Corwin Mathematics Series – serie

Practical and proven math tasks to maximize student thinking and learning

Building upon the blockbuster success of Building Thinking Classrooms in Mathematics, Peter Liljedahl has joined forces with co-author Kyle Webb to bring the Building Thinking Classrooms (BTC) framework to life in this new book, Mathematics Tasks for the Thinking Classroom, Grades 6-12.

But this book is so much more than simply a collection of good thinking tasks. It delves deeper into the implementation of the 14 practices from the BTC framework by updating the practices with the newest research, and focusing on the practice through the lens of rich math tasks that address specific mathematical learning outcomes or standards. Across the 20 non-curricular tasks and 30 curricular tasks used as models, this book:

Helps you choose tasks to fit your particular math standards, goals, and the competencies you want your students to buildWalks you through all the steps and scripts to launch, facilitate, and consolidate each taskShares examples of possible student solutions along with hints you might offer to help their thinking alongOffers tasks for consolidation, example notes to my future forgetful self, and mild, medium, and spicy check-your-understanding questions (CYUs) for every thin sliced sequences of curricular tasksImparts reflections from the authors on each task

The book closes with specific guidance on how to find more tasks or craft your own non-curricular and curricular tasks, along with answers to educators’ frequently asked questions. It includes access to a companion website that includes downloadables and a task template for creating your own tasks.

Whether you are new to BTC or a seasoned user, Mathematics Tasks for the Thinking Classroom, Grades 6-12 will help teachers, coaches, and specialists transform traditional math classrooms into dynamic and thought-provoking learning spaces. Mathematics Tasks for the Thinking Classroom, Grades K-5 is also available to create district-wide thinking classrooms!

Keep thinking…keep learning in different settings In Peter Liljedahl’s bestselling Building Thinking Classrooms in Mathematics: 14 Teaching Practices for Enhancing Learning, readers discovered that thinking is a precursor to learning. Translating 15 years of research, the anchor book introduced 14 practices that have the most potential to increase student thinking in the classroom and can work for any teacher in any setting.  But how do these practices work in a classroom with social distancing or in settings that are not always face-to-face? This follow-up supplement will answer those questions, and more. It walks teachers through how to adapt the 14 practices for 12 distinct settings, some of which came about as a result of the COVID-19 pandemic. This guide:

Provides the what, why, and how to adapt each practice in face-to-face settings that require social distancing, fixed seating, or small class sizes; synchronous and asynchronous virtual settings; synchronous and asynchronous hybrid settings; independent learning; and homeschooling. Includes guidance on using thinking classroom practices to support students in unfinished learning in small groups and one-on-one teaching or tutoring. Offers updated toolkits and a recommended order for the implementation of the practices for each of the settings. This supplement allows teachers to dip in as needed and continually modify the practices as their own classroom situations change and evolve, always keeping the thinking at the forefront of their mathematics teaching and learning.

Math is not rote-memorizable. Math is not random-guessable. Math is figure-out-able.

Author Pam Harris argues that teaching real math—math that is free of distortions–will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do.

Memorization tricks and algorithms meant to make math “easier” are full of traps that sacrifice long-term student growth for short-lived gains. Students and teachers alike have been led to believe that they’ve learned more and more math, but in reality their brains never get any stronger. 

Using these tricks may make facts easier to memorize in isolation, but that very disconnect distorts the reality of math. The mountain of trivia piles up until students hit a breaking point. Humanity's most powerful system of understanding, organizing, and making an impact on the world becomes a soul-draining exercise in confusion, chaos, and lost opportunities.

Developing Mathematical Reasoning: Avoiding the Trap of Algorithms emphasizes the importance of teaching students increasingly sophisticated mathematical reasoning and understanding underlying concepts rather than relying on a set rule for solving problems. This book illuminates a hierarchy of mathematical reasoning to help teachers guide students through various domains of math development, from basic counting and adding to more complex proportional and functional reasoning.

Everyone is capable of understanding and doing real math. This book:

Highlights the important mathematical relationships, strategies, and models for students to developOffers personal stories, reflection sections, and extensive practical exercises for easy implementationIncludes real math—a lot of it—to provide teachers with examples they can put to use in their classrooms immediately

This book is a valuable resource for educators looking to reach more students by building a strong foundation of mathematical thinking in their students. By addressing common misconceptions about math and providing practical strategies for teaching real math, this book shows that everyone can use the mathematical relationships they already know to reason about new relationships. In other words, everyone can math.

