Mental Imagery In Mathematics

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Exploiting Mental Imagery with Computers in Mathematics Education

Author : Rosamund Sutherland
Publisher : Springer Science & Business Media
ISBN 13 : 3642577717
Total Pages : 337 pages
Book Rating : 4.6/5 (425 download)

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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 2012-12-06 with total page 337 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.

Fundamental Constructs in Mathematics Education

Author : John Mason
Publisher : Psychology Press
ISBN 13 : 9780415326971
Total Pages : 360 pages
Book Rating : 4.3/5 (269 download)

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Book Synopsis Fundamental Constructs in Mathematics Education by : John Mason

Download or read book Fundamental Constructs in Mathematics Education written by John Mason and published by Psychology Press. This book was released on 2004 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together a collection of classic tasks, extracts and texts that have been quoted repeatedly in mathematics education literature.

Visualization in Mathematics, Reading and Science Education

Author : Linda M. Phillips
Publisher : Springer Science & Business Media
ISBN 13 : 9048188164
Total Pages : 112 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis Visualization in Mathematics, Reading and Science Education by : Linda M. Phillips

Download or read book Visualization in Mathematics, Reading and Science Education written by Linda M. Phillips and published by Springer Science & Business Media. This book was released on 2010-09-02 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Science education at school level worldwide faces three perennial problems that have become more pressing of late. These are to a considerable extent interwoven with concerns about the entire school curriculum and its reception by students. The rst problem is the increasing intellectual isolation of science from the other subjects in the school curriculum. Science is too often still taught didactically as a collection of pre-determined truths about which there can be no dispute. As a con- quence, many students do not feel any “ownership” of these ideas. Most other school subjects do somewhat better in these regards. For example, in language classes, s- dents suggest different interpretations of a text and then debate the relative merits of the cases being put forward. Moreover, ideas that are of use in science are presented to students elsewhere and then re-taught, often using different terminology, in s- ence. For example, algebra is taught in terms of “x, y, z” in mathematics classes, but students are later unable to see the relevance of that to the meaning of the universal gas laws in physics, where “p, v, t” are used. The result is that students are c- fused and too often alienated, leading to their failure to achieve that “extraction of an education from a scheme of instruction” which Jerome Bruner thought so highly desirable.

Models of the Mind

Author : Grace Lindsay
Publisher : Bloomsbury Publishing
ISBN 13 : 1472966457
Total Pages : 401 pages
Book Rating : 4.4/5 (729 download)

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Book Synopsis Models of the Mind by : Grace Lindsay

Download or read book Models of the Mind written by Grace Lindsay and published by Bloomsbury Publishing. This book was released on 2021-03-04 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The human brain is made up of 85 billion neurons, which are connected by over 100 trillion synapses. For more than a century, a diverse array of researchers searched for a language that could be used to capture the essence of what these neurons do and how they communicate – and how those communications create thoughts, perceptions and actions. The language they were looking for was mathematics, and we would not be able to understand the brain as we do today without it. In Models of the Mind, author and computational neuroscientist Grace Lindsay explains how mathematical models have allowed scientists to understand and describe many of the brain's processes, including decision-making, sensory processing, quantifying memory, and more. She introduces readers to the most important concepts in modern neuroscience, and highlights the tensions that arise when the abstract world of mathematical modelling collides with the messy details of biology. Each chapter of Models of the Mind focuses on mathematical tools that have been applied in a particular area of neuroscience, progressing from the simplest building block of the brain – the individual neuron – through to circuits of interacting neurons, whole brain areas and even the behaviours that brains command. In addition, Grace examines the history of the field, starting with experiments done on frog legs in the late eighteenth century and building to the large models of artificial neural networks that form the basis of modern artificial intelligence. Throughout, she reveals the value of using the elegant language of mathematics to describe the machinery of neuroscience.

Math Made Visual

Author : Claudi Alsina
Publisher : MAA
ISBN 13 : 9780883857465
Total Pages : 202 pages
Book Rating : 4.8/5 (574 download)

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Book Synopsis Math Made Visual by : Claudi Alsina

Download or read book Math Made Visual written by Claudi Alsina and published by MAA. This book was released on 2006-07-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being

Author : George Lakoff
Publisher :
ISBN 13 :
Total Pages : 520 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being by : George Lakoff

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.

