Download or read book Early Fraction Learning written by Robert P. Hunting and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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?
Download or read book Early Fraction Learning written by Robert P Hunting and published by . This book was released on 1991-10-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Cambridge Handbook of Cognition and Education written by John Dunlosky and published by Cambridge University Press. This book was released on 2019-02-07 with total page 1130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Let s Play Math written by Denise Gaskins and published by Tabletop Academy Press. This book was released on 2012-09-04 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Developing Fractions Knowledge written by Amy J. Hackenberg and published by SAGE. This book was released on 2016-07-21 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Writing in Math Class written by Marilyn Burns and published by Math Solutions. This book was released on 1995 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Writing in Math Class presents a clear and persuasive case for making writing a part of math instruction. Author and master teacher Marilyn Burns explains why students should write in math class, describes five different types of writing assignments for math, and offer tips and suggestions for teachers. In her usual engaging style, Marilyn Burns tells what happened in actual classrooms when writing was incorporated into math lessons. Illustrated throughout with student work. With a foreword by Susan Ohanian.
Download or read book Developing Fractions Knowledge written by Amy J. Hackenberg and published by SAGE. This book was released on 2016-07-21 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Development of Children s Fraction Thinking in a First grade Classroom written by Susan Carol Baker and published by . This book was released on 1994 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Children s Fractional Knowledge written by Leslie P. Steffe and published by Springer Science & Business Media. This book was released on 2009-12-02 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantitative Development in Infancy and Early Childhood written by Kelly S. Mix and published by Oxford University Press. This book was released on 2002-04-04 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to define and discuss the key issues raised by new findings in the study of quantitative development. One basic question addressed is how the abilities reported in infants and young children relate to later development. In some accounts, one is left with the impression that infants possess all the fundamental skills that make up mature quantitative reasoning. According to this view, subsequent development seems to consist of little more than the gradual expression of these skills in increasing complex and explicit tasks. This is a major departure from previously held views of quantitative development, such as that of Piaget. To evaluate these new claims, authors will first review the abilities attributed to infants and then define the parameters of early childhood competencies. Comparing the two developmental periods, the authors will evaluate the finding, discuss the transition between these age periods, and offer a framework for understanding later development of quantitative skills, such as counting and calculation. Underlying the argument throughout will be an examination of the nativist versus empiricist debate that has taken center stage in infancy research.
Download or read book What Children Can Teach Adults About Mathematics written by Robert P Hunting and published by PALM-Ed Pty Ltd. This book was released on 2013-10-29 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ways adults think about mathematics and the ways children think about mathematics are not necessarily the same. Listening, observing, and talking with children is necessary so that teachers, parents, and carers can figure out where they are coming from mathematically. If children’s mathematics encompasses their own meanings and understandings, and those meanings and understandings may be different to mine, then to provide effective assistance and support, I must make every effort to see mathematics from their perspective. In this book I highlight important aspects of children’s beginning understandings of mathematics, illustrated with examples taken from observations of children. In Chapter 1 I discuss the origins of mathematics in infants with illustrations provided from three major strands of mathematics: number, space, and measurement. In Chapter 2 I give examples of different ways young children use fingers in their efforts to solve simple mathematical problems, looking in detail at one child’s behavior. Chapter 3 focuses on a 4-year-old’s views about numbers. There is a commonly held belief that before children start school they have not really thought about numbers; that young children’s mathematical minds are a blank slate. Nothing could be further from the case. In Chapter 4 I discuss the topic of counting, focusing firstly on the spontaneous counting behavior of a 4-year-old, followed by interviews that further reveal how his knowledge of numbers and counting are related. Chapter 5 further discusses how children learn about numbers; in particular the various conceptions children have of the number 10. I explain the significance of part-whole knowledge in children’s numerical thinking in Chapter 6, with examples taken from preschool, the 2nd grade, and 5th grade. Chapter 7 is about sharing, its origins, contexts when sharing arises, types of sharing, and the relationship between sharing and counting, sharing and division, and sharing as a platform for learning fractions. In Chapter 8 I begin by discussing early geometric ideas, including basic operations for moving items in two dimensions, followed by three-dimensional activities. I discuss the key notion of conservation of quantity and conclude with comments about scale and distance. Chapter 9 begins with the question “What is measurement?” I discuss the issue of measurement error, then sketch out a general development of measurement thinking. Types of conservation are described, as are unit systems. Finally, children’s thinking in area situations, including common misconceptions, are discussed. In Chapter 10, after a story showing how fractions can be introduced naturally, I focus on the fraction knowledge of an 11-year-old, who responded to a range of tasks designed to tease out this child’s conceptual understanding of fractions.
Download or read book Research in Mathematics Education in Australasia 2008 2011 written by Bob Perry and published by Springer Science & Business Media. This book was released on 2012-09-11 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the eighth edition of the four-yearly review of mathematics education research in Australasia. Commissioned by the Mathematics Education Research Group of Australasia (MERGA), this review critiques the most current Australasian research in mathematics education in the four years from 2008-2011. The main objective of this review is to celebrate and recognise significant findings; highlight relationships between research; identify themes; and forecast further research directions. This theme-based review has produced a comprehensive analysis of Australasian research in a politically challenging time—producing a manuscript with implications for a wider, international, audience. As the 2009 Felix Klein medal winner Gilah Leder states: A substantial body of research is captured in the chapters of this review. It encompasses the labours of a community of active researchers, with varied interests and diverse theoretical perspectives. Some of the issues explored in the period covered by this volume clearly resonate with questions and concerns particularly pertinent to the changing educational environment; others are more aptly described as continuing or renewed explorations of areas of long standing concern.
Download or read book Engaging Young Children in Mathematics written by Douglas H. Clements and published by Routledge. This book was released on 2003-10-17 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of conclusions drawn from the expertise shared at the Conference on Standards for Prekindergarten and Kindergarten Mathematics Education. It offers substantive detail regarding young students' understandings of mathematical ideas.
Download or read book The Origins of Mathematical Knowledge in Childhood written by Catherine Sophian and published by Routledge. This book was released on 2017-09-25 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book My Family Reunion written by Christine Clement and published by The Rosen Publishing Group, Inc. This book was released on 2010-01-01 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: BookMath that students can relate to!This full-color, photo-illustrated math reader seamlessly integrates Math with the curriculum areas of Science and Social Studies. Grab your students' attention and inspire a love of Math and of learning.
Download or read book Getting the Buggers to Add Up written by Mike Ollerton and published by Bloomsbury Publishing. This book was released on 2012-02-23 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition brings the book right up to date in line with the new Mathematics and Functional Mathematics GCSES and IGCSES.
Download or read book A Focus on Fractions written by Marjorie M. Petit and published by . This book was released on 2010 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: "To watch teachers interact with the research and practical suggestions in this book is exhilarating. The real joy, however, is seeing them use this learned knowledge as they instruct their students. This is a book for all of us who have struggled to help students make sense of fractions."---Mary Montgomery Lindquist, Fuller E. Callaway Professor of Mathematics Education, Emeritus, Past President of the National Council of Teachers of Mathematics "A Focus on Fractions draws on research from mathematics education to produce a classroom-friendly system of formative assessment. Classroom teachers, mathematics educators, teacher education students, and researchers in the field will find what is in this book useful and interesting."---Judith Zawojewski, Associate Professor, Illinois Institute of Technology "This book is a tour de force in relating research and practice in mathematics education, and as such it should also be of great interest to researchers and graduate students in the field."---Edward A. Silver, William A. Brownell Professor of Education, University of Michigan 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. 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.
