Children S Fractional Knowledge

Author : Leslie P. Steffe,John Olive
Publisher : Springer Science & Business Media
Page : 379 pages
File Size : 50,9 Mb
Release : 2009-12-02
Category : Education
ISBN : 9781441905918

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Children's Fractional Knowledge by Leslie P. Steffe,John Olive Pdf

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.

Author : Robert P. Hunting,Gary Davis
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Education
ISBN : 9781461231943

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Early Fraction Learning by Robert P. Hunting,Gary Davis Pdf

Early Fraction learning is centrally of interest to students and researchersin mathematics education, tackling as it does one of that discipline's most vexing problems: why are fractions so difficult to learn and to teach?

Author : Amy J. Hackenberg,Anderson Norton,Robert J Wright
Publisher : SAGE
Page : 225 pages
File Size : 46,8 Mb
Release : 2016-07-21
Category : Juvenile Nonfiction
ISBN : 9781473986855

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Developing Fractions Knowledge by Amy J. Hackenberg,Anderson Norton,Robert J Wright Pdf

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.

Author : Susan B. Empson,Linda Levi
Publisher : Heinemann Educational Books
Page : 0 pages
File Size : 41,6 Mb
Release : 2011
Category : Education
ISBN : 0325030537

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Extending Children's Mathematics by Susan B. Empson,Linda Levi Pdf

"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.

Author : Sarah K Major
Publisher : Child1st Publications LLC
Page : 228 pages
File Size : 43,8 Mb
Release : 2014-11-30
Category : Education
ISBN : 1936981971

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Right-Brained Fractions by Sarah K Major Pdf

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.

Author : Susan J. Lamon
Publisher : Routledge
Page : 280 pages
File Size : 52,5 Mb
Release : 2006-08-15
Category : Education
ISBN : 9781135606770

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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 : Robert J Wright,David Ellemor-Collins,Pamela D Tabor
Publisher : SAGE
Page : 313 pages
File Size : 45,8 Mb
Release : 2011-11-04
Category : Education
ISBN : 9781446253687

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Developing Number Knowledge by Robert J Wright,David Ellemor-Collins,Pamela D Tabor Pdf

Following the great success of the earlier books, this fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasising computational fluency and the progressive development of students′ mathematical sophistication. The book is organized in key domains of number instruction, including structuring numbers 1 to 20, knowledge of number words and numerals, conceptual place value, mental computation, written computation methods, fractions, and early algebraic reasoning. Features include: fine-grained progressions of instruction within each domain; detailed descriptions of students′ strategies and difficulties; assessment tasks with notes on students′ responses; classroom-ready instructional activities; This book is designed for classroom and intervention teachers, special education teachers and classroom assistants. The book is an invaluable resource for mathematics advisors and coaches, learning support staff, numeracy consultants, curriculum developers, teacher educators and researchers.

Author : Janette Maree Bobis
Publisher : Unknown
Page : 201 pages
File Size : 55,8 Mb
Release : 2011
Category : Fractions
ISBN : 1875900683

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Fractions by Janette Maree Bobis Pdf

Author : Amy J. Hackenberg,Anderson Norton,Robert J Wright
Publisher : SAGE
Page : 347 pages
File Size : 54,6 Mb
Release : 2016-07-21
Category : Education
ISBN : 9781473987616

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Developing Fractions Knowledge by Amy J. Hackenberg,Anderson Norton,Robert J Wright Pdf

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.

Author : Catherine Sophian
Publisher : Routledge
Page : 212 pages
File Size : 46,9 Mb
Release : 2017-09-25
Category : Education
ISBN : 9781351541756

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The Origins of Mathematical Knowledge in Childhood by Catherine Sophian Pdf

This book examines the origins and development of children's mathematical knowledge. It contrasts the widely held view that counting is the starting point for mathematical development with an alternative comparison-of-quantities position. According to the comparison-of-quantities position, the concept of number builds upon more basic concepts of equality, inequality, and less-than and greater-than relations, which derive from comparisons between unenumerated quantities such as lengths. The concept of number combines these basic comparative concepts with the concept of a unit of measure, which allows one quantity to be described as a multiple of another. Sophian examines these alternative accounts of children's developing mathematical knowledge in the light of research: on children's counting; on their reasoning about continuous quantities such as length and area; on the development of the concept of unit; on additive and multiplicative reasoning; and on knowledge about fractions. In the closing chapters, Sophian draws out the developmental and the educational implications of the research and theory presented. Developmentally, the comparison-of-quantities position undermines the idea that numerical knowledge develops through domain-specific learning mechanisms in that it links numerical development both to physical knowledge about objects, which is the starting point for the concept of unit, and to the acquisition of linguistic number terms. Instructionally, the comparison-of-quantities perspective diverges from the counting-first perspective in that it underscores the continuity between whole-number arithmetic and fraction learning that stems from the importance of the concept of unit for both. Building on this idea, Sophian advances three instructional recommendations: First, instruction about numbers should always be grounded in thinking about quantities and how numbers represent the relations between them; second, instruction in the early years should always be guided by a long-term perspective in which current objectives are shaped by an understanding of their role in the overall course of mathematics learning; and third, instruction should be directly toward promoting the acquisition of the most general mathematical knowledge possible. The Origins of Mathematical Knowledge in Childhood is intended for researchers, professionals, and graduate students in developmental psychology, educational psychology, and mathematics education, and as a supplementary text for advanced undergraduate courses in cognitive development, educational psychology, and mathematics education.

