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The Origins Of Mathematical Knowledge In Childhood
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Book Synopsis The Origins of Mathematical Knowledge in Childhood by : Catherine Sophian
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 212 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.
Book Synopsis Why is Math So Hard for Some Children? by : Daniel B. Berch
Download or read book Why is Math So Hard for Some Children? written by Daniel B. Berch and published by Brookes Publishing Company. This book was released on 2007 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Helping Children Learn Mathematics by : National Research Council
Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.
Book Synopsis Psychological Perspectives on Early Childhood Education by : Susan L. Golbeck
Download or read book Psychological Perspectives on Early Childhood Education written by Susan L. Golbeck and published by Routledge. This book was released on 2001-03 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brings together the work of leading researchers in the field of child development and early education to examine current problems from the perspective of psychological theory and research.
Book Synopsis Mathematics Learning in Early Childhood by : National Research Council
Download or read book Mathematics Learning in Early Childhood written by National Research Council and published by National Academies Press. This book was released on 2009-11-13 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Early childhood mathematics is vitally important for young children's present and future educational success. Research demonstrates that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success. Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children.
Book Synopsis EBOOK: Assessing Children's Mathematical Knowledge by : Barry Cooper
Download or read book EBOOK: Assessing Children's Mathematical Knowledge written by Barry Cooper and published by McGraw-Hill Education (UK). This book was released on 1999-12-16 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'this work is highly relevant to the proliferation of accountability measures worldwide' James Scheurich and Douglas Foley In many countries, the lives of teachers and children are increasingly dominated by programmes of national testing of mathematics and other subjects. In England, the majority of the items in such tests have set mathematical tasks in every day situations such as 'shopping'. This requires children to make decisions about whether to use or not their own every day knowledge and experience in their problem-solving. Some children are likely to have a better 'feel for this game' than others. Assessing Children's Mathematical Knowledge draws on the analysis of national curriculum test data from more than 600 children of 10-11 and 13-14 years of age, as well as in-depth interviews with 250 of these as they attempt to solve test problems, in order to explore the nature of the difficulties children experience with 'realistic' items. The book shows, by comparing test and interview data, that many children, as a consequence of their confusion over the requirements of 'realistic' test items, fail in tests to demonstrate mathematical knowledge and understanding that they actually possess. The book also explores whether this problem of invalid measurement is equally spread across children from different social backgrounds, and across the sexes. The book will be of interest to academics and teachers studying for advanced degrees in mathematics education, sociology of education and educational assessment.
Book Synopsis Early Childhood Mathematics by : Robert J. Jensen
Download or read book Early Childhood Mathematics written by Robert J. Jensen and published by Simon & Schuster Books For Young Readers. This book was released on 1993 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In this volume useful information for the teacher is presented concerning the importance of language and the communication of ideas, how to enhance classroom dynamics, and the use of alternate assessment and evaluation approaches in the early childhood grades."--Back cover.
Book Synopsis The Absorbent Mind by : Maria Montessori
Download or read book The Absorbent Mind written by Maria Montessori and published by Simon and Schuster. This book was released on 2013-03-25 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Absorbent Mind was Maria Montessori's most in-depth work on her educational theory, based on decades of scientific observation of children. Her view on children and their absorbent minds was a landmark departure from the educational model at the time. This book helped start a revolution in education. Since this book first appeared there have been both cognitive and neurological studies that have confirmed what Maria Montessori knew decades ago.
Book Synopsis Cognitive Foundations for Improving Mathematical Learning by : David C. Geary
Download or read book Cognitive Foundations for Improving Mathematical Learning written by David C. Geary and published by Academic Press. This book was released on 2019-01-03 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fifth volume in the Mathematical Cognition and Learning series focuses on informal learning environments and other parental influences on numerical cognitive development and formal instructional interventions for improving mathematics learning and performance. The chapters cover the use of numerical play and games for improving foundational number knowledge as well as school math performance, the link between early math abilities and the approximate number system, and how families can help improve the early development of math skills. The book goes on to examine learning trajectories in early mathematics, the role of mathematical language in acquiring numeracy skills, evidence-based assessments of early math skills, approaches for intensifying early mathematics interventions, the use of analogies in mathematics instruction, schema-based diagrams for teaching ratios and proportions, the role of cognitive processes in treating mathematical learning difficulties, and addresses issues associated with intervention fadeout. - Identifies the relative influence of school and family on math learning - Discusses the efficacy of numerical play for improvement in math - Features learning trajectories in math - Examines the role of math language in numeracy skills - Includes assessments of math skills - Explores the role of cognition in treating math-based learning difficulties
Book Synopsis How Students Learn by : National Research Council
Download or read book How Students Learn written by National Research Council and published by National Academies Press. This book was released on 2005-01-23 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do you get a fourth-grader excited about history? How do you even begin to persuade high school students that mathematical functions are relevant to their everyday lives? In this volume, practical questions that confront every classroom teacher are addressed using the latest exciting research on cognition, teaching, and learning. How Students Learn: History, Mathematics, and Science in the Classroom builds on the discoveries detailed in the bestselling How People Learn. Now, these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. Organized for utility, the book explores how the principles of learning can be applied in teaching history, science, and math topics at three levels: elementary, middle, and high school. Leading educators explain in detail how they developed successful curricula and teaching approaches, presenting strategies that serve as models for curriculum development and classroom instruction. Their recounting of personal teaching experiences lends strength and warmth to this volume. The book explores the importance of balancing students' knowledge of historical fact against their understanding of concepts, such as change and cause, and their skills in assessing historical accounts. It discusses how to build straightforward science experiments into true understanding of scientific principles. And it shows how to overcome the difficulties in teaching math to generate real insight and reasoning in math students. It also features illustrated suggestions for classroom activities. How Students Learn offers a highly useful blend of principle and practice. It will be important not only to teachers, administrators, curriculum designers, and teacher educators, but also to parents and the larger community concerned about children's education.
