Constructivism In Mathematics Vol 1

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Constructivism in Mathematics, Vol 1

Author : A.S. Troelstra
Publisher : Elsevier
ISBN 13 : 0080570887
Total Pages : 378 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Constructivism in Mathematics, Vol 1 by : A.S. Troelstra

Download or read book Constructivism in Mathematics, Vol 1 written by A.S. Troelstra and published by Elsevier. This book was released on 1988-07-01 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two volumes cover the principal approaches to constructivism in mathematics. They present a thorough, up-to-date introduction to the metamathematics of constructive mathematics, paying special attention to Intuitionism, Markov's constructivism and Martin-Lof's type theory with its operational semantics. A detailed exposition of the basic features of constructive mathematics, with illustrations from analysis, algebra and topology, is provided, with due attention to the metamathematical aspects. Volume 1 is a self-contained introduction to the practice and foundations of constructivism, and does not require specialized knowledge beyond basic mathematical logic. Volume 2 contains mainly advanced topics of a proof-theoretical and semantical nature.

Radical Constructivism in Mathematics Education

Author : E. Glasersfeld
Publisher : Springer Science & Business Media
ISBN 13 : 0306472015
Total Pages : 264 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Radical Constructivism in Mathematics Education by : E. Glasersfeld

Download or read book Radical Constructivism in Mathematics Education written by E. Glasersfeld and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is the science of acts without things - and through this, of things one can define by acts. 1 Paul Valéry The essays collected in this volume form a mosaik of theory, research, and practice directed at the task of spreading mathematical knowledge. They address questions raised by the recurrent observation that, all too frequently, the present ways and means of teaching mathematics generate in the student a lasting aversion against numbers, rather than an understanding of the useful and sometimes enchanting things one can do with them. Parents, teachers, and researchers in the field of education are well aware of this dismal situation, but their views about what causes the wide-spread failure and what steps should be taken to correct it have so far not come anywhere near a practicable consensus. The authors of the chapters in this book have all had extensive experience in teaching as well as in educational research. They approach the problems they have isolated from their own individual perspectives. Yet, they share both an overall goal and a specific fundamental conviction that characterized the efforts about which they write here. The common goal is to find a better way to teach mathematics. The common conviction is that knowledge cannot simply be transferred ready-made from parent to child or from teacher to student but has to be actively built up by each learner in his or her own mind.

Constructivism in Mathematics, Vol 2

Author : A.S. Troelstra
Publisher : Elsevier
ISBN 13 : 008095510X
Total Pages : 607 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Constructivism in Mathematics, Vol 2 by : A.S. Troelstra

Download or read book Constructivism in Mathematics, Vol 2 written by A.S. Troelstra and published by Elsevier. This book was released on 2014-06-28 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras. The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The text then examines proof theory of intuitionistic logic, theory of types and constructive set theory, and choice sequences. The book elaborates on semantical completeness, sheaves, sites, and higher-order logic, and applications of sheaf models. Topics include a derived rule of local continuity, axiom of countable choice, forcing over sites, sheaf models for higher-order logic, and complete Heyting algebras. The publication is a valuable reference for mathematicians and researchers interested in mathematics and logic.

Beyond Constructivism

Author : Richard A. Lesh
Publisher : Routledge
ISBN 13 : 1317438515
Total Pages : 614 pages
Book Rating : 4.3/5 (174 download)

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Book Synopsis Beyond Constructivism by : Richard A. Lesh

Download or read book Beyond Constructivism written by Richard A. Lesh and published by Routledge. This book was released on 2003-05-01 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has two primary goals. On the level of theory development, the book clarifies the nature of an emerging "models and modeling perspective" about teaching, learning, and problem solving in mathematics and science education. On the level of emphasizing practical problems, it clarifies the nature of some of the most important elementary-but-powerful mathematical or scientific understandings and abilities that Americans are likely to need as foundations for success in the present and future technology-based information age. Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching features an innovative Web site housing online appendices for each chapter, designed to supplement the print chapters with digital resources that include example problems, relevant research tools and video clips, as well as transcripts and other samples of students' work: http://tcct.soe.purdue.edu/booksULandULjournals/modelsULandUL modeling/ This is an essential volume for graduate-level courses in mathematics and science education, cognition and learning, and critical and creative thinking, as well as a valuable resource for researchers and practitioners in these areas.

