More Teaching Fractions And Ratios For Understanding

Author : Susan J. Lamon
Publisher : Routledge
Page : 254 pages
File Size : 54,7 Mb
Release : 2006-08-15
Category : Education
ISBN : 9781135606787

Get Book

Teaching Fractions and Ratios for Understanding by Susan J. Lamon Pdf

This popular text addresses the urgent need for curriculum materials that cross traditional boundaries to include many of the elements that are integrated in the teaching/learning enterprise: mathematics content, teacher understanding, student thinking, teaching methods, instructional activities, and assessment. The book pushes readers beyond the limits of their current understanding of rational numbers, challenging them to refine and explain their thinking--without falling back on rules and procedures they have relied on throughout their lives. Written in a conversational and easy to understand style, this is not a textbook as much as it is a resource book. An underlying assumption is that facilitating teacher understanding using the same questions and activities that may be used with children is one way to help teachers build the comfort and confidence they need to begin talking to children about complex ideas. Unlike a textbook that is used to study formal theory and then discarded when it comes to putting ideas into practice, the many problems and activities included to facilitate teacher learning are valuable resources for use in elementary and middle school classrooms. Changes in the second edition include: *even more student work incorporated in every chapter; *discussion of the connectivity between the topics addressed in the book and the elementary and middle school mathematics curricula; *an increased emphasis on measurement; *expansion of some topics, including number sense, percent, scale factors, similarity, and linear graphs; *clarification of the characteristics of ratio and proportions and how to use these to generate discussion with children; and *content-related interview questions for exploring children's thinking. This book is a valuable resource for researchers and curriculum developers in mathematics education, pre-service and in-service teachers of mathematics, those involved in the mathematical and pedagogical preparation of mathematics teachers, and graduate students in mathematics education. The methods and activities it includes have been tested with students in grades 3-8 and with pre-service and in-service teachers and other adults. This text is accompanied by MORE--a supplement that is not merely an answer key but a resource that includes in-depth discussions of all the problems in the text; develops and extends discussion of the issues, teaching problems, and other considerations raised in the chapters; and contains additional problems--with and without solutions--that instructors may find helpful for assessment purposes.

Author : Susan J. Lamon
Publisher : Routledge
Page : 347 pages
File Size : 41,9 Mb
Release : 2020-03-23
Category : Education
ISBN : 9781000037333

Get Book

Teaching Fractions and Ratios for Understanding by Susan J. Lamon Pdf

Written in a user-friendly, conversational style, the fourth edition of this groundbreaking text helps pre-service and in-service mathematics teachers build the comfort and confidence they need to begin talking to children about fractions and ratios, distilling complex ideas and translating research into usable ideas for the classroom. For two decades, Teaching Fractions and Ratios for Understanding has pushed readers beyond the limits of their current understanding of fractions and rational numbers, challenging them to refine and explain their thinking without falling back on rules and procedures they have relied on throughout their lives. All of the material offered in the book has been used with students, and is presented so that readers can see the brilliance of their insights as well as the issues that challenge their understanding. Each chapter includes children’s strategies and samples of student work for teacher analysis, as well as activities for practicing each thinking strategy, designed to be solved without rules or algorithms, using reasoning alone. The fourth edition of this popular text has been updated throughout and includes new examples of student work, updated artwork, and more. As with previous editions, an equally valuable component of this text is the companion book MORE! Teaching Fractions and Ratios for Understanding (2012), a supplement that is not merely an answer key but a resource that provides the scaffolding for the groundbreaking approach to fraction and ratio instruction explored here. MORE! includes in-depth discussions of selected problems in the main text, supplementary activities, Praxis preparation questions, more student work, and templates for key manipulatives.

