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Because fluency practice is not a worksheet. Fluency in mathematics
is more than adeptly using basic facts or implementing algorithms.
Real fluency involves reasoning and creativity, and it varies by
the situation at hand. Figuring Out Fluency in Mathematics Teaching
and Learning offers educators the inspiration to develop a deeper
understanding of procedural fluency, along with a plethora of
pragmatic tools for shifting classrooms toward a fluency approach.
In a friendly and accessible style, this hands-on guide empowers
educators to support students in acquiring the repertoire of
reasoning strategies necessary to becoming versatile and nimble
mathematical thinkers. It includes: "Seven Significant Strategies"
to teach to students as they work toward procedural fluency.
Activities, fluency routines, and games that encourage learning the
efficiency, flexibility, and accuracy essential to real fluency.
Reflection questions, connections to mathematical standards, and
techniques for assessing all components of fluency. Suggestions for
engaging families in understanding and supporting fluency. Fluency
is more than a toolbox of strategies to choose from; it's also a
matter of equity and access for all learners. Give your students
the knowledge and power to become confident mathematical thinkers.
Finally! A book that helps solve the problem of teaching
problem-solving! Learning to be a problem solver is hard. Teaching
students how to be problem solvers themselves can be even harder.
Some students may learn to mimic procedures to come up with correct
answers, but are they really learning to solve problems? To become
independent problem solvers, students need to practice exploring,
tinkering, and most importantly thinking!! The bite-size routines
in this guide are perfect for teachers looking for the interesting,
engaging, and doable practice students need to become
problem-solving masters. These flexible, modifiable bursts of
quality practice are designed to get students to look at problems
in different ways, spark discussion, make connections, and boost
mathematics achievement. This collection addresses the common
challenges students and teachers face when learning to problem
solve by Developing students’ mathematical reasoning and
conceptual understanding Building students’ skills with various
problem-solving strategies Nurturing mathematical confidence and
improving identity and agency Fortified with standards for math
practices and processes, the ideas in this guide develop the
reasoning and critical-thinking skills for students to become
independent problem-solvers for life!
Because fluency practice is not a worksheet. Fluency in mathematics
is more than adeptly using basic facts or implementing algorithms.
It is not about speed or recall. Real fluency is about choosing
strategies that are efficient, flexible, lead to accurate
solutions, and are appropriate for the given situation. Developing
fluency is also a matter of equity and access for all learners. The
landmark book Figuring Out Fluency in Mathematics Teaching and
Learning offered educators the inspiration to develop a deeper
understanding of procedural fluency, along with a plethora of
pragmatic tools for shifting classrooms toward a fluency approach.
Now, teachers have the chance to apply that inspiration through
explicit instruction and practice every day with the classroom
companion Figuring Out Fluency: Addition and Subtraction with
Fractions and Decimals. With this book, teachers can: Dive deeper
into the Significant Strategies for fluency explained in the anchor
book Learn how these strategies grow from and relate to the basic
fact strategies children learn Access over 100 strategy-aligned and
classroom-ready activities for fluency instruction and practice in
adding and subtracting fractions and decimals, including worked
examples, routines, games, and centers Find activities for
assessing all components of addition and subtraction fluency for
fractions and decimals, plus support for engaging families Download
all of the needed support tools, game boards, and other resources
from the companion website for immediate implementation. Give each
and every student the knowledge and power to become skilled and
confident mathematical thinkers and doers.
"This book is awesome! What stood out to me was the deep
understanding I was able to have about what fluency actually means.
Too often the message has been fluency and accuracy, especially at
the middle school level. By providing teachers with tools for
building fluency with integers, expressions, and algebra, this book
shifts that message to also focus on flexibility and strategy
selection." Lindsey Henderson Secondary Mathematics Specialist,
Utah State Board of Education Salt Lake City, UT Because fluency
practice is not a worksheet. Fluency in mathematics is more than
adeptly using basic facts or implementing algorithms. It is not
about speed or recall. Real fluency is about choosing strategies
that are efficient, flexible, lead to accurate solutions, and are
appropriate for the given situation. Developing fluency is also a
matter of equity and access for all learners. The landmark book
Figuring Out Fluency in Mathematics Teaching and Learning offered
educators the inspiration to develop a deeper understanding of
procedural fluency, along with a plethora of pragmatic tools for
shifting classrooms toward a fluency approach. Now, teachers have
the chance to apply that inspiration through explicit instruction
and practice every day with the classroom companion Figuring Out
Fluency-Operations With Rational Numbers and Algebraic Equations.
