Visual Thinking In Mathematics
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Visual Thinking In Mathematics
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Author : Marcus Giaquinto
language : en
Publisher: Oxford University Press
Release Date : 2007-07-05
Visual Thinking In Mathematics written by Marcus Giaquinto and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-05 with Mathematics categories.
Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis.
Visual Thinking In Mathematics
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Author : Marcus Giaquinto
language : en
Publisher: Clarendon Press
Release Date : 2007-07-05
Visual Thinking In Mathematics written by Marcus Giaquinto and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-05 with Philosophy categories.
Visual thinking - visual imagination or perception of diagrams and symbol arrays, and mental operations on them - is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual thinking in mathematics is rarely just a superfluous aid; it usually has epistemological value, often as a means of discovery. Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis. He shows how we can discern abstract general truths by means of specific images, how synthetic a priori knowledge is possible, and how visual means can help us grasp abstract structures. Visual Thinking in Mathematics reopens the investigation of earlier thinkers from Plato to Kant into the nature and epistemology of an individual's basic mathematical beliefs and abilities, in the new light shed by the maturing cognitive sciences. Clear and concise throughout, it will appeal to scholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking.
Visual Thinking In Mathematics
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Author : M. Giaquinto
language : en
Publisher:
Release Date : 2007
Visual Thinking In Mathematics written by M. Giaquinto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Arithmetic categories.
Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis.
Proofs Without Words
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Author : Roger B. Nelsen
language : en
Publisher: MAA
Release Date : 1993
Proofs Without Words written by Roger B. Nelsen and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Logic, Symbolic and mathematical categories.
Proofs Without Words Iii
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Author : Roger B. Nelsen
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-31
Proofs Without Words Iii written by Roger B. Nelsen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-31 with Mathematics categories.
Proofs without words (PWWs) are figures or diagrams that help the reader see why a particular mathematical statement is true, and how one might begin to formally prove it true. PWWs are not new, many date back to classical Greece, ancient China, and medieval Europe and the Middle East. PWWs have been regular features of the MAA journals Mathematics Magazine and The College Mathematics Journal for many years, and the MAA published the collections of PWWs Proofs Without Words: Exercises in Visual Thinking in 1993 and Proofs Without Words II: More Exercises in Visual Thinking in 2000. This book is the third such collection of PWWs.
Math Made Visual
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Author : Claudi Alsina
language : en
Publisher: MAA
Release Date : 2006-07-06
Math Made Visual written by Claudi Alsina and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-06 with Education categories.
The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication and teaching of mathematics. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece and India but only in the last thirty years has there been a growing interest in so-called 'proofs without words.' In this book the authors show that behind most of the pictures 'proving' mathematical relations are some well-understood methods. The first part of the book consists of twenty short chapters, each one describing a method to visualize some mathematical idea (a proof, a concept, an operation,...) and several applications to concrete cases. Following this the book examines general pedagogical considerations concerning the development of visual thinking, practical approaches for making visualizations in the classroom and a discussion of the role that hands-on material plays in this process.
Thinking Visually
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Author : Stephen K. Reed
language : en
Publisher: Psychology Press
Release Date : 2013-08-21
Thinking Visually written by Stephen K. Reed and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-21 with Psychology categories.
Language is a marvelous tool for communication, but it is greatly overrated as a tool for thought. This volume documents the many ways pictures, visual images, and spatial metaphors influence our thinking. It discusses both classic and recent research that support the view that visual thinking occurs not only where we expect to find it, but also where we do not. Much of comprehending language, for instance, depends on visual simulations of words or on spatial metaphors that provide a foundation for conceptual understanding. Thinking Visually supports comprehension by reducing jargon and by providing many illustrations, educational applications, and problems for readers to solve. It provides a broad overview of topics that range from the visual images formed by babies to acting classes designed for the elderly, from visual diagrams created by children to visual diagrams created by psychologists, from producing and manipulating images to viewing animations. The final chapters discuss examples of instructional software and argue that the lack of such software in classrooms undermines the opportunity to develop visual thinking. The book includes the Animation TutorTM downloadable resources to illustrate the application of research on visual thinking to improve mathematical reasoning.
Toward A Visually Oriented School Mathematics Curriculum
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Author : Ferdinand Rivera
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-06
Toward A Visually Oriented School Mathematics Curriculum written by Ferdinand Rivera and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-06 with Education categories.
What does it mean to have a visual representation of a mathematical object, concept, or process? What visualization strategies support growth in mathematical thinking, reasoning, generalization, and knowledge? Is mathematical seeing culture-free? How can information drawn from studies in blind subjects help us understand the significance of a multimodal approach to learning mathematics? Toward a Visually-Oriented School Mathematics Curriculum explores a unified theory of visualization in school mathematical learning via the notion of progressive modeling. Based on the author’s longitudinal research investigations in elementary and middle school classrooms, the book provides a compelling empirical account of ways in which instruction can effectively orchestrate the transition from personally-constructed visuals, both externally-drawn and internally-derived, into more structured visual representations within the context of a socioculturally grounded mathematical activity. Both for teachers and researchers, a discussion of this topic is relevant in the history of the present. The ubiquity of technological tools and virtual spaces for learning and doing mathematics has aroused interest among concerned stakeholders about the role of mathematics in these contexts. The book begins with a prolegomenon on the author’s reflections on past and present visual studies in mathematics education. In the remaining seven chapters, visualization is pursued in terms of its role in bringing about progressions in mathematical symbolization, abduction, pattern generalization, and diagrammatization. Toward a Visually-Oriented School Mathematics Curriculum views issues surrounding visualization through the eyes of a classroom teacher-researcher; it draws on findings within and outside of mathematics education that help practitioners and scholars gain a better understanding of what it means to pleasurably experience the symmetric visual/symbolic reversal phenomenon – that is, seeing the visual in the symbolic and the symbolic in the visual."
Proofs Without Words Ii
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Author : Roger B. Nelsen
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-02-22
Proofs Without Words Ii written by Roger B. Nelsen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-22 with Mathematics categories.
Like its predecessor, Proofs without Words, this book is a collection of pictures or diagrams that help the reader see why a particular mathematical statement may be true and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: geometry and algebra; trigonometry, calculus and analytic geometry; inequalities; integer sums; and sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.
Shape Understanding System
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Author : Zbigniew Les
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-11
Shape Understanding System written by Zbigniew Les and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-11 with Mathematics categories.
This book presents the results of research into one of the most complex and difficult areas - research into thinking and understanding. The research was carried out at the newly founded Queen Jadwiga Research Institute of Understanding and is focused on the problem of visual understanding and visual thinking. The authors believe this is the first book to attempt to investigate the complexity of visual thinking problems in the context of building the thinking machine.