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A schoolwide solution for students' mathematics success! Do you
sometimes start to teach a mathematics concept and feel like you're
staring at a sea of bewildered faces? What happens when you
discover students previously learned a calculation trick or a
mnemonic that has muddied their long-term understanding? When
"rules" seem to change from year to year, teacher to teacher, or
school to school, mathematics can seem like a disconnected mystery
for students. Clear up the confusion with a Mathematics
Whole-School Agreement! Expanded from the highly popular "Rules
that Expire" series of NCTM articles, this essential guide leads
educators through the collaborative step-by-step process of
establishing a coherent and consistent learner-centered and
equitable approach to mathematics instruction. Through this work,
you will identify, streamline, and become passionate about using
clear and consistent mathematical language, notations,
representations, rules, and generalizations within and across
classrooms and grades. Importantly, you'll learn to avoid "rules
that expire"-tricks that may seem to help students in one grade but
hurt in the long run. Features of this book include * Abundant
grade-specific examples * Effective working plans for
sustainability * Barrier-busting tips, to-dos, and try-it-outs *
Practical templates and checklists * PLC prompts and discussion
points When teachers unite across grades, students hit the ground
running every year. Take the next step together as a team and help
all your students build on existing understanding to find new
success and most importantly, love learning and doing mathematics!
A schoolwide solution for students' mathematics success! Do you
sometimes start to teach a mathematics concept and feel like you're
staring at a sea of bewildered faces? What happens when you
discover students previously learned a calculation trick or a
mnemonic that has muddied their long-term understanding? When
"rules" seem to change from year to year, teacher to teacher, or
school to school, mathematics can seem like a disconnected mystery
for students. Clear up the confusion with a Mathematics
Whole-School Agreement! Expanded from the highly popular "Rules
that Expire" series of NCTM articles, this essential guide leads
educators through the collaborative step-by-step process of
establishing a coherent and consistent learner-centered and
equitable approach to mathematics instruction. Through this work,
you will identify, streamline, and become passionate about using
clear and consistent mathematical language, notations,
representations, rules, and generalizations within and across
classrooms and grades. Importantly, you'll learn to avoid "rules
that expire"-tricks that may seem to help students in one grade but
hurt in the long run. Features of this book include: * Abundant
grade-specific examples * Effective working plans for
sustainability * Barrier-busting tips, to-dos, and try-it-outs *
Practical templates and checklists * PLC prompts and discussion
points When teachers unite across grades, students hit the ground
running every year. Take the next step together as a team and help
all your students build on existing understanding to find new
success and most importantly, love learning and doing mathematics!
A school-wide solution for students' mathematics success! Do you
sometimes start to teach a mathematics concept and feel like you're
staring at a sea of bewildered faces? What happens when you
discover students previously learned a calculation trick or a
mnemonic that has muddied their long-term understanding? When
"rules" seem to change from year to year, teacher to teacher, or
school to school, mathematics can seem like a disconnected mystery
for students. Clear up the confusion with a Mathematics
Whole-School Agreement! Expanded from the highly popular "Rules
that Expire" series of NCTM articles, this essential guide leads
educators through the collaborative step-by-step process of
establishing a coherent and consistent learner-centered and
equitable approach to mathematics instruction. Through this work,
you will identify, streamline, and become passionate about using
clear and consistent mathematical language, notations,
representations, rules, and generalizations within and across
classrooms and grades. Importantly, you'll learn to avoid "rules
that expire"-tricks that may seem to help students in one grade but
hurt in the long run. Features of this book include * Abundant
grade-specific examples * Effective working plans for
sustainability * Barrier-busting tips, to-dos, and try-it-outs *
Practical templates and checklists * PLC prompts and discussion
points When teachers unite across grades, students hit the ground
running every year. Take the next step together as a team and help
all your students build on existing understanding to find new
success and most importantly, love learning and doing mathematics!
A volume in Research in Mathematics Education Series Editor Barbara
J. Dougherty, Iowa State University This volume contains papers
from the Second International Curriculum Conference sponsored by
the Center for the Study of Mathematics Curriculum (CSMC). The
intended audience includes policy makers, curriculum developers,
researchers, teachers, teacher trainers, and anyone else interested
in school mathematics curricula.
