Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8 PDF Download

Author: Joanne Elizabeth Lobato
Publisher: National Council of Teachers of English
ISBN: 9780873536226
Category : Curriculum planning
Languages : en
Pages : 0

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

Author: Sheldon Erickson
Publisher: Aims Educational Foundation
ISBN: 9781881431787
Category : Mathematics
Languages : en
Pages : 212

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Book Description

Author: Carmen Whitman
Publisher: Math Solutions
ISBN: 9781935099246
Category : Education
Languages : en
Pages : 271

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Book Description
"Presents 18 proportional reasoning lessons for middle-school students; each lesson contains standards correlations, vocabulary, teacher notes, student connections, and reproducible pages, with the goal of seeing inclusive proportionality as the big idea that helps educators to make a unifying connection across all mathematics strands"--Provided by publisher.

Author: Marian Small
Publisher: Teachers College Press
ISBN: 0807756601
Category : Education
Languages : en
Pages : 129

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Book Description
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: Marjorie M. Petit
Publisher: Routledge
ISBN: 1000071448
Category : Education
Languages : en
Pages : 242

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Book Description
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: Contemporary
Publisher: McGraw-Hill Education
ISBN: 9780076620937
Category : Mathematics
Languages : en
Pages : 152

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Book Description
Students use various tools—objects, diagrams, tables, graphs, and equations—to understand proportional and non-proportional relationships.

Author: Susan J. Lamon
Publisher: Routledge
ISBN: 1135606781
Category : Education
Languages : en
Pages : 254

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Book Description
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: Guershon Harel
Publisher: SUNY Press
ISBN: 9780791417638
Category : Education
Languages : en
Pages : 448

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Book Description
Two of the most important concepts children develop progressively throughout their mathematics education years are additivity and multiplicativity. Additivity is associated with situations that involve adding, joining, affixing, subtracting, separating and removing. Multiplicativity is associated with situations that involve duplicating, shrinking, stressing, sharing equally, multiplying, dividing, and exponentiating. This book presents multiplicativity in terms of a multiplicative conceptual field (MCF), not as individual concepts. It is presented in terms of interrelations and dependencies within, between, and among multiplicative concepts. The authors share the view that research on the mathematical, cognitive, and instructional aspects of multiplicative concepts must be situated in an MCF framework.

Author: Andrew Ravenscroft
Publisher: Springer
ISBN: 9783642332623
Category : Computers
Languages : en
Pages : 553

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Book Description
This book constitutes the refereed proceedings of the 7th European Conference on Technology Enhanced Learning, EC-TEL 2012, held in Saarbrücken, Germany, in September 2012. The 26 revised full papers presented were carefully reviewed and selected from 130 submissions. The book also includes 12 short papers, 16 demonstration papers, 11 poster papers, and 1 invited paper. Specifically, the programme and organizing structure was formed through the themes: mobile learning and context; serious and educational games; collaborative learning; organisational and workplace learning; learning analytics and retrieval; personalised and adaptive learning; learning environments; academic learning and context; and, learning facilitation by semantic means.

Author: Dirk de Bock
Publisher: Springer Science & Business Media
ISBN: 0387711643
Category : Education
Languages : en
Pages : 191

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Book Description
This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity. It discusses: how the illusion of linearity appears in diverse domains of mathematics and science; what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon; and how the illusion of linearity can be remedied.