Rose Mary Zbiek – författare

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.

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.

The depth and breadth of a mathematics teacher’s understanding of mathematics matter most as the teacher engages in the daily work of teaching. One of the major challenges to teachers is to be ready to draw on the relevant mathematical ideas from different areas of the school curriculum and from their postsecondary mathematics experiences that can be helpful in explaining ideas to students, making instructional decisions, creating examples, and engaging in other aspects of their daily work. Being mathematically ready and confident requires teachers to engage in ongoing professional learning that helps them to connect mathematics to events like those they live on a daily basis. The purpose of this volume is to provide teachers, teacher educators, and other facilitators of professional learning opportunities with examples of authentic events and tools for discussing those events in professional learning settings.The work shared in Facilitator’s Guidebook for Use of Mathematics Situations in Professional Learning (Guidebook) resulted from a collaborative effort of school mathematics supervisors and university mathematics educators. The collaborators joined their varied experiences as teachers, coaches, supervisors, teacher educators, and researchers to suggest ways to scaffold activities, encourage discussion, and instigate reflection with teacher–participants of differing mathematics backgrounds and with varying teaching assignments. Each guide has ideas for engaging and furthering mathematical thought across a range of facilitator and participant mathematics backgrounds and draws on the collaborators’ uses of the Situations with in-service and prospective teachers.The events and mathematical ideas connected to each event come from Situations in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations. A Situation is a description of a classroom-related event and the mathematics related to it. For each of six Situations, school and university collaborators developed a facilitator’s guide that presents ideas and options for engaging teachers with the event and the mathematical ideas. The Guidebook also contains suggestions for how teachers and others might develop new Situations based on events from their own classrooms as a form of professional learning. Both teacher educators and school-based facilitators can use this volume to structure sessions and inspire ideas for professional learning activities that are rooted in the daily work of mathematics teachers and students.

The depth and breadth of a mathematics teacher’s understanding of mathematics matter most as the teacher engages in the daily work of teaching. One of the major challenges to teachers is to be ready to draw on the relevant mathematical ideas from different areas of the school curriculum and from their postsecondary mathematics experiences that can be helpful in explaining ideas to students, making instructional decisions, creating examples, and engaging in other aspects of their daily work. Being mathematically ready and confident requires teachers to engage in ongoing professional learning that helps them to connect mathematics to events like those they live on a daily basis. The purpose of this volume is to provide teachers, teacher educators, and other facilitators of professional learning opportunities with examples of authentic events and tools for discussing those events in professional learning settings.The work shared in Facilitator’s Guidebook for Use of Mathematics Situations in Professional Learning (Guidebook) resulted from a collaborative effort of school mathematics supervisors and university mathematics educators. The collaborators joined their varied experiences as teachers, coaches, supervisors, teacher educators, and researchers to suggest ways to scaffold activities, encourage discussion, and instigate reflection with teacher–participants of differing mathematics backgrounds and with varying teaching assignments. Each guide has ideas for engaging and furthering mathematical thought across a range of facilitator and participant mathematics backgrounds and draws on the collaborators’ uses of the Situations with in-service and prospective teachers.The events and mathematical ideas connected to each event come from Situations in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations. A Situation is a description of a classroom-related event and the mathematics related to it. For each of six Situations, school and university collaborators developed a facilitator’s guide that presents ideas and options for engaging teachers with the event and the mathematical ideas. The Guidebook also contains suggestions for how teachers and others might develop new Situations based on events from their own classrooms as a form of professional learning. Both teacher educators and school-based facilitators can use this volume to structure sessions and inspire ideas for professional learning activities that are rooted in the daily work of mathematics teachers and students.

The depth and breadth of a mathematics teacher's understanding of mathematics matter most as the teacher engages in the daily work of teaching. One of the major challenges to teachers is to be ready to draw on the relevant mathematical ideas from different areas of the school curriculum and from their postsecondary mathematics experiences that can be helpful in explaining ideas to students, making instructional decisions, creating examples, and engaging in other aspects of their daily work. Being mathematically ready and confident requires teachers to engage in ongoing professional learning that helps them to connect mathematics to events like those they live on a daily basis. The purpose of this volume is to provide teachers, teacher educators, and other facilitators of professional learning opportunities with examples of authentic events and tools for discussing those events in professional learning settings.The work shared in Facilitator's Guidebook for Use of Mathematics Situations in Professional Learning (Guidebook) resulted from a collaborative effort of school mathematics supervisors and university mathematics educators. The collaborators joined their varied experiences as teachers, coaches, supervisors, teacher educators, and researchers to suggest ways to scaffold activities, encourage discussion, and instigate reflection with teacher-participants of differing mathematics backgrounds and with varying teaching assignments. Each guide has ideas for engaging and furthering mathematical thought across a range of facilitator and participant mathematics backgrounds and draws on the collaborators' uses of the Situations with in-service and prospective teachers.The events and mathematical ideas connected to each event come from Situations in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations. A Situation is a description of a classroom-related event and the mathematics related to it. For each of six Situations, school and university collaborators developed a facilitator's guide that presents ideas and options for engaging teachers with the event and the mathematical ideas. The Guidebook also contains suggestions for how teachers and others might develop new Situations based on events from their own classrooms as a form of professional learning. Both teacher educators and school-based facilitators can use this volume to structure sessions and inspire ideas for professional learning activities that are rooted in the daily work of mathematics teachers and students.