Author : Susan J. Lamon
Publisher : Routledge
Page : 172 pages
File Size : 53,9 Mb
Release : 2014-04-04
Category : Education
ISBN : 9781135606701

Get Book

More Teaching Fractions and Ratios for Understanding by Susan J. Lamon Pdf

This book is a supplement to the text Teaching Fractions and Ratios for Understanding. It is not merely an answer key, but a resource that includes in-depth discussions of the problems in the text; develops and extends discussion of the issues, teaching problems, and other considerations raised in the chapters; and contains additional problems--with and without solutions--that instructors may find helpful for assessment purposes. In the second edition, MORE has been reorganized so that supplementary activities immediately follow the discussions of the activities from the text. Solutions to these supplemental activities have been removed to facilitate the use of MORE in courses. Nevertheless, because the number of activities in each chapter of the text has increased and complete discussions of all of them are provided in MORE, there is ample opportunity to learn reasoning methods.

Author : Susan J. Lamon
Publisher : Unknown
Page : 138 pages
File Size : 54,9 Mb
Release : 2012
Category : Electronic books
ISBN : 1315045540

Get Book

More! Teaching Fractions and Ratios for Understanding by Susan J. Lamon Pdf

"More is not an answer key but a resource that provides the scaffolding for the groundbreaking approach to fraction and ratio instruction presented in its companion text, Teaching Fractions and Ratios. Keeping the focus on the reasoning needed to properly understand and teach rational numbers, More shows teachers how to engage in powerful ways of thinking so that they can, in turn, enhance the mathematical education of their students. Like its companion text, More has been heavily expanded and reorganized, including even more student work, templates for key manipulatives, and an emphasis on applications to everyday life. Based on the content chapters in Teaching Fractions and Ratios, each chapter includes:In-depth Discussions of selected problems and their solutions. Supplementary Activities and a collection of challenging problems involving fractions. Praxis Preparation Questions geared to the content of each chapter"--Provided by publisher.

Author : Susan J. Lamon
Publisher : Routledge
Page : 348 pages
File Size : 47,9 Mb
Release : 2005-10-01
Category : Education
ISBN : 0805852123

Get Book

Teaching Fractions and More Set 2nd Ed by Susan J. Lamon Pdf

This popular text addresses the urgent need for curriculum materials that cross traditional boundaries to include many of the elements that are integrated in the teaching/learning enterprise: mathematics content, teacher understanding, student thinking, teaching methods, instructional activities, and assessment. The book pushes readers beyond the limits of their current understanding of rational numbers, challenging them to refine and explain their thinking--without falling back on rules and procedures they have relied on throughout their lives. By facilitating teacher understanding through the same kinds of questions and activities that may be used with children in grades 3-8, this book helps teachers build the comfort and confidence they need to begin talking to children about fractions and ratios. The many problems and activities included her, plus the clear distillation of complex ideas make this text a valuable resources for both pre- and in-service mathematics teachers. New features and coverage in the third edition include: Even more student work and mathematical content incorporated into every chapter An increased emphasis on technology in the mathematics classroom More explicit connection to how teachers support students with a focus on sequencing instructional activities and differentiating tasks for various levels of thinking A companion website with additional examples, exam questions, and hand-outs of key visuals from the text. a This text is accompanied by an updated MORE--a supplement that is not merely an answer key but a resource that includes in-depth discussions of all the problems in the text; develops and extends discussion of the issues, teaching problems, and other considerations raised in the chapters; and contains additional problems--with and without solutions--that instructors may find helpful for assessment purposes.

Author : Susan J. Lamon
Publisher : Routledge
Page : 178 pages
File Size : 55,7 Mb
Release : 2005-10-01
Category : Education
ISBN : 9781135667740

Get Book

More: in-depth Discussion of the Reasoning Activities in teaching Fractions and Ratios for Understanding by Susan J. Lamon Pdf

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

Author : Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles
Publisher : National Council of Teachers of English
Page : 0 pages
File Size : 42,6 Mb
Release : 2010
Category : Curriculum planning
ISBN : 0873536223

Get Book

Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8 by Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles Pdf

"A series for teaching mathematics."--P. [1] of cover.

Author : Marjorie M. Petit,Robert E. Laird,Edwin L. Marsden,Caroline B. Ebby
Publisher : Routledge
Page : 208 pages
File Size : 54,5 Mb
Release : 2015-07-24
Category : Education
ISBN : 9781317597308

Get Book

A Focus on Fractions by Marjorie M. Petit,Robert E. Laird,Edwin L. Marsden,Caroline B. Ebby Pdf

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.

