Download or read book Proportional Reasoning by Young Children written by Alan Christopher Schorn and published by . This book was released on 1989 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Developing Essential Understanding of Ratios Proportions and Proportional Reasoning for Teaching Mathematics in Grades 6 8 written by Joanne Elizabeth Lobato and published by National Council of Teachers of English. This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A series for teaching mathematics."--P. [1] of cover.
Download or read book 21st Century Learning for 21st Century Skills written by Andrew Ravenscroft and published by Springer. This book was released on 2012-08-14 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 7th European Conference on Technology Enhanced Learning, EC-TEL 2012, held in Saarbrücken, Germany, in September 2012. The 26 revised full papers presented were carefully reviewed and selected from 130 submissions. The book also includes 12 short papers, 16 demonstration papers, 11 poster papers, and 1 invited paper. Specifically, the programme and organizing structure was formed through the themes: mobile learning and context; serious and educational games; collaborative learning; organisational and workplace learning; learning analytics and retrieval; personalised and adaptive learning; learning environments; academic learning and context; and, learning facilitation by semantic means.
Download or read book Analogical Reasoning in Children written by Usha Goswami and published by Psychology Press. This book was released on 2013-10-23 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analogical reasoning is a fundamental cognitive skill, involved in classification, learning, problem-solving and creative thinking, and should be a basic building block of cognitive development. However, for a long time researchers have believed that children are incapable of reasoning by analogy. This book argues that this is far from the case, and that analogical reasoning may be available very early in development. Recent research has shown that even 3-year-olds can solve analogies, and that infants can reason about relational similarity, which is the hallmark of analogy. The book traces the roots of the popular misconceptions about children's analogical abilities and argues that when children fail to use analogies, it is because they do not understand the relations underlying the analogy rather than because they are incapable of analogical reasoning. The author argues that young children spontaneously use analogies in learning, and that their analogies can sometimes lead them into misconceptions. In the "real worlds" of their classrooms, children use analogies when learning basic skills like reading, and even babies seem to use analogies to learn about the world around them.
Download or read book Handbook of Research on the Education of Young Children written by Olivia N. Saracho and published by Routledge. This book was released on 2013-01-17 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Research on the Education of Young Children is the essential reference on research on early childhood education throughout the world. This singular resource provides a comprehensive overview of important contemporary issues as well as the information necessary to make informed judgments about these issues. The field has changed significantly since the publication of the second edition, and this third edition of the handbook takes care to address the entirety of vital new developments. A valuable tool for all those who work and study in the field of early childhood education, this volume addresses critical, cutting edge research on child development, curriculum, policy, and research and evaluation strategies. With a multitude of new and updated chapters, The Handbook of Research on the Education of Young Children, 3rd Edition makes the expanding knowledge base related to early childhood education readily available and accessible.
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.
Download or read book Mathematical Challenges For All written by Roza Leikin and published by Springer Nature. This book was released on 2023-03-17 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book argues that mathematical challenge can be found at any level and at every age and constitutes an essential characteristic of any mathematics classroom aimed at developing the students’ mathematical knowledge and skills. Since each mathematics classroom is heterogeneous with respect to students’ mathematical potential, quality mathematical instruction results from matching the level of mathematical challenge to different students’ potential. Thus, effective integration of mathematical challenge in the instructional process is strongly connected to the equity principle of mathematics education. In the three sections in this volume readers can find diverse views on mathematical challenges in curriculum and instructional design, kinds and variation of mathematically challenging tasks and collections of mathematical problems. Evidence-based analysis is interwoven with theoretical positions expressed by the authors of the chapters. Cognitive, social and affective characteristics of challenging mathematical activities are observed and analyzed. The volume opens new avenues of research in mathematics education, and pose multiple questions about mathematical instruction rich in mathematical challenge for all. The authors invite readers to explore and enjoy mathematical challenges at different levels.