Using strengths-based approaches to support development in mathematics  It’s time to re-imagine what’s possible and celebrate the brilliance multilingual learners bring to today’s classrooms. Innovative teaching strategies can position these learners as leaders in mathematics. Yet, as the number of multilingual learners in North American schools grows, many teachers have not had opportunities to gain the competencies required to teach these learners effectively, especially in disciplines such as mathematics. Multilingual learners—historically called English Language Learners—are expected to interpret the meaning of problems, analyze, make conjectures, evaluate their progress, and discuss and understand their own approaches and the approaches of their peers in mathematics classrooms. Thus, language plays a vital role in mathematics learning, and demonstrating these competencies in a second (or third) language is a challenging endeavor. Based on best practices and the authors’ years of research, this guide offers practical approaches that equip grades K-8 teachers to draw on the strengths of multilingual learners, partner with their families, and position these learners for success. Readers will find:  • A focus on multilingual students as leaders • A strength-based approach that draws on students’ life experiences and cultural backgrounds • An emphasis on maintaining high expectations for learners’ capacity for mastering rigorous content • Strategies for representing concepts in different formats  • Stop and Think questions throughout and reflection questions at the end of each chapter • Try It! Implementation activities, student work examples, and classroom transcripts With case studies and activities that provide a solid foundation for teachers’ growth and exploration, this groundbreaking book will help teachers and teacher educators engage in meaningful, humanized mathematics instruction.  

How to build productive relationships in math education  I wasn’t taught this way. I can’t help my child! These are common refrains from today’s parents and guardians, who are often overwhelmed, confused, worried, and frustrated about how to best support their children with what they see as the “new math.” The problem has been compounded by the shift to more distance learning in response to a global pandemic. Partnering With Parents in Elementary School Math provides educators with long overdue guidance on how to productively partner and communicate with families about their children’s mathematics learning. It includes reproducible surveys, letters, and planning documents that can be used to improve the home-school relationship, which in turn helps students, parents, teachers, and education leaders alike. Readers will find guidance on how to:    · Understand and empathize with what fuels parents’ anxieties and concerns · Align as a school and set parents’ expectations about what math instruction their children will experience and how it will help them · Communicate clearly and productively with parents about their students’ progress, strengths, and needs in math  · Run informative and fun family events  · support homework  · Coach parents to portray a productive disposition about math in front of their children Educators, families, and students are best served when proactive, productive, and healthy relationships have been developed with each other and with the realities of today's math education. This guide shows how these relationships can be built.

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.

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. 

“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: 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.

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.

Empower your students as they reimagine the world around them through mathematicsCulturally relevant mathematics teaching engages students by helping them learn and understand math more deeply, and make connections to themselves, their communities, and the world around them. The mathematics task provides opportunities for a direct pathway to this goal. But many teachers ask, how can you find, adapt, and implement math tasks that build powerful learners?Engaging in Culturally Relevant Math Tasks helps teachers to design and refine inspiring mathematics learning experiences driven by the kind of high-quality and culturally relevant mathematics tasks that connect students to their world. With the goal of inspiring all students to see themselves as doers of mathematics, this book provides intensive, in-the-moment guidance and practical classroom tools that empower educators to shape culturally relevant experiences while systematically building tasks that are standards-based. It includes A pathway for moving through the process of asking, imagining, planning, creating, and improving culturally relevant math tasks.Tools and strategies for designing culturally relevant math tasks that preservice, novice, and veteran teachers can use to grow their practice day by day.Research-based teaching practices seen through the lens of culturally relevant instruction that help students develop deep conceptual understanding, procedural knowledge, fluency, and application in 6-12 mathematical content.Examples, milestones, opportunities for reflection, and discussion questions guide educators to strengthen their classroom practices, and to reimagine math instruction in response. This book is for any educator who wants to teach mathematics in a more authentic, inclusive, and meaningful way, and it is especially beneficial for teachers whose students are culturally different from them.

“A very compelling set of fresh ideas are offered that prepare educators to turn the corner on advocating for social justice in the mathematics classroom. Each book is full of engaging activities, frameworks and standards that centers instruction on community, worldview, and the developmental needs of all students, a must needed resource to reboot our commitment to the next generation.”

