-Explores the development of elementary students’ understanding of the mathematics of measure, demonstrating how measurement can serve as an anchor for supporting a deeper understanding of future mathematics learning, as well as learning in other STEM disciplines. -Describes a learning progression built on benchmarks of student learning about measure in length, angle, area, volume, and rational number, exploring related concepts, classroom experiences, and instructional practices at each stage—an approach relevant for scholars, teacher educators, and specialists in math education. -Written by two leading researchers in math and science education, who draw from decades of experience in K-5 classroom research. -Accompanied by online resources developed for practitioners, including instructional guides, examples of student thinking, and other teacher-focused materials, helping clarify how to bring concepts of measure and rational number to life in classrooms.

-Explores the development of elementary students’ understanding of the mathematics of measure, demonstrating how measurement can serve as an anchor for supporting a deeper understanding of future mathematics learning, as well as learning in other STEM disciplines. -Describes a learning progression built on benchmarks of student learning about measure in length, angle, area, volume, and rational number, exploring related concepts, classroom experiences, and instructional practices at each stage—an approach relevant for scholars, teacher educators, and specialists in math education. -Written by two leading researchers in math and science education, who draw from decades of experience in K-5 classroom research. -Accompanied by online resources developed for practitioners, including instructional guides, examples of student thinking, and other teacher-focused materials, helping clarify how to bring concepts of measure and rational number to life in classrooms.

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.

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.

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.

First Published in 2004. This special issue of Cognition and Instruction features three manuscripts investigating particular aspects of classroom participant structures, specifically in the context of science instruction. Participant structures is a term introduced four decades ago to describe the roles, rights, and responsibilities regarding who can say what, to whom, and when in the course of classroom activity.

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.

First Published in 2004. This special issue of Cognition and Instruction features three manuscripts investigating particular aspects of classroom participant structures, specifically in the context of science instruction. Participant structures is a term introduced four decades ago to describe the roles, rights, and responsibilities regarding who can say what, to whom, and when in the course of classroom activity.

How can you introduce terms from geometry and measurement so that your students' vocabulary will enhance their understanding of concepts and definitions? What can you say to clarify the thinking of a student who claims that perimeter is always an even number? How does knowing what changes or stays the same when shapes are transformed help you support and extend your students' understanding of shapes and the space that they occupy? How much do you know ... and how much do you need to know? Helping your students develop a robust understanding of geometry and measurement requires that you understand fundamental statistical concepts deeply. But what does that mean? This book focuses on essential knowledge for mathematics teachers about geometry and measurement. It is organized around three big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to geometry and measurement, the book will broaden and deepen your understanding of one of the most challenging topics for students-and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students' understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.