Barbara Dougherty

Get a deeper understanding of teaching functions, 9–12 with our concise and comprehensive Go-To Guide. Based on Developing Essential Understanding of Functions 9–12 and Putting Essential Understanding of Functions into Practice 9–12, this summary distills the key concepts and ideas into a quick-reference guide that's perfect for supplementing your reading of Developing Essential Understanding of Functions 9–12 and Putting Essential Understanding of Functions into Practice 9–12, reviewing the basics before diving deeper into the subject, refreshing your knowledge and filling in gaps in your understanding, and identifying areas where you need more information and want to learn more. Go-To Guides are designed to provide you with a thorough grasp of the mathematical ideas and principles needed to teach functions, 9–12 by focusing on the core concepts and relationships that underlie the subject. This Go-To Guide is perfect for those looking to develop a deeper understanding of functions, 9–12, create targeted lessons and activities that meet the needs of students, anticipate common student misconceptions and errors, design effective assessments and evaluations, and enhance your own math knowledge and skills. Whether you're new to teaching functions 9–12, or an experienced educator, our Go-To Guides will be your trusted resource for teaching with confidence and clarity.

NSights Math Games for Conceptual Understanding is a resource for teachers to use with any mathematics curriculum. The games in this book are developed to support students as they acquire a deeper understanding of number relationships and generalizations that lead to conceptual knowledge and robust procedural skills. These types of concepts and skills are foundational to accessing more sophisticated mathematical ideas. The learning outcomes for each game are closely aligned to late elementary through high school grades. In some games, there are different levels or versions that may range from simple to more complex mathematical ideas and are, therefore, appropriate for use in diverse classrooms. This will allow you to match the game's mathematical ideas and complexity to the levels of your students. Sometimes, you may want to review previously learned skills to focus on the number sense ideas. Or, you can use the level or version that more closely fits with the content you are teaching at grade level. Each game in this volume includes learning outcome(s), instructions, and a recording sheet or game board. Sometimes, suggestions about organizing your classroom (such as playing in pairs or teacher-led) are included to assist you in making the game a success with your students. The games in this volume are user-friendly and accessible for all students. They have been classroom tested by students and teachers, and their suggestions have contributed to creating games that are highly engaging while at the same time promoting robust mathematical learning.

How can you introduce terms from geometry and measurement so that your students’ vocabulary will enhance their understanding of concepts and definitions? What can you say to clarify the thinking of a student who claims that perimeter is always an even number? How does knowing what changes or stays the same when shapes are transformed help you support and extend your students’ understanding of shapes and the space that they occupy? How much do you know … and how much do you need to know? Helping your students develop a robust understanding of geometry and measurement requires that you understand fundamental statistical concepts deeply. But what does that mean? This book focuses on essential knowledge for mathematics teachers about geometry and measurement. It is organized around three big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry and measurement, the book will broaden and deepen your understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.

How can you build on young children’s interactions with the world to develop their geometric thinking? What can you say to a student who claims that a diamond isn’t a square because it “stands on a point”? How can knowing what does not change when shapes are transformed help you extend your students’ thinking about the area of geometric figures? How much do you know … and how much do you need to know? Helping your students develop a robust understanding of geometry and measurement requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry and measurement. It is organized around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry and measurement, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic. About the Series: Focus on the ideas that you need to understand thoroughly to teach confidently. Move beyond the mathematics you expect your students to learn. Students who fail to get a solid grounding in pivotal concepts struggle in subsequent work in mathematics and related disciplines. By bringing a deeper understanding to your teaching, you can help students who don’t get it the first time by presenting the mathematics in multiple ways. The Essential Understanding Series addresses topics in school mathematics that are critical to the mathematical development of students but are often difficult to teach. Each book in the series gives an overview of the topic, highlights the differences between what teachers and students need to know, examines the big ideas and related essential understandings, reconsiders the ideas presented in light of connections with other mathematical ideas, and includes questions for readers’ reflection.

Do your students have the incorrect idea that addition “makes numbers bigger” and subtraction “makes numbers smaller”? Do they believe that subtraction is always “taking away”? What tasks can you offer - what questions can you ask - to determine what your students 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 addition and subtraction effectively in prekindergarten–grade 2. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with these computations - 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 addition and subtraction. 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 reaction 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.

Do your students believe that division ""doesn't make sense"" if the divisor is greater than the dividend? Explore rich, researched-based strategies and tasks that show how students are reasoning about and making sense of mulitplication and division. This book focuses on the specialised pedagogical content knowledge that you need to teach multiplication and division effectively in grades 3-5.