|
Showing 1 - 14 of
14 matches in All Departments
To define better techniques of mathematics education, this book
combines a knowledge of cognitive science with mathematics
curriculum theory and research. The concept of the human reasoning
process has been changed fundamentally by cognitive science in the
last two decades. The role of memory retrieval, domain-specific and
domain-general skills, analogy, and mental models is better
understood now than previously. The authors believe that cognitive
science provides the most accurate account thus far of the actual
processes that people use in mathematics and offers the best
potential for genuine increases in efficiency. As such, they
suggest that a cognitive science approach enables constructivist
ideas to be analyzed and further developed in the search for
greater understanding of children's mathematical learning.
Not simply an application of cognitive science, however, this book
provides a new perspective on mathematics education by examining
the nature of mathematical concepts and processes, how and why they
are taught, why certain approaches appear more effective than
others, and how children might be assisted to become more
mathematically powerful. The authors use recent theories of analogy
and knowledge representation -- combined with research on teaching
practice -- to find ways of helping children form links and
correspondences between different concepts, so as to overcome
problems associated with fragmented knowledge. In so doing, they
have capitalized on new insights into the values and limitations of
using concrete teaching aids which can be analyzed in terms of
analogy theory.
In addition to addressing the role of understanding, the authors
have analyzed skill acquisition models in terms of their
implications for the development of mathematical competence. They
place strong emphasis on the development of students' mathematical
reasoning and problem solving skills to promote flexible use of
knowledge. The book further demonstrates how children have a number
of general problem solving skills at their disposal which they can
apply independently to the solution of novel problems, resulting in
the enhancement of their mathematical knowledge.
The Handbook of Research on STEM Education represents a
groundbreaking and comprehensive synthesis of research and
presentation of policy within the realm of science, technology,
engineering, and mathematics (STEM) education. What distinguishes
this Handbook from others is the nature of integration of the
disciplines that is the founding premise for the work - all
chapters in this book speak directly to the integration of STEM,
rather than discussion of research within the individual content
areas. The Handbook of Research on STEM Education explores the most
pressing areas of STEM within an international context. Divided
into six sections, the authors cover topics including: the nature
of STEM, STEM learning, STEM pedagogy, curriculum and assessment,
critical issues in STEM, STEM teacher education, and STEM policy
and reform. The Handbook utilizes the lens of equity and access by
focusing on STEM literacy, early childhood STEM, learners with
disabilities, informal STEM, socio-scientific issues, race-related
factors, gender equity, cultural-relevancy, and parental
involvement. Additionally, discussion of STEM education policy in a
variety of countries is included, as well as a focus on engaging
business/industry and teachers in advocacy for STEM education. The
Handbook's 37 chapters provide a deep and meaningful landscape of
the implementation of STEM over the past two decades. As such, the
findings that are presented within provide the reader with clear
directions for future research into effective practice and supports
for integrated STEM, which are grounded in the literature to date.
This third edition of the Handbook of International Research in
Mathematics Education provides a comprehensive overview of the most
recent theoretical and practical developments in the field of
mathematics education. Authored by an array of internationally
recognized scholars and edited by Lyn English and David Kirshner,
this collection brings together overviews and advances in
mathematics education research spanning established and emerging
topics, diverse workplace and school environments, and globally
representative research priorities. New perspectives are presented
on a range of critical topics including embodied learning, the
theory-practice divide, new developments in the early years,
educating future mathematics education professors, problem solving
in a 21st century curriculum, culture and mathematics learning,
complex systems, critical analysis of design-based research,
multimodal technologies, and e-textbooks. Comprised of 12 revised
and 17 new chapters, this edition extends the Handbook's original
themes for international research in mathematics education and
remains in the process a definitive resource for the field.