Linda M. Fulmore TODOS: Mathematics For ALL Cave Creek, AZ

Empower students to be the change—join the teaching mathematics for social justice movement!

We live in an era in which students of all ages have—through media and their lived experiences— a more visceral experience of social injustices. However, when people think of social justice, mathematics rarely comes to mind. With a teacher-friendly design, this book brings upper elementary mathematics content to life by connecting it to student curiosity, empathy, and issues students see or experience.

Tested in Grades 3-5 classrooms, the model lessons in this book walk teachers through the process of applying critical frameworks to instruction, using standards-based mathematics to explore, understand, and respond to social justice issues. Learn to plan instruction that engages students in mathematics explorations through age-appropriate, culturally relevant topics, such as valuing differences, health and pay inequality, bullying, voting rights, and environmental justice. Features include:

Content cross-referenced by mathematical concept and social issues Connection to Learning for Justice’s social justice standards Downloadable instructional materials and lesson resources Guidance for lessons driven by students’ unique passions and challenges Connections between research and practice

Written for teachers committed to developing equitable and just practices through the lens of mathematics content and practice standards as well as social justice standards, this book will help connect content to students’ daily lives, fortify their mathematical understanding, and expose them to issues that will support them in becoming active citizens and leaders.

"If you teach middle school math and have wanted to promote social justice, but haven’t been sure how to get started, you need to check out this book. It incorporates lessons you can use immediately as well as how to foster the kind of classroom community where students will thrive. It’s the kind of book you’ll want to have alongside you to support you throughout your journey." Robert Kaplinsky Author and Consultant Long Beach, CA

Empower young adolescents to be the change—join the teaching mathematics for social justice movement!

Students of all ages and intersecting identities—through media and their lived experiences— bear witness to and experience social injustices and movements around the world for greater justice. However, when people think of social justice, mathematics rarely comes to mind. With a user-friendly design, this book brings middle school mathematics content to life by connecting it to issues students see or experience.

Developed for use by Grades 6-8 educators, the contributed model lessons in this book walk teachers through the process of applying critical frameworks to instruction, using standards-based mathematics to explore, understand, and respond to social injustices. Learn to plan daily instruction that engages young adolescents in mathematics explorations through age-appropriate, culturally relevant topics such as health and economic inequality, human and civil rights, environmental justice, and accessibility. Features include:

Content cross-referenced by mathematical concept and social issues Connection to Learning for Justice’s social justice standards Downloadable teacher materials and lesson resources Guidance for lessons driven by young adolescents’ unique passions and challenges Connections between research and practice

Written for teachers committed to developing equitable and empowering practices through the lens of mathematics content and practice standards as well as social justice standards, this book will help connect content to young adolescents’ daily lives, strengthen their mathematical understanding, and expose them to issues that will support them in becoming active agents of change and responsible leaders.

Your journey to becoming a social justice mathematics educator begins here.

Every journey has a beginning—a starting point—where you take a moment to set your sights on your next destination carefully. Teaching mathematics for social justice (TMSJ) means reimagining your mathematics classroom in a way that serves more children better–as a place that lifts mathematics up as a tool for students to analyze and understand the worlds around them, celebrate their unique identities and their communities, and become agents of change. For any K-12 educator who values these goals Teaching Mathematics for Social Justice, Grades: A Guide for Moving from Mindset to Action can be the start of a transformational journey.

Guiding you in planning, implementing, assessing, and showcasing social justice mathematics lessons and helping children apply their learning beyond the classroom, this book:

Encourages self-reflection on the “why” of your teaching and examines your own mindset about mathematicsProvides a step-by-step action plan for creating equitable and socially just mathematics classrooms that focus on rich and collaborative mathematics learningIncorporates interactive reflection prompts, self-assessments, and activities throughout the journeyDescribes culturally responsive teaching practices to better respond to the instructional needs of the diverse individuals in your classroomOffers activities to identify what current events and social issues are important to children and their familiesInspires you to remain steadfast in their journey of growth toward becoming a social justice mathematics educator

Complete with sample lessons, online resources, and practical tools, this guide will empower you to better understand the children in your classroom, leverage their strengths, and make mathematics learning relevant and useful as they use mathematics to address the issues they care about. Start your journey towards becoming a social justice mathematics educator today.

Help students see their whole selves in the math they're learning with culturally responsive teaching.

