A Focus on Fractions

A Focus on Fractions

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  • Author: Marjorie M. Petit
  • Publisher: Routledge
  • ISBN: 1317597303
  • Category : Education
  • Languages : en
  • Pages : 208

A Focus on Fractions is a groundbreaking effort to make the mathematics education research on how students develop their understanding of fraction concepts readily accessible and understandable to pre- and in-service K– 8 mathematics educators. Using extensive annotated samples of student work, as well as vignettes characteristic of classroom teachers’ experiences, this book equips educators with the knowledge and tools to reveal students’ thinking so that they can modify their teaching and improve student learning of fraction concepts. A Focus on Fractions 2nd edition includes sections on the Common Core State Standards for Mathematics and the Ongoing Assessment Project (OGAP) Fraction Framework integrated into each chapter as well as a new chapter on the OGAP Fraction Progression and how it can be used for formative assessment purposes. This updated edition assists teachers in translating research findings into their classroom practice by conveying detailed information about how students develop fraction understandings. Additional images and examples serve to flesh out and supplement the newly-introduced concepts in this updated and expanded edition. Special Features: Looking Back Questions at the end of each chapter provide teachers the opportunity to analyze student thinking and consider instructional strategies for their own students. Instructional Links help teachers relate concepts from the chapter to their own instructional materials and programs. Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of fractions. Answer Key posted online offers extensive explanations of in-chapter questions. New sections devoted to the CCSSM and OGAP Fraction Progression are woven throughout the book as well as a new stand alone chapter on the OGAP Fraction Progression. The OGAP Fraction Framework is an all-new eResource, now available as a free download from the book’s website: www.routledge.com/9781138816442.


A Focus on Fractions

A Focus on Fractions

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  • Author: Marjorie M. Petit
  • Publisher: Routledge
  • ISBN: 1136998098
  • Category : Education
  • Languages : en
  • Pages : 264

A Focus on Fractions is the first book to make cognitive research on how students develop their understanding of fraction concepts readily accessible and understandable to pre- and in-service K– 8 mathematics educators. This important resource assists teachers in translating research findings into their classroom practice by conveying detailed information about how students develop fraction understandings as well as common student misconceptions, errors, preconceptions, and partial understandings that may interfere with students learning. Using extensive annotated samples of student work, as well as vignettes characteristic of classroom teachers’ experiences, this book equips educators with knowledge and tools to reveal students’ thinking so that they can modify their teaching to improve student learning of fractions concepts. Special Features: End of Chapter Questions provide teachers the opportunity to analyze student thinking and consider instructional strategies for their own students. Instructional Links help teachers relate concepts from the chapter to their own instructional materials and programs. Big Ideas and Research Reviews frame the chapters and provide a platform for meaningful exploration of the teaching of fractions. Answer Key posted online offers extensive explanations of in-chapter questions. A Focus on Fractions bridges the gap between what mathematics education researchers have discovered about the learning of fraction concepts and what teachers need to know to make effective instructional decisions.


A Focus on Multiplication and Division

A Focus on Multiplication and Division

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  • Author: Elizabeth T. Hulbert
  • Publisher: Taylor & Francis
  • ISBN: 1351671707
  • Category : Education
  • Languages : en
  • Pages : 213

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.


A Focus on Ratios and Proportions

A Focus on Ratios and Proportions

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  • Author: Marjorie M. Petit
  • Publisher: Routledge
  • ISBN: 1000071448
  • Category : Education
  • Languages : en
  • Pages : 264

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.


Beyond Pizzas & Pies

Beyond Pizzas & Pies

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  • Author: Julie McNamara
  • Publisher: Math Solutions
  • ISBN: 1935099132
  • Category : Education
  • Languages : en
  • Pages : 186

"This resource combines current research and practical strategies to support teachers in understanding and addressing the most common misconceptions that students have about fractions and presents opportunities to help students investigate, discuss, revise, expand, and refine their understanding of fractions. Includes reproducibles, bibliography, and index"--


Eating Fractions

Eating Fractions

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  • Author:
  • Publisher: Scholastic Inc.
  • ISBN: 0590437704
  • Category : Big books
  • Languages : en
  • Pages : 44

Food is cut into halves, quarters, and thirds to illustrate how parts make a whole. Simple recipes included.