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 Space Time and Number in the Brain written by Elizabeth Brannon and published by Academic Press. This book was released on 2011-05-31 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of mathematical cognition and the ways in which the ideas of space, time and number are encoded in brain circuitry has become a fundamental issue for neuroscience. How such encoding differs across cultures and educational level is of further interest in education and neuropsychology. This rapidly expanding field of research is overdue for an interdisciplinary volume such as this, which deals with the neurological and psychological foundations of human numeric capacity. A uniquely integrative work, this volume provides a much needed compilation of primary source material to researchers from basic neuroscience, psychology, developmental science, neuroimaging, neuropsychology and theoretical biology. The first comprehensive and authoritative volume dealing with neurological and psychological foundations of mathematical cognition Uniquely integrative volume at the frontier of a rapidly expanding interdisciplinary field Features outstanding and truly international scholarship, with chapters written by leading experts in a variety of fields
Download or read book A Study of Proportional Reasoning as it Relates to the Development of Multiplication Concepts written by Judith Flowers and published by . This book was released on 1998 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Study of Children s Understanding of Fraction Size and Its Relationship to Proportional Reasoning written by Tzu-Ta Yiu and published by . This book was released on 1992 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: One purpose of this study was to investigate children's understanding of fraction size; specifically, their ability to order fractions and to relate the size of a fraction to whole numbers. Other purposes were to examine the relationships between children's understanding of fraction size and their knowledge of the multiplicative relationship between numbers as measured by a proportional-reasoning task and to explore the commonality among children's strategies for tasks involving multiplicative structures. Three different written tasks, two fraction-size tasks and one proportion-reasoning (PR) task, were administered to sixty fourth- and fifth-grade children from three schools in east-central Illinois. The two fraction-size tasks assessed children's ability in relating the size of fractions to whole numbers (FW) and comparing the size of fraction pairs (FF). The proportion-reasoning tasks were based on Noelting's orange-juice tasks and required knowledge of the multiplicative relationship between numbers. Twelve students from each grade were individually interviewed to explore their strategies. The results revealed the following: (1) Children's performance on the fraction-and-whole-number-relation (FW) tasks revealed several misconceptions, including the dominance of whole-number concepts, detachment of conceptual understanding from mathematical procedures, using fraction models without knowledge of fraction size, and deficiency of estimation skill. Children's performance on the fraction-fraction comparison tasks (FF) tasks revealed an additive type of thinking. Results also showed that children performed better on the FF tasks than on the FW tasks. (2) There was a significant correlation between children's performance on the two fraction-size tasks and their knowledge of the multiplicative relationships between numbers measured by the proportional-reasoning task. (3) Children employed parallel strategies across different types of tasks involving fractions or ratios. Children used parallel strategies on the two fraction-size tasks. Moreover, these strategies were reliably associated with levels of performance on the proportional-reasoning tasks. Put differently, strategies that required multiplicative thinking were related to success on the fraction-size and proportional-reasoning tasks. The findings implied that instruction of fractions needs to help children recognize the differences between the concept of whole numbers and the concept of fractions, develop an understanding of the size of a fraction in relation to other numbers including whole numbers, and construct an understanding of the multiplicative relationship. Efforts need to be taken to help children build the connections between the concrete representations of fractions and the ideas of fractions as numbers.
Download or read book Analogical Reasoning in Children written by Usha Goswami and published by Psychology Press. This book was released on 2013-10-23 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analogical reasoning is a fundamental cognitive skill, involved in classification, learning, problem-solving and creative thinking, and should be a basic building block of cognitive development. However, for a long time researchers have believed that children are incapable of reasoning by analogy. This book argues that this is far from the case, and that analogical reasoning may be available very early in development. Recent research has shown that even 3-year-olds can solve analogies, and that infants can reason about relational similarity, which is the hallmark of analogy. The book traces the roots of the popular misconceptions about children's analogical abilities and argues that when children fail to use analogies, it is because they do not understand the relations underlying the analogy rather than because they are incapable of analogical reasoning. The author argues that young children spontaneously use analogies in learning, and that their analogies can sometimes lead them into misconceptions. In the "real worlds" of their classrooms, children use analogies when learning basic skills like reading, and even babies seem to use analogies to learn about the world around them.