Cultivating Mathematical Hearts: Culturally Responsive Mathematics Teaching in Elementary Classrooms, aims to re-center mathematics as a humanizing endeavor because putting children and their humanity at the heart of mathematics education can result in more engaged, meaningful, and joyful learning.

This book introduces a model and a tool for Culturally Responsive Mathematics Teaching, constructed to create a safe, inclusive space where all learners can come together in their own educational journey and develop a love for math that centers their experiences and comes from the heart. Implementing the Culturally Responsive Mathematics Teaching Tool (CRMT2) will help you cultivate and sustain meaningful, rich, and rigorous mathematical learning spaces for all your students–experiences that foster mathematical curiosity and joy. The book walks you through each aspect of the framework and tool, guiding you to consider how your classroom structures, lessons, tasks, and assessments:

Honor the existing cultural strengths, experiences, and lived realities of all your studentsElicit diverse mathematical thinking and ideasSupport equitable access to rigorous mathematical learning and discourse for all studentsInvite a sense of agency in each student’s learning experiencePromote high engagement and excitement while learning mathematicsNurture an understanding that mathematics is a powerful tool for making sense of the world

By weaving these strategies into classroom lessons, teachers can humanize mathematics instruction to successfully build a love for math while providing equitable learning opportunities that empower student voice and promote success in mathematics.

Target the Math…Support the Students…Provide Access for All

The need for focused small group math instruction has never been greater. Today’s education landscape is fraught with learning divides unlike anything we’ve faced in recent years. We need new ways of teaching students who have remarkably varying levels of understanding and vastly different needs.

Meaningful Small Groups in Math, Grades K-5 offers practical guidance on how to meet the diverse needs of today’s students. Written for K-5 classroom teachers, math interventionists and instructional coaches, this user-friendly, accessible book provides guidance on the necessary components of small group instruction in math, trajectories for small-group instruction on specific concepts, and practical steps for getting started. Readers will find

Checklists and templates for implementing small group, sample lessons in the major content domains Emphasis on flexible groups Intervention and extension ideas for differentiating learning A chapter devoted to developing small-group programs across a school or organization

Small group instruction in mathematics has not been as well-developed as its counterpart in the reading world. In K-5 math classrooms, small-group instruction has typically been reduced to learning centers and rotation stations, with little emphasis on differentiated, small-group, teacher-facilitated learning. To meet the needs of today’s students, a more focused approach is needed.

A strengths and assets-based approach to multilingual learner success

As the number of multilingual learners (MLLs) in US schools continues to grow, educators need to learn the moves necessary to support the success of these students in mathematics and science.

Equity Moves to Support Multilingual Learners in Mathematics and Science, Grades K-8 focuses on the literacy opportunities that MLLs can achieve when language scaffolds are taught alongside rigorous math and science content. It provides a framework teachers can use to develop equity-centered, scaffolded math, science, or STEAM lessons. Readers will find

Anchor phenomena that demonstrate issues with lesson design and delivery and highlight areas to include language and content scaffoldsExamples for honoring the languages of students, families, and communitiesCulturally responsive techniques and easy-to-use tables featuring the equity movesVignettes showcasing the equity move in the classroom settingA focus on four language demands: vocabulary, discourse, multiple modes of representation, and text features

With an assets-based approach to what MLLs can do, this book helps teachers unpack the language demands of mathematics and science and encourages reflection of their own practices in scaffolding for language and culture.

Go beyond problem-solving and performance tasks.  Bring project-based learning to life!

Do you want your students to be more engaged in their mathematics lessons while also amplifying cultural relevancy and equity? If so, proceed to the next level of instruction with project-based learning (PBL)! This book provides the whole PBL game plan designed by an experienced, award-winning teacher and researcher. Whether you want to start with small steps or you are ready for full implementation in your classroom, project-based learning experiences can lead to forever memories and deeper learning for your students. Answering the why, what, and how of embarking on the journey toward PBL, readers will find

Need-to-Know questions to open each chapterStudent and educator vignettes to identify stumbling blocks and successesPBL Plus Tips that identify those small steps teachers can make to gradually shift toward PBLYour Turn prompts to actively connect ideas to your practice

This approachable guide includes everything you need to move from tasks to memorable project-based experiences that leverage student voice and choice and build a welcoming classroom culture!

