Download or read book Foundations of Geometric Cognition written by Mateusz Hohol and published by Routledge. This book was released on 2019-09-12 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers. Foundations of Geometric Cognition shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object recognition. These capacities, shared with non-human animals and appearing in early stages of the human ontogeny, cannot, however, fully explain a uniquely human form of geometric cognition. In the book, Hohol argues that Euclidean geometry would not be possible without the human capacity to create and use abstract concepts, demonstrating how language and diagrams provide cognitive scaffolding for abstract geometric thinking, within a context of a Euclidean system of thought. Taking an interdisciplinary approach and drawing on research from diverse fields including psychology, cognitive science, and mathematics, this book is a must-read for cognitive psychologists and cognitive scientists of mathematics, alongside anyone interested in mathematical education or the philosophical and historical aspects of geometry.
Download or read book Foundations of Geometric Cognition written by Mateusz Hohol and published by Routledge. This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Geometric Cognition presents an empirically inspired theory of geometric cognition. The book explains how language and diagrams provide cognitive scaffolding for abstract geometric thinking within a context of Euclidean systems of thought.
Download or read book Foundations of Geometric Cognition written by Mateusz Hohol and published by Routledge. This book was released on 2019-09-12 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers. Foundations of Geometric Cognition shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object recognition. These capacities, shared with non-human animals and appearing in early stages of the human ontogeny, cannot, however, fully explain a uniquely human form of geometric cognition. In the book, Hohol argues that Euclidean geometry would not be possible without the human capacity to create and use abstract concepts, demonstrating how language and diagrams provide cognitive scaffolding for abstract geometric thinking, within a context of a Euclidean system of thought. Taking an interdisciplinary approach and drawing on research from diverse fields including psychology, cognitive science, and mathematics, this book is a must-read for cognitive psychologists and cognitive scientists of mathematics, alongside anyone interested in mathematical education or the philosophical and historical aspects of geometry.
Download or read book Cognitive Science Foundations of Instruction written by Mitchell Rabinowitz and published by Routledge. This book was released on 2020-02-13 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents and discusses current research that makes the connection between cognitive theory and instructional application. Addressing two general issues, the first set of chapters specifies the relation between cognitive theory and the development and evaluation of instruction, while the second set deals with the questions involved in understanding and assessing cognitive skills. The outstanding feature of these chapters is that they all present in-depth discussions of the theoretical issues underlying instructional decisions. Many present specific implementations that provide examples of concrete applications of theory. In addition, the settings for implementing these examples span a broad range of instructional areas and environments, illustrating the generality and transferability of the application of theory to practice.
Download or read book Conceptual Spaces written by Peter Gardenfors and published by MIT Press. This book was released on 2004-01-30 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within cognitive science, two approaches currently dominate the problem of modeling representations. The symbolic approach views cognition as computation involving symbolic manipulation. Connectionism, a special case of associationism, models associations using artificial neuron networks. Peter Gärdenfors offers his theory of conceptual representations as a bridge between the symbolic and connectionist approaches. Symbolic representation is particularly weak at modeling concept learning, which is paramount for understanding many cognitive phenomena. Concept learning is closely tied to the notion of similarity, which is also poorly served by the symbolic approach. Gärdenfors's theory of conceptual spaces presents a framework for representing information on the conceptual level. A conceptual space is built up from geometrical structures based on a number of quality dimensions. The main applications of the theory are on the constructive side of cognitive science: as a constructive model the theory can be applied to the development of artificial systems capable of solving cognitive tasks. Gärdenfors also shows how conceptual spaces can serve as an explanatory framework for a number of empirical theories, in particular those concerning concept formation, induction, and semantics. His aim is to present a coherent research program that can be used as a basis for more detailed investigations.
