Proof And Other Dilemmas

Author : Bonnie Gold
Publisher : MAA
ISBN 13 : 9780883855676
Total Pages : 392 pages
Book Rating : 4.74/5 ( download)

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Download or read book Proof and Other Dilemmas written by Bonnie Gold and published by MAA. This book was released on 2008 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sixteen original essays exploring recent developments in the philosophy of mathematics, written in a way mathematicians will understand.

Author : Gila Hanna
Publisher : Springer Science & Business Media
ISBN 13 : 9400721293
Total Pages : 468 pages
Book Rating : 4.96/5 ( download)

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Download or read book Proof and Proving in Mathematics Education written by Gila Hanna and published by Springer Science & Business Media. This book was released on 2012-06-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: *THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.

Author : M. Jablonowski
Publisher : Springer
ISBN 13 : 0230288596
Total Pages : 147 pages
Book Rating : 4.91/5 ( download)

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Download or read book Risk Dilemmas written by M. Jablonowski and published by Springer. This book was released on 2007-10-23 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book identifies the pitfalls of applying precautionary strategies to high-stakes risks that have already become entrenched. Precaution must be applied on a precautionary basis, considering alternative paths to progress that maintain natural risk levels. This requires a radical rethinking of the way we define and achieve progress.

Author : Bharath Sriraman
Publisher : Springer Nature
ISBN 13 : 3031408462
Total Pages : 3221 pages
Book Rating : 4.65/5 ( download)

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Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Sepideh Stewart
Publisher : Springer
ISBN 13 : 3319668110
Total Pages : 382 pages
Book Rating : 4.16/5 ( download)

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Download or read book Challenges and Strategies in Teaching Linear Algebra written by Sepideh Stewart and published by Springer. This book was released on 2018-02-01 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book originated from a Discussion Group (Teaching Linear Algebra) that was held at the 13th International Conference on Mathematics Education (ICME-13). The aim was to consider and highlight current efforts regarding research and instruction on teaching and learning linear algebra from around the world, and to spark new collaborations. As the outcome of the two-day discussion at ICME-13, this book focuses on the pedagogy of linear algebra with a particular emphasis on tasks that are productive for learning. The main themes addressed include: theoretical perspectives on the teaching and learning of linear algebra; empirical analyses related to learning particular content in linear algebra; the use of technology and dynamic geometry software; and pedagogical discussions of challenging linear algebra tasks. Drawing on the expertise of mathematics education researchers and research mathematicians with experience in teaching linear algebra, this book gathers work from nine countries: Austria, Germany, Israel, Ireland, Mexico, Slovenia, Turkey, the USA and Zimbabwe.

Author : Catarina Dutilh Novaes
Publisher : Cambridge University Press
ISBN 13 : 110847988X
Total Pages : 287 pages
Book Rating : 4.82/5 ( download)

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Download or read book The Dialogical Roots of Deduction written by Catarina Dutilh Novaes and published by Cambridge University Press. This book was released on 2020-12-17 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive account of the concept and practices of deduction covering philosophy, history, cognition and mathematical practice.

Author : Rod Downey
Publisher : Cambridge University Press
ISBN 13 : 1139916831
Total Pages : 540 pages
Book Rating : 4.37/5 ( download)

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Download or read book Turing's Legacy written by Rod Downey and published by Cambridge University Press. This book was released on 2014-05-01 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alan Turing was an inspirational figure who is now recognised as a genius of modern mathematics. In addition to leading the Allied forces' code-breaking effort at Bletchley Park in World War II, he proposed the theoretical foundations of modern computing and anticipated developments in areas from information theory to computer chess. His ideas have been extraordinarily influential in modern mathematics and this book traces such developments by bringing together essays by leading experts in logic, artificial intelligence, computability theory and related areas. Together, they give insight into this fascinating man, the development of modern logic, and the history of ideas. The articles within cover a diverse selection of topics, such as the development of formal proof, differing views on the Church–Turing thesis, the development of combinatorial group theory, and Turing's work on randomness which foresaw the ideas of algorithmic randomness that would emerge many years later.

Author : Hardy Grant
Publisher : Birkhäuser
ISBN 13 : 1493932640
Total Pages : 109 pages
Book Rating : 4.41/5 ( download)

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Download or read book Turning Points in the History of Mathematics written by Hardy Grant and published by Birkhäuser. This book was released on 2016-04-15 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation. Some of the turning points considered are the rise of the axiomatic method (most famously in Euclid), and the subsequent major changes in it (for example, by David Hilbert); the “wedding,” via analytic geometry, of algebra and geometry; the “taming” of the infinitely small and the infinitely large; the passages from algebra to algebras, from geometry to geometries, and from arithmetic to arithmetics; and the revolutions in the late nineteenth and early twentieth centuries that resulted from Georg Cantor’s creation of transfinite set theory. The origin of each turning point is discussed, along with the mathematicians involved and some of the mathematics that resulted. Problems and projects are included in each chapter to extend and increase understanding of the material. Substantial reference lists are also provided. Turning Points in the History of Mathematics will be a valuable resource for teachers of, and students in, courses in mathematics or its history. The book should also be of interest to anyone with a background in mathematics who wishes to learn more about the important moments in its development.

Author : Rina Zazkis
Publisher : Springer
ISBN 13 : 3319626922
Total Pages : 425 pages
Book Rating : 4.25/5 ( download)

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Download or read book Scripting Approaches in Mathematics Education written by Rina Zazkis and published by Springer. This book was released on 2017-10-30 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how the practice of script writing can be used both as a pedagogical approach and as a research tool in mathematics education. It provides an opportunity for script-writers to articulate their mathematical arguments and/or their pedagogical approaches. It further provides researchers with a corpus of narratives that can be analyzed using a variety of theoretical perspectives. Various chapters argue for the use of dialogical method and highlight its benefits and special features. The chapters examine both “low tech” implementations as well as the use of a technological platform, LessonSketch. The chapters present results of and insights from several recent studies, which utilized scripting in mathematics education research and practice.

Author : Jonathan M. Borwein
Publisher : Springer Science & Business Media
ISBN 13 : 1461442532
Total Pages : 237 pages
Book Rating : 4.30/5 ( download)

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Download or read book An Introduction to Modern Mathematical Computing written by Jonathan M. Borwein and published by Springer Science & Business Media. This book was released on 2012-08-07 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thirty years ago mathematical, as opposed to applied numerical, computation was difficult to perform and so relatively little used. Three threads changed that: the emergence of the personal computer; the discovery of fiber-optics and the consequent development of the modern internet; and the building of the Three “M’s” Maple, Mathematica and Matlab. We intend to persuade that Mathematica and other similar tools are worth knowing, assuming only that one wishes to be a mathematician, a mathematics educator, a computer scientist, an engineer or scientist, or anyone else who wishes/needs to use mathematics better. We also hope to explain how to become an "experimental mathematician" while learning to be better at proving things. To accomplish this our material is divided into three main chapters followed by a postscript. These cover elementary number theory, calculus of one and several variables, introductory linear algebra, and visualization and interactive geometric computation.