Book Synopsis Contemporary Perspectives on Mathematics in Early Childhood Education by : Olivia Saracho
Download or read book Contemporary Perspectives on Mathematics in Early Childhood Education written by Olivia Saracho and published by IAP. This book was released on 2008-02-01 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Maths is all Around You by : Marianne Knaus
Download or read book Maths is all Around You written by Marianne Knaus and published by Bloomsbury Publishing. This book was released on 2015-04-23 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: We encounter mathematics on a regular basis in one form or another. For some people, maths is 'scary' and not something they feel confident about. Even though many educators and parents attempt to provide good mathematics experiences, there is still a high level of anxiety about the teaching and learning of mathematics. This book presents a broad range of concepts and aims to widen the narrow view that maths for young children is just about numbers and shapes. The content includes pattern (early algebra), counting, number, early operations, measurement, shape and spatial awareness (geometry), matching, sorting, data analysis and the introduction of chance (statistics and probability). This book is intended for educators and parents who would like to explore and investigate maths concepts to enrich children's experiences and extend their current thinking and learning.
Book Synopsis The Nature of Mathematical Knowledge by : Philip Kitcher
Download or read book The Nature of Mathematical Knowledge written by Philip Kitcher and published by Oxford University Press, USA. This book was released on 1984 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book argues against the view that mathematical knowledge is a priori, contending that mathematics is an empirical science and develops historically, just as natural sciences do. Kitcher presents a complete, systematic, and richly detailed account of the nature of mathematical knowledge and its historical development, focusing on such neglected issues as how and why mathematical language changes, why certain questions assume overriding importance, and how standards of proof are modified.
Book Synopsis Learning and Teaching Early Math by : Douglas H. Clements
Download or read book Learning and Teaching Early Math written by Douglas H. Clements and published by Routledge. This book was released on 2009-04-01 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this important new book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help teachers become more effective professionals. By opening up new windows to seeing young children and the inherent delight and curiosity behind their mathematical reasoning, learning trajectories ultimately make teaching more joyous. They help teachers understand the varying level of knowledge and thinking of their classes and the individuals within them as key in serving the needs of all children. In straightforward, no-nonsense language, this book summarizes what is known about how children learn mathematics, and how to build on what they know to realize more effective teaching practice. It will help teachers understand the learning trajectories of early mathematics and become quintessential professionals.
Book Synopsis The Nature and Origin of Mathematical Skills by : J.I.D. Campbell
Download or read book The Nature and Origin of Mathematical Skills written by J.I.D. Campbell and published by Elsevier. This book was released on 1992-08-07 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: A broad range of current experimental research on numerical cognition and the acquisition of mathematical skills is covered in this volume. The individual chapters provide in-depth analysis of specific issues, methodologies, phenomena, and theory. The book is divided into two parts. In the first part the focus is on the acquisition and development of numerical skills. Part 2 of the book contains research on the information-processing basis of numerical skills, focusing on the mechanisms of perception, attention, and memory that support number skills.The range of theoretical and methodological orientations represented in the volume captures both the diversity and coherence of contemporary research into mathematical skills. The research of educational psychologists, cognitive psychologists, and cognitive neuropsychologists mutually informs and reinforces theoretical developments within each area. The multidisciplinary interest in mathematics skills reflects the pervasiveness and importance of mathematics in education, technology, and science, and also indicates that questions about mathematical competence address important issues in diverse areas of psychology and cognitive science.
Book Synopsis Transforming the Workforce for Children Birth Through Age 8 by : National Research Council
Download or read book Transforming the Workforce for Children Birth Through Age 8 written by National Research Council and published by National Academies Press. This book was released on 2015-07-23 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Children are already learning at birth, and they develop and learn at a rapid pace in their early years. This provides a critical foundation for lifelong progress, and the adults who provide for the care and the education of young children bear a great responsibility for their health, development, and learning. Despite the fact that they share the same objective - to nurture young children and secure their future success - the various practitioners who contribute to the care and the education of children from birth through age 8 are not acknowledged as a workforce unified by the common knowledge and competencies needed to do their jobs well. Transforming the Workforce for Children Birth Through Age 8 explores the science of child development, particularly looking at implications for the professionals who work with children. This report examines the current capacities and practices of the workforce, the settings in which they work, the policies and infrastructure that set qualifications and provide professional learning, and the government agencies and other funders who support and oversee these systems. This book then makes recommendations to improve the quality of professional practice and the practice environment for care and education professionals. These detailed recommendations create a blueprint for action that builds on a unifying foundation of child development and early learning, shared knowledge and competencies for care and education professionals, and principles for effective professional learning. Young children thrive and learn best when they have secure, positive relationships with adults who are knowledgeable about how to support their development and learning and are responsive to their individual progress. Transforming the Workforce for Children Birth Through Age 8 offers guidance on system changes to improve the quality of professional practice, specific actions to improve professional learning systems and workforce development, and research to continue to build the knowledge base in ways that will directly advance and inform future actions. The recommendations of this book provide an opportunity to improve the quality of the care and the education that children receive, and ultimately improve outcomes for children.
Book Synopsis Early Childhood Mathematics Education Research by : Julie Sarama
Download or read book Early Childhood Mathematics Education Research written by Julie Sarama and published by Routledge. This book was released on 2009-04-01 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