With this book, teachers can Dive deeper into the Significant
Strategies for fluency explained in the anchor book as they apply
to rational number operations Explore how these strategies can be
applied for proportional reasoning, solving equations for unknowns,
and solving systems of linear equations Access over 100
classroom-ready activities, including worked examples, routines,
and games. Find activities to explicitly teach students how to use
and choose strategies to operate on rational numbers and solve
algebraic equations Download all of the needed support tools, game
boards, and other resources from the companion website for
immediate implementation Give each and every student the knowledge
and power to become skilled and confident mathematical thinkers and
doers.
Because fluency practice is not a worksheet. Fluency in mathematics
is more than adeptly using basic facts or implementing algorithms.
It is not about speed or recall. Real fluency is about choosing
strategies that are efficient, flexible, lead to accurate
solutions, and are appropriate for the given situation. Developing
fluency is also a matter of equity and access for all learners. The
landmark book Figuring Out Fluency in Mathematics Teaching and
Learning offered educators the inspiration to develop a deeper
understanding of procedural fluency, along with a plethora of
pragmatic tools for shifting classrooms toward a fluency approach.
Now, teachers have the chance to apply that inspiration through
explicit instruction and practice every day with the classroom
companion Figuring Out Fluency: Addition and Subtraction with Whole
Numbers. With this book, teachers can: * Dive deeper into the
Significant Strategies for fluency explained in the anchor book *
Learn how these strategies grow from and relate to the basic fact
strategies children learn * Access over 100 strategy-aligned and
classroom-ready activities for fluency instruction and practice in
adding and subtracting multi-digit whole numbers, including worked
examples, routines, games, and centers * Find activities for
assessing all components of addition and subtraction fluency plus
support for engaging families * Download all of the needed support
tools, game boards, and other resources from the companion website
for immediate implementation. Give each and every student the
knowledge and power to become skilled and confident mathematical
thinkers and doers.
Your guide to grow and learn as a math teacher! Let's face it,
teaching elementary math can be hard. So much about how we teach
math today may look and feel different from how we learned it.
Today, we recognize placing the student at the center of their
learning increases engagement, motivation, and academic achievement
soars. Teaching math in a student-centered way changes the role of
the teacher from one who traditionally "delivers knowledge" to one
who fosters thinking. Most importantly, we must ensure our practice
gives each and every student the opportunity to learn, grow, and
achieve at high levels, while providing opportunities to develop
their agency and authority in the classroom which results in a
positive math identity. Whether you are a brand new teacher or a
veteran, if you find teaching math to be quite the challenge, this
is the guide you want by your side. Designed for just-in-time
learning and support, this practical resource gives you brief,
actionable answers to your most pressing questions about teaching
elementary math. Written by four experienced math educators
representing diverse experiences, these authors offer the practical
advice they wish they received years ago, from lessons they've
learned over decades of practice, research, coaching, and through
collaborating with teams, teachers and colleagues-especially new
teachers-every day. Questions and answers are organized into five
areas of effort that will help you most thrive in your elementary
math classroom: 1. How do I build a positive math community? 2. How
do I structure, organize, and manage my math class? 3. How do I
engage my students in math? 4. How do I help my students talk about
math? 5. How do I know what my students know and move them forward?
Woven throughout, you'll find helpful sidebar notes on fostering
identity and agency; access and equity; teaching in different
settings; and invaluable resources for deeper learning. The final
question-Where do I go from here?- offers guidance for growing your
practice over time. Strive to become the best math educator you can
be; your students are counting on it! What will be your first step
on the journey?
