Foundations Of Geometric Cognition PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Foundations Of Geometric Cognition PDF full book. Access full book title Foundations Of Geometric Cognition.
| Author | : Mateusz Hohol |
| Publisher | : Routledge |
| Total Pages | : 315 |
| Release | : 2019-09-12 |
| Genre | : Psychology |
| ISBN | : 0429509219 |
Download Foundations of Geometric Cognition Book in PDF, ePub and Kindle
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.
| Author | : Mateusz Hohol |
| Publisher | : Routledge |
| Total Pages | : 0 |
| Release | : 2020 |
| Genre | : PSYCHOLOGY |
| ISBN | : 9780367173449 |
Download Foundations of Geometric Cognition Book in PDF, ePub and Kindle
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.
| Author | : Mateusz Hohol |
| Publisher | : Routledge |
| Total Pages | : 188 |
| Release | : 2019-09-12 |
| Genre | : Psychology |
| ISBN | : 042950859X |
Download Foundations of Geometric Cognition Book in PDF, ePub and Kindle
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.
| Author | : Mitchell Rabinowitz |
| Publisher | : Routledge |
| Total Pages | : 250 |
| Release | : 2020-02-13 |
| Genre | : Education |
| ISBN | : 1135443661 |
Download Cognitive Science Foundations of Instruction Book in PDF, ePub and Kindle
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.
| Author | : Peter Gardenfors |
| Publisher | : MIT Press |
| Total Pages | : 324 |
| Release | : 2004-01-30 |
| Genre | : Psychology |
| ISBN | : 9780262572194 |
Download Conceptual Spaces Book in PDF, ePub and Kindle
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.
| Author | : Sue Johnston-Wilder |
| Publisher | : Paul Chapman Educational Publishing |
| Total Pages | : 300 |
| Release | : 2005-09-14 |
| Genre | : Business & Economics |
| ISBN | : 9781412911696 |
Download Developing Thinking in Geometry Book in PDF, ePub and Kindle
"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
| Author | : Garret Sobczyk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 373 |
| Release | : 2012-10-26 |
| Genre | : Mathematics |
| ISBN | : 0817683852 |
Download New Foundations in Mathematics Book in PDF, ePub and Kindle
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.
| Author | : David C. Geary |
| Publisher | : Academic Press |
| Total Pages | : 377 |
| Release | : 2019-01-03 |
| Genre | : Psychology |
| ISBN | : 0128159537 |
Download Cognitive Foundations for Improving Mathematical Learning Book in PDF, ePub and Kindle
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
| Author | : National Research Council |
| Publisher | : National Academies Press |
| Total Pages | : 399 |
| Release | : 2009-11-13 |
| Genre | : Education |
| ISBN | : 0309147433 |
Download Mathematics Learning in Early Childhood Book in PDF, ePub and Kindle
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.
| Author | : George Mather |
| Publisher | : Psychology Press |
| Total Pages | : 830 |
| Release | : 2016-08-12 |
| Genre | : Psychology |
| ISBN | : 1317372549 |
Download Foundations of Sensation and Perception Book in PDF, ePub and Kindle
Do you wonder how movies – sequences of static frames – appear to move, or why 3-D films look different from traditional movies? Why does ventriloquism work, and why can airliner flights make you feel disoriented? The answers to these and other questions about the human senses can be found within the pages of Foundations of Sensation and Perception. This third edition maintains the standard for clarity and accessibility combined with rigor which was set in previous editions, making it suitable for a wide range of students. As in the previous editions, the early chapters allow students to grasp fundamental principles in relation to the relatively simple sensory systems (smell, taste, touch and balance) before moving on to more complex material in hearing and vision. The text has been extensively updated, and this new edition includes: a new chapter devoted to attention and perception over 200 new references over 30 new figures and improved, more colorful, visual presentation a new companion website with a range of resources for students and lecturers The book contains a range of pedagogical features, including tutorial sections at the end of each chapter. This distinctive feature introduces areas of the subject which are rarely included in student texts, but are crucial for establishing a firm foundation of knowledge. Some tutorials are devoted to more advanced and technical topics (optics, light measurement, Bayesian inference), but treated in an accessible manner, while others cover topics a little outside of the mainstream (music perception, consciousness, visual art). Foundations of Sensation and Perception will enable the reader to achieve a firm grasp of current knowledge concerning the processes that underlie our perception of the world and will be an invaluable resource for those studying psychology, neuroscience, and related disciplines.
