Visualization Explanation And Reasoning Styles In Mathematics

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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.

The Philosophy of Mathematical Practice

Author : Paolo Mancosu
Publisher : Oxford University Press on Demand
ISBN 13 : 0199296456
Total Pages : 460 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis The Philosophy of Mathematical Practice by : Paolo Mancosu

Download or read book The Philosophy of Mathematical Practice written by Paolo Mancosu and published by Oxford University Press on Demand. This book was released on 2008-06-19 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.

The Logical Status of Diagrams

Author : Sun-Joo Shin
Publisher : Cambridge University Press
ISBN 13 : 052146157X
Total Pages : 211 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis The Logical Status of Diagrams by : Sun-Joo Shin

Download or read book The Logical Status of Diagrams written by Sun-Joo Shin and published by Cambridge University Press. This book was released on 1994 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: The validity of the transformation rules ensures that the correct application of the rules will not lead to fallacies. The book concludes with a discussion of some fundamental differences between graphical systems and linguistic systems.

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.

Eyes on Math

Author : Marian Small
Publisher : Teachers College Press
ISBN 13 : 0807753912
Total Pages : 241 pages
Book Rating : 4.8/5 (77 download)

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Book Synopsis Eyes on Math by : Marian Small

Download or read book Eyes on Math written by Marian Small and published by Teachers College Press. This book was released on 2012-12-30 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book is an exciting follow-up to the authors bestsellers on differentiated math instruction, Good Questions and More Good Questions. Eyes on Math is a unique teaching resource that provides engaging, full-color graphics and pictures with text showing teachers how to use each image to stimulate mathematical teaching conversations around key K–8 concepts. Teachers using the book can download the images for projection onto classroom white boards or screens. The questions and answers will help both students and teachers look more deeply and see the math behind the math!

Toward a Visually-Oriented School Mathematics Curriculum

Author : Ferdinand Rivera
Publisher : Springer Science & Business Media
ISBN 13 : 9400700148
Total Pages : 319 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Toward a Visually-Oriented School Mathematics Curriculum by : Ferdinand Rivera

Download or read book Toward a Visually-Oriented School Mathematics Curriculum written by Ferdinand Rivera and published by Springer Science & Business Media. This book was released on 2011-01-06 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Philosophy of Mathematics: Oxford Bibliographies Online Research Guide

Author : Otavio Bueno
Publisher : Oxford University Press
ISBN 13 : 0199810516
Total Pages : 42 pages
Book Rating : 4.1/5 (998 download)

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Book Synopsis Philosophy of Mathematics: Oxford Bibliographies Online Research Guide by : Otavio Bueno

Download or read book Philosophy of Mathematics: Oxford Bibliographies Online Research Guide written by Otavio Bueno and published by Oxford University Press. This book was released on 2010-06 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.

Intelligent Computer Mathematics

Author : Jacques Carette
Publisher : Springer
ISBN 13 : 3642393209
Total Pages : 398 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Intelligent Computer Mathematics by : Jacques Carette

Download or read book Intelligent Computer Mathematics written by Jacques Carette and published by Springer. This book was released on 2013-07-01 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 20th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2013, 6th International Workshop on Digital Mathematics Libraries, DML 2013, Systems and Projects, held in Bath, UK as part of CICM 2013, the Conferences on Intelligent Computer Mathematics. The 7 revised full papers out of 18 submissions for MKM 2013, 5 revised full papers out of 12 submissions for Calculemus 2013, 6 revised full papers out of 8 submissions for DML 2013, and 12 revised full papers out of 16 submissions for Systems and Project track presented together with 3 invited talks were carefully reviewed and selected, resulting in 33 papers from a total of 73 submissions.

Philosophy of Mathematics

Author : James Robert Brown
Publisher : Routledge
ISBN 13 : 1135902399
Total Pages : 260 pages
Book Rating : 4.1/5 (359 download)

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Book Synopsis Philosophy of Mathematics by : James Robert Brown

Download or read book Philosophy of Mathematics written by James Robert Brown and published by Routledge. This book was released on 2010-03-17 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value? This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis.

