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A Focus on Multiplication and Division is a groundbreaking effort
to make mathematics education research readily accessible and
understandable to pre- and in-service K-6 mathematics educators.
Revealing students' thought processes with extensive annotated
samples of student work and vignettes characteristic of teachers'
experiences, this book is sure to equip educators with the
knowledge and tools needed to modify their lessons and to improve
student learning of multiplication and division. Special Features:
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 help teachers relate
concepts from each chapter to their own instructional materials and
programs. Big Ideas frame the chapters and provide a platform for
meaningful exploration of the teaching of multiplication and
division. Answer Key posted online offers extensive explanations of
in-chapter questions. Each chapter includes sections on the Common
Core State Standards for Mathematics and integrates the Ongoing
Assessment Project (OGAP) Multiplicative Reasoning Progression for
formative assessment purposes. Centered on the question of how
students develop their understanding of mathematical concepts, this
innovative book places math teachers in the mode of ongoing action
researchers.
-Makes mathematics education research on multiplication and
division accessible and understandable to pre-service and
in-service teachers of grades K-6, allowing teachers to understand
evidence in student work and make better instructional decisions.
-Uses extensive annotated samples of student work, helping teachers
improve their ability to recognize and assess student errors and
misconceptions, as well as their understanding, learning, and
fluency of multiplicative reasoning. -Built off the wide-scale
research gathered in the Ongoing Assessment Project (OGAP), drawn
from hundreds of teachers and thousands of examples of student
work. -Each chapter includes student work samples and vignettes to
illuminate the research, guidance on CCSSM standards, end of
chapter questions, professional development activities, and
instructional links that help teachers relate concepts back to
their own instructional materials and programs. -This edition has
been updated throughout with the latest research, CCSSM standards,
additional examples and vignettes, and more.
-Makes mathematics education research on fraction concepts
accessible and understandable to pre-service and in-service
teachers of grades K-8, allowing teachers to understand evidence in
student work and make better instructional decisions. -Uses
extensive annotated samples of student work, helping teachers
improve their ability to recognize and assess student errors and
misconceptions, as well as their understanding, learning, and
fluency of fraction concepts. -Built off the wide-scale research
gathered in the Ongoing Assessment Project (OGAP), drawn from
hundreds of teachers and thousands of examples of student work.
-Each chapter includes student work samples and vignettes to
illuminate the research, guidance on CCSSM standards, end of
chapter questions, professional development activities, and
instructional links that help teachers relate concepts back to
their own instructional materials and programs. -This edition has
been updated throughout with the latest research, CCSSM standards,
additional examples and vignettes, and more.
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 pre-service 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: 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 (CCSSM) are supported by math education research
Case Studies are presented, 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 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 Multiplication and Division 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 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.
-Makes mathematics education research on fraction concepts
accessible and understandable to pre-service and in-service
teachers of grades K-8, allowing teachers to understand evidence in
student work and make better instructional decisions. -Uses
extensive annotated samples of student work, helping teachers
improve their ability to recognize and assess student errors and
misconceptions, as well as their understanding, learning, and
fluency of fraction concepts. -Built off the wide-scale research
gathered in the Ongoing Assessment Project (OGAP), drawn from
hundreds of teachers and thousands of examples of student work.
-Each chapter includes student work samples and vignettes to
illuminate the research, guidance on CCSSM standards, end of
chapter questions, professional development activities, and
instructional links that help teachers relate concepts back to
their own instructional materials and programs. -This edition has
been updated throughout with the latest research, CCSSM standards,
additional examples and vignettes, and more.
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.
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