The Handbook of Research on STEM Education represents a
groundbreaking and comprehensive synthesis of research and
presentation of policy within the realm of science, technology,
engineering, and mathematics (STEM) education. What distinguishes
this Handbook from others is the nature of integration of the
disciplines that is the founding premise for the work - all
chapters in this book speak directly to the integration of STEM,
rather than discussion of research within the individual content
areas. The Handbook of Research on STEM Education explores the most
pressing areas of STEM within an international context. Divided
into six sections, the authors cover topics including: the nature
of STEM, STEM learning, STEM pedagogy, curriculum and assessment,
critical issues in STEM, STEM teacher education, and STEM policy
and reform. The Handbook utilizes the lens of equity and access by
focusing on STEM literacy, early childhood STEM, learners with
disabilities, informal STEM, socio-scientific issues, race-related
factors, gender equity, cultural-relevancy, and parental
involvement. Additionally, discussion of STEM education policy in a
variety of countries is included, as well as a focus on engaging
business/industry and teachers in advocacy for STEM education. The
Handbook's 37 chapters provide a deep and meaningful landscape of
the implementation of STEM over the past two decades. As such, the
findings that are presented within provide the reader with clear
directions for future research into effective practice and supports
for integrated STEM, which are grounded in the literature to date.
Mathematical and Analogical Reasoning of Young Learners provides
foundational knowledge of the nature, development, and assessment
of mathematical and analogical reasoning in young children.
Reasoning is fundamental to understanding mathematics and is
identified as one of the 10 key standards for school mathematics
for the new millennium. The book draws on longitudinal and
cross-cultural studies, conducted in the United States and
Australia, of children's reasoning development as they progressed
from preschool through the end of second grade. The multifaceted
analysis of young children's development of mathematical and
analogical reasoning focuses on individual learners, their learning
environments, and the interaction between the two. The
multidisciplinary team of authors present multiple perspectives and
multiple methodologies, and provide valuable information on
organizing and sustaining interdisciplinary and cross-cultural
inquiry. Key issues addressed include: *the relationship between
mathematical and analogical reasoning; *how changes in children's
reasoning relate to the implicit instruction they receive in their
classrooms; *analyses of the participating teachers' knowledge,
beliefs, and practices with respect to mathematical and analogical
reasoning of young learners; and *ways in which we might promote
development of mathematical and analogical reasoning in young
children. This volume is highly relevant for mathematics educators,
researchers in mathematics education, educational psychologists,
early childhood teachers, and others interested in mathematical
development of young children, in particular, the development of
their reasoning processes.
"Mathematical and Analogical Reasoning of Young Learners" provides
foundational knowledge of the nature, development, and assessment
of mathematical and analogical reasoning in young children.
Reasoning is fundamental to understanding mathematics and is
identified as one of the 10 key standards for school mathematics
for the new millennium. The book draws on longitudinal and
cross-cultural studies, conducted in the United States and
Australia, of children's reasoning development as they progressed
from preschool through the end of second grade.
The multifaceted analysis of young children's development of
mathematical and analogical reasoning focuses on individual
learners, their learning environments, and the interaction between
the two. The multidisciplinary team of authors present multiple
perspectives and multiple methodologies, and provide valuable
information on organizing and sustaining interdisciplinary and
cross-cultural inquiry. Key issues addressed include:
*the relationship between mathematical and analogical reasoning;
*how changes in children's reasoning relate to the implicit
instruction they receive in their classrooms;
*analyses of the participating teachers' knowledge, beliefs, and
practices with respect to mathematical and analogical reasoning of
young learners; and
*ways in which we might promote development of mathematical and
analogical reasoning in young children.
This volume is highly relevant for mathematics educators,
researchers in mathematics education, educational psychologists,
early childhood teachers, and others interested in mathematical
development of young children, in particular, the development of
their reasoning processes.
How we reason with mathematical ideas continues to be a fascinating
and challenging topic of research--particularly with the rapid and
diverse developments in the field of cognitive science that have
taken place in recent years. Because it draws on multiple
disciplines, including psychology, philosophy, computer science,
linguistics, and anthropology, cognitive science provides rich
scope for addressing issues that are at the core of mathematical
learning.
Drawing upon the interdisciplinary nature of cognitive science,
this book presents a broadened perspective on mathematics and
mathematical reasoning. It represents a move away from the
traditional notion of reasoning as "abstract" and "disembodied," to
the contemporary view that it is "embodied" and "imaginative." From
this perspective, mathematical reasoning involves reasoning with
structures that emerge from our bodily experiences as we interact
with the environment; these structures extend beyond finitary
propositional representations. Mathematical reasoning is
imaginative in the sense that it utilizes a number of powerful,
illuminating devices that structure these concrete experiences and
transform them into models for abstract thought. These "thinking
tools"--analogy, metaphor, metonymy, and imagery--play an important
role in mathematical reasoning, as the chapters in this book
demonstrate, yet their potential for enhancing learning in the
domain has received little recognition.