A Focus on Addition and Subtraction

A Focus on Addition and Subtraction

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  • Author: Caroline Ebby
  • Publisher: Routledge
  • ISBN: 1000220931
  • Category : Education
  • Languages : en
  • Pages : 261

This innovative text offers a unique approach to making mathematics education research on addition, subtraction, and number concepts readily accessible and understandable to pre-service and in-service teachers of grades K–3. Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of teachers’ experiences, this book provides educators with the knowledge and tools needed to modify their lessons and improve student learning of additive reasoning in the primary grades. Based on research gathered in the Ongoing Assessment Project (OGAP), this engaging, easy-to-use resource features practical resources such as: 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 Addition, Subtraction, and Base Ten Number Progressions, based on research conducted with hundreds of teachers and thousands of pieces of student work; In-chapter sections on how Common Core State Standards for Math (CCSSM) are supported by math education research; End-of-chapter 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; An accompanying eResource, available online, offers an answer key to Looking Back questions, as well as a copy of the OGAP Additive Framework and the OGAP Number Line Continuum. A Focus on Addition and Subtraction marks the fourth installment of the popular A Focus on... collection, designed to aid the professional development of pre-service and in-service mathematics teachers. Following from previous volumes on ratios and proportions, multiplication and division, and fractions, this newest addition 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.


Unpacking Fractions

Unpacking Fractions

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  • Author: Monica Neagoy
  • Publisher: ASCD
  • ISBN: 1416621237
  • Category : Education
  • Languages : en
  • Pages : 301

For years, the teaching and learning of fractions has been associated with rote memorization. But this mechanical approach to instruction—which strips students of an ability to reason or make sense of math—has resulted in a failure of understanding. Author Monica Neagoy, drawing on decades of research studies, evidence from teacher practice, and 25 years of experience working around the world with teachers, students, and parents, addresses seven big ideas in the teaching and learning of fractions in grades 2–6. Each idea is supported by a vignette from a real classroom, common misconceptions, a thorough unpacking of productive mathematical thinking, and several multistep and thought-provoking problems for teachers to explore. She offers three fundamental reasons why it’s imperative for us to take a closer look at how we teach fractions: 1. Fractions play a key role in students’ feelings about mathematics. 2. Fractions are fundamental to school math and daily life. 3. Fractions are foundational to success in algebra. While a solid grounding in algebra is necessary for a STEM career, the worthy goal of “algebra for all” will not be possible until “fractions for all” is a reality. Unpacking Fractions provides teachers with concrete strategies for achieving that reality—in short, helping all students gain the knowledge they need to feel at ease with fractions.


Fractions in Disguise

Fractions in Disguise

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  • Author: Edward Einhorn
  • Publisher: Charlesbridge
  • ISBN: 1607347288
  • Category : Juvenile Nonfiction
  • Languages : en
  • Pages : 36

Equal parts action and humor add up to a wholly entertaining introduction to simplifying fractions, in this one-of-a-kind math picture book story. When a valuable fraction goes missing, George Cornelius Factor (a.k.a. GCF) vows to track it down. Knowing that the villainous Dr. Brok likes to disguise his ill-gotten fractions, G.C.F. invents a Reducer—half ray gun, half calculator— that strips away the disguise, reducing the fraction to its lowest common denominator and revealing its true form. With the Reducer in hand, George seeks out Dr. Brok in hopes of retrieving the missing fraction. David Clark’s illustrations are packed with humorous details as well as clearly defined fractions and their corresponding reduction equations.


Number Talks

Number Talks

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  • Author: Sherry Parrish
  • Publisher: Math Solutions Publications
  • ISBN: 9781935099758
  • Category : Education
  • Languages : en
  • Pages : 0

"This resource was created in response to the requests of teachers--those who want to implement number talks but are unsure of how to begin, and those with experience who want more guidance in crafting purposeful problems."--Page 4 de la couverture.