A volume in Research in Mathematics Education Series Editor Barbara
J. Dougherty, Iowa State University This volume contains papers
from the Second International Curriculum Conference sponsored by
the Center for the Study of Mathematics Curriculum (CSMC). The
intended audience includes policy makers, curriculum developers,
researchers, teachers, teacher trainers, and anyone else interested
in school mathematics curricula.
A volume in Research in Mathematics Education Series Editor Barbara
J. Dougherty, University of Mississippi The purpose of this book is
to document the work of the Show-Me Project (1997-2007) and to
highlight lessons learned about curriculum implementation. Although
the Show-Me Project was charged with promoting the dissemination
and implementation of four distinct comprehensive curriculum
programs (Connected Mathematics, Mathematics in Context, MathScape,
and MathThematics), most of the lessons learned from this work are
not curriculum specific. Rather, they cut across the four programs
and share commonalities with standards-based curriculum reform at
any level. We believe that documenting these lessons learned will
be one of the legacies of the Show-Me Project We anticipate that
the comprehensive nature of this work will attract readers from
multiple audiences that include state and district mathematics
supervisors, middle grades mathematics teachers and administrators
involved in curriculum reform, as well as mathematics teacher
educators. Those about to embark on the review of curriculum
materials will appreciate reading about the processes employed by
other districts. Readers with interests in a particular curriculum
program will be able to trace the curriculum-specific chapters to
gain insights into how the design of the curricula relate to
professional development, adoption and implementation issues, and
teachers' personal experience using the curriculum materials.
Individuals who provide professional development at the middle
grades level will find chapters that they can use for both general
and focused discussions. Teachers at all stages of implementation
will recognize their own experiences in reading and reflecting on
the stories of teacher change. Mathematics educators will find
ideas on how these curricula can be used in the preparation of
preservice middle grades teachers.
A volume in Research in Mathematics Education Series Editor Barbara
J. Dougherty, University of Mississippi The purpose of this book is
to document the work of the Show-Me Project (1997-2007) and to
highlight lessons learned about curriculum implementation. Although
the Show-Me Project was charged with promoting the dissemination
and implementation of four distinct comprehensive curriculum
programs (Connected Mathematics, Mathematics in Context, MathScape,
and MathThematics), most of the lessons learned from this work are
not curriculum specific. Rather, they cut across the four programs
and share commonalities with standards-based curriculum reform at
any level. We believe that documenting these lessons learned will
be one of the legacies of the Show-Me Project We anticipate that
the comprehensive nature of this work will attract readers from
multiple audiences that include state and district mathematics
supervisors, middle grades mathematics teachers and administrators
involved in curriculum reform, as well as mathematics teacher
educators. Those about to embark on the review of curriculum
materials will appreciate reading about the processes employed by
other districts. Readers with interests in a particular curriculum
program will be able to trace the curriculum-specific chapters to
gain insights into how the design of the curricula relate to
professional development, adoption and implementation issues, and
teachers' personal experience using the curriculum materials.
Individuals who provide professional development at the middle
grades level will find chapters that they can use for both general
and focused discussions. Teachers at all stages of implementation
will recognize their own experiences in reading and reflecting on
the stories of teacher change. Mathematics educators will find
ideas on how these curricula can be used in the preparation of
preservice middle grades teachers.
A volume in Research in Mathematics Education Series Editor Barbara
J. Dougherty, University of Mississippi This volume contains the
proceedings of the First International Curriculum Conference
sponsored by the Center for the Study of Mathematics Curriculum
(CSMC). The CSMC is one of the National Science Foundation Centers
for Learning and Teaching (Award No. ESI-0333879). The
countries-China, Japan, Korea, and Singapore (in alphabetical
order, which also happens to be the order of their
populations)-have each been in the news because of their
performance on international tests and/or their economic
performance and potential. They also have centralized education
ministries that create a single mathematics curriculum framework
followed in the entire country.
A volume in Research in Mathematics Education Series Editor Barbara
J. Dougherty, University of Mississippi This volume contains the
proceedings of the First International Curriculum Conference
sponsored by the Center for the Study of Mathematics Curriculum
(CSMC). The CSMC is one of the National Science Foundation Centers
for Learning and Teaching (Award No. ESI-0333879). The
countries-China, Japan, Korea, and Singapore (in alphabetical
order, which also happens to be the order of their
populations)-have each been in the news because of their
performance on international tests and/or their economic
performance and potential. They also have centralized education
ministries that create a single mathematics curriculum framework
followed in the entire country.