Get a deeper understanding of teaching number and numeration, PK-2 with our concise and comprehensive Go-To Guide.Based on Developing Essential Understanding of Number and Numeration PK-2 and Putting Essential Understanding of Number and Numeration into Practice PK-2, 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 Number and Numeration PK-2 and Putting Essential Understanding of Number and Numeration into Practice PK-2,reviewing the basics before diving deeper into the subject,refreshing your knowledge and filling in gaps in your understanding, andidentifying 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 number and numeration in grades PK-2, 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 number and numeration, PK-2,create targeted lessons and activities that meet the needs of students,anticipate common student misconceptions and errors,design effective assessments and evaluations, andenhance your own math knowledge and skills.Whether you're new to teaching number and numeration PK–2, or an experienced educator, our Go-To Guides will be your trusted resource for teaching with confidence and clarity.

Get a deeper understanding of teaching fractions and rational numbers, 3–5 with our concise and comprehensive Go-To Guide.Based on Developing Essential Understanding of Rational Numbers 3–5 and Putting Essential Understanding of Fractions into Practice 3–5, 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 Rational Numbers 3–5 and Putting Essential Understanding of Fractions into Practice 3–5, 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 fractions and rational numbers, 3–5 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 fractions and rational numbers, 3–5create targeted lessons and activities that meet the needs of students,anticipate common student misconceptions and errors,design effective assessments and evaluations, andenhance your own math knowledge and skills.Whether you're new to teaching fractions and rational numbers 3–5, or an experienced educator, our Go-To Guides will be your trusted resource for teaching with confidence and clarity.

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.

Get a deeper understanding of Expressions, Equations, and Functions with our concise and comprehensive Go-To Guide.Based on Developing Essential Understanding of Expressions, Equations, and Functions and Putting Essential Understanding of Expressions and Equations 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 Expressions, Equations, and Functions and Putting Essential Understanding of Expressions and Equations into PracticeReviewing the basics before diving deeper into the subjectRefreshing your knowledge and filling in gaps in your understanding Identifying 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 Expressions, Equations, and Functions 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 Expressions, Equations, and Functions Create 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 Expressions, Equations, and Functions 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.

Get a deeper understanding of teaching Statistics, 9–12 with our concise and comprehensive Go-To Guide.Based on Developing Essential Understanding of Statistics 9–12 and Putting Essential Understanding of Statistics 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 Statistics 9–12 and Putting Essential Understanding of Statistics into Practice 9–12,reviewing the basics before diving deeper into the subject,refreshing your knowledge and filling in gaps in your understanding, andidentifying 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 Statistics in grades 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 Statistics, 9–12,create targeted lessons and activities that meet the needs of students,anticipate common student misconceptions and errors,design effective assessments and evaluations, andenhance your own math knowledge and skills.Whether you're new to teaching Statistics 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 teaching Statistics, 6–8 with our concise and comprehensive Go-To Guide.Based on Developing Essential Understanding of Statistics 6–8, 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 Statistics 6-8reviewing the basics before diving deeper into the subject,refreshing your knowledge and filling in gaps in your understanding, andidentifying 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 Statistics in grades 6–8, by focusing on the core concepts and relationships that underlie the subject.This Go-To Guide is perfect for those looking todevelop a deeper understanding of Statistics, 6–8,create targeted lessons and activities that meet the needs of students,anticipate common student misconceptions and errors,design effective assessments and evaluations, andenhance your own math knowledge and skills.Whether you're new to teaching Statistics 6–8, or an experienced educator, our Go-To Guides will be your trusted resource for teaching with confidence and clarity.

The depth and breadth of a mathematics teacher's understanding of mathematics matter most as the teacher engages in the daily work of teaching. One of the major challenges to teachers is to be ready to draw on the relevant mathematical ideas from different areas of the school curriculum and from their postsecondary mathematics experiences that can be helpful in explaining ideas to students, making instructional decisions, creating examples, and engaging in other aspects of their daily work. Being mathematically ready and confident requires teachers to engage in ongoing professional learning that helps them to connect mathematics to events like those they live on a daily basis. The purpose of this volume is to provide teachers, teacher educators, and other facilitators of professional learning opportunities with examples of authentic events and tools for discussing those events in professional learning settings.The work shared in Facilitator's Guidebook for Use of Mathematics Situations in Professional Learning (Guidebook) resulted from a collaborative effort of school mathematics supervisors and university mathematics educators. The collaborators joined their varied experiences as teachers, coaches, supervisors, teacher educators, and researchers to suggest ways to scaffold activities, encourage discussion, and instigate reflection with teacher-participants of differing mathematics backgrounds and with varying teaching assignments. Each guide has ideas for engaging and furthering mathematical thought across a range of facilitator and participant mathematics backgrounds and draws on the collaborators' uses of the Situations with in-service and prospective teachers.The events and mathematical ideas connected to each event come from Situations in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations. A Situation is a description of a classroom-related event and the mathematics related to it. For each of six Situations, school and university collaborators developed a facilitator's guide that presents ideas and options for engaging teachers with the event and the mathematical ideas. The Guidebook also contains suggestions for how teachers and others might develop new Situations based on events from their own classrooms as a form of professional learning. Both teacher educators and school-based facilitators can use this volume to structure sessions and inspire ideas for professional learning activities that are rooted in the daily work of mathematics teachers and students.