Meaning in Mathematics

Author: John Polkinghorne

Publisher: OUP Oxford

ISBN: 0191621293

Category: Mathematics

Page: 176

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Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics. The chapters are written by some of the world's finest mathematicians, mathematical physicists and philosophers of mathematics, each giving their perspective on this fascinating debate. Every chapter is followed by a short response from another member of the author team, reinforcing the main theme and raising further questions. Accessible to anyone interested in what mathematics really means, and useful for mathematicians and philosophers of science at all levels, Meaning in Mathematics offers deep new insights into a subject many people take for granted.
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Meaning in Mathematics Education

Author: Jeremy Kilpatrick,Celia Hoyles,Ole Skovsmose

Publisher: Springer Science & Business Media

ISBN: 0387240403

Category: Education

Page: 260

View: 9947

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What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding the complexity of meaning in mathematics education is a matter of huge importance. There are twin directions in which discussions have developed—theoretical and practical—and this book seeks to move the debate forward along both dimensions while seeking to relate them where appropriate. A discussion of meaning can start from a theoretical examination of mathematics and how mathematicians over time have made sense of their work. However, from a more practical perspective, anybody involved in teaching mathematics is faced with the need to orchestrate the myriad of meanings derived from multiple sources that students develop of mathematical knowledge. This book presents a wide variety of theoretical reflections and research results about meaning in mathematics and mathematics education based on long-term and collective reflection by the group of authors as a whole. It is the outcome of the work of the BACOMET (BAsic COmponents of Mathematics Education for Teachers) group who spent several years deliberating on this topic. The ten chapters in this book, both separately and together, provide a substantial contribution to clarifying the complex issue of meaning in mathematics education. This book is of interest to researchers in mathematics education, graduate students of mathematics education, under graduate students in mathematics, secondary mathematics teachers and primary teachers with an interest in mathematics.
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Perspectives on Practice and Meaning in Mathematics and Science Classrooms

Author: D. Clarke

Publisher: Springer Science & Business Media

ISBN: 0306472287

Category: Education

Page: 358

View: 583

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This is a variegated picture of science and mathematics classrooms that challenges a research tradition that converges on the truth. The reader is surrounded with different images of the classroom and will find his beliefs confirmed or challenged. The book is for educational researchers, research students, and practitioners with an interest in optimizing the effectiveness of classrooms as environments for learning.
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Meaning and Existence in Mathematics

Author: Charles Castonguay

Publisher: Springer Science & Business Media

ISBN: 370917113X

Category: Juvenile Nonfiction

Page: 160

View: 1116

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The take-over of the philosophy of mathematics by mathematical logic is not complete. The central problems examined in this book lie in the fringe area between the two, and by their very nature will no doubt continue to fall partly within the philosophical re mainder. In seeking to treat these problems with a properly sober mixture of rhyme and reason, I have tried to keep philosophical jargon to a minimum and to avoid excessive mathematical compli cation. The reader with a philosophical background should be familiar with the formal syntactico-semantical explications of proof and truth, especially if he wishes to linger on Chapter 1, after which it is easier philosophical sailing; while the mathematician need only know that to "explicate" a concept consists in clarifying a heretofore vague notion by proposing a clearer (sometimes formal) definition or formulation for it. More seriously, the interested mathematician will find occasional recourse to EDWARD'S Encyclopedia of Philos ophy (cf. bibliography) highly rewarding. Sections 2. 5 and 2. 7 are of interest mainly to philosophers. The bibliography only contains works referred to in the text. References are made by giving the author's surname followed by the year of publication, the latter enclosed in parentheses. When the author referred to is obvious from the context, the surname is dropped, and even the year of publication or "ibid. " may be dropped when the same publication is referred to exclusively over the course of several paragraphs.
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Perspectives on Mathematics Education

Papers Submitted by Members of the Bacomet Group

Author: H. Christiansen,A.G. Howson,M. Otte

Publisher: Springer Science & Business Media

ISBN: 9400945043

Category: Education

Page: 371

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BACOMET cannot be evaluated solely on the basis of its publications. It is important then that the reader, with only this volume on which to judge both the BACOMET activities and its major outcome to date, should know some thing of what preceded this book's publication. For it is the story of how a group of educators, mainly tutors of student-teachers of mathematics, com mitted themselves to a continuing period of work and self-education. The concept of BACOMET developed during a series of meetings held in 1978-79 between the three editors, Bent Christiansen, Geoffrey Howson and Michael Otte, at which we expressed our concern about the contributions from mathematics education as a discipline to teacher education, both as we observed it and as we participated in it. The short time which was at the teacher-educator's disposal, allied to the limited knowledge and experience of the students on which one had to build, raised puzzling problems concerning priorities and emphases. The recognition that these problems were shared by educators from many different countries was matched by the fact that it would be fruitless to attempt to search for an internationally (or even nationally) acceptable solution to our problems. Different contexts and traditions rule this out.
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Mind, Meaning and Mathematics

