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.

'Elevate' is a brand new Key Stage 3 Mathematics course which has been written specifically to embrace the principles of the new KS3 2008 curriculum. 'Elevate' provides a flexible blend of differentiated resources that work perfectly together to encourage pupils to progress whatever their ability level.

This edited volume will help educators better analyze methodological and practical tools designed to aid classroom instruction. It features papers that explore the need to create a system in order to fully meet the uncertainties and developments of modern educational phenomena. These have emerged due to the abundance of digital resources and new forms of collective work. The collected papers offer new perspectives to a rising field of research known as the Documentational Approach to Didactics. This framework was first created by the editors of this book. It seeks to develop a deeper understanding of mathematics teaching expertise. Readers will gain insight into how to meet the theoretical questions brought about by digitalization. These include: how to analyze teachers’ work when they prepare for their teaching, how to conceptualize the relationships between individual and collective work, and how to follow the related processes over the long term. The contributors also provide a comparative view in terms of contrasting selected phenomena across different educational cultures and education systems. For instance, they consider how differences in curriculum resources are available to teachers and how teachers make use of them to shape instruction. Coverage also considers the extent to which teachers make use of additional material, particularly those available through the global marketplace on the Internet. This book builds on works from the Re(s)sources 2018 Conference, Understanding teachers’ work through their interactions with resources for teaching, held in Lyon, France.

Teaching Secondary and Middle School Mathematics combines the latest developments in research, technology, and standards with a vibrant writing style to help teachers prepare for the excitement and challenges of teaching secondary and middle school mathematics. The book explores the mathematics teaching profession by examining the processes of planning, teaching, and assessing student progress through practical examples and recommendations. Beginning with an examination of what it means to teach and learn mathematics, the reader is led through the essential components of teaching, concluding with an examination of how teachers continue with professional development throughout their careers. Hundreds of citations are used to support the ideas presented in the text, and specific websites and other resources are presented for future study by the reader. Classroom scenarios are presented to engage the reader in thinking through specific challenges that are common in mathematics classrooms. The seventh edition has been updated and expanded with particular emphasis on the latest technology, standards, and other resources. The reader is introduced to the ways that students think and how to best meet their needs through planning that involves attention to differentiation, as well as how to manage a classroom for success. Features include: • Following on from the sixth edition, assessment takes a central role in planning and teaching. Unit 3 (of 5) addresses the use of summative and formative assessments to inform classroom teaching practices. • A new appendix is included that lists websites that can be used in a methods class to view other teachers interacting with students for discussion of effective teaching practices. • The feature entitled “Links and Resources” has been updated in each of the 13 chapters. Five strongly recommended and practical resources are spotlighted at the end of each chapter as an easy reference to some of the most important materials on the topic. • Approximately 150 new citations have either replaced or been added to the text to reflect the latest in research, materials, and resources that support the teaching of mathematics. • Significant revisions have been made to Chapter 12, which now includes updated research and practices as well as a discussion on culturally responsive pedagogy. Likewise, Chapter 8 now includes a description of best and high-leverage teaching practices, and a discussion in Chapter 11 on alternative high school mathematics electives for students has been added. • Chapter 9, on the practical use of classroom technology, has again been revised to reflect the latest tools available to classroom teachers, including apps that can be run on handheld personal devices, in light of changes in education resulting from the global pandemic. An updated Instructor’s Manual features a test bank, sample classroom activities, PowerPoint slide content, chapter summaries, and learning outcomes for each chapter, and can be accessed by instructors online at www.routledge.com/9781032472867.

Teach math lessons through the creative means of a life storyProvide 36 weeks of instruction based on skill levels rather than grade levelsGuide students by the use of inexpensive manipulatives, including index cards, dried beans, and construction paper! We often tend to compartmentalize when teaching children. In real life, there aren’t artificial barriers between “subjects.” For example, when you are cooking or baking, you have to use the skills of reading, logical thinking, and measuring, just to name a few. In driving a car, you see and read road signs, read maps, and count miles. So why do we say to children, “This is math, this is language, this is about science and nature, and this is history”? The most natural and effective means to teach children is through life examples. Content, story, and the ability to show math in real life make a living math book!