A volume in Research in Mathematics Education Series Editor Barbara
J. Dougherty, University of Mississippi This volume investigates
the evolution of the geometry curriculum in the United States over
the past 150 years. A primary goal is to increase awareness of the
nature of the current geometry curriculum by investigating the
historical, mathematical and pedagogical influences that it has
sustained since its inception. Given the limited access to
first-hand accounts of the enacted geometry curriculum during the
past 150 years, the book relies on textbooks to provide a record of
the implemented curriculum at any given point in time and on policy
documents and journal articles to provide insight into the
prevalent issues and arguments of the day. The book is organized in
a chronological sequence of ""notable events"" leading to
discernable changes in thinking about the geometry curriculum over
the past century and a half-roughly the extent of time during which
geometry has been taught in American schools. Notable events
include important reports or commissions, influential texts, new
schools of thought, and developments in learning technologies.
These events affected, among other things: content and aims of the
geometry curriculum; the nature of mathematical activity as
construed by both mathematicians and mathematics educators; and,
the resources students are given for engaging in mathematical
activity. Before embarking through the notable events, it is
necessary to consider the ""big bang"" of geometry, namely the
moment in time that shaped the future life of the geometry
curriculum. This corresponds to the emergence of Euclidean
geometry. Given its influence on the shape of the geometry
curriculum, familiarity with the nature of the geometry articulated
in Euclid's Elements is essential to understanding the many
tensions that surround the school geometry curriculum. Several
themes emerge over the course of the monograph, and include: the
aims and means of the geometry curriculum, the importance of proof
in geometry, the role of visualization and tactile experiences, the
fusion between solid and plane geometry, the curricular connections
between geometry and algebra, and the use of motion and continuity.
The intended audience would include curriculum developers,
researchers, teachers, and curriculum supervisors.
A volume in Research in Mathematics Education Series Editor Barbara
J. Dougherty, University of Mississippi This volume investigates
the evolution of the geometry curriculum in the United States over
the past 150 years. A primary goal is to increase awareness of the
nature of the current geometry curriculum by investigating the
historical, mathematical and pedagogical influences that it has
sustained since its inception. Given the limited access to
first-hand accounts of the enacted geometry curriculum during the
past 150 years, the book relies on textbooks to provide a record of
the implemented curriculum at any given point in time and on policy
documents and journal articles to provide insight into the
prevalent issues and arguments of the day. The book is organized in
a chronological sequence of ""notable events"" leading to
discernable changes in thinking about the geometry curriculum over
the past century and a half-roughly the extent of time during which
geometry has been taught in American schools. Notable events
include important reports or commissions, influential texts, new
schools of thought, and developments in learning technologies.These
events affected, among other things: content and aims of the
geometry curriculum; the nature of mathematical activity as
construed by both mathematicians and mathematics educators; and,
the resources students are given for engaging in mathematical
activity. Before embarking through the notable events, it is
necessary to consider the ""big bang"" of geometry, namely the
moment in time that shaped the future life of the geometry
curriculum. This corresponds to the emergence of Euclidean
geometry. Given its influence on the shape of the geometry
curriculum, familiarity with the nature of the geometry articulated
in Euclid's Elements is essential to understanding the many
tensions that surround the school geometry curriculum. Several
themes emerge over the course of the monograph, and include: the
aims and means of the geometry curriculum, the importance of proof
in geometry, the role of visualization and tactile experiences, the
fusion between solid and plane geometry, the curricular connections
between geometry and algebra, and the use of motion and continuity.
The intended audience would include curriculum developers,
researchers, teachers, and curriculum supervisors.
