Terry Crites – författare

Like algebra at any level, early algebra is a way to explore, analyse, represent and generalise mathematical ideas and relationships. This book shows that children can and do engage in generalising about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential understandings for developing algebraic thinking in grades 3-5. The big ideas relate to the fundamental properties of number and operations, the use of the equals sign to represent equivalence, variables as efficient tools for representing mathematical ideas, quantitative reasoning as a way to understand mathematical relationships and functional thinking to generalise relationships between covarying quantities. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.

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.

Do your students suppose that if the perimeter of a shape increases, the area also increases? Do they think that area is the product of base and height, without understanding that this applies only to parallelograms? Do they believe that a transformation happens only on or to a particular object and not the entire plane?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 effectively in grades 6–8. 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—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. 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.

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.

Get a deeper understanding of Geometry with our concise and comprehensive Go-To Guide.Based on Developing Essential Understanding of Geometry and Putting Essential Understanding of Geometry into Practice, 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 Geometry and Putting Essential Understanding of Geometry into PracticeReviewing the basics before diving deeper into the subjectRefreshing your knowledge and filling in gaps in your understandingIdentifying areas where you need more information and want to learn moreGo-To Guides are designed to provide you with a thorough grasp of the mathematical ideas and principles needed to teach Geometry 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 GeometryCreate targeted lessons and activities that meet the needs of studentsAnticipate common student misconceptions and errorsDesign effective assessments and evaluationsEnhance your own math knowledge and skillsWhether you're new to teaching Geometry or an experienced educator, our Go-To Guides will be your trusted resource for teaching with confidence and clarity.