Constructivist Views on the Teaching and Learning of Mathematics

Author : Robert Benjamin Davis
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Constructivist Views on the Teaching and Learning of Mathematics by : Robert Benjamin Davis

Download or read book Constructivist Views on the Teaching and Learning of Mathematics written by Robert Benjamin Davis and published by . This book was released on 1990 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constructivist views on the teaching and learning of mathematics (Journal for research in mathematics education).

Radical Constructivism in Action

Author : Leslie P. Steffe
Publisher : Routledge
ISBN 13 : 1135699461
Total Pages : 344 pages
Book Rating : 4.1/5 (356 download)

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Book Synopsis Radical Constructivism in Action by : Leslie P. Steffe

Download or read book Radical Constructivism in Action written by Leslie P. Steffe and published by Routledge. This book was released on 2002-11 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last twenty-five years Ernst von Glasersfeld has had a tremendous impact on mathematics and science education through his fundamental insights into the nature of knowledge and knowing. Radical Constructivism in Action is a new volume of papers honouring his work by building on his model of knowing. The contributions by leading researchers present constructivism in action, tying the authors' actions regarding practical problems of mathematics and science education, philosophy, and sociology to their philosophical constraints, giving meaning to constructivism operationally. The book begins with a retrospective analogy between radical constructivism's emergence and changes in what is thought of as "certain" scientific knowledge. It aims to increase understanding of constructivism and Glasersfeld's achievement, and is vibrant evidence of the continued vitality of research in the constructivism tradition.

Constructivism in Mathematics, Vol 2

Author : A.S. Troelstra
Publisher : Elsevier Science
ISBN 13 : 9780444703583
Total Pages : 129 pages
Book Rating : 4.7/5 (35 download)

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Book Synopsis Constructivism in Mathematics, Vol 2 by : A.S. Troelstra

Download or read book Constructivism in Mathematics, Vol 2 written by A.S. Troelstra and published by Elsevier Science. This book was released on 1988-11-15 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras. The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The text then examines proof theory of intuitionistic logic, theory of types and constructive set theory, and choice sequences. The book elaborates on semantical completeness, sheaves, sites, and higher-order logic, and applications of sheaf models. Topics include a derived rule of local continuity, axiom of countable choice, forcing over sites, sheaf models for higher-order logic, and complete Heyting algebras. The publication is a valuable reference for mathematicians and researchers interested in mathematics and logic.

Nominalism and Constructivism in Seventeenth-Century Mathematical Philosophy

Author : David Sepkoski
Publisher : Routledge
ISBN 13 : 1136768688
Total Pages : 186 pages
Book Rating : 4.1/5 (367 download)

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Book Synopsis Nominalism and Constructivism in Seventeenth-Century Mathematical Philosophy by : David Sepkoski

Download or read book Nominalism and Constructivism in Seventeenth-Century Mathematical Philosophy written by David Sepkoski and published by Routledge. This book was released on 2013-05-24 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: What was the basis for the adoption of mathematics as the primary mode of discourse for describing natural events by a large segment of the philosophical community in the seventeenth century? In answering this question, this book demonstrates that a significant group of philosophers shared the belief that there is no necessary correspondence between external reality and objects of human understanding, which they held to include the objects of mathematical and linguistic discourse. The result is a scholarly reliable, but accessible, account of the role of mathematics in the works of (amongst others) Galileo, Kepler, Descartes, Newton, Leibniz, and Berkeley. This impressive volume will benefit scholars interested in the history of philosophy, mathematical philosophy and the history of mathematics.