Offering a year's worth of daily instructional material that you
can use each class period to promote student reasoning and number
sense, this resource will help students: Frequently revisit
essential mathematical concepts Foster and shore up conceptual
understanding Engage in mental mathematics, leading to efficiency
and fluency Engage in mathematical discourse by constructing viable
arguments and critiquing the reasoning of others Reason
mathematically, which can improve performance on high-stakes
assessments Move learning beyond "correctness" by valuing mistakes
and discourse to encourage a growth mindset
Do your students need more practice to develop number sense and
reasoning? Are you looking to engage your students with activities
that are uncomplicated, worthwhile, and doable? Have you had
success with number talks but do your students crave more variety?
Have you ever thought, "What can I do differently?" Swap out
traditional warmup practices and captivate your elementary students
with these new, innovative, and ready-to-go routines! Trusted
elementary math expert John J. SanGiovanni details 20
classroom-proven practice routines to help you ignite student
engagement, reinforce learning, and prepare students for the lesson
ahead. Each quick and lively activity spurs mathematics discussion
and provides a structure for talking about numbers, number
concepts, and number sense. Designed to jump-start mathematics
reasoning in any elementary classroom, the routines are: Rich with
content-specific examples and extensions Modifiable to work with
math content at any K-5 grade level Compatible with any textbook or
core mathematics curriculum Practical, easy-to-implement, and
flexible for use as a warm-up or other activity Accompanied by
online slides and video demonstrations, the easy 5-10 minute
routines become your go-to materials for a year's work of daily
plug-and-play short-burst reasoning and fluency instruction that
reinforces learning and instills mathematics confidence in
students. Students' brains are most ready to learn in the first few
minutes of math class. Give math practice routines a makeover in
your classroom with these 20 meaningful and energizing warmups for
learning crucial mathematics skills and concepts, and make every
minute count.
Because fluency practice is not a worksheet. Fluency in mathematics
is more than adeptly using basic facts or implementing algorithms.
It is not about speed or recall. Real fluency is about choosing
strategies that are efficient, flexible, lead to accurate
solutions, and are appropriate for the given situation. Developing
fluency is also a matter of equity and access for all learners. The
landmark book Figuring Out Fluency in Mathematics Teaching and
Learning offered educators the inspiration to develop a deeper
understanding of procedural fluency, along with a plethora of
pragmatic tools for shifting classrooms toward a fluency approach.
Now, teachers have the chance to apply that inspiration through
explicit instruction and practice every day with the classroom
companion Figuring Out Fluency: Multiplication and Division with
Whole Numbers. With this book, teachers can: * Dive deeper into the
Significant Strategies for fluency explained in the anchor book *
Learn how these strategies grow from and relate to the basic fact
strategies children learn * Access over 100 strategy-aligned and
classroom-ready activities for fluency instruction and practice in
multiplying and dividing multi-digit whole numbers, including
worked examples, routines, games, and centers * Find activities for
assessing all components of multiplication and division fluency
plus support for engaging families * Download all of the needed
support tools, game boards, and other resources from the companion
website for immediate implementation. Give each and every student
the knowledge and power to become skilled and confident
mathematical thinkers and doers.
Misconceptions and incomplete mathematical thinking often go
undetected, as teachers are rarely trained to consider why or how
an answer was generated. They often respond to incorrect answers by
re-teaching the correct processes, and the underlying problem
persists. Unrecognized misconceptions then become permanent ways of
thinking; each new layer of mathematics knowledge builds upon on
flawed foundations. This book addresses that problem head on. By
covering the essential content or "big ideas" of K-2 mathematics,
it turns elementary teachers into experts in diagnosis,
intervention, and evaluation, and delivers the tasks and tools to
use in the classroom day-to-day.
Because fluency practice is not a worksheet. Fluency in mathematics
is more than adeptly using basic facts or implementing algorithms.
