Caroline B. Ebby – författare

The third edition of this book offers a unique approach to making mathematics education research on the teaching and learning of fraction concepts readily accessible and understandable to pre-service and in-service K-8 mathematics teachers.

Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers’ experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction and ultimately improve student learning. Based on research gathered in the Ongoing Assessment Project (OGAP), and updated throughout, this engaging and easy-to-use resource also features:

Two new chapters dedicated to understanding the OGAP Fraction Framework and Progression—based on research conducted with hundreds of teachers—to gather and interpret evidence of student learning along a learning progression, referenced throughout the book so readers can apply the concepts to their instruction;

A close focus on student work, including 180+ annotated pieces of student work, to help teachers improve their ability to recognize, assess, and monitor their students’ errors and misconceptions, as well as their developing conceptual understanding;

A discussion of decimal fractions, also new to the third edition;

In-chapter sections on how Common Core State Standards for Math (CCSSM) are supported by math education research;

End-of-chapter Looking Back questions to allow teachers to analyze student thinking and consider instructional strategies for their own students;

Instructional links to help teachers relate concepts from each chapter to their own instructional materials and programs;

Accompanying online Support Material includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and Progression.

A Focus on Fractions is part of the popular A Focus on . . . collection, designed to aid the professional development of pre-service and in-service mathematics teachers. As with the other volumes on addition and subtraction, ratios and proportions, and multiplication and division, this updated new edition bridges the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.

The third edition of this book offers a unique approach to making mathematics education research on the teaching and learning of fraction concepts readily accessible and understandable to pre-service and in-service K-8 mathematics teachers.

Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers’ experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction and ultimately improve student learning. Based on research gathered in the Ongoing Assessment Project (OGAP), and updated throughout, this engaging and easy-to-use resource also features:

Two new chapters dedicated to understanding the OGAP Fraction Framework and Progression—based on research conducted with hundreds of teachers—to gather and interpret evidence of student learning along a learning progression, referenced throughout the book so readers can apply the concepts to their instruction;

A close focus on student work, including 180+ annotated pieces of student work, to help teachers improve their ability to recognize, assess, and monitor their students’ errors and misconceptions, as well as their developing conceptual understanding;

A discussion of decimal fractions, also new to the third edition;

In-chapter sections on how Common Core State Standards for Math (CCSSM) are supported by math education research;

End-of-chapter Looking Back questions to allow teachers to analyze student thinking and consider instructional strategies for their own students;

Instructional links to help teachers relate concepts from each chapter to their own instructional materials and programs;

Accompanying online Support Material includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and Progression.

A Focus on Fractions is part of the popular A Focus on . . . collection, designed to aid the professional development of pre-service and in-service mathematics teachers. As with the other volumes on addition and subtraction, ratios and proportions, and multiplication and division, this updated new edition bridges the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.

The second edition of this book offers a unique approach to making mathematics education research on the teaching and learning of multiplication and division concepts readily accessible and understandable to preservice and in-service K-6 mathematics teachers.

Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers’ experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction, and ultimately improve student learning. Based on research gathered in the Ongoing Assessment Project (OGAP) and updated throughout, this engaging and easy-to-use resource also features the following:

New chapters on the OGAP Multiplicative Reasoning Framework and Learning Progressions and Using the OGAP Multiplicative Progression to inform instruction and support student learning In-chapter sections on how Common Core State Standards for Math are supported by math education research Case Studies focusing on a core mathematical idea and different types of instructional responses to illustrate how teachers can elicit evidence of student thinking and use that information to inform instruction Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and division Looking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own students Instructional Links to help teachers relate concepts from each chapter to their own instructional materials and programs Accompanying online Support Material that includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and Progression

A Focus on Multiplication and Division is part of the popular A Focus on . . . collection, designed to aid the professional development of preservice and in-service mathematics teachers. As with the other volumes on addition and subtraction, ratios and proportions, and fractions, this updated new edition bridges the gap between what math education researchers know and what teachers need to know to better understand evidence in student work and make effective instructional decisions.

The second edition of this book offers a unique approach to making mathematics education research on the teaching and learning of multiplication and division concepts readily accessible and understandable to preservice and in-service K-6 mathematics teachers.

Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers’ experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction, and ultimately improve student learning. Based on research gathered in the Ongoing Assessment Project (OGAP) and updated throughout, this engaging and easy-to-use resource also features the following:

New chapters on the OGAP Multiplicative Reasoning Framework and Learning Progressions and Using the OGAP Multiplicative Progression to inform instruction and support student learning In-chapter sections on how Common Core State Standards for Math are supported by math education research Case Studies focusing on a core mathematical idea and different types of instructional responses to illustrate how teachers can elicit evidence of student thinking and use that information to inform instruction Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and division Looking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own students Instructional Links to help teachers relate concepts from each chapter to their own instructional materials and programs Accompanying online Support Material that includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and Progression

A Focus on Multiplication and Division is part of the popular A Focus on . . . collection, designed to aid the professional development of preservice and in-service mathematics teachers. As with the other volumes on addition and subtraction, ratios and proportions, and fractions, this updated new edition bridges the gap between what math education researchers know and what teachers need to know to better understand evidence in student work and make effective instructional decisions.

The third edition of this book offers a unique approach to making mathematics education research on the teaching and learning of fraction concepts readily accessible and understandable to pre-service and in-service K-8 mathematics teachers.Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers’ experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction and ultimately improve student learning. Based on research gathered in the Ongoing Assessment Project (OGAP), and updated throughout, this engaging and easy-to-use resource also features:Two new chapters dedicated to understanding the OGAP Fraction Framework and Progression—based on research conducted with hundreds of teachers—to gather and interpret evidence of student learning along a learning progression, referenced throughout the book so readers can apply the concepts to their instructionA close focus on student work, including 180+ annotated pieces of student work, to help teachers improve their ability to recognize, assess, and monitor their students’ errors and misconceptions, as well as their developing conceptual understandingA discussion of decimal fractions, also new to the third editionIn-chapter sections on how Common Core State Standards for Math (CCSSM) are supported by math education researchEnd-of-chapter Looking Back questions to allow teachers to analyze student thinking and consider instructional strategies for their own studentsInstructional links to help teachers relate concepts from each chapter to their own instructional materials and programsAccompanying online Support Material includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and ProgressionA Focus on Fractions is part of the popular A Focus on... collection, designed to aid the professional development of pre-service and in-service mathematics teachers. As with the other volumes on addition and subtraction, ratios and proportions, and multiplication and division, this updated new edition bridges the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.

The third edition of this book offers a unique approach to making mathematics education research on the teaching and learning of fraction concepts readily accessible and understandable to pre-service and in-service K-8 mathematics teachers.Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers’ experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction and ultimately improve student learning. Based on research gathered in the Ongoing Assessment Project (OGAP), and updated throughout, this engaging and easy-to-use resource also features:Two new chapters dedicated to understanding the OGAP Fraction Framework and Progression—based on research conducted with hundreds of teachers—to gather and interpret evidence of student learning along a learning progression, referenced throughout the book so readers can apply the concepts to their instructionA close focus on student work, including 180+ annotated pieces of student work, to help teachers improve their ability to recognize, assess, and monitor their students’ errors and misconceptions, as well as their developing conceptual understandingA discussion of decimal fractions, also new to the third editionIn-chapter sections on how Common Core State Standards for Math (CCSSM) are supported by math education researchEnd-of-chapter Looking Back questions to allow teachers to analyze student thinking and consider instructional strategies for their own studentsInstructional links to help teachers relate concepts from each chapter to their own instructional materials and programsAccompanying online Support Material includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and ProgressionA Focus on Fractions is part of the popular A Focus on... collection, designed to aid the professional development of pre-service and in-service mathematics teachers. As with the other volumes on addition and subtraction, ratios and proportions, and multiplication and division, this updated new edition bridges the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.

The second edition of this book offers a unique approach to making mathematics education research on the teaching and learning of multiplication and division concepts readily accessible and understandable to preservice and in-service K-6 mathematics teachers.Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers’ experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction, and ultimately improve student learning. Based on research gathered in the Ongoing Assessment Project (OGAP) and updated throughout, this engaging and easy-to-use resource also features the following:New chapters on the OGAP Multiplicative Reasoning Framework and Learning Progressions and Using the OGAP Multiplicative Progression to inform instruction and support student learningIn-chapter sections on how Common Core State Standards for Math are supported by math education researchCase Studies focusing on a core mathematical idea and different types of instructional responses to illustrate how teachers can elicit evidence of student thinking and use that information to inform instructionBig Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and divisionLooking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own studentsInstructional Links to help teachers relate concepts from each chapter to their own instructional materials and programsAccompanying online Support Material that includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and Progression A Focus on Multiplication and Division is part of the popular A Focus on . . . collection, designed to aid the professional development of preservice and in-service mathematics teachers. As with the other volumes on addition and subtraction, ratios and proportions, and fractions, this updated new edition bridges the gap between what math education researchers know and what teachers need to know to better understand evidence in student work and make effective instructional decisions.

