Constructivism in Mathematics, Vol 2

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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.

Constructivism in Mathematics, Vol 1

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Author :
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.

Constructivism in Mathematics

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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:

Beyond Constructivism

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Author :
Publisher : Routledge
ISBN 13 : 1317438523
Total Pages : 610 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 610 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.

Beyond Constructivism

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Publisher : Psychology Press
ISBN 13 : 9780805838220
Total Pages : 614 pages
Book Rating : 4.8/5 (382 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 Psychology Press. This book was released on 2003 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.

Constructivism in Mathematics

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Author :
Publisher : Elsevier Science
ISBN 13 : 9780444702661
Total Pages : 355 pages
Book Rating : 4.7/5 (26 download)

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Book Synopsis Constructivism in Mathematics by : A.S. Troelstra

Download or read book Constructivism in Mathematics written by A.S. Troelstra and published by Elsevier Science. This book was released on 1988-07-15 with total page 355 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 Action

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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.

Radical Constructivism in Mathematics Education

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Author :
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.

Social Constructivism as a Philosophy of Mathematics

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Author :
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.

Investigating Mathematics Teaching

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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.

Categorical Logic and Type Theory

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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.

Constructivism in Mathematics

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Author :
Publisher : North Holland
ISBN 13 : 9780444705068
Total Pages : 0 pages
Book Rating : 4.7/5 (5 download)

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Book Synopsis Constructivism in Mathematics by : A.S. Troelstra

Download or read book Constructivism in Mathematics written by A.S. Troelstra and published by North Holland. This book was released on 1988-08-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Constructivism

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Author :
Publisher : Teachers College Press
ISBN 13 : 0807772593
Total Pages : 576 pages
Book Rating : 4.8/5 (77 download)

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Book Synopsis Constructivism by : Catherine Twomey Fosnot

Download or read book Constructivism written by Catherine Twomey Fosnot and published by Teachers College Press. This book was released on 2013-09-18 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This enduring bestseller remains the most comprehensive examination of constructivism and its relationship to teaching and learning. Closing the gap between theory and practice, well-known scholars make constructivism accessible by showing its application in everyday classrooms. Building on the success of the first edition, the authors have completely updated this popular text and expanded its scope to include examples of constructivist teaching across all grade levels and disciplines. An ambitious revision of a now classic text, Constructivism: Theory, Perspectives, and Practice, Second Edition is an invaluable resource for practicing teachers, teacher educators, and curriculum specialists in mathematics, science, social studies, and language arts. New for the Second Edition! An updated theory section that adds further contemporary biological evidence to go beyond the theories of Piaget and Vygotsky—offering a more contemporary framework for a psychological theory of learning.New chapters reflecting the school-based reforms that have been initiated since the writing of the first edition—specifically addressing the changes in mathematics, social studies, and teacher education.A new chapter on the emerging field of disability studies—including a critique that unmasks current practices and assumptions that better serve schools rather than students and their families. Contributors: Paul Cobb • Susan Cowey • Rheta DeVries • Eleanor Duckworth • Dewey I. Dykstra, Jr. • George Forman • Catherine Twomey Fosnot • Catherine A. Franklin • June S. Gould • Maxine Greene • Candace Julyan • Randall Stewart Perry • D. Kim Reid • Deborah Schifter • Jan Weatherly Valle • Ernst von Glasersfeld • Betty Zan. Praise for the First Edition! “Provides the reader with many ways of connecting to the central ideas of constructivism . . . highly readable.” —Gifted Child Quarterly “Shows how constructivist theory can inform classroom practices, and . . . provides teachers with a deeper understanding that gives substance to the rhetoric of school reform.” —Journal of Curriculum Studies

Constructivism in Mathematics, Vol 1

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Author :
Publisher : Elsevier Science
ISBN 13 : 9780444702661
Total Pages : 355 pages
Book Rating : 4.7/5 (26 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 Science. This book was released on 1988-07-15 with total page 355 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.

New Computational Paradigms

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Publisher : Springer Science & Business Media
ISBN 13 : 0387685464
Total Pages : 560 pages
Book Rating : 4.3/5 (876 download)

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Book Synopsis New Computational Paradigms by : S.B. Cooper

Download or read book New Computational Paradigms written by S.B. Cooper and published by Springer Science & Business Media. This book was released on 2007-11-28 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.

Nominalism and Constructivism in Seventeenth-Century Mathematical Philosophy

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Author :
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.

Constructivism in mathematics

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Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (633 download)

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Book Synopsis Constructivism in mathematics by : Anne S. Troelstra

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