Create a pathway to equity by detracking mathematics 

The tracked mathematics system has been operating in US schools for decades. However, research demonstrates negative effects on subgroups of students by keeping them in a single math track, thereby denying them access to rigorous coursework needed for college and career readiness. The journey to change this involves confronting some long-standing beliefs and structures in education.

When supported with the right structures, instructional shifts, coalition building, and educator training and support, the detracking of mathematics courses can be a primary pathway to equity. The ultimate goal is to increase more students’ access to and achievement in higher levels of mathematics learning–especially for students who are historically marginalized. Based on the stories and lessons learned from the San Francisco Unified School District educators who have talked the talk and walked the walk, this book provides a model for all those involved in taking on detracking efforts from policymakers and school administrators, to math coaches and teachers.

By sharing stories of real-world examples, lessons learned, and prompts to provoke discussion about your own context, the book walks you through: 

Designing and gaining support for a policy of detracked math coursesImplementing the policy through practical shifts in scheduling, curriculum, professional development, and coachingSupporting and improving the policy through continuous research, monitoring, and maintenance. 

This book offers the big ideas that help you in your own unique journey to advance equity in your school or district’s mathematics education and also provides practical information to help students in a detracked system thrive.

Math really is for everyone—so let’s prove it.

You’ve heard it from kids, from friends, and from celebrities: “I’m bad at math.” It’s a line that society tends to accept without examination—after all, some people just aren’t “math people,” right?

Wrong. As we do with other essential skills, we need to expose the stereotypes, challenge the negative mindsets, and finally confront the systemic opportunity gaps in math education, and replace them with a new vision for what math is, who it’s for, and who can excel at it. In this book you’ll find

Research on teacher and student mindsets and their effect on student achievementAudience-specific and differentiated tools, reflection questions, and suggested actions for educators at all levels of the systemExamples from popular media, as well as personal stories and anecdotesQuotes, data-driven figures, and suggestions for deeper learning on all aspects of a positive and equitable vision of math education

Both social commentary and a toolkit of solutions, this bold new book directly challenges the constructs that have historically dictated our perceptions of what makes someone a “math person”. Only by dismantling those misplaced assumptions can we reform math education so it works for everyone. Because in truth, we are all math people.

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 byDeveloping students’ mathematical reasoning and conceptual understandingBuilding students’ skills with various problem-solving strategiesNurturing mathematical confidence and improving identity and agencyFortified 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!

Stop algebra from being a mathematical gatekeeper. With rich math tasks, all students can succeed. 

Every teacher strives to make instruction effective and interesting, yet traditional methods of teaching algebra are not working for many students! That’s a problem. But the answer isn’t to supplement the curriculum with random tasks. Classroom Ready-Rich Math Tasks for Grades 6-12 equips you with a cohesive solution--50+ mathematical tasks that are rich, research-based, standards-aligned, and classroom-tested. The tasks:

Are organized into learning progressions that help all students make the leap from arithmetic to algebraOffer students interesting mathematics problems to think about and solve so math is investigative, interactive, and engagingProvide opportunities for you to connect new content to prior knowledge or focus on an underdeveloped conceptEngage students in conceptual understanding, procedural practice, and problem solving through critical thinking and applicationCome with downloadable planning tools, student resource pages,  and extension questionsInclude additional support for students who may be struggling

Every learner deserves opportunities to engage in meaningful, rigorous mathematics. And every teacher can develop mathematical thinking and reasoning abilities in students. Part of the bestselling series spanning elementary and middle school, Classroom-Ready Rich Algebra Tasks, Grades 6-12 is a powerful add-on to any core mathematics program at your school.

A thinking student is an engaged student

Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling “non-thinking” student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.

Practical and proven math tasks to maximize student thinking and learning

Building upon the blockbuster success of Building Thinking Classrooms in Mathematics, Peter Liljedahl has joined forces with co-author Maegan Giroux to bring the Building Thinking Classrooms (BTC) framework to life in this new book, Mathematics Tasks for the Thinking Classroom, Grades K-5.

