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Mental Geometry
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Book Synopsis Geometry of Grief by : Michael Frame
Download or read book Geometry of Grief written by Michael Frame and published by University of Chicago Press. This book was released on 2021-09-08 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry -- Grief -- Beauty -- Story -- Fractal -- Beyond -- Appendix: More Math.
Book Synopsis Molecular Origins of Brain and Body Geometry by : Antonio Lima-de-Faria
Download or read book Molecular Origins of Brain and Body Geometry written by Antonio Lima-de-Faria and published by Springer. This book was released on 2014-10-07 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: New concepts arise in science when apparently unrelated fields of knowledge are put together in a coherent way. The recent results in molecular biology allow to explain the emergence of body patterns in animals that before could not be understood by zoologists. There are no ”fancy curiosities” in nature. Every pattern is a product of a molecular cascade originating in genes and a living organism arises from the collaboration of these genes with the outer physical environment. Tropical fishes are as startling in their colors and geometric circles as peacocks. Tortoises are covered with the most regular triangles, squares and concentric circles that can be green, brown or yellow. Parallel scarlet bands are placed side by side of black ones along the body of snakes. Zebras and giraffes have patterns which are lessons in geometry, with their transversal and longitudinal stripes, their circles and other geometric figures. Monkeys, like the mandrills, have a spectacularly colored face scarlet nose with blue parallel flanges and yellow beard. All this geometry turns out to be highly molecular. The genes are many and have been DNA sequenced. Besides they not only deal with the coloration of the body but with the development of the brain and the embryonic process. A precise scenario of molecular events unravels in the vertebrates. It may seem far-fetched, but the search for the origin of this geometry made it mandatory to study the evolution of matter and the origin of the brain. It turned out that matter from its onset is pervaded by geometry and that the brain is also a prisoner of this ordered construction. Moreover, the brain is capable of altering the body geometry and the geometry of the environment changes the brain. Nothing spectacular occurred when the brain arrived in evolution. Not only it came after the eye, which had already established itself long ago, but it had a modest origin. It started from sensory cells on the skin that later aggregated into clusters of neurons that formed ganglia. It also became evident that pigment cells, that decide the establishment of the body pattern, originate from the same cell population as neurons (the neural crest cells). This is a most revealing result because it throws light on the power that the brain has to rapidly redirect the coloration of the body and to change its pattern. Recent experiments demonstrate how the brain changes the body geometry at will and within seconds, an event that could be hardly conceived earlier. Moreover, this change is not accidental it is related to the surrounding environment and is also used as a mating strategy. Chameleons know how to do it as well as flat fishes and octopuses. No one would have dared to think that the brain had its own geometry. How could the external geometry of solids or other figures of our environment be apprehended by neurons if these had no architecture of their own? Astonishing was that the so called ”simple cells”, in the neurons of the primary visual cortex, responded to a bar of light with an axis of orientation that corresponded to the axis of the cell’s receptive field. We tend to consider our brain a reliable organ. But how reliable is it? From the beginning the brain is obliged to transform reality. Brain imagery involves: form, color, motion and sleep. Unintentionally these results led to unexpected philosophical implications. Plato’s pivotal concept that ”forms” exist independently of the material world is reversed. Atoms have been considered to be imaginary for 2,000 years but at present they can be photographed, one by one, with electron microscopes. The reason why geometry has led the way in this inquiry is due to the fact that where there is geometry there is utter simplicity coupled to rigorous order that underlies the phenomenon where it is recognized. Order allows variation but imposes at the same time a canalization that is patent in what we call evolution.
Book Synopsis Mathematics and Cognition by : Pearla Nesher
Download or read book Mathematics and Cognition written by Pearla Nesher and published by CUP Archive. This book was released on 1990-02-23 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1990 book is aimed at teachers, mathematics educators and general readers who are interested in mathematics education from a psychological point of view.