Visualization, Explanation and Reasoning Styles in Mathematics

Author : P. Mancosu
Publisher : Springer Science & Business Media
ISBN 13 : 1402033354
Total Pages : 315 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Visualization, Explanation and Reasoning Styles in Mathematics by : P. Mancosu

Download or read book Visualization, Explanation and Reasoning Styles in Mathematics written by P. Mancosu and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.

Visual Thinking in Mathematics

Author : Marcus Giaquinto
Publisher : Oxford University Press
ISBN 13 : 0199285942
Total Pages : 298 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Visual Thinking in Mathematics by : Marcus Giaquinto

Download or read book Visual Thinking in Mathematics written by Marcus Giaquinto and published by Oxford University Press. This book was released on 2007-07-05 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

How Not to Be Wrong

Author : Jordan Ellenberg
Publisher : Penguin Press
ISBN 13 : 1594205221
Total Pages : 480 pages
Book Rating : 4.5/5 (942 download)

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Book Synopsis How Not to Be Wrong by : Jordan Ellenberg

Download or read book How Not to Be Wrong written by Jordan Ellenberg and published by Penguin Press. This book was released on 2014-05-29 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.

Handbook of Research on the Psychology of Mathematics Education

Author : Angel Gutiérrez
Publisher : Sense Publishers
ISBN 13 : 9077874194
Total Pages : 538 pages
Book Rating : 4.0/5 (778 download)

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Book Synopsis Handbook of Research on the Psychology of Mathematics Education by : Angel Gutiérrez

Download or read book Handbook of Research on the Psychology of Mathematics Education written by Angel Gutiérrez and published by Sense Publishers. This book was released on 2006 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compilation of the research produced by the International Group for the Psychology of Mathematics Education (PME) since its creation in 1976. The first three sections summarize cognitively-oriented research on learning and teaching specific content areas, transversal areas, and based on technology-rich environments. The fourth section is devoted to the research on social, affective, cultural and cognitive aspects of mathematics education. The fifth section includes two chapters summarizing the PME research on teacher training and professional life of mathematics teachers.

Secrets of Mental Math

Author : Arthur Benjamin
Publisher : Crown
ISBN 13 : 030734746X
Total Pages : 306 pages
Book Rating : 4.3/5 (73 download)

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Book Synopsis Secrets of Mental Math by : Arthur Benjamin

Download or read book Secrets of Mental Math written by Arthur Benjamin and published by Crown. This book was released on 2008-06-03 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: These simple math secrets and tricks will forever change how you look at the world of numbers. Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun. Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.

Proofs from THE BOOK

Author : Martin Aigner
Publisher : Springer Science & Business Media
ISBN 13 : 3662223430
Total Pages : 194 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis Proofs from THE BOOK by : Martin Aigner

Download or read book Proofs from THE BOOK written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Critical Issues in Mathematics Education

Author : Philip Clarkson
Publisher : Springer Science & Business Media
ISBN 13 : 0387096736
Total Pages : 252 pages
Book Rating : 4.3/5 (87 download)

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Book Synopsis Critical Issues in Mathematics Education by : Philip Clarkson

Download or read book Critical Issues in Mathematics Education written by Philip Clarkson and published by Springer Science & Business Media. This book was released on 2008-09-22 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Critical Issues in Mathematics Education presents the significant contributions of Professor Alan Bishop within the mathematics education research community. Six critical issues, each of which have had paramount importance in the development of mathematics education research, are reviewed and include a discussion of current developments in each area. Teacher decision making, spatial/visualizing geometry, teachers and research, cultural/social aspects of mathematics education, sociopolitical issues, and values serve as the basic issues discussed in this examination of mathematics education over the last fifty years during which Professor Bishop has been active in the field. A comprehensive discussion of each of these topics is realized by offering the reader a classic research contribution of Professor Bishop’s together with commentary and invited chapters from leading experts in the field of mathematics education. Critical Issues in Mathematics Education will make an invaluable contribution to the ongoing reflection of mathematic education researchers worldwide, but also to policy makers and teacher educators who wish to understand some of the key issues with which mathematics education has been and still is concerned, and the context within which Professor Bishop’s key contributions to these research issues were made.

