How do your students determine whether a mathematical statement is true? Do they rely on a teacher, a textbook, or various examples? How can you encourage them to connect examples, extend their ideas to new situations that they have not yet considered, and reason more generally? How much do you know...and how much do you need to know? Helping your students develop a robust understanding of mathematical reasoning requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about mathematical reasoning. It is organized around one big idea, supported by multiple smaller, interconnected ideas essential understandings.Taking you beyond a simple introduction to mathematical reasoning, 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. Focus on the ideas that you need to understand thoroughly to teach confidently.

Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Grades Pre-K–8

John Lannin

Amy Ellis

Rebekah Elliott

Rose Mary Zbiek

NCTM

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 specialized pedagogical content knowledge that you need to teach multiplication and division effectively in grades 3-5. 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 math 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 multipliacation and division. 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. About the Series: 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 refl¬ection 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, understanding into practice, instructional strategies, and assessment that pedagogical content knowledge entails. Resources and tasks are available at nctm.org/more4U.

Putting Essential Understanding of Multiplication and Division into Practice in Grades 3–5

Barbara J. Dougherty

Kathryn Chval

Dustin Jones

Do your students suppose that 1/3 is greater than 1/2, since 3 is greater than 2? Do they believe that having halves means having two, and only two, congruent pieces of a whole? 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 fractions effectively in grades 3 5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with fractions 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 fractions. 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. About the Series: 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 refl¬ection 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, understanding into practice, 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

Putting Essential Understanding of Fractions into Practice in Grades 3–5

Dusty Jones

Do your students have concept images that limit their ideas of shapes to specific examples, oriented in particular ways? Do they confuse the size of an angle with the length of the rays in a drawing of an angle? When solving problems, do they mix up the concepts of perimeter the distance around a shape, measured in linear units and area the region within the shape, measured in square units? 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 geometry and measurement effectively in grades 3-5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with geometry and measurement 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 geometry and measurement. 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. Putting Essential Understanding of Geometry and Measurement into Practice in Grades 3-5 is the eighth title in NCTM s highly useful and very readable Putting Essential Understanding into Practice Series, edited by Barbara J. Dougherty. Each volume in the series builds on the companion volume in the earlier Essential Understanding Series to show teachers how to implement their understanding of mathematics in the classroom.

Putting Essential Understanding of Geometry and Measurement Into Practice in Grades 3–5

See the best price to sell, buy, or rent books by John Lannin. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by John Lannin

See the best price to sell, buy, or rent books by John Lannin. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Grades Pre-K–8

Putting Essential Understanding of Multiplication and Division into Practice in Grades 3–5

Putting Essential Understanding of Fractions into Practice in Grades 3–5

Putting Essential Understanding of Geometry and Measurement Into Practice in Grades 3–5