The Origins Of Mathematical Knowledge In Childhood
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The Origins Of Mathematical Knowledge In Childhood
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Author : Catherine Sophian
language : en
Publisher: Routledge
Release Date : 2017-09-25
The Origins Of Mathematical Knowledge In Childhood written by Catherine Sophian and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-25 with Education categories.
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.
The Origins Of Mathematical Knowledge In Childhood
DOWNLOAD
Author : Catherine Sophian
language : en
Publisher: Routledge
Release Date : 2017-09-25
The Origins Of Mathematical Knowledge In Childhood written by Catherine Sophian and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-25 with Education categories.
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.
Why Is Math So Hard For Some Children
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Author : Daniel B. Berch
language : en
Publisher: Brookes Publishing Company
Release Date : 2007
Why Is Math So Hard For Some Children written by Daniel B. Berch and has been published by Brookes Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Education categories.
This landmark resource gives educational decision-makers and researchers theoretical and practical insight into mathematical learning difficulties and disabilities, combining diverse perspectives from fields such as special education, developmental
Understanding Children S Mathematical Graphics Beginnings In Play
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Author : Carruthers, Elizabeth
language : en
Publisher: McGraw-Hill Education (UK)
Release Date : 2011-04-01
Understanding Children S Mathematical Graphics Beginnings In Play written by Carruthers, Elizabeth and has been published by McGraw-Hill Education (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-01 with Education categories.
Key features include: --
Fostering Children S Mathematical Power
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Author : Arthur J. Baroody
language : en
Publisher: Routledge
Release Date : 1998-09-01
Fostering Children S Mathematical Power written by Arthur J. Baroody and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-01 with Education categories.
Teachers have the responsibility of helping all of their students construct the disposition and knowledge needed to live successfully in a complex and rapidly changing world. To meet the challenges of the 21st century, students will especially need mathematical power: a positive disposition toward mathematics (curiosity and self confidence), facility with the processes of mathematical inquiry (problem solving, reasoning and communicating), and well connected mathematical knowledge (an understanding of mathematical concepts, procedures and formulas). This guide seeks to help teachers achieve the capability to foster children's mathematical power - the ability to excite them about mathematics, help them see that it makes sense, and enable them to harness its might for solving everyday and extraordinary problems. The investigative approach attempts to foster mathematical power by making mathematics instruction process-based, understandable or relevant to the everyday life of students. Past efforts to reform mathematics instruction have focused on only one or two of these aims, whereas the investigative approach accomplishes all three. By teaching content in a purposeful context, an inquiry-based fashion, and a meaningful manner, this approach promotes chilren's mathematical learning in an interesting, thought-provoking and comprehensible way. This teaching guide is designed to help teachers appreciate the need for the investigative approach and to provide practical advice on how to make this approach happen in the classroom. It not only dispenses information, but also serves as a catalyst for exploring, conjecturing about, discussing and contemplating the teaching and learning of mathematics.
Early Childhood Mathematics Education Research
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Author : Julie Sarama
language : en
Publisher: Routledge
Release Date : 2009-04-01
Early Childhood Mathematics Education Research written by Julie Sarama and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-01 with Education categories.
This important new book synthesizes relevant research on the learning of mathematics from birth into the primary grades from the full range of these complementary perspectives. At the core of early math experts Julie Sarama and Douglas Clements's theoretical and empirical frameworks are learning trajectories—detailed descriptions of children’s thinking as they learn to achieve specific goals in a mathematical domain, alongside a related set of instructional tasks designed to engender those mental processes and move children through a developmental progression of levels of thinking. Rooted in basic issues of thinking, learning, and teaching, this groundbreaking body of research illuminates foundational topics on the learning of mathematics with practical and theoretical implications for all ages. Those implications are especially important in addressing equity concerns, as understanding the level of thinking of the class and the individuals within it, is key in serving the needs of all children.
Transforming Children S Mathematics Education
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Author : Leslie P. Steffe
language : en
Publisher: Routledge
Release Date : 2013-11-05
Transforming Children S Mathematics Education written by Leslie P. Steffe and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-05 with Education categories.
