 pages

Geometric Curve-Drawing Devices as an Alternative Approach to Analytic Geometry

An Analysis of the Methods, Voice, and Epistemology of a High-School Senior

part 3|139 pages

Defining A New Semantics of Space

chapter 17|20 pages

Mapping the Classroom Using a CAD Program

Geometry as Applied Mathematics

part |6 pages

Epilogue