But this book is so much more than simply a collection of good thinking tasks. It delves deeper into the implementation of the 14 practices from the BTC framework by updating the practices with the newest research, and focusing on the practice through the lens of rich math tasks that address specific mathematical learning outcomes or standards. Across the 20 non-curricular tasks and 30 curricular tasks used as models, this book:

Helps you choose tasks to fit your particular math standards, goals, and the competencies you want your students to buildWalks you through all the steps and scripts to launch, facilitate, and consolidate each taskShares examples of possible student solutions along with hints you might offer to help their thinking alongOffers tasks for consolidation, example notes to my future forgetful self, and mild, medium, and spicy check-your-understanding questions (CYUs) for every thin sliced sequences of curricular tasksImparts reflections from the authors on each task

The book closes with specific guidance on how to find more tasks or craft your own non-curricular and curricular tasks, along with answers to educators’ frequently asked questions. It includes access to a companion website that includes downloadables and a task template for creating your own tasks.

Whether you are new to BTC or a seasoned user, Mathematics Tasks for the Thinking Classroom, Grades K-5 will help teachers, coaches, and specialists transform traditional math classrooms into dynamic and thought-provoking learning spaces.

Because fluency practice is not a worksheet.

Fluency in mathematics is more than basic facts or using algorithms. It is not about recall or speed. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is 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. It explained the seven Significant Strategies for fluency and offered a plethora of pragmatic tools for shifting classrooms toward a greater fluency approach. However, in order to become truly adept with these strategies, children must first have certain underlying foundational concepts and skills in place. 

Figuring Out Fluency-Ten Underlying Foundations for Reasoning Strategies with Whole Numbers explores the ideas that are essential to reasoning: Number Relationships; Subitizing and Decomposing; Distance to 10, 100, and 1,000; Counting and Skip-Counting; Properties of Addition and Its Inverse Relationship with Subtraction; Properties of Multiplication and Its Inverse Relationship with Division; Multiplying by 10s and 100s; Multiples and Factors; Doubling and Halving; and Computational Estimation. With this book, elementary teachers can

Help children develop these foundational understandings, critical to reasoning and number sense.Leverage over 100 classroom-ready routines, centers, and games to develop these concepts both in first instruction, practice, and intervention.Download all of the needed support tools, game boards, and other resources from the companion website for immediate implementation

Develop each and every students’ knowledge and power to become skilled and confident mathematical thinkers and doers.

Ambitious teaching requires ambitious coaching

Over a decade ago, the National Council of Teachers of Mathematics (NCTM) and Corwin co-published the modern classic, 5 Practices for Orchestrating Productive Mathematics Discussions, aimed at guiding teachers to improve the quality of mathematics discussions in their classrooms and create an equitable learning environment for students. The bestselling series, The 5 Practices in Practice series, followed to further explore the five practices within grade bands, empowering teachers to overcome challenges in orchestrating mathematics discussions. And now, esteemed mathematics expert Peg Smith and her author team, take the 5 practices to the next level with Coaching the 5 Practices.

Written for coaches, instructional leaders, professional developers, and teacher educators, Coaching the 5 Practices: Supporting Mathematics Teachers in Orchestrating Productive Discussions will be the lynchpin to supporting teachers who are committed to engaging students in productive discussions in mathematics classrooms. The book introduces a coaching model that creates opportunities for teacher learning through one-on-one interactions with a coach. This model focuses on the specific challenges teachers face and opportunities they can lean into as they are learning to support productive mathematics discussions around the 5 practices of anticipating, monitoring, selecting, sequencing, and connecting (as well as Practice 0 of setting goals and selecting tasks).

Through three phases of a coaching cycle—before a lesson, during a lesson, and after a lesson, this coaching model

Focuses on ambitious teaching in mathematics, aiming to ensure that every student succeeds in high-quality academic workFollows iterative cycles of various touchpoints between the coach and a teacherEmphasizes what a coach needs to do to support teacher learning throughout the cycle

With narrative examples and vignettes, lesson plans, pre-lesson and post-lesson conference plans, and other artifacts collected from real coaching sessions and classrooms, Coaching the 5 Practices is a valuable resource for education professionals who work with teachers to improve the quality of mathematics instruction. Through the efforts of Coaching the 5 Practices, teachers will continue to refine their craft and become increasingly more skilled at implementing the 5 practices in ways that support the learning of each and every student.

Every child has a right to make sense of math, and to use math to make sense of their worlds. 

