Barbara J. Dougherty – författare

Do your students say that one object is “bigger” than another without attending more precisely to the attribute they are comparing? Do they have difficulty naming numbers from 11 to 19? Do some students still count all while their classmates are counting on or counting by tens?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 number and numeration 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 number and numeration. 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.Maximize the potential of student-centered learning and teaching by putting essential understanding into practice.

This book, the eleventh in the Putting Essential Understanding into Practice Series, focuses on misconceptions about variables, expressions, equations, and functions that students often bring to grades 6–8. The authors present tasks given to middle-grades students and examine sample responses to them to show how teachers can bring misconceptions to the surface, where they and their students can inspect them, recognize errors and limitations, and replace faulty thinking with robust ideas.

Stop algebra from being a mathematical gatekeeper. With rich math tasks, all students can succeed. 

Every teacher strives to make instruction effective and interesting, yet traditional methods of teaching algebra are not working for many students! That’s a problem. But the answer isn’t to supplement the curriculum with random tasks. Classroom Ready-Rich Math Tasks for Grades 6-12 equips you with a cohesive solution--50+ mathematical tasks that are rich, research-based, standards-aligned, and classroom-tested. The tasks:

Are organized into learning progressions that help all students make the leap from arithmetic to algebraOffer students interesting mathematics problems to think about and solve so math is investigative, interactive, and engagingProvide opportunities for you to connect new content to prior knowledge or focus on an underdeveloped conceptEngage students in conceptual understanding, procedural practice, and problem solving through critical thinking and applicationCome with downloadable planning tools, student resource pages,  and extension questionsInclude additional support for students who may be struggling

Every learner deserves opportunities to engage in meaningful, rigorous mathematics. And every teacher can develop mathematical thinking and reasoning abilities in students. Part of the bestselling series spanning elementary and middle school, Classroom-Ready Rich Algebra Tasks, Grades 6-12 is a powerful add-on to any core mathematics program at your school.

A schoolwide solution for students’ mathematics success!

Do you sometimes start to teach a mathematics concept and feel like you’re staring at a sea of bewildered faces? What happens when you discover students previously learned a calculation trick or a mnemonic that has muddied their long-term understanding? When “rules” seem to change from year to year, teacher to teacher, or school to school, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement! 

Expanded from the highly popular “Rules that Expire” series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. Through this work, you will identify, streamline, and become passionate about using clear and consistent mathematical language, notations, representations, rules, and generalizations within and across classrooms and grades. Importantly, you’ll learn to avoid “rules that expire”—tricks that may seem to help students in one grade but hurt in the long run. Features of this book include

·         Abundant grade-specific examples

·         Effective working plans for sustainability

·         Barrier-busting tips, to-dos, and try-it-outs

·         Practical templates and checklists

·         PLC prompts and discussion points

 

When teachers unite across grades, students hit the ground running every year. Take the next step together as a team and help all your students build on existing understanding to find new success and most importantly, love learning and doing mathematics! 

A schoolwide solution for students’ mathematics success! Do you sometimes start to teach a mathematics concept and feel like you’re staring at a sea of bewildered faces? What happens when you discover students previously learned a calculation trick or a mnemonic that has muddied their long-term understanding? When “rules” seem to change from year to year, teacher to teacher, or school to school, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement!  Expanded from the highly popular “Rules that Expire” series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. Through this work, you will identify, streamline, and become passionate about using clear and consistent mathematical language, notations, representations, rules, and generalizations within and across classrooms and grades. Importantly, you’ll learn to avoid “rules that expire”—tricks that may seem to help students in one grade but hurt in the long run. Features of this book include: • Abundant grade-specific examples • Effective working plans for sustainability • Barrier-busting tips, to-dos, and try-it-outs • Practical templates and checklists • PLC prompts and discussion points When teachers unite across grades, students hit the ground running every year. Take the next step together as a team and help all your students build on existing understanding to find new success and most importantly, love learning and doing mathematics! 

 

Teaching Ratios, Proportions and Proportional Reasoning 6–8Get a deeper understanding of Ratios and Proportions with our concise and comprehensive Go-To Guide.Based on Developing Essential Understanding of Ratios, Proportions, and Proportionality and Putting Essential Understanding of Ratios and Proportions 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 Ratios, Proportions, and Proportionality and Putting Essential Understanding of Ratios and Proportions 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 Ratios and Proportions 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 Ratios and ProportionsCreate 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 Ratios and Proportions or an experienced educator, our Go-To Guides will be your trusted resource for teaching with confidence and clarity.

Teaching Geometry and Measurement 3–5Get a deeper understanding of Geometry and Measurement with our concise and comprehensive Go-To Guide.Based on Developing Essential Understanding of Geometry and Measurement and Putting Essential Understanding of Geometry and Measurement 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 Measurement and Putting Essential Understanding of Geometry and Measurement 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 and Measurement 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 Geometry and MeasurementCreate 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 and Measurement or an experienced educator, our Go-To Guides will be your trusted resource for teaching with confidence and clarity.