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-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.
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