Author : John Dunlosky,Katherine A. Rawson
Publisher : Cambridge University Press
Page : 748 pages
File Size : 50,7 Mb
Release : 2019-02-07
Category : Psychology
ISBN : 1108416012

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The Cambridge Handbook of Cognition and Education by John Dunlosky,Katherine A. Rawson Pdf

This Handbook reviews a wealth of research in cognitive and educational psychology that investigates how to enhance learning and instruction to aid students struggling to learn and to advise teachers on how best to support student learning. The Handbook includes features that inform readers about how to improve instruction and student achievement based on scientific evidence across different domains, including science, mathematics, reading and writing. Each chapter supplies a description of the learning goal, a balanced presentation of the current evidence about the efficacy of various approaches to obtaining that learning goal, and a discussion of important future directions for research in this area. It is the ideal resource for researchers continuing their study of this field or for those only now beginning to explore how to improve student achievement.

Author : Fateen Masad
Publisher : Unknown
Page : 436 pages
File Size : 50,8 Mb
Release : 1988
Category : Electronic
ISBN : WISC:89015530934

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Young Children's Intuitive Knowledge of Identification, Ordering, Equivalence, and Addition of Fractions by Fateen Masad Pdf

Author : Baby Iq Builder Books
Publisher : Baby IQ Builder Books
Page : 128 pages
File Size : 50,7 Mb
Release : 2016-04-22
Category : Electronic
ISBN : 1683740610

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Fractions for 4th Grade Math Essentials by Baby Iq Builder Books Pdf

Learning fractions can be so much fun if only the right motivators are used. This workbook is one of those motivators. It is pleasant to the eyes, it is age-appropriate and it contains just the right mix of relaxed and challenging equations. At the end of this book, expect a stronger grasp of fraction knowledge. Grab a copy now!

Author : Paul Christian Dawkins,Amy J. Hackenberg,Anderson Norton
Publisher : Springer Nature
Page : 620 pages
File Size : 48,9 Mb
Release : 2024-01-22
Category : Education
ISBN : 9783031473869

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Piaget’s Genetic Epistemology for Mathematics Education Research by Paul Christian Dawkins,Amy J. Hackenberg,Anderson Norton Pdf

The book provides an entry point for graduate students and other scholars interested in using the constructs of Piaget’s genetic epistemology in mathematics education research. Constructs comprising genetic epistemology form the basis for some of the most well-developed theoretical frameworks available for characterizing learning, particularly in mathematics. The depth and complexity of Piaget’s work can make it challenging to find adequate entry points for learners, not least because it requires a reorientation regarding the nature of mathematical knowledge itself. This volume gathers leading scholars to help address that challenge. The main section of the book presents key Piagetian constructs for mathematics education research such as schemes and operations, figurative and operative thought, images and meanings, and decentering. The chapters that discuss these constructs include examples from research and address how these constructs can be used in research. There are two chapters on various types of reflective abstraction, because this construct is Piaget’s primary tool for characterizing the advancement of knowledge. The later sections of the book contain commentaries reflecting on the contributions of the body of theory developed in the first section. They connect genetic epistemology to current research domains such as equity and the latest in educational psychology. Finally, the book closes with short chapters portraying how scholars are using these tools in specific arenas of mathematics education research, including in special education, early childhood education, and statistics education.

Author : Prodigy Wizard Books
Publisher : Prodigy Wizard Books
Page : 40 pages
File Size : 41,5 Mb
Release : 2016-03-03
Category : Electronic
ISBN : 1683232267

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Fractions Books for Kids Math Essentials by Prodigy Wizard Books Pdf

Fight the Big C with those suffering from it! This educational book will take your child through a possibly ugly journey of pain and diseases. But why should your child still go through with it? It's because of the knowledge that comes with the experience. You want your child to understand the what's, whys and how's questions are answered satisfa