Investigating Mathematics Teaching

Author : Barbara Jaworski
Publisher : Routledge
ISBN 13 : 1135716110
Total Pages : 254 pages
Book Rating : 4.1/5 (357 download)

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Book Synopsis Investigating Mathematics Teaching by : Barbara Jaworski

Download or read book Investigating Mathematics Teaching written by Barbara Jaworski and published by Routledge. This book was released on 2002-11-01 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Barbara Jaworski addresses a number of questions that are central to research on reform in mathematics education today. In this volume she attempts to chart critically yet honestly her own developing ideas as she undertakes a several-year-long enquiry into mathematics teaching and gives a very personal account of her developing conceptions, conjectures, thoughts and reflections. The author accounts for her research both genetically and biographically, simultaneously restructuring the development of her ideas and giving a rigorous, critical and reflective account.

Constructivism in Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (88 download)

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Book Synopsis Constructivism in Mathematics by :

Download or read book Constructivism in Mathematics written by and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Social Constructivism as a Philosophy of Mathematics

Author : Paul Ernest
Publisher : SUNY Press
ISBN 13 : 9780791435878
Total Pages : 336 pages
Book Rating : 4.4/5 (358 download)

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Book Synopsis Social Constructivism as a Philosophy of Mathematics by : Paul Ernest

Download or read book Social Constructivism as a Philosophy of Mathematics written by Paul Ernest and published by SUNY Press. This book was released on 1998-01-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.

Undead Theories

Author : David Geelan
Publisher : BRILL
ISBN 13 : 9087903642
Total Pages : 167 pages
Book Rating : 4.0/5 (879 download)

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Book Synopsis Undead Theories by : David Geelan

Download or read book Undead Theories written by David Geelan and published by BRILL. This book was released on 2006-01-01 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory is dead. . . long live theory! In this collection of linked essays, David Geelan explores the contentious relationship between theory and research in education. The first chapter proclaims the 'death of theory' in educational research, but the remainder of the book explores a number of the ways in which theory survives and thrives. A commitment to conducting educational research that directly serves students and teachers, and that changes the life in classrooms through negotiation and collaboration, not through prescription, requires new tools and new ways of using them. Such tools include narrative modes of conducting and representing research as well as a 'disciplined eclecticism' that emphasises choosing and using competing theories in intentional ways. Metaphorical descriptions from the philosophy of science - particularly Kuhn and Popper - have been influential in science education. David explores the value of such perspectives, and argues that although they have offered important insights for science education, their use has also 'forced other perspectives into blindness’. In the contexts of research methodology, educational philosophy, science education and educational technology, David talks about new 'places to stand and ways to look' but, more importantly, gives specific examples of the ways in which these methodological tools and philosophical perspectives have been used in his own teaching and research practices.

Constructivism and Education

Author : Marie Larochelle
Publisher : Cambridge University Press
ISBN 13 : 9780521621359
Total Pages : 332 pages
Book Rating : 4.6/5 (213 download)

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Book Synopsis Constructivism and Education by : Marie Larochelle

Download or read book Constructivism and Education written by Marie Larochelle and published by Cambridge University Press. This book was released on 1998-08-13 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: An international collection dealing with the constructivist approach to education.

A Journey in Mathematics Education Research

Author : Erna Yackel
Publisher : Springer Science & Business Media
ISBN 13 : 9048197295
Total Pages : 255 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis A Journey in Mathematics Education Research by : Erna Yackel