Author : Monica Neagoy
Publisher : ASCD
Page : 301 pages
File Size : 45,6 Mb
Release : 2017-03-10
Category : Education
ISBN : 9781416621232

Get Book

Unpacking Fractions by Monica Neagoy Pdf

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.

Author : Carne Barnett-Clarke
Publisher : National Council of Teachers of English
Page : 83 pages
File Size : 47,6 Mb
Release : 2010
Category : Mathematics
ISBN : 0873536304

Get Book

Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3/5 by Carne Barnett-Clarke Pdf

What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades? How much do you know… and how much do you need to know? Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about rational numbers. It is organised around four big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to rational numbers, 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. Focus on the ideas that you need to understand thoroughly to teach confidently.

Author : Marjorie M. Petit,Robert E. Laird,Matthew F. Wyneken,Frances R. Huntoon,Mary D. Abele-Austin,Jean D. Sequeira
Publisher : Routledge
Page : 242 pages
File Size : 43,7 Mb
Release : 2020-05-17
Category : Education
ISBN : 9781000071443

Get Book

A Focus on Ratios and Proportions by Marjorie M. Petit,Robert E. Laird,Matthew F. Wyneken,Frances R. Huntoon,Mary D. Abele-Austin,Jean D. Sequeira Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 48,9 Mb
Release : 1994
Category : Electronic
ISBN : OCLC:1106733872

Get Book

Fractions, Decimals, Ratios, and Percents by Anonim Pdf

Author : David Ben-Chaim,Yaffa Keret,Bat-Sheva Ilany
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 40,9 Mb
Release : 2012-07-30
Category : Education
ISBN : 9789460917844

Get Book

Ratio and Proportion by David Ben-Chaim,Yaffa Keret,Bat-Sheva Ilany Pdf

Ratio and Proportion—Research and Teaching in Mathematics Teachers’ Education offers its readers an intellectual adventure where they can acquire invaluable tools to turn teaching ratio and proportion to professionals and school children into an enjoyable experience. Based on in-depth research, it presents a deep, comprehensive view of the topic, focusing on both the mathematical and psychological-didactical aspects of teaching it. The unique teaching model incorporates both theoretical and practical knowledge, allowing instructors to custom-design teacher courses according to their speci?c needs. The book reports on hands-on experience in the college classes plus teachers’ experience in the actual classroom setting. An important feature is the extensive variety of interesting, meaningful authentic activities. While these activities are on a level that will engage pre- and in-service mathematics teachers in training, most can also be utilized in upper elementary and middle school classes. Accompanying the majority of these activities are detailed remarks, explanations, and solutions, along with creative ideas on how to conduct and expand the learning adventure. While primarily written for educators of mathematics teachers, this book can be an invaluable source of information for mathematics teachers of elementary and middle school classes, pre-service teachers, and mathematics education researchers.

Author : Marian Small
Publisher : Teachers College Press
Page : 129 pages
File Size : 46,6 Mb
Release : 2015-04-10
Category : Education
ISBN : 9780807756607

Get Book

Building Proportional Reasoning Across Grades and Math Strands, K-8 by Marian Small Pdf

Although proportional reasoning is not formally introduced as a topic in the Common Core and other mathematics curricula until 6th grade, introducing its fundamental ideas in the early grades helps students develop essential skills in ratios, percentages, and other proportional representations when they reach the upper grades. The author takes this complex subject and crafts examples and questions that help teachers see the larger purpose in teaching concepts, such as unitizing, and how that understanding is essential for more complex ideas, such as ratios. Teachers and vertical teams can see how the concepts can build year after year. This new resource by well-known professional developer Marian Small suggests questions that are both interesting for students and useful for providing diagnostic information to teachers. Chapters are organized by grade level (K-8) around the Common Core State Standards for Mathematics to help teachers use the resource more easily.

Author : Susan J Lamon
Publisher : Routledge
Page : 186 pages
File Size : 50,6 Mb
Release : 2005-10
Category : Education
ISBN : 9781135667757

Get Book

More: In-depth Discussion of the Reasoning Activities in Teaching Fractions and Ratios for Understanding by Susan J Lamon Pdf

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.