Essays on the Philosophical Views of Husserl and Frege

Author: L. Haaparanta

Publisher: Springer Science & Business Media

ISBN: 940158334X

Category: Philosophy

Page: 284

View: 7011

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At the turn of the century, Gottlob Frege and Edmund Husserl both participated in the discussion concerning the foundations of logic and mathematics. Since the 1960s, comparisons have been made between Frege's semantic views and Husserl's theory of intentional acts. In quite recent years, new approaches to the two philosophers' views have appeared. This collection of articles opens with the first English translation of Dagfinn Føllesdal's early classic on Husserl and Frege of 1958. The book brings together a number of new contributions by well-known authors and gives a survey of recent developments in the field. It shows that Husserl's thought is coming to occupy a central role in the philosophy of logic and mathematics, as well as in the philosophy of mind and cognitive science. The work is primarily meant for philosophers, especially for those working on the problems of language, logic, mathematics, and mind. It can also be used as a textbook in advanced courses in philosophy.
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Vital Directions for Mathematics Education Research

Author: Keith R Leatham

Publisher: Springer Science & Business Media

ISBN: 1461469775

Category: Education

Page: 207

View: 3465

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This book provides a collection of chapters from prominent mathematics educators in which they each discuss vital issues in mathematics education and what they see as viable directions research in mathematics education could take to address these issues. All of these issues are related to learning and teaching mathematics. The book consists of nine chapters, seven from each of seven scholars who participated in an invited lecture series (Scholars in Mathematics Education) at Brigham Young University, and two chapters from two other scholars who are writing reaction papers that look across the first seven chapters. The recommendations take the form of broad, overarching principles and ideas that cut across the field. In this sense, this book differs from classical “research agenda projects,” which seek to outline specific research questions that the field should address around a central topic.
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The Infinite in Mathematics

Logico-mathematical writings

Author: Felix Kaufmann

Publisher: Springer Science & Business Media

ISBN: 9400997957

Category: Science

Page: 237

View: 4629

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The main item in the present volume was published in 1930 under the title Das Unendliche in der Mathematik und seine Ausschaltung. It was at that time the fullest systematic account from the standpoint of Husserl's phenomenology of what is known as 'finitism' (also as 'intuitionism' and 'constructivism') in mathematics. Since then, important changes have been required in philosophies of mathematics, in part because of Kurt Godel's epoch-making paper of 1931 which established the essential in completeness of arithmetic. In the light of that finding, a number of the claims made in the book (and in the accompanying articles) are demon strably mistaken. Nevertheless, as a whole it retains much of its original interest and value. It presents the issues in the foundations of mathematics that were under debate when it was written (and in some cases still are); , and it offers one alternative to the currently dominant set-theoretical definitions of the cardinal numbers and other arithmetical concepts. While still a student at the University of Vienna, Felix Kaufmann was greatly impressed by the early philosophical writings (especially by the Logische Untersuchungen) of Edmund Husser!' He was never an uncritical disciple of Husserl, and he integrated into his mature philosophy ideas from a wide assortment of intellectual sources. But he thought of himself as a phenomenologist, and made frequent use in all his major publications of many of Husserl's logical and epistemological theses.
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Meaning in Absurdity

What bizarre phenomena can tell us about the nature of reality

Author: Bernard Kastrup

Publisher: John Hunt Publishing

ISBN: 1846948606

Category: Philosophy

Page: 134

View: 1037

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This book is an experiment. Inspired by the bizarre and uncanny, it is an attempt to use science and rationality to lift the veil off the irrational. Its ways are unconventional: weaving along its path one finds UFOs and fairies, quantum mechanics, analytic philosophy, history, mathematics, and depth psychology. The enterprise of constructing a coherent story out of these incommensurable disciplines is exploratory. But if the experiment works, at the end these disparate threads will come together to unveil a startling scenario about the nature of reality. The payoff is handsome: a reason for hope, a boost for the imagination, and the promise of a meaningful future. Yet this book may confront some of your dearest notions about truth and reason. Its conclusions cannot be dismissed lightly, because the evidence this book compiles and the philosophy it leverages are solid in the orthodox, academic sense.
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