Download or read book A Journey in Mathematics Education Research written by Erna Yackel and published by Springer Science & Business Media. This book was released on 2010-11-30 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our objective is to publish a book that lays out the theoretical constructs and research methodologies within mathematics education that have been developed by Paul Cobb and explains the process of their development. We propose to do so by including papers in which Cobb introduced new theoretical perspectives and methodologies into the literature, each preceded by a substantive accompanying introductory paper that explains the motivation/rationale for developing the new perspectives and/or methodologies and the processes through which they were developed, and Cobb’s own retrospective comments. In this way the book provides the reader with heretofore unpublished material that lays out in considerable detail the issues and problems that Cobb has confronted in his work, that, from his viewpoint, required theoretical and methodological shifts/advances and provides insight into how he has achieved the shifts/advances. The result will be a volume that, in addition to explaining Cobb’s contributions to the field of mathematics education, also provides the reader with insight into what is involved in developing an aggressive and evolving research program. When Cobb confronts problems and issues in his work that cannot be addressed using his existing theories and frameworks, he looks to other fields for theoretical inspiration. A critical feature of Cobb’s work is that in doing so, he consciously appropriates and adapts ideas from these other fields to the purpose of supporting processes of learning and teaching mathematics; He does not simply accept the goals or motives of those fields. As a result, Cobb reconceptualizes and reframes issues and concepts so that they result in new ways of investigating, exploring, and explaining phenomena that he encounters in the practical dimensions of his work, which include working in classrooms, with teachers, and with school systems. The effect is that the field of mathematics education is altered. Other researchers have found his "new ways of looking" useful to them. And they, in turn, adapt these ideas for their own use. The complexity of many of the ideas that Cobb has introduced into the field of mathematics education can lead to a multiplicity of interpretations by practitioners and by other researchers, based on their own experiential backgrounds. Therefore, by detailing the development of Cobb’s work, including the tensions involved in coming to grips with and reconciling apparently contrasting perspectives, the book will shed additional light on the processes of reconceptualization and thus help the reader to understand the reasons, mechanisms, and outcomes of researchers’ constant pursuit of new insights.

L.E.J. Brouwer – Topologist, Intuitionist, Philosopher

Author : Dirk van Dalen
Publisher : Springer Science & Business Media
ISBN 13 : 1447146166
Total Pages : 877 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis L.E.J. Brouwer – Topologist, Intuitionist, Philosopher by : Dirk van Dalen

Download or read book L.E.J. Brouwer – Topologist, Intuitionist, Philosopher written by Dirk van Dalen and published by Springer Science & Business Media. This book was released on 2012-12-04 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main protagonists in the ‘foundation crisis’ of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.

Relatively and Philosophically Earnest

Author : Bharath Sriraman
Publisher : IAP
ISBN 13 : 1607523361
Total Pages : 259 pages
Book Rating : 4.6/5 (75 download)

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Book Synopsis Relatively and Philosophically Earnest by : Bharath Sriraman

Download or read book Relatively and Philosophically Earnest written by Bharath Sriraman and published by IAP. This book was released on 2009-10-01 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paul Ernest’s name is synonymous with social constructivism as a philosophy of mathematics. His contributions to mathematics education have occurred at a very fundamental level and to a extent shaped theory development in this field. His research addresses fundamental questions about the nature of mathematics and how it relates to teaching, learning and society. For the last three decades Paul has been a prolific scholar who has published in a wide array of topics such as the relationship between the philosophy of mathematics and mathematics education, and more generally the philosophy of mathematics education, ethics and values in mathematics education, and the philosophy of research methodology. The title of this Festschrift is meant to be a pun to convey the sometimes relativistic dimension to mathematical certainty that Paul argued for in developing his philosophy, and also a play on words for the fact that absolute “earnestness” may perhaps be a Platonic construct, and not possible in the realm of language and human discourse! Paul Ernest’s scholarly evolution and life can best be summarized in the words of Walt Whitman “Do I contradict myself? Very well then I contradict myself” (I am large, I contain multitudes). Indeed his presence has been large and multitudinous and this Festschrift celebrates his 65th Birthday with numerous contributions coming from the mathematics, philosophy and mathematics education communities around the world.

Categorical Logic and Type Theory

Author : B. Jacobs
Publisher : Gulf Professional Publishing
ISBN 13 : 9780444508539
Total Pages : 784 pages
Book Rating : 4.5/5 (85 download)

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Book Synopsis Categorical Logic and Type Theory by : B. Jacobs

Download or read book Categorical Logic and Type Theory written by B. Jacobs and published by Gulf Professional Publishing. This book was released on 2001-05-10 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.