Despite their gifts, students with disabilities are often viewed from a deficit standpoint in mathematics classrooms. These students are often conceptualized as needing to be fixed or remediated. Rethinking Disability and Mathematics argues that mathematics should be a transformative space for these students, a place where they can discover their power and potential and be appreciated for their many strengths. Author Rachel Lambert introduces Universal Design for Learning for Math (UDL Math), a way to design math classrooms that empowers disabled and neurodiverse students to engage in mathematics in ways that lead to meaningful and joyful math learning. The book showcases how UDL Math can open up mathematics classrooms so that they provide access to meaningful understanding and an identity as a math learner to a wider range of students. Weaved throughout the book are the voices of neurodiverse learners telling their own stories of math learning. 

Through stories of real teachers recognizing the barriers in their own math classrooms and redesigning to increase access, the book:

Reframes students with disabilities from a deficit to an asset perspective, paving the way for trusting their mathematical thinkingOffers equitable math instruction for all learners, including those with disabilities, neurodiverse students, and/or multilingual learnersApplies UDL to the math classroom, providing practical tips and techniques to support students' cognitive, affective, and strategic developmentImmerses readers in math classrooms where all students are engaged in meaningful mathematics, from special education day classes to inclusive general education classrooms, from grades K-8. Integrates research on mathematical learning including critical math content such as developing number sense and place value, fluency with math facts and operations, and understanding fractions and algebraic thinking.Explores critical issues such as writing IEP goals in math

This book is designed for all math educators, both those trained as general education teachers and those trained as special education teachers. The UDL Math approach is adapted to work for all learners because everyone varies in how they perceive the world and in how they approach mathematical problem solving. When we rethink mathematics to include multiple ways of being a math learner, we make math accessible and engaging for a wider group of learners.

Foster a love of mathematics by creating a more inclusive and empowering learning environment through asset-based teaching!

An asset-based perspective on math education means starting with what students already know instead of focusing on what’s missing. This approach elevates student thinking and reasoning skills. In this way, educators acknowledge that all students bring prior experiences, strengths, talents, and resources to the learning process and can contribute meaningfully in an authentic learning environment. Transform Your Math Class Using Asset-Based Teaching for Grades 6-12 provides insight into asset-based perspectives in mathematics education to create an environment where all students feel valued and capable of being doers of mathematics. In the book, Michael Steele and Joleigh Honey highlight the importance of using language, instructional routines, and systemic structure that positively impact student engagement, their math identity, and ultimately their outcomes.

Providing a wealth of knowledge and practical strategies that can be used to transform math classrooms into inclusive, supportive, and empowering learning environments, this book:

Introduces an asset-based perspective that focuses on students' strengths, assets, and potential to learn mathematicsIncludes a variety of frameworks and tools that teachers can use to build and grow their sense of asset-based perspectivesOffers strategies for promoting a growth mindset in mathematics, encouraging productive struggle in math, and promoting equitable math instructionSupports teachers in reflecting on their decisions, self-awareness, and self-managementIncludes a companion online study guide to support teachers individually or as part of a professional learning community

Adopting asset-based perspectives is about movement over time, not about flipping a switch. This book paves the path for an asset-based journey that ultimately helps to transform our math classrooms and advance all students’ learning and development.

Take math instruction to the next level by truly meeting the needs of ALL learners

Today's classrooms are more diverse than ever, and teachers face the challenge of meeting not only the academic needs of their students but also their social and emotional growth. Math Workshop Plus, Grades K-8 by Alison J. Mello and Dr. Nicki Newton is here to help educators elevate their math instruction for all learners by more intentionally integrating Universal Design for Learning (UDL) and Social and Emotional Learning (SEL) into the popular Math Workshop model.

By reimagining Math Workshop through an equity lens, this book offers practical guidance to designing instruction that meets every child where they are. It addresses unfinished learning, fostering positive math identities, and building the competencies students need to succeed academically and socially.

Offering an actionable approach to promote learning environments where every student can thrive, Math Workshop Plus, Grades K-8 includes

Practical strategies to seamlessly incorporate UDL and SEL into your Math Workshop for more accessible and inclusive instruction.Classroom-ready resources such as example activities, vignettes, and tools at all grade levels to help you implement changes immediately.Guidance for fostering equity by meeting the diverse needs of all learners, including strategies for differentiation, scaffolding, and supporting students' social-emotional growth.Real-world success stories from educators who have transformed their classrooms with the Math Workshop Plus approach.

With Math Workshop Plus, you'll gain the tools and confidence to create a classroom environment that promotes access and excellence for all students. Learn how to personalize instruction, remove barriers to learning, and inspire a love for math in every child.