A volume in Research in Mathematics Education Series Editor Barbara
J. Dougherty, University of Mississippi This monograph reports on
an analysis of a small part of the mathematics curriculum, the
definitions given to quadrilaterals. This kind of research, which
we call micro-curricular analysis, is often undertaken by those who
create curriculum, but it is not usually done systematically and it
is rarely published. Many terms in mathematics education can be
found to have different definitions in mathematics books. Among
these are ""natural number,"" ""parallel lines"" and ""congruent
triangles,"" ""trapezoid"" and ""isosceles trapezoid,"" the formal
definitions of the trigonometric functions and absolute value, and
implicit definitions of the arithmetic operations addition,
subtraction, multiplication, and division. Yet many teachers and
students do not realize there is a choice of definitions for
mathematical terms. And even those who realize there is a choice
may not know who decides which definition of any mathematical term
is better, and under what criteria. Finally, rarely are the
mathematical implications of various choices discussed.As a result,
many students misuse and otherwise do not understand the role of
definition in mathematics. We have chosen in this monograph to
examine a bit of mathematics for its definitions: the
quadrilaterals. We do so because there is some disagreement in the
definitions and, consequently, in the ways in which quadrilaterals
are classified and relate to each other. The issues underlying
these differences have engaged students, teachers, mathematics
educators, and mathematicians. There have been several articles and
a number of essays on the definitions and classification of
quadrilaterals. But primarily we chose this specific area of
definition in mathematics because it demonstrates how broad
mathematical issues revolving around definitions become reflected
in curricular materials. While we were undertaking this research,
we found that the area of quadrilaterals supplied grist for broader
and richer discussions than we had first anticipated. The intended
audience includes curriculum developers, researchers, teachers,
teacher trainers, and anyone interested in language and its use.
A volume in Research in Mathematics Education Series Editor Barbara
J. Dougherty, University of Mississippi This monograph reports on
an analysis of a small part of the mathematics curriculum, the
definitions given to quadrilaterals. This kind of research, which
we call micro-curricular analysis, is often undertaken by those who
create curriculum, but it is not usually done systematically and it
is rarely published. Many terms in mathematics education can be
found to have different definitions in mathematics books. Among
these are ""natural number,"" ""parallel lines"" and ""congruent
triangles,"" ""trapezoid"" and ""isosceles trapezoid,"" the formal
definitions of the trigonometric functions and absolute value, and
implicit definitions of the arithmetic operations addition,
subtraction, multiplication, and division. Yet many teachers and
students do not realize there is a choice of definitions for
mathematical terms. And even those who realize there is a choice
may not know who decides which definition of any mathematical term
is better, and under what criteria. Finally, rarely are the
mathematical implications of various choices discussed. As a
result, many students misuse and otherwise do not understand the
role of definition in mathematics. We have chosen in this monograph
to examine a bit of mathematics for its definitions: the
quadrilaterals. We do so because there is some disagreement in the
definitions and, consequently, in the ways in which quadrilaterals
are classified and relate to each other. The issues underlying
these differences have engaged students, teachers, mathematics
educators, and mathematicians. There have been several articles and
a number of essays on the definitions and classification of
quadrilaterals. But primarily we chose this specific area of
definition in mathematics because it demonstrates how broad
mathematical issues revolving around definitions become reflected
in curricular materials. While we were undertaking this research,
we found that the area of quadrilaterals supplied grist for broader
and richer discussions than we had first anticipated. The intended
audience includes curriculum developers, researchers, teachers,
teacher trainers, and anyone interested in language and its use.
This book, the eleventh in the Putting Essential Understanding into
Practice Series, focuses on misconceptions about variables,
expressions, equations, and functions that students often bring to
grades 6–8. The authors present tasks given to middle-grades
students and examine sample responses to them to show how teachers
can bring misconceptions to the surface, where they and their
students can inspect them, recognize errors and limitations, and
replace faulty thinking with robust ideas.
Do your students have “concept images” that limit their ideas
of shapes to specific examples, oriented in particular ways? Do
they confuse the size of an angle with the length of the rays in a
drawing of an angle? When solving problems, do they mix up the
concepts of perimeter—the distance around a shape, measured in
linear units—and area—the region within the shape, measured in
square units? What tasks can you offer—what questions can you
ask—to determine what they know or don’t know—and move them
forward in their thinking? This book focuses on the specialized
pedagogical content knowledge that you need to teach geometry and
measurement effectively in grades 3–5. The authors demonstrate
how to use this multifaceted knowledge to address the big ideas and
essential understandings that students must develop for success
with geometry and measurement—not only in their current work, but
also in higher-level mathematics and a myriad of real-world
contexts. Explore rich, research-based strategies and tasks that
show how students are reasoning about and making sense of geometry
and measurement. Use the opportunities that these and similar tasks
provide to build on their understanding while identifying and
correcting misunderstandings that may be keeping them from taking
the next steps in learning. Putting Essential Understanding of
Geometry and Measurement into Practice in Grades 3–5 is the
eighth title in NCTM’s highly useful and very readable Putting
Essential Understanding into Practice Series, edited by Barbara J.
Dougherty. Each volume in the series builds on the companion volume
in the earlier Essential Understanding Series to show teachers how
to implement their understanding of mathematics in the classroom.
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