This book is an attempt to fill this void. Drawing upon
backgrounds in mathematics education, educational psychology,
philosophy, linguistics, and cognitive science, the chapter authors
provide a rich and comprehensive analysis of mathematical
reasoning. New and exciting perspectives are presented on the
nature of mathematics (e.g., "mind-based mathematics"), on the
array of powerful cognitive tools for reasoning (e.g., "analogy and
metaphor"), and on the different ways these tools can facilitate
mathematical reasoning. Examples are drawn from the reasoning of
the preschool child to that of the adult learner.
How we reason with mathematical ideas continues to be a fascinating
and challenging topic of research--particularly with the rapid and
diverse developments in the field of cognitive science that have
taken place in recent years. Because it draws on multiple
disciplines, including psychology, philosophy, computer science,
linguistics, and anthropology, cognitive science provides rich
scope for addressing issues that are at the core of mathematical
learning.
Drawing upon the interdisciplinary nature of cognitive science,
this book presents a broadened perspective on mathematics and
mathematical reasoning. It represents a move away from the
traditional notion of reasoning as "abstract" and "disembodied," to
the contemporary view that it is "embodied" and "imaginative." From
this perspective, mathematical reasoning involves reasoning with
structures that emerge from our bodily experiences as we interact
with the environment; these structures extend beyond finitary
propositional representations. Mathematical reasoning is
imaginative in the sense that it utilizes a number of powerful,
illuminating devices that structure these concrete experiences and
transform them into models for abstract thought. These "thinking
tools"--analogy, metaphor, metonymy, and imagery--play an important
role in mathematical reasoning, as the chapters in this book
demonstrate, yet their potential for enhancing learning in the
domain has received little recognition.
This book is an attempt to fill this void. Drawing upon
backgrounds in mathematics education, educational psychology,
philosophy, linguistics, and cognitive science, the chapter authors
provide a rich and comprehensive analysis of mathematical
reasoning. New and exciting perspectives are presented on the
nature of mathematics (e.g., "mind-based mathematics"), on the
array of powerful cognitive tools for reasoning (e.g., "analogy and
metaphor"), and on the different ways these tools can facilitate
mathematical reasoning. Examples are drawn from the reasoning of
the preschool child to that of the adult learner.
To define better techniques of mathematics education, this book
combines a knowledge of cognitive science with mathematics
curriculum theory and research. The concept of the human reasoning
process has been changed fundamentally by cognitive science in the
last two decades. The role of memory retrieval, domain-specific and
domain-general skills, analogy, and mental models is better
understood now than previously. The authors believe that cognitive
science provides the most accurate account thus far of the actual
processes that people use in mathematics and offers the best
potential for genuine increases in efficiency. As such, they
suggest that a cognitive science approach enables constructivist
ideas to be analyzed and further developed in the search for
greater understanding of children's mathematical learning.
Not simply an application of cognitive science, however, this book
provides a new perspective on mathematics education by examining
the nature of mathematical concepts and processes, how and why they
are taught, why certain approaches appear more effective than
others, and how children might be assisted to become more
mathematically powerful. The authors use recent theories of analogy
and knowledge representation -- combined with research on teaching
practice -- to find ways of helping children form links and
correspondences between different concepts, so as to overcome
problems associated with fragmented knowledge. In so doing, they
have capitalized on new insights into the values and limitations of
using concrete teaching aids which can be analyzed in terms of
analogy theory.
In addition to addressing the role of understanding, the authors
have analyzed skill acquisition models in terms of their
implications for the development of mathematical competence. They
place strong emphasis on the development of students' mathematical
reasoning and problem solving skills to promote flexible use of
knowledge. The book further demonstrates how children have a number
of general problem solving skills at their disposal which they can
apply independently to the solution of novel problems, resulting in
the enhancement of their mathematical knowledge.
This book conceptualizes the nature of mathematical modeling in the
early grades from both teaching and learning perspectives.
Mathematical modeling provides a unique opportunity to engage
elementary students in the creative process of mathematizing their
world. A diverse community of internationally known researchers and
practitioners share studies that advance the field with respect to
the following themes: The Nature of Mathematical Modeling in the
Early Grades Content Knowledge and Pedagogy for Mathematical
Modeling Student Experiences as Modelers Teacher Education and
Professional Development in Modeling Experts in the field provide
commentaries that extend and connect ideas presented across
chapters. This book is an invaluable resource in illustrating what
all young children can achieve with mathematical modeling and how
we can support teachers and families in this important work.