Reflective practice is at the heart of effective teaching, and this book helps you develop into a reflective teacher of mathematics. Everything you need is here: guidance on developing your analysis and self-evaluation skills, the knowledge of what you are trying to achieve and why, and examples of how experienced teachers deliver successful lessons. The book shows you how to plan lessons, how to make good use of resources and how to assess pupils' progress effectively. Each chapter contains points for reflection, which encourage you to break off from your reading and think about the challenging questions that you face as a new teacher. The book is supplemented by a companion website, with: " Videos of real lessons so you can see the skills discussed in the text in action " Links to a range of sites that provide useful additional support " Extra planning and resource materials. If you are training to teach mathematics this book will help you to improve your classroom performance, by providing you with practical advice, but also by helping you to think in depth about the key issues. It also provides examples of the research evidence that is needed in academic work at Masters level, essential for anyone undertaking an M-level PGCE. Paul Chambers was formerly course leader for PGCE mathematics at Edge Hill University.

Achieve High-Quality Mathematics Discourse With Purposeful Talk Techniques Many mathematics teachers agree that engaging students in high quality discourse is important for their conceptual learning, but successfully promoting such discourse in elementary classrooms—with attention to the needs of every learner—can be a challenge. Activating Math Talk tackles this challenge by bringing practical, math-specific, productive discourse techniques that are applicable to any lesson or curriculum. Framed around 11 student-centered discourse techniques, this research-based book connects purposeful instructional techniques to specific lesson goals and includes a focus on supporting emergent multilingual learners. You will be guided through each technique with Classroom examples of tasks and techniques spanning grades K–5 Reflection moments to help you consider how key ideas relate to your own instruction Classroom vignettes that illustrate the techniques in action and provide opportunities to analyze and prepare for your own implementation Group discussion questions for engaging with colleagues in your professional community Achieving high-quality mathematics discourse is within your reach using the clear-cut techniques that activates your math talk efforts to promote every student’s conceptual learning.

Have you ever noticed that we tend to compartmentalize when teaching our children? In real life, there aren’t artificial barriers between “subjects.” For example, when you are cooking or baking, you have to use the skills of reading, logical thinking, and measuring, just to name a few. In driving a car, you see and read road signs, read maps, and count miles. It has become quite clear that there is an abundance of math curriculums available that are nothing but monotonous drill sheets dressed up in pretty colors. Pretty colors do not make a living book. Content, story, and the ability to show math in real life make a living math book. Math Level 1: Teach math lessons through the creative means of a life storyProvides a link for the downloadable answer keyHas a scope and sequence that contains learning numbers 0 to 100, circles and patterns, counting and addition, days of the week, and telling time. This book was written to be used by you and your young student together. It is the story of a twin brother and sister, Charlie and Charlotte, who are visiting their grandparents’ farm. They soon learn that the farm is full of learning opportunities! As you read their story, your students will be drawn into the adventure along with the twins. They will learn about numbers, shapes, place value, adding, and subtracting. They will also learn about gardening, baby animals on the farm, nature, and the love of family. They will hear exciting stories from Grandpa and Grandma, and they will be invited to join the twins on their living math adventures. We hope you have a grand time on this adventure!

"This book is a must-have for anyone who has faced the challenge of teaching problem solving. The ideas to be learned are supported with a noticeably rich collection of classroom-ready problems, examples of student thinking, and videos. Problem solving is at the center of learning and doing mathematics. And so, Mathematize It! should be at the center of every teacher’s collection of instructional resources." John SanGiovanni Coordinator, Elementary Mathematics Howard County Public School System, Ellicott City, MD Help students reveal the math behind the words "I don’t get what I’m supposed to do!" This is a common refrain from students when asked to solve word problems. Solving problems is about more than computation. Students must understand the mathematics of a situation to know what computation will lead to an appropriate solution. Many students often pluck numbers from the problem and plug them into an equation using the first operation they can think of (or the last one they practiced). Students also tend to choose an operation by solely relying on key words that they believe will help them arrive at an answer, which without careful consideration of what the problem is actually asking of them. Mathematize It! Going Beyond Key Words to Make Sense of Word Problems, Grades K-2 shares a reasoning approach that helps students dig into the problem to uncover the underlying mathematics, deeply consider the problem’s context, and employ strong operation sense to solve it. Through the process of mathematizing, the authors provide an explanation of a consistent method—and specific instructional strategies—to take the initial focus off specific numbers and computations and put it on the actions and relationships expressed in the problem. Sure to enhance teachers’ own operation sense, this user-friendly resource for Grades K-2 · Offers a systematic mathematizing process for students to use when solving word problems · Gives practice opportunities and dozens of problems to leverage in the classroom · Provides specific examples of questions and explorations for addition and subtraction of whole numbers as well as early thinking for multiplication and division · Demonstrates the use of concrete manipulatives to model problems with dozens of short videos · Includes end-of-chapter activities and reflection questions How can you help your students understand what is happening mathematically when solving word problems? Mathematize it!

"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.