Download or read book Developing Thinking in Geometry written by Sue Johnston-Wilder and published by Paul Chapman Educational Publishing. This book was released on 2005-09-14 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: "All readers can use this book to reignite their fascination with mathematics. Fosters not only a curiosity about geometry itself but crucially focuses on how learners can actively engage in thinking about geometry and its central key ideas."-Sylvia Johnson, Professor, Sheffield Hallam University"Exudes activity and interactivity. A book for learning geometry, learning to think more deeply about geometry, and also about its teaching and learning."-David Pimm, Professor, University of AlbertaDeveloping Thinking in Geometry enables teachers and their support staff to experience and teach geometric thinking. Discussing key teaching principles, the book and its accompanying interactive CD-ROM include many activities encouraging readers to extend their own learning, and teaching practices.Drawing on innovative approaches for teaching and learning geometry developed by the Open University's Centre for Mathematics Education, this resource is constructed around the following key themes:InvarianceLanguage and points of viewReasoning using invarianceVisualizing and representing
Download or read book New Foundations in Mathematics written by Garret Sobczyk and published by Springer Science & Business Media. This book was released on 2012-10-26 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
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.
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 377 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
Download or read book Knowledge under Construction written by Daniel Ness and published by Rowman & Littlefield Publishers. This book was released on 2007-03-26 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knowledge under Construction investigates how young children develop spatial, geometric, and scientific thinking skills-particularly those associated with architecture. Based on original research and analysis of videotapes of children's play with blocks, the authors' findings suggest that such play is anything but pointless. Their conclusions fill in gaps in our current understanding of how children learn to think spatially and scientifically even while challenging portions of that understanding, including some of Piaget's thesis about the primacy of topological space in children's learning. A system of measurement developed to identify and categorize children's spontaneous behavior at play allows adults to observe patterns of behavior as children play and record the development of process skills and cognitive abilities, enhancing our understanding of how children begin to learn about space and architectural relationships. The book also examines the educational implications of our enhanced understanding. One possible development is a new, alternative way to measure cognitive abilities and development in children based on their work with blocks.
Download or read book Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being written by George Lakoff and published by . This book was released on 2000-11-02 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of the cognitive science of mathematical ideas.
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 Special Issues in Early Childhood Mathematics Education Research written by and published by BRILL. This book was released on 2022-02-14 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, 23 contributors offer new insights on key issues in mathematics education in early childhood.
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 Acquisition of Complex Arithmetic Skills and Higher Order Mathematics Concepts written by David C. Geary and published by Academic Press. This book was released on 2017-02-08 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts focuses on typical and atypical learning of complex arithmetic skills and higher-order math concepts. As part of the series Mathematical Cognition and Learning, this volume covers recent advances in the understanding of children’s developing competencies with whole-number arithmetic, fractions, and rational numbers. Each chapter covers these topics from multiple perspectives, including genetic disorders, cognition, instruction, and neural networks. Covers innovative measures and recent methodological advances in mathematical thinking and learning Contains contributions that improve instruction and education in these domains Informs policy aimed at increasing the level of mathematical proficiency in the general public
Download or read book A Geometric Approach to the Unification of Symbolic Structures and Neural Networks written by Tiansi Dong and published by Springer Nature. This book was released on 2020-08-24 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unification of symbolist and connectionist models is a major trend in AI. The key is to keep the symbolic semantics unchanged. Unfortunately, present embedding approaches cannot. The approach in this book makes the unification possible. It is indeed a new and promising approach in AI. -Bo Zhang, Director of AI Institute, Tsinghua It is indeed wonderful to see the reviving of the important theme Nural Symbolic Model. Given the popularity and prevalence of deep learning, symbolic processing is often neglected or downplayed. This book confronts this old issue head on, with a historical look, incorporating recent advances and new perspectives, thus leading to promising new methods and approaches. -Ron Sun (RPI), on Governing Board of Cognitive Science Society Both for language and humor, approaches like those described in this book are the way to snickerdoodle wombats. -Christian F. Hempelmann (Texas A&M-Commerce) on Executive Board of International Society for Humor Studies
Download or read book Relativity and Geometry written by Roberto Torretti and published by Elsevier. This book was released on 2014-05-20 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relativity and Geometry aims to elucidate the motivation and significance of the changes in physical geometry brought about by Einstein, in both the first and the second phases of relativity. The book contains seven chapters and a mathematical appendix. The first two chapters review a historical background of relativity. Chapter 3 centers on Einstein's first Relativity paper of 1905. Subsequent chapter presents the Minkowskian formulation of special relativity. Chapters 5 and 6 deal with Einstein's search for general relativity from 1907 to 1915, as well as some aspects and subsequent developments of the theory. The last chapter explores the concept of simultaneity, geometric conventionalism, and a few other questions concerning space time structure, causality, and time.