Eminent scholars from around the globe gathered to discuss how educational systems would change if the prevailing principles of constructivism were applied to three major aspects of those systems -- knowledge and learning, communication, and environment. This volume provides documentation of the proceedings of this important meeting - - the Early Childhood Action Group of the Sixth International Congress on Mathematics Education. This international assembly, representing such diverse disciplines as mathematics and math education, epistemology, philosophy, cognitive science, psycholinguistics, and science education, is the first to examine early childhood mathematics education from constructivist and international perspectives in addition to formulating recommendations for future work in the field.
Engaging Young Children In Mathematics
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Author : Douglas H. Clements
language : en
Publisher: Routledge
Release Date : 2004
Engaging Young Children In Mathematics written by Douglas H. Clements and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Education categories.
Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education brings together the combined wisdom of a diverse group of experts involved with early childhood mathematics. The book originates from the landmark 2000 Conference on Standards for Pre-kindergarten and Kindergarten Mathematics Education, attended by representatives from almost every state developing standards for young children's mathematics; federal government officials; mathematicians; mathematics educators; researchers from mathematics education, early childhood education, and psychology; curriculum developers; teachers; policymakers; and professionals from organizations such as the National Conference of Teachers of Mathematics and the National Association for the Education of Young Children. The main goal of the Conference was to work collectively to help those responsible for framing and implementing early childhood mathematics standards. Although it has its roots in the Conference, the expanded scope of the standards and recommendations covered in this book includes the full range of kindergarten to grade 2. The volume is organized into two main parts and an online appendix (http://www.gse.buffalo.edu/org/conference/). Part One, Major Themes and Recommendations, offers a framework for thinking about pre-kindergarten - grade 2 mathematics education and specific recommendations. Part Two, Elaboration of Major Themes and Recommendations, provides substantive detail regarding young students' understandings of mathematical ideas. Each Part includes five parallel subsections: "Standards in Early Childhood Education"; "Math Standards and Guidelines"; "Curriculum, Learning, Teaching, and Assessment"; "Professional Development"; and "Toward the Future: Implementation and Policy." As a whole the book: * presents comprehensive summaries of research that provide specific guidelines for standards, curriculum, and teaching; * takes the recent reports and recommendations for early childhood mathematics education to the next level; * integrates practical details and research throughout; and * provides a succinct, but thorough review of research on the topics, sequences, and learning trajectories that children can and should learn at each of their first years of life, with specific developmental guidelines that suggest appropriate content for each topic for each year from 2-year-olds to 7-year-olds. This is an indispensable volume for mathematics educators, researchers, curriculum developers, teachers and policymakers, including those who create standards, scope and sequences, and curricula for young children and professional teacher development materials, and students in mathematics education, early childhood trainers, teacher educators, and faculty in mathematics education.
What Children Can Teach Adults About Mathematics
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Author : Robert P Hunting
language : en
Publisher: PALM-Ed Pty Ltd
Release Date : 2013-10-29
What Children Can Teach Adults About Mathematics written by Robert P Hunting and has been published by PALM-Ed Pty Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-29 with Education categories.
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.
Contemporary Perspectives On Mathematics In Early Childhood Education
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Author : Olivia Saracho
language : en
Publisher: IAP
Release Date : 2008-02-01
Contemporary Perspectives On Mathematics In Early Childhood Education written by Olivia Saracho and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-01 with Education categories.
This volume provides a comprehensive critical analysis of the research in mathematics education for young children. The researchers who conducted the critical analysis focused on the relationship between (1) mathematics learning in the early years and domain specific approaches to cognitive development, (2) the children’s social learning and their developing understanding of math, and (3) the children’s learning in a natural context and their understanding of mathematics concepts. The work of these scholars can help guide those researchers who are interested in pursuing studies in early childhood mathematics in a specific area of study. This volume will facilitate the research conducted by both novice and expert researchers. The volume has accomplished its major goals, which consists of critically analyzing important research in a specific area that would be most useful in advancing the field and provide recommendations for both researchers and educators.