Book Synopsis Space and Geometry in the Light of Physiological, Psychological and Physical Inquiry by : Ernst Mach
Download or read book Space and Geometry in the Light of Physiological, Psychological and Physical Inquiry written by Ernst Mach and published by . This book was released on 1906 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Learning and Teaching of Geometry in Secondary Schools by : Pat Herbst
Download or read book The Learning and Teaching of Geometry in Secondary Schools written by Pat Herbst and published by Taylor & Francis. This book was released on 2017-03-16 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education. The Learning and Teaching of Geometry in Secondary Schools reviews past and present research on the teaching and learning of geometry in secondary schools and proposes an approach for design research on secondary geometry instruction. Areas covered include: teaching and learning secondary geometry through history; the representations of geometric figures; students’ cognition in geometry; teacher knowledge, practice and, beliefs; teaching strategies, instructional improvement, and classroom interventions; research designs and problems for secondary geometry. Drawing on a team of international authors, this new text will be essential reading for experienced teachers of mathematics, graduate students, curriculum developers, researchers, and all those interested in exploring students’ study of geometry in secondary schools.
Book Synopsis Mathematical Imagining by : Christof Weber
Download or read book Mathematical Imagining written by Christof Weber and published by Taylor & Francis. This book was released on 2023-10-10 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imagine a plastic cup lying on the floor. Give the cup a nudge so that it begins to roll. What does the path it takes look like? So begins the journey that Christof Weber takes you on in Mathematical Imagining: A Routine for Secondary Classrooms . Along the way, he makes the case that the ability to imagine, manipulate, and explain mathematical images and situations is fundamental to all mathematics and particularly important to higher level study. Most importantly, drawing on years of experiments in his own classroom, Weber shows that mathematical imagining is a skill that can be taught efficiently and effectively. Mathematical Imagining describes an original routine that gives students space and time to imagine a mathematical situation and then revise, discuss, and act upon the mental images they create. You can use this creative routine to glimpse into your students' thinking and discover teaching opportunities, while empowering them to create their own mathematics.Inside you’ll find the following: An introduction to the routine including the rationale behind it, facilitation guidance, and classroom examples Modifications to implement the routine in your classroom, even with varying time constraints 37 exercises broken into four categories: constructions, problem-solving, reasoning, and paradoxes Discussions of the mathematics involved in each exercise, including possible follow-up questions Instructions on how to create your own exercises beyond the book This one-of-a-kind resource is for secondary teachers looking to inspire student creativity and curiosity, deepen their own subject matter knowledge and pedagogical content knowledge, and invite all students to access the power of their own mathematical imaginations.
Book Synopsis Handbook of Behavioral and Cognitive Geography by : Daniel R. Montello
Download or read book Handbook of Behavioral and Cognitive Geography written by Daniel R. Montello and published by Edward Elgar Publishing. This book was released on 2018-04-27 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive Handbook summarizes existing work and presents new concepts and empirical results from leading scholars in the multidisciplinary field of behavioral and cognitive geography, the study of the human mind, and activity in and concerning space, place, and environment. It provides the broadest and most inclusive coverage of the field so far, including work relevant to human geography, cartography, and geographic information science.
Author :Rosamund Sutherland Publisher :Springer Science & Business Media ISBN 13 :9783540585824 Total Pages :348 pages Book Rating :4.5/5 (858 download)
Book Synopsis Exploiting Mental Imagery with Computers in Mathematics Education by : Rosamund Sutherland
Download or read book Exploiting Mental Imagery with Computers in Mathematics Education written by Rosamund Sutherland and published by Springer Science & Business Media. This book was released on 1995 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.
Book Synopsis Space, Time and Number in the Brain by : Stanislas Dehaene
Download or read book Space, Time and Number in the Brain written by Stanislas Dehaene and published by Academic Press. This book was released on 2011-07-13 with total page 374 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
Book Synopsis EBOOK: Enhancing Primary Mathematics Teaching by : Ian Thompson
Download or read book EBOOK: Enhancing Primary Mathematics Teaching written by Ian Thompson and published by McGraw-Hill Education (UK). This book was released on 2003-09-16 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is the third in an important trilogy of edited collections on the teaching and learning of primary mathematics. To each book the editor, Ian Thompson, has attracted a team of expert contributors, and himself set the characteristically high standard of writing and clarity... When, in 10 or 20 years' time, people want to know about the state of English primary mathematics at the turn of the 21st century, they will turn to this volume. You would do well to read it now." Mathematics in Schools "This is the third book in the popular series edited by Ian Thompson that brings together an impressive array of contributing authors. Current issues are discussed in an informed but concise way that makes research accessible to the wider community of mathematics educators." Julia Anghileri, University of Cambridge This book explores the effect that the National Numeracy Strategy and its successor, the Primary Strategy, have had on the way in which mathematics is taught in primary schools. Prominent contributors examine the Strategies' recommendations from the perspective of their own research areas or interests, and discuss the issues involved, including: Ideas for extending current practice Suggestions of important aspects of mathematics teaching that are being given little or no emphasis Alternative approaches that could be integrated into current practice Aspects of current practice that need to take account of recent research findings or emerging issues. Each chapter discusses implications for teaching and learning primary mathematics. The book will be particularly useful for trainees, practising teachers, mathematics coordinators and numeracy consultants. Contributors: Mundher Adhami, Mike Askew, Carol Aubrey, Margaret Brown, Ann Dowker, Rosemary Hafeez, Steve Higgins, Keith Jones, Lesley Jones, Valsa Koshy, Alison Millett, Claire Mooney, Laurie Rousham, Malcolm Swan, Ian Thompson, Helen J Williams.
