Children's Fractional Knowledge

Children's Fractional Knowledge

Author: Leslie P. Steffe

Publisher: Springer Science & Business Media

Published: 2009-12-02

Total Pages: 379

ISBN-13: 144190591X

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Children’s Fractional Knowledge elegantly tracks the construction of knowledge, both by children learning new methods of reasoning and by the researchers studying their methods. The book challenges the widely held belief that children’s whole number knowledge is a distraction from their learning of fractions by positing that their fractional learning involves reorganizing—not simply using or building upon—their whole number knowledge. This hypothesis is explained in detail using examples of actual grade-schoolers approaching problems in fractions including the schemes they construct to relate parts to a whole, to produce a fraction as a multiple of a unit part, to transform a fraction into a commensurate fraction, or to combine two fractions multiplicatively or additively. These case studies provide a singular journey into children’s mathematics experience, which often varies greatly from that of adults. Moreover, the authors’ descriptive terms reflect children’s quantitative operations, as opposed to adult mathematical phrases rooted in concepts that do not reflect—and which in the classroom may even suppress—youngsters’ learning experiences. Highlights of the coverage: Toward a formulation of a mathematics of living instead of being Operations that produce numerical counting schemes Case studies: children’s part-whole, partitive, iterative, and other fraction schemes Using the generalized number sequence to produce fraction schemes Redefining school mathematics This fresh perspective is of immediate importance to researchers in mathematics education. With the up-close lens onto mathematical development found in Children’s Fractional Knowledge, readers can work toward creating more effective methods for improving young learners’ quantitative reasoning skills.


Extending Children's Mathematics

Extending Children's Mathematics

Author: Susan B. Empson

Publisher: Heinemann Educational Books

Published: 2011

Total Pages: 0

ISBN-13: 9780325030531

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"With the collaboration of a number of dedicated teachers and their students, Susan Empson and Linda Levi have produced a volume that is faithful to the basic principles of CGI while at the same time covering new ground with insight and innovation." -Thomas P. Carpenter This highly anticipated follow-up volume to the landmark Children's Mathematics: Cognitively Guided Instruction addresses the urgent need to help teachers understand and teach fraction concepts. Fractions remain one of the key stumbling blocks in math education, and here Empson and Levi lay a foundation for understanding fractions and decimals in ways that build conceptual learning. They show how the same kinds of intuitive knowledge and sense making that provides the basis for children's learning of whole number arithmetic can be extended to fractions and decimals. Just as they did in Children's Mathematics and Thinking Mathematically, Empson and Levi provide important insights into children's thinking and alternative approaches to solving problems. Three themes appear throughout the book: building meaning for fractions and decimals through discussing and solving word problems the progression of children's strategies for solving fraction word problems and equations from direct modeling through relational thinking designing instruction that capitalizes on students' relational thinking strategies to integrate algebra into teaching and learning fractions. With illuminating examples of student work, classroom vignettes, "Teacher Commentaries" from the field, sample problems and instructional guides provided in each chapter, you'll have all the tools you need to teach fractions and decimals with understanding and confidence.


Preschool Math

Preschool Math

Author: Robert A. Williams

Publisher: Gryphon House, Inc.

Published: 2005

Total Pages: 244

ISBN-13: 9780876590003

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Children will delight in the 140 activities that bring math to life in the classroom. This collection is organized by curriculum area, making it easy for teachers to integrate the activities into their daily plans. Teachers/parents.


A Focus on Fractions

A Focus on Fractions

Author: Marjorie M. Petit

Publisher: Routledge

Published: 2015-07-24

Total Pages: 208

ISBN-13: 1317597303

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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.


Children's Mathematics

Children's Mathematics

Author: Thomas P. Carpenter

Publisher: Heinemann Educational Books

Published: 2015

Total Pages: 0

ISBN-13: 9780325052878

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With a focus on children's mathematical thinking, this second edition adds new material on the mathematical principles underlying children's strategies, a new online video that illustrates student teacher interaction, and examines the relationship between CGI and the Common Core State Standards for Mathematics.


Right-Brained Fractions

Right-Brained Fractions

Author: Sarah K Major

Publisher: Child1st Publications LLC

Published: 2014-11-30

Total Pages: 228

ISBN-13: 9781936981977

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Come on a fun filled fractions adventure with the Ator brothers! Num Ator loves to count! He shares a house with his twin brother Nom Ator who lives downstairs. Nom loves to name things! This dynamic duo is the missing link for students who struggle with fractions. With wonderful storytelling, vibrant images, and exciting activities Right-Brained Fractions provides the groundwork to develop and reinforce fraction skills, which is achieved by students being able to create their own models to visualize each problem being solved. This valuable resource is specifically designed to engage and support any child's unique style of learning.


Developing Fractions Knowledge

Developing Fractions Knowledge

Author: Amy J. Hackenberg

Publisher: SAGE

Published: 2016-07-21

Total Pages: 343

ISBN-13: 147398761X

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Supporting and understanding your students’ fractional knowledge is crucial to their overall grasp of numbers and mathematics. By centralizing around three key stages of development, this effective guide will help you to assess your students’ understanding of fractions and modify your teaching accordingly. These key stages are identified as: Stage 1a: Fair Sharing Stage 1b: Part-Whole Stage 2a: Disembedding and IteratingStage 2b: Measuring with Unit Fractions Stage 2c: Reversing Fractions Stage 3a: Fractions as Numbers Stage 3b: Operating with Fractions As the newest addition to the bestselling Maths Recovery Series, this book will be a useful guide for all primary classroom teachers and assistants, including experienced Mathematics Recovery instructors.


Teaching Fractions and Ratios for Understanding

Teaching Fractions and Ratios for Understanding

Author: Susan J. Lamon

Publisher: Routledge

Published: 2006-08-15

Total Pages: 254

ISBN-13: 1135606781

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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.


Give Me Half!

Give Me Half!

Author: Stuart J. Murphy

Publisher: Harper Collins

Published: 1996-03-27

Total Pages: 44

ISBN-13: 0064467015

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Splitting things in half may seem like an easy thing to do, but when two siblings and a pizza are involved, things can get messy. Children learn about fractions at school but fractions are also an important part of everyday life outside the classroom.In this riotous book, Stuart J. Murphy and G. Brian Karas introduce the simplest of fractions, 1/2.


Whole-y Cow!

Whole-y Cow!

Author: Taryn Souders

Publisher: Sleeping Bear Press

Published: 2010-10-15

Total Pages: 34

ISBN-13: 1585366234

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Learning about fractions isn't always easy, but who says it can't be fun? Using one very entertaining cow, math teacher Taryn Souders has devised a very clever (and fun) way of explaining fractions to beginning learners. One whole cow, calmly eating hay, decided to act differently on this particular day. One whole cow - what should we do? I know! Let's paint one half blue! Prompted by a poem and a visual clue, students are asked to answer what fraction is illustrated in the cow's antics, starting with halves and progressing into thirds, fourths, eighths, and tenths. What fraction of the cow is blue? Answer: ½ What fraction of the cow is white? Answer: ½ With the math problem featured as part of the artwork, students get an immediate sense of how to apply and understand the concept of fractions. How moo-velous! Taryn J. Souders lives in Winter Park, Florida. With a background in math education, she is passionate about keeping math fun for young students. This is her first children's book. Tatjana Mai-Wyss was born in Switzerland. She remembers learning about fractions with the help of a typical Swiss cake. Tatjana has illustrated several children's books and her work has been published in books and magazines in the United States and abroad. She lives in South Carolina.