Inside Arguments

Author : Henrique Jales Ribeiro
Publisher : Cambridge Scholars Publishing
ISBN 13 : 1443839310
Total Pages : 420 pages
Book Rating : 4.4/5 (438 download)

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Book Synopsis Inside Arguments by : Henrique Jales Ribeiro

Download or read book Inside Arguments written by Henrique Jales Ribeiro and published by Cambridge Scholars Publishing. This book was released on 2012-04-25 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes a collection of eighteen essays that provide a decisive input to the study of logic and argumentation theory by some of the finest specialists in these areas, covering the main schools of thought and contemporary trends at the beginning of the 21st century. In these essays, the authors clarify the status of what we currently call, ambiguously and problematically, “logic” and “argumentation theory”, and discuss the no less controversial issue of the relationship between these two concepts when applied to the study of argumentation and its problems. At the same time, they take stock of the most recent developments of argumentation theory considered as an ongoing research subject. It is the first time in the last few decades that a work this comprehensive and up-to-date on such matters has been published. This volume is an essential tool for all of those interested in the study of the relations between logic and argumentation, particularly at the university level. It provides not only an introduction to these subjects, but also the necessary framework for further specialised research development in the future.

Representation and Productive Ambiguity in Mathematics and the Sciences

Author : Emily R. Grosholz
Publisher : Oxford University Press
ISBN 13 : 0199299730
Total Pages : 332 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Representation and Productive Ambiguity in Mathematics and the Sciences by : Emily R. Grosholz

Download or read book Representation and Productive Ambiguity in Mathematics and the Sciences written by Emily R. Grosholz and published by Oxford University Press. This book was released on 2007-08-30 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emily Grosholz offers an original investigation of demonstration in mathematics and science, examining how it works and why it is persuasive. Focusing on geometrical demonstration, she shows the roles that representation and ambiguity play in mathematical discovery. She presents a wide range of case studies in mechanics, topology, algebra, logic, and chemistry, from ancient Greece to the present day, but focusing particularly on the seventeenth and twentieth centuries. She argues that reductive methods are effective not because they diminish but because they multiply and juxtapose modes of representation. Such problem-solving is, she argues, best understood in terms of Leibnizian 'analysis' - the search for conditions of intelligibility. Discovery and justification are then two aspects of one rational way of proceeding, which produces the mathematician's formal experience. Grosholz defends the importance of iconic, as well as symbolic and indexical, signs in mathematical representation, and argues that pragmatic, as well as syntactic and semantic, considerations are indispensable for mathematical reasoning. By taking a close look at the way results are presented on the page in mathematical (and biological, chemical, and mechanical) texts, she shows that when two or more traditions combine in the service of problem solving, notations and diagrams are sublty altered, multiplied, and juxtaposed, and surrounded by prose in natural language which explains the novel combination. Viewed this way, the texts yield striking examples of language and notation that are irreducibly ambiguous and productive because they are ambiguous. Grosholtz's arguments, which invoke Descartes, Locke, Hume, and Kant, will be of considerable interest to philosophers and historians of mathematics and science, and also have far-reaching consequences for epistemology and philosophy of language.

Math Made Visual

Author : Claudi Alsina
Publisher : American Mathematical Soc.
ISBN 13 : 1614441006
Total Pages : 173 pages
Book Rating : 4.6/5 (144 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 American Mathematical Soc.. This book was released on 2006-12-31 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is it possible to make mathematical drawings that help to understand mathematical ideas, proofs, and arguments? The [Author];s of this book are convinced that the answer is yes and the objective of this book is to show how some visualization techniques may be employed to produce pictures that have both mathematical and pedagogical interest. 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''. Hundreds of these have been published in Mathematics Magazine and The College Mathematics Journal, as well as in other journals, books, and on the internet. Often a person encountering a ``proof without words'' may have the feeling that the pictures involved are the result of a serendipitous discovery or the consequence of an exceptional ingenuity on the part of the picture's creator. In this book, the [Author];s show that behind most of the pictures, ``proving'' mathematical relations are some well-understood methods. As the reader shall see, a given mathematical idea or relation may have many different images that justify it, so that depending on the teaching level or the objectives for producing the pictures, one can choose the best alternative.

