Robert E. Laird – författare

This resource offers a groundbreaking effort to make mathematics education research on ratios and proportions readily accessible and understandable to preservice and in-service teachers of grades 6 to 8. Using extensive annotated samples of student work and based on research gathered in the Ongoing Assessment Project (OGAP), A Focus on Ratios and Proportions teaches readers how students develop understanding and fluency involving ratio and proportion concepts.Special features include:A close focus on student work, including 150+ 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 focus on the OGAP Ratios and Proportions Progression, based on research conducted with hundreds of teachers and thousands of pieces of student work.Sections on how Common Core State Standards for Math (CCSSM) are supported by math education research.Student work samples and vignettes to illuminate the research, as well as end of chapter Looking Back questions and Instructional Links, which allow teachers to analyze evidence of student thinking and strategies and consider instructional responses.An accompanying eResource, available online, offers an answer key as well as extensive explanation of the Looking Back questions.Like A Focus on Multiplication and Division and A Focus on Fractions, this book is designed to bridge 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.

This resource offers a groundbreaking effort to make mathematics education research on ratios and proportions readily accessible and understandable to preservice and in-service teachers of grades 6 to 8. Using extensive annotated samples of student work and based on research gathered in the Ongoing Assessment Project (OGAP), A Focus on Ratios and Proportions teaches readers how students develop understanding and fluency involving ratio and proportion concepts.Special features include:A close focus on student work, including 150+ 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 focus on the OGAP Ratios and Proportions Progression, based on research conducted with hundreds of teachers and thousands of pieces of student work.Sections on how Common Core State Standards for Math (CCSSM) are supported by math education research.Student work samples and vignettes to illuminate the research, as well as end of chapter Looking Back questions and Instructional Links, which allow teachers to analyze evidence of student thinking and strategies and consider instructional responses.An accompanying eResource, available online, offers an answer key as well as extensive explanation of the Looking Back questions.Like A Focus on Multiplication and Division and A Focus on Fractions, this book is designed to bridge 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.

This resource offers a groundbreaking effort to make mathematics education research on ratios and proportions readily accessible and understandable to preservice and in-service teachers of grades 6 to 8. Using extensive annotated samples of student work and based on research gathered in the Ongoing Assessment Project (OGAP), A Focus on Ratios and Proportions teaches readers how students develop understanding and fluency involving ratio and proportion concepts.

Special features include:

A close focus on student work, including 150+ 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 focus on the OGAP Ratios and Proportions Progression, based on research conducted with hundreds of teachers and thousands of pieces of student work. Sections on how Common Core State Standards for Math (CCSSM) are supported by math education research. Student work samples and vignettes to illuminate the research, as well as end of chapter Looking Back questions and Instructional Links, which allow teachers to analyze evidence of student thinking and strategies and consider instructional responses. An accompanying eResource, available online, offers an answer key as well as extensive explanation of the Looking Back questions.

Like A Focus on Multiplication and Division and A Focus on Fractions, this book is designed to bridge 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.

This resource offers a groundbreaking effort to make mathematics education research on ratios and proportions readily accessible and understandable to preservice and in-service teachers of grades 6 to 8. Using extensive annotated samples of student work and based on research gathered in the Ongoing Assessment Project (OGAP), A Focus on Ratios and Proportions teaches readers how students develop understanding and fluency involving ratio and proportion concepts.

Special features include:

A close focus on student work, including 150+ 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 focus on the OGAP Ratios and Proportions Progression, based on research conducted with hundreds of teachers and thousands of pieces of student work. Sections on how Common Core State Standards for Math (CCSSM) are supported by math education research. Student work samples and vignettes to illuminate the research, as well as end of chapter Looking Back questions and Instructional Links, which allow teachers to analyze evidence of student thinking and strategies and consider instructional responses. An accompanying eResource, available online, offers an answer key as well as extensive explanation of the Looking Back questions.

Like A Focus on Multiplication and Division and A Focus on Fractions, this book is designed to bridge 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 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.