Mathematics for Human Flourishing

Author : Francis Su
Publisher : Yale University Press
ISBN 13 : 0300248814
Total Pages : 287 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis Mathematics for Human Flourishing by : Francis Su

Download or read book Mathematics for Human Flourishing written by Francis Su and published by Yale University Press. This book was released on 2020-01-07 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the Mathematics Association of America's 2021 Euler Book Prize, this is an inclusive vision of mathematics—its beauty, its humanity, and its power to build virtues that help us all flourish“This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart.”—James Tanton, Global Math Project"A good book is an entertaining read. A great book holds up a mirror that allows us to more clearly see ourselves and the world we live in. Francis Su’s Mathematics for Human Flourishing is both a good book and a great book."—MAA Reviews For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity’s most beautiful ideas.In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award‑winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires—such as for play, beauty, freedom, justice, and love—and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother’s, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher’s letters to the author appear throughout the book and show how this intellectual pursuit can—and must—be open to all.

The Case for Mental Imagery

Author : Stephen M. Kosslyn
Publisher : Oxford University Press
ISBN 13 : 0195179080
Total Pages : 257 pages
Book Rating : 4.1/5 (951 download)

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Book Synopsis The Case for Mental Imagery by : Stephen M. Kosslyn

Download or read book The Case for Mental Imagery written by Stephen M. Kosslyn and published by Oxford University Press. This book was released on 2006-03-09 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: When we try to remember whether we left a window open or closed, do we actually see the window in our mind? If we do, does this mental image play a role in how we think? For almost a century, scientists have debated whether mental images play a functional role in cognition. In The Case for Mental Imagery, Stephen Kosslyn, William Thompson, and Giorgio Ganis present a complete and unified argument that mental images do depict information, and that these depictions do play a functional role in human cognition. They outline a specific theory of how depictive representations are used in information processing, and show how these representations arise from neural processes. To support this theory, they seamlessly weave together conceptual analyses and the many varied empirical findings from cognitive psychology and neuroscience. In doing so, they present the conceptual grounds for positing this type of internal representation and summarize and refute arguments to the contrary. Their argument also serves as a historical review of the imagery debate from its earliest inception to its most recent phases, and provides ample evidence that significant progress has been made in our understanding of mental imagery. In illustrating how scientists think about one of the most difficult problems in psychology and neuroscience, this book goes beyond the debate to explore the nature of cognition and to draw out implications for the study of consciousness. Student and professional researchers in vision science, cognitive psychology, philosophy, and neuroscience will find The Case for Mental Imagery to be an invaluable resource for understanding not only the imagery debate, but also and more broadly, the nature of thought, and how theory and research shape the evolution of scientific debates.

Teaching Mathematics in the Primary School

Author : Gill Bottle
Publisher : Bloomsbury Publishing
ISBN 13 : 1441158588
Total Pages : 220 pages
Book Rating : 4.4/5 (411 download)

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Book Synopsis Teaching Mathematics in the Primary School by : Gill Bottle

Download or read book Teaching Mathematics in the Primary School written by Gill Bottle and published by Bloomsbury Publishing. This book was released on 2005-01-01 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title highlights aspects of progression and continuity in the teaching of Mathematics across the elementary years and encourages readers to develop an understanding of key principles and the confidence to apply these appropriately to their classroom practice. It addresses the connections between teaching, managing, planning, and assessment, and presents ideas about how practitioners can enhance children's mathematical understanding and ability to use mathematics in a variety of contexts

How We Understand Mathematics

Author : Jacek Woźny
Publisher : Springer
ISBN 13 : 3319776886
Total Pages : 122 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis How We Understand Mathematics by : Jacek Woźny

Download or read book How We Understand Mathematics written by Jacek Woźny and published by Springer. This book was released on 2018-04-25 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested in the engaging question of how mathematics works and why it works so well.