Advances in Mathematics Education Research on Proof and Proving

Author : Andreas J. Stylianides
Publisher : Springer
ISBN 13 : 3319709968
Total Pages : 298 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Advances in Mathematics Education Research on Proof and Proving by : Andreas J. Stylianides

Download or read book Advances in Mathematics Education Research on Proof and Proving written by Andreas J. Stylianides and published by Springer. This book was released on 2018-01-10 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores new trends and developments in mathematics education research related to proof and proving, the implications of these trends and developments for theory and practice, and directions for future research. With contributions from researchers working in twelve different countries, the book brings also an international perspective to the discussion and debate of the state of the art in this important area. The book is organized around the following four themes, which reflect the breadth of issues addressed in the book: • Theme 1: Epistemological issues related to proof and proving; • Theme 2: Classroom-based issues related to proof and proving; • Theme 3: Cognitive and curricular issues related to proof and proving; and • Theme 4: Issues related to the use of examples in proof and proving. Under each theme there are four main chapters and a concluding chapter offering a commentary on the theme overall.

Visualization in the Age of Computerization

Author : Annamaria Carusi
Publisher : Routledge
ISBN 13 : 1135077371
Total Pages : 292 pages
Book Rating : 4.1/5 (35 download)

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Book Synopsis Visualization in the Age of Computerization by : Annamaria Carusi

Download or read book Visualization in the Age of Computerization written by Annamaria Carusi and published by Routledge. This book was released on 2014-08-21 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Digitalization and computerization are now pervasive in science. This has deep consequences for our understanding of scientific knowledge and of the scientific process, and challenges longstanding assumptions and traditional frameworks of thinking of scientific knowledge. Digital media and computational processes challenge our conception of the way in which perception and cognition work in science, of the objectivity of science, and the nature of scientific objects. They bring about new relationships between science, art and other visual media, and new ways of practicing science and organizing scientific work, especially as new visual media are being adopted by science studies scholars in their own practice. This volume reflects on how scientists use images in the computerization age, and how digital technologies are affecting the study of science.

An Aristotelian Realist Philosophy of Mathematics

Author : J. Franklin
Publisher : Springer
ISBN 13 : 1137400730
Total Pages : 316 pages
Book Rating : 4.1/5 (374 download)

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Book Synopsis An Aristotelian Realist Philosophy of Mathematics by : J. Franklin

Download or read book An Aristotelian Realist Philosophy of Mathematics written by J. Franklin and published by Springer. This book was released on 2014-04-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.

The Richness of the History of Mathematics

Author : Karine Chemla
Publisher : Springer Nature
ISBN 13 : 3031408551
Total Pages : 702 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis The Richness of the History of Mathematics by : Karine Chemla

Download or read book The Richness of the History of Mathematics written by Karine Chemla and published by Springer Nature. This book was released on 2023-11-27 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines. Many different approaches to the study of the history of mathematics have been developed. Understanding this diversity is central to learning about these fields, but very few books deal with their richness and concrete suggestions for the “what, why and how” of these domains of inquiry. The editors and authors approach the basic question of what the history of mathematics is by means of concrete examples. For the “how” question, basic methodological issues are addressed, from the different perspectives of mathematicians and historians. Containing essays by leading scholars, this book provides a multitude of perspectives on mathematics, its role in culture and development, and connections with other sciences, making it an important resource for students and academics in the history and philosophy of mathematics.