Book Synopsis Space, Time and Number in the Brain by : Elizabeth Brannon
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
Book Synopsis Geometry and the Imagination by : D. Hilbert
Download or read book Geometry and the Imagination written by D. Hilbert and published by American Mathematical Soc.. This book was released on 2021-03-17 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This remarkable book has endured as a true masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer—even after more than half a century has passed! The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. “Hilbert and Cohn-Vossen” is full of interesting facts, many of which you wish you had known before. It's also likely that you have heard those facts before, but surely wondered where they could be found. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in R 3 R3. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: π/4=1−1/3+1/5−1/7+−… π/4=1−1/3+1/5−1/7+−…. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is “Projective Configurations”. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. Here, we see regular polyhedra again, from a different perspective. One of the high points of the chapter is the discussion of Schlafli's Double-Six, which leads to the description of the 27 lines on the general smooth cubic surface. As is true throughout the book, the magnificent drawings in this chapter immeasurably help the reader. A particularly intriguing section in the chapter on differential geometry is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? Many mathematicians are familiar with the plaster models of surfaces found in many mathematics departments. The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained! The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the “pantheon” of great mathematics books.
Book Synopsis Catalogue by : University of Delaware
Download or read book Catalogue written by University of Delaware and published by . This book was released on 1856 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Foundations of Geometric Cognition by : Mateusz Hohol
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 Mental Imagery written by R.G. Kunzendorf and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current book presents select proceedings from the Eleventh Annual Conference of AASMI (The American Association for the Study of Mental Imagery) in Washington, DC, 1989, and from the Twelfth Annual Conference of AASMI in Lowell and Boston, MA, 1990. This presentation of keynote addresses, research papers, and clinical workshops reflects a broad range of theoretical positions and a diverse repertoire of methodological approaches. Within this breadth and diversity, however, four aspects of the nature of imagery stand out: its mental nature, its private nature, its conscious nature, and its symbolic nature. The mental nature of imagery--i.e., its epistemological aspect--is explored in the book's first section of articles by Marcia Johnson, Laura Snodgrass, Leonard Giambra and Alicia Grodsky, Vija Lusebrink, Selina Kassels, Helane Rosenberg and Yakov Epstein, M. Elizabeth D'Zamko and Lynne Schwab, and Laurence Martel. These first eight articles fall, essentially, into various domains of cognitive psychology, including the psychology of art and educational psychology. In the second section, the private nature of imagery is studied by Ernest Hartmann, Nicholas Spanos, Benjamin Wallace, Deirdre Barrett, John Connolly, James Honeycutt, Dominique Gendrin, and James Honeycutt and J. Michael Gotcher. These studies, which fall within the realm of personality and social psychology, bring to light the fact that many very public interpersonal behaviors reflect very private images. Such behaviors range from interpersonal rapport with a hypnotist, to rapport with a forensic jury.
Book Synopsis The Principles of Education by : Thomas Raymont
Download or read book The Principles of Education written by Thomas Raymont and published by . This book was released on 1904 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Cognitive Mathematics by : Marcel Danesi
Download or read book Handbook of Cognitive Mathematics written by Marcel Danesi and published by Springer Nature. This book was released on 2022-10-31 with total page 1392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cognitive mathematics provides insights into how mathematics works inside the brain and how it is interconnected with other faculties through so-called blending and other associative processes. This handbook is the first large collection of various aspects of cognitive mathematics to be amassed into a single title, covering decades of connection between mathematics and other figurative processes as they manifest themselves in language, art, and even algorithms. It will be of use to anyone working in math cognition and education, with each section of the handbook edited by an international leader in that field.
