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Designing Learning Environments for Developing Understanding of Geometry and Space : Studies in Mathematical Thinking and Learning - Richard Lehrer

Designing Learning Environments for Developing Understanding of Geometry and Space

Studies in Mathematical Thinking and Learning

By: Richard Lehrer (Editor), Daniel Chazan (Editor)

Paperback Published: 1st October 1998
ISBN: 9780805819496
Number Of Pages: 518

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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.

Preface
Why Teach Geometry?
A Role for Geometry in General Education
From a Different Perspective: Building on Students' Informal Knowledge
Charting a Course for Secondary Geometry
Chaos in the Classroom
Studies of Conceptual Development.
Interpreting Student Understanding in Geometry: A Synthesis of Two Models
Longitudinal Study of Children's Reasoning About Space and Geometry
Developing Understanding of Space and Geometry in the Primary Grades
Development of Geometric and Measurement Ideas
Students' Understanding of Three-Dimensional Cube Arrays: Findings From a Research and Curriculum Development Project
Sixth Grade Students' Conceptions of Stability in Engineering Contexts
Interconnecting Science and Mathematics Concepts: Area and Volume
Geometric Curve-Drawing Devices as an Alternative Approach to Analytic Geometry: An Analysis of the Methods, Voice, and Epistemology of a High School Senior
Conjecturing and Argumentation in High School Geometry Students
Defining a New Semantics of Space: Computers, Software, and the Electronic World.
What Is Dynamic Geometry?
An Alternative Approach to Proof in Dynamic Geometry
Opportunities to Explore and Integrate Mathematics With the Geometer's Sketchpad
Mapping the Classroom Using CAD Program: Geometry as Applied Mathematics
The Cognition and Technology Group at Vanderbilt
An Introduction to Geometry Through Anchored Instruction
Teachers and Students Investigating and Communicating About Geometry: The Math Forum
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780805819496
ISBN-10: 0805819495
Series: Studies in Mathematical Thinking and Learning
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 518
Published: 1st October 1998
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 23.5 x 14.61  x 3.18
Weight (kg): 0.81
Edition Number: 1