Download or read book Building Proportional Reasoning Across Grades and Math Strands K 8 written by Marian Small and published by Teachers College Press. This book was released on 2014-04-15 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although proportional reasoning is not formally introduced as a topic in the Common Core and other mathematics curricula until 6th grade, introducing its fundamental ideas in the early grades helps students develop essential skills in ratios, percentages, and other proportional representations when they reach the upper grades. The author takes this complex subject and crafts examples and questions that help teachers see the larger purpose in teaching concepts, such as unitizing, and how that understanding is essential for more complex ideas, such as ratios. Teachers and vertical teams can see how the concepts can build year after year. This new resource by well-known professional developer Marian Small suggests questions that are both interesting for students and useful for providing diagnostic information to teachers. Chapters are organized by grade level (K–8) around the Common Core State Standards for Mathematics to help teachers use the resource more easily. Math teachers can use this resource to help students develop a solid foundation for more proficient and more confident work with multiplicative thinking and proportionality. It will also help math coaches as they assist teachers in their transition to teaching mathematics within the more demanding framework of the CCSS. This book will also help preservice teachers and their instructors as they prepare themselves and their students to understand and teach math with a deep level of understanding. “Once again, Marian Small has created an outstanding resource for anyone working with elementary or middle grades mathematics students. With her trademark ‘good questions to ask,’ clear explanations of underlying ideas, and rich activities, Dr. Small gets at the heart of ways to correct often misunderstood and poorly taught concepts of proportional reasoning, starting with the rarely mentioned primary level.” —Linda Sheffield, Regents Professor Emerita, Northern Kentucky University
Download or read book Large Scale Studies in Mathematics Education written by James A. Middleton and published by Springer. This book was released on 2015-05-05 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, funding agencies like the Institute of Educational Sciences and the National Science Foundation have increasingly emphasized large-scale studies with experimental and quasi-experimental designs looking for 'objective truths'. Educational researchers have recently begun to use large-scale studies to understand what really works, from developing interventions, to validation studies of the intervention, and then to efficacy studies and the final "scale-up" for large implementation of an intervention. Moreover, modeling student learning developmentally, taking into account cohort factors, issues of socioeconomics, local political context and the presence or absence of interventions requires the use of large data sets, wherein these variables can be sampled adequately and inferences made. Inroads in quantitative methods have been made in the psychometric and sociometric literatures, but these methods are not yet common knowledge in the mathematics education community. In fact, currently there is no volume devoted to discussion of issues related to large-scale studies and to report findings from them. This volume is unique as it directly discusses methodological issue in large-scale studies and reports empirical data from large-scale studies.
Download or read book An Open Book What and How Young Children Learn From Picture and Story Books written by Jessica S. Horst and published by Frontiers Media SA. This book was released on 2016-01-21 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Looking at and listening to picture and story books is a ubiquitous activity, frequently enjoyed by many young children and their parents. Well before children can read for themselves they are able to learn from books. Looking at and listening to books increases children’s general knowledge, understanding about the world and promotes language acquisition. This collection of papers demonstrates the breadth of information pre-reading children learn from books and increases our understanding of the social and cognitive mechanisms that support this learning. Our hope is that this Research Topic/eBook will be useful for researchers as well as educational practitioners and parents who are interested in optimizing children’s learning.
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 Rational Numbers written by Thomas P. Carpenter and published by Routledge. This book was released on 2012-10-12 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until recently there had been relatively little integration of programs of research on teaching, learning, curriculum, and assessment. However, in the last few years it has become increasingly apparent that a more unified program of research is needed to acquire an understanding of teaching and learning in schools that will inform curriculum development and assessment. The chapters in this volume represent a first step toward an integration of research paradigms in one clearly specified mathematical domain. Integrating a number of different research perspectives is a complex task, and ways must be found to reduce the complexity without sacrificing the integration. The research discussed in this volume is tied together because it deals with a common content strand. During the last ten years specific content domains have served as focal points for research on the development of mathematical concepts in children. The areas of addition and subtraction, algebra, rational numbers, and geometry are notable examples. Whether a similar organizational structure will prevail for programs of research that integrate the study of teaching, learning, curriculum, and assessment is an open question. The perspectives presented in this volume illustrate the potential for adopting this perspective.
