Do your students think that the vertical line test is indispensable and foolproof for determining whether a relationship is a function? Do they believe that every function can be modeled by an equation? Do they interpret the graph of a function as the function itself? 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 functions effectively in grades 9–12. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with functions - 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 functions. 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. You have essential understanding. It’s time to put it into practice in your teaching. The Putting Essential Understanding into Practice Series moves NCTM’s Essential Understanding Series into the classroom. The new series details and explores best practices for teaching the essential ideas that students must grasp about fundamental topics in mathematics - topics that are challenging to learn and teach but are critical to the development of mathematical understanding. Classroom vignettes and samples of student work bring each topic to life, and questions for reader reflection open it up for hands-on exploration. Each volume underscores connections with the Common Core State Standards for Mathematics while highlighting the knowledge of learners, curriculum, instructional strategies, and assessment that pedagogical content knowledge entails. Resources and tasks are available at nctm.org/more4U. Maximize the potential of student-centered learning and teaching by putting essential understanding into practice.

Let’s face it, teaching secondary math can be hard. So much about how we teach math today may look and feel different from how we learned it. 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 secondary 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 secondary math classroom: How do I build a positive math community? How do I structure, organize, and manage my math class? How do I engage my students in math? How do I help my students talk about math? 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?

Transforming the standards into learning outcomes just got a lot easier In this resource, you can see in an instant how teaching to your state standards should look and sound in the classroom. Under the premise that math is math, the authors provide a Cross-Referencing Index for states implementing their own specific mathematics standards, allowing you to see and understand which page number to turn to for standards-based teaching ideas. It’s all here, page by page: The mathematical progression of each conceptual category, starting with modeling as a unifying theme and moving through number and quantity, algebra, functions, geometry, and statistics and probability, building from eighth-grade standards The mathematics embedded in each conceptual category for a deeper understanding of the content How standards connect within and across domains and to previous grade standards, so teachers can better appreciate how they relate How content standards connect with the standards for mathematical practice, with a focus on modeling as a unifying theme Example tasks, progressions of tasks, and descriptions of what teachers and students should be doing to foster deep learning Your Mathematics Standards Companion is your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful high school mathematics curriculum in any state or district.

Your User’s Guide to the Mathematics Standards When it comes to mathematics, standards aligned is achievement aligned... In the short time since The Common Core Mathematics Companions for grades K–2, 3–5 and 6–8 burst on the scene, they have been lauded as the best resources for making critical mathematics ideas easy to teach. With this brand-new volume, high school mathematics success is at your fingertips. Page by page, the authors lay out the pieces of an in-depth explanation, including The mathematical progression of each conceptual category, starting with modeling as a unifying theme, and moving through number & quantity, algebra, functions, geometry, and statistics and probability, building from the 8th grade standards The mathematics embedded in each conceptual category for a deeper understanding of the content How standards connect within and across domains, and to previous grade standards, so teachers can better appreciate how they relate How standards connect with the standards for mathematical practice, with a focus on modeling as a unifying theme Example tasks, progressions of tasks, and descriptions of what teachers and students should be doing to foster deep learning The Common Core Mathematics Companion: The Standards Decoded, High School has what every high school teacher needs to provide students with the foundation for the concepts and skills they will be expected to know .

Give math students the connections between what they learn and how they do math—and suddenly math makes sense If your secondary-school students are fearful of or frustrated by math, it’s time for a new approach. When you teach concepts rather than rote processes, you show students math’s essential elegance, as well as its practicality—and help them discover their own natural mathematical abilities. This book is a road map to retooling how you teach math in a deep, clear, and meaningful way —through a conceptual lens—helping students achieve higher-order thinking skills. Jennifer Wathall shows you how to plan units, engage students, assess understanding, incorporate technology, and even guides you through an ideal concept-based classroom. Practical tools include: Examples from arithmetic to calculus Inquiry tasks, unit planners, templates, and activities Sample assessments with examples of student work Vignettes from international educators A dedicated companion website with additional resources, including a study guide, templates, exemplars, discussion questions, and other professional development activities. Everyone has the power to understand math. By extending Erickson and Lanning’s work on Concept-Based Curriculum and Instruction specifically to math, this book helps students achieve the deep understanding and skills called for by global standards and be prepared for the 21st century workplace. "Jennifer Wathall’s book is one of the most forward thinking mathematics resources on the market. While highlighting the essential tenets of Concept-Based Curriculum design, her accessible explanations and clear examples show how to move students to deeper conceptual understandings. This book ignites the mathematical mind!" — Lois A. Lanning, Author of Designing Concept-based Curriculum for English-Language Arts, K-12 "Wathall is a master at covering all the bases here; this book is bursting with engaging assessment examples, discussion questions, research, and resources that apply specifically to mathematical topics. Any math teacher or coach would be hard-pressed to read it and not come away with scores of ideas, assessments, and lessons that she could use instantly in the classroom. As an IB Workshop Leader and instructional coach, I want this book handy on a nearby shelf for regular referral – it′s a boon to any educator who wants to bring math to life for students." — Alexis Wiggins, Instructional Coach, IB Workshop Leader and Consultant

"A series for teaching mathematics."--P. [1] of cover.

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 sixth edition has been updated and expanded with particular emphasis on the latest technology, resources, and standards. 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: The entire text has been reorganized so that assessment takes a more central role in planning and teaching. Unit 3 (of 5) now addresses the use of summative and formative assessments to inform classroom teaching practices. ● A new feature, "Links and Resources," has been added to each of the 13 chapters. While the book includes a substantial listing of citations and resources after the 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. ● A Quick Reference Guide has been added to the front of the book to assist the reader in identifying the most useful chapter features by topic. ● A significant revision to Chapter 13 now includes discussions of common teaching assessments used for field experiences and licensure, as well as a discussion of practical suggestions for success in methods and student teaching experiences. ● Chapter 9 on the practical use of classroom technology has been revised to reflect the latest tools available to classroom teachers, including apps that can be run on handheld, personal devices. An updated Instructor’s Manual features a test bank, sample classroom activities, Powerpoint slides, chapter summaries, and learning outcomes for each chapter, and can be accessed by instructors online at www.routledge.com/9780367146511