This book conceptualizes the nature of mathematical modeling in the
early grades from both teaching and learning perspectives.
Mathematical modeling provides a unique opportunity to engage
elementary students in the creative process of mathematizing their
world. A diverse community of internationally known researchers and
practitioners share studies that advance the field with respect to
the following themes: The Nature of Mathematical Modeling in the
Early Grades Content Knowledge and Pedagogy for Mathematical
Modeling Student Experiences as Modelers Teacher Education and
Professional Development in Modeling Experts in the field provide
commentaries that extend and connect ideas presented across
chapters. This book is an invaluable resource in illustrating what
all young children can achieve with mathematical modeling and how
we can support teachers and families in this important work.
This book emanated primarily from concerns that the mathematical
capabilities of young children continue to receive inadequate
attention in both the research and instructional arenas. Research
over many years has revealed that young children have sophisticated
mathematical minds and a natural eagerness to engage in a range of
mathematical activities. As the chapters in this book attest,
current research is showing that young children are developing
complex mathematical knowledge and abstract reasoning a good deal
earlier than previously thought. A range of studies in prior to
school and early school settings indicate that young learners do
possess cognitive capacities which, with appropriately designed and
implemented learning experiences, can enable forms of reasoning not
typically seen in the early years. Although there is a large and
coherent body of research on individual content domains such as
counting and arithmetic, there have been remarkably few studies
that have attempted to describe characteristics of structural
development in young students' mathematics. Collectively, the
chapters highlight the importance of providing more exciting,
relevant, and challenging 21st century mathematics learning for our
young students. The chapters provide a broad scope in their topics
and approaches to advancing young children's mathematical learning.
They incorporate studies that highlight the importance of pattern
and structure across the curriculum, studies that target particular
content such as statistics, early algebra, and beginning number,
and studies that consider how technology and other tools can
facilitate early mathematical development. Reconceptualising the
professional learning of teachers in promoting young children's
mathematics, including a consideration of the role of play, is also
addressed.
This third edition of the Handbook of International Research in
Mathematics Education provides a comprehensive overview of the most
recent theoretical and practical developments in the field of
mathematics education. Authored by an array of internationally
recognized scholars and edited by Lyn English and David Kirshner,
this collection brings together overviews and advances in
mathematics education research spanning established and emerging
topics, diverse workplace and school environments, and globally
representative research priorities. New perspectives are presented
on a range of critical topics including embodied learning, the
theory-practice divide, new developments in the early years,
educating future mathematics education professors, problem solving
in a 21st century curriculum, culture and mathematics learning,
complex systems, critical analysis of design-based research,
multimodal technologies, and e-textbooks. Comprised of 12 revised
and 17 new chapters, this edition extends the Handbook's original
themes for international research in mathematics education and
remains in the process a definitive resource for the field.
This book emanated primarily from concerns that the mathematical
capabilities of young children continue to receive inadequate
attention in both the research and instructional arenas. Research
over many years has revealed that young children have sophisticated
mathematical minds and a natural eagerness to engage in a range of
mathematical activities. As the chapters in this book attest,
current research is showing that young children are developing
complex mathematical knowledge and abstract reasoning a good deal
earlier than previously thought. A range of studies in prior to
school and early school settings indicate that young learners do
possess cognitive capacities which, with appropriately designed and
implemented learning experiences, can enable forms of reasoning not
typically seen in the early years. Although there is a large and
coherent body of research on individual content domains such as
counting and arithmetic, there have been remarkably few studies
that have attempted to describe characteristics of structural
development in young students' mathematics. Collectively, the
chapters highlight the importance of providing more exciting,
relevant, and challenging 21st century mathematics learning for our
young students. The chapters provide a broad scope in their topics
and approaches to advancing young children's mathematical learning.
They incorporate studies that highlight the importance of pattern
and structure across the curriculum, studies that target particular
content such as statistics, early algebra, and beginning number,
and studies that consider how technology and other tools can
facilitate early mathematical development. Reconceptualising the
professional learning of teachers in promoting young children's
mathematics, including a consideration of the role of play, is also
addressed."
|
|