The second edition of this book offers a unique approach to making mathematics education research on the teaching and learning of multiplication and division concepts readily accessible and understandable to preservice and in-service K-6 mathematics teachers.Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers’ experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction, and ultimately improve student learning. Based on research gathered in the Ongoing Assessment Project (OGAP) and updated throughout, this engaging and easy-to-use resource also features the following:New chapters on the OGAP Multiplicative Reasoning Framework and Learning Progressions and Using the OGAP Multiplicative Progression to inform instruction and support student learningIn-chapter sections on how Common Core State Standards for Math are supported by math education researchCase Studies focusing on a core mathematical idea and different types of instructional responses to illustrate how teachers can elicit evidence of student thinking and use that information to inform instructionBig Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and divisionLooking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own studentsInstructional Links to help teachers relate concepts from each chapter to their own instructional materials and programsAccompanying online Support Material that includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and Progression A Focus on Multiplication and Division is part of the popular A Focus on . . . collection, designed to aid the professional development of preservice and in-service mathematics teachers. As with the other volumes on addition and subtraction, ratios and proportions, and fractions, this updated new edition bridges the gap between what math education researchers know and what teachers need to know to better understand evidence in student work and make effective instructional decisions.

This resource presents and describes a model for teaching and learning mathematics responsively in the elementary and middle grades. Developed through the Responsive Math Teaching (RMT) project—a seven-year collaboration between teachers, teacher leaders, school and district administrators, and researchers from a network of K-8 urban schools—this book equips any mathematics educator with the tools to enhance instruction and increase equitable outcomes for students and communities historically underrepresented in mathematics. Chapters pair research-based instructional practices with real examples to show how this model has been successfully implemented in actual schools, often under challenging conditions. Each chapter includes classroom vignettes and then breaks down the topic into jobs or responsibilities for teachers, indicating their specific role in supporting their students. The authors provide tools to assist teachers in the decision-making needed to carry out these responsibilities in the classroom. Topics include the components of a responsive mathematics lesson, comprehensive lesson planning guidance, building a responsive classroom community, and supporting responsive teaching as an instructional leader. Whether you are a classroom teacher, teacher educator, or leader, this book can guide you in understanding and reframing your responsibilities, challenge existing norms around mathematics, empower your students as problem-solvers, and ultimately cultivate joy in mathematics teaching and learning.

This resource presents and describes a model for teaching and learning mathematics responsively in the elementary and middle grades. Developed through the Responsive Math Teaching (RMT) project—a seven-year collaboration between teachers, teacher leaders, school and district administrators, and researchers from a network of K-8 urban schools—this book equips any mathematics educator with the tools to enhance instruction and increase equitable outcomes for students and communities historically underrepresented in mathematics. Chapters pair research-based instructional practices with real examples to show how this model has been successfully implemented in actual schools, often under challenging conditions. Each chapter includes classroom vignettes and then breaks down the topic into jobs or responsibilities for teachers, indicating their specific role in supporting their students. The authors provide tools to assist teachers in the decision-making needed to carry out these responsibilities in the classroom. Topics include the components of a responsive mathematics lesson, comprehensive lesson planning guidance, building a responsive classroom community, and supporting responsive teaching as an instructional leader. Whether you are a classroom teacher, teacher educator, or leader, this book can guide you in understanding and reframing your responsibilities, challenge existing norms around mathematics, empower your students as problem-solvers, and ultimately cultivate joy in mathematics teaching and learning.

This resource presents and describes a model for teaching and learning mathematics responsively in the elementary and middle grades. Developed through the Responsive Math Teaching (RMT) project-a seven-year collaboration between teachers, teacher leaders, school and district administrators, and researchers from a network of K-8 urban schools-this book equips any mathematics educator with the tools to enhance instruction and increase equitable outcomes for students and communities historically underrepresented in mathematics. Chapters pair research-based instructional practices with real examples to show how this model has been successfully implemented in actual schools, often under challenging conditions. Each chapter includes classroom vignettes and then breaks down the topic into jobs or responsibilities for teachers, indicating their specific role in supporting their students. The authors provide tools to assist teachers in the decision-making needed to carry out these responsibilities in the classroom. Topics include the components of a responsive mathematics lesson, comprehensive lesson planning guidance, building a responsive classroom community, and supporting responsive teaching as an instructional leader. Whether you are a classroom teacher, teacher educator, or leader, this book can guide you in understanding and reframing your responsibilities, challenge existing norms around mathematics, empower your students as problem-solvers, and ultimately cultivate joy in mathematics teaching and learning.