Richard Lehrer

Daniel Chazan

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.

Designing Learning Environments for Developing Understanding of Geometry and Space

Adrienne Lehrer

Eva Feder Kittay

Recently, there has been a surge of interest in the lexicon. The demand for a fuller and more adequate understanding of lexical meaning required by developments in computational linguistics, artificial intelligence, and cognitive science has stimulated a refocused interest in linguistics, psychology, and philosophy. Different disciplines have studied lexical structure from their own vantage points, and because scholars have only intermittently communicated across disciplines, there has been little recognition that there is a common subject matter. The conference on which this volume is based brought together interested thinkers across the disciplines of linguistics, philosophy, psychology, and computer science to exchange ideas, discuss a range of questions and approaches to the topic, consider alternative research strategies and methodologies, and formulate interdisciplinary hypotheses concerning lexical organization. The essay subjects discussed include: * alternative and complementary conceptions of the structure of the lexicon, * the nature of semantic relations and of polysemy, * the relation between meanings, concepts, and lexical organization, * critiques of truth-semantics and referential theories of meaning, * computational accounts of lexical information and structure, and * the advantages of thinking of the lexicon as ordered.

Richard Lehrer

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