Proof And Other Dilemmas
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Proof And Other Dilemmas
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Author : Bonnie Gold
language : en
Publisher: MAA
Release Date : 2008
Proof And Other Dilemmas written by Bonnie Gold and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
During the first 75 years of the twentieth century almost all work in the philosophy of mathematics concerned foundational questions. In the last quarter of the century, philosophers of mathematics began to return to basic questions concerning the philosophy of mathematics such as, what is the nature of mathematical knowledge and of mathematical objects, and how is mathematics related to science? Two new schools of philosophy of mathematics, social constructivism and structuralism, were added to the four traditional views (formalism, intuitionalism, logicism, and platonism). The advent of the computer led to proofs and the development of mathematics assisted by computer, and to questions of the role of the computer in mathematics. This book of 16 essays, all written specifically for this volume, is the first to explore this range of new developments in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers are not yet discussing. The other half, written by philsophers of mathematics, summarize the discussion in that community during the last 35 years. In each case, a connection is made to issues relevant to the teach of mathematics.
Proof And Proving In Mathematics Education
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Author : Gila Hanna
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-14
Proof And Proving In Mathematics Education written by Gila Hanna 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 2012-06-14 with Education categories.
*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.
Risk Dilemmas
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Author : M. Jablonowski
language : en
Publisher: Springer
Release Date : 2007-10-23
Risk Dilemmas written by M. Jablonowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-23 with Business & Economics categories.
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.
Advances In Mathematics Education Research On Proof And Proving
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Author : Andreas J. Stylianides
language : en
Publisher: Springer
Release Date : 2018-01-10
Advances In Mathematics Education Research On Proof And Proving written by Andreas J. Stylianides and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-10 with Education categories.
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.
Profunedu 2019
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Author : Naufal Ishartono
language : en
Publisher: European Alliance for Innovation
Release Date : 2019-08-06
Profunedu 2019 written by Naufal Ishartono and has been published by European Alliance for Innovation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-06 with Education categories.
The 4th Progressive and Fun Education (The 4th Profunedu) International Conference is a forum for researchers and lecturers within the ALPTK Muhammadiyah College to disseminate their best research results. This conference aims to provide a platform for researchers and academics to share their research findings with others and meet lecturers and researchers from other institutions and to strengthen the collaboration and networking amongs the participants. The 4th Profunedu was held on 6-8 August 2019 in Makassar, Indonesia. It is hoped that this proceeding can help improve the quality of education, especially the quality of education in Indonesia.
Mathematical Rigour And Informal Proof
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Author : Fenner Stanley Tanswell
language : en
Publisher: Cambridge University Press
Release Date : 2024-03-28
Mathematical Rigour And Informal Proof written by Fenner Stanley Tanswell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-28 with Philosophy categories.
This Element looks at the contemporary debate on the nature of mathematical rigour and informal proofs as found in mathematical practice. The central argument is for rigour pluralism: that multiple different models of informal proof are good at accounting for different features and functions of the concept of rigour. To illustrate this pluralism, the Element surveys some of the main options in the literature: the 'standard view' that rigour is just formal, logical rigour; the models of proofs as arguments and dialogues; the recipe model of proofs as guiding actions and activities; and the idea of mathematical rigour as an intellectual virtue. The strengths and weaknesses of each are assessed, thereby providing an accessible and empirically-informed introduction to the key issues and ideas found in the current discussion.
A Century Of Advancing Mathematics
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Author : Paul Zorn
language : en
Publisher: The Mathematical Association of America
Release Date : 2015-08-23
A Century Of Advancing Mathematics written by Paul Zorn and has been published by The Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-23 with Mathematics categories.
The MAA was founded in 1915 to serve as a home for The American Mathematical Monthly. The mission of the Association-to advance mathematics, especially at the collegiate level-has, however, always been larger than merely publishing world-class mathematical exposition. MAA members have explored more than just mathematics; we have, as this volume tries to make evident, investigated mathematical connections to pedagogy, history, the arts, technology, literature, every field of intellectual endeavor. Essays, all commissioned for this volume, include exposition by Bob Devaney, Robin Wilson, and Frank Morgan; history from Karen Parshall, Della Dumbaugh, and Bill Dunham; pedagogical discussion from Paul Zorn, Joe Gallian, and Michael Starbird, and cultural commentary from Bonnie Gold, Jon Borwein, and Steve Abbott. This volume contains 35 essays by all-star writers and expositors writing to celebrate an extraordinary century for mathematics-more mathematics has been created and published since 1915 than in all of previous recorded history. We've solved age-old mysteries, created entire new fields of study, and changed our conception of what mathematics is. Many of those stories are told in this volume as the contributors paint a portrait of the broad cultural sweep of mathematics during the MAA's first century. Mathematics is the most thrilling, the most human, area of intellectual inquiry; you will find in this volume compelling proof of that claim.
Handbook Of The History And Philosophy Of Mathematical Practice
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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date : 2024-04-26
Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.
The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques
The Philosophy Of Mathematics Education Today
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Author : Paul Ernest
language : en
Publisher: Springer
Release Date : 2018-06-09
The Philosophy Of Mathematics Education Today written by Paul Ernest and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-09 with Education categories.
This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in the 21st century? How do students learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future.
New Directions For Mathematics Education Research On Proving
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Author : Keith Weber
language : en
Publisher: Springer Nature
Release Date : 2025-08-03
New Directions For Mathematics Education Research On Proving written by Keith Weber and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-03 with Education categories.
This book summarizes new directions in mathematics education research on proving at the university level, thereby providing contemporary extensions of the sub-fields of proof that Annie and John Selden introduced to the field. The chapters each describe an emerging new area of proof research, review the relevant findings in this area, present open research questions and the tools to address them. The book also discusses proof as a literary genre, and how students' feelings during the proof writing process can influence their behavior. The concluding chapter of the book reflects on new directions for research on proving. As such, this book provides mathematics educators, who have extensive experience researching proof, with an up-to-date review of the new methodologies and research questions with regard to proof, and young scholars, interested in proof, can use these chapters as primers on which they can build a research program.