It is not about speed or recall. Real fluency is about choosing
strategies that are efficient, flexible, lead to accurate
solutions, and are appropriate for the given situation. Developing
fluency is also a matter of equity and access for all learners. The
landmark book Figuring Out Fluency in Mathematics Teaching and
Learning offered educators the inspiration to develop a deeper
understanding of procedural fluency, along with a plethora of
pragmatic tools for shifting classrooms toward a fluency approach.
Now, teachers have the chance to apply that inspiration through
explicit instruction and practice every day with the classroom
companion Figuring Out Fluency: Multiplication and Division with
Fractions and Decimals. With this book, teachers can: Dive deeper
into the Significant Strategies for fluency explained in the anchor
book Learn how these strategies grow from and relate to the basic
fact strategies children learn Access over 100 strategy-aligned and
classroom-ready activities for fluency instruction and practice in
multiplying and dividing fractions and decimals, including worked
examples, routines, games, and centers Find activities for
assessing all components of multiplication and division fluency for
fractions and decimals, plus support for engaging families Download
all of the needed support tools, game boards, and other resources
from the companion website for immediate implementation. Give each
and every student the knowledge and power to become skilled and
confident mathematical thinkers and doers.
"Seldom has a book been as timely or as necessary as Productive
Math Struggle is today. . . One of the remarkable accomplishments
of SanGiovanni, Katt, and Dykema's work lies in how they seamlessly
connect the research on high-quality tasks, high expectations,
identity, and equity to productive math struggle. This is perhaps
their greatest contribution. The authors see productive math
struggle as a critical feature of mathematics classrooms that
support access, equity, and empowerment, specifically arguing that
every student is 'worthy of struggle.'" From the Foreword by Matt
Larson, Ph.D. Past President (2016-2018), National Council of
Teachers of Mathematics Associate Superintendent for Instruction,
Lincoln Public Schools, Nebraska Struggle is hard. Productive
struggle is power. All students face struggle, and they should-it
is how they learn and grow. The teacher's job is not to remove
struggle, but rather to value and harness it, helping students
develop good habits of productive struggle. But what's missing for
many educators is an action plan for how to achieve this,
especially when it comes to math. Persevering through difficult
challenges to reach new learning is the core of Productive Math
Struggle. When left unsupported, struggle can become unproductive
and demoralizing, negatively influencing students' mathematical
identities. The authors guide teachers through six specific
actions-including valuing, fostering, building, planning,
supporting, and reflecting on struggle-to create a game plan for
overcoming obstacles by sharing Actionable steps, activities, and
tools for implementation Instructional tasks and vignettes
representative of each grade level Real-world examples showcasing
classroom photos and student work samples A book study guide is
available under the Free Resources tab that helps math educators to
learn together on how to incorporate productive math struggle in
their classrooms. Revolving around the idea that math is a way of
thinking and understanding, and not just the pursuit of answers and
procedures, this book empowers students to embrace productive
struggle to build essential skills for learning and living-both
inside and outside the classroom.
This bank of carefully selected tasks to discover what students
know - and don't quite grasp - about big ideas in grades 3-5
mathematics. 180 in all, downloadable, standards-aligned, and
augmented with sample student work, commentary on strengths and
gaps, and next instructional steps so teachers can swiftly spot the
teachable moments in students' misunderstandings.
The routines in this book will help students: Frequently revisit
essential mathematical concepts Foster and shore up conceptual
understanding Engage in mental mathematics, leading to efficiency
and fluency Engage in mathematical discourse by constructing viable
arguments and critiquing the reasoning of others Reason
mathematically, and prepare for high stakes assessments Move
learning beyond "correctness" by valuing mistakes and discourse and
encouraging a growth mindset
Being an effective math educator is one part based on the quality
of the tasks we give, one part how we diagnose what we see, and one
part what we do with what we find. Yet with so many students and
big concepts to cover, it can be hard to slow down enough to look
for those moments when students' responses tell us what we need to
know about next best steps. In this remarkable book, John
SanGiovanni helps us value our students' misconceptions and
incomplete understandings as much as their correct ones-because
it's the gap in their understanding today that holds the secrets to
planning tomorrow's best teaching.
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