Constructivism In Mathematics Vol 2
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Constructivism In Mathematics Vol 2
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Author : A.S. Troelstra
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Constructivism In Mathematics Vol 2 written by A.S. Troelstra and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
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
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Author :
language : en
Publisher:
Release Date : 1988
Constructivism In Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Constructive mathematics categories.
Constructivism In Mathematics Vol 1
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Author : A.S. Troelstra
language : en
Publisher: Elsevier
Release Date : 1988-07-01
Constructivism In Mathematics Vol 1 written by A.S. Troelstra and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-07-01 with Computers categories.
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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Author : Anne Sjerp Troelstra
language : en
Publisher:
Release Date : 1988
Constructivism In Mathematics written by Anne Sjerp Troelstra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Constructive mathematics categories.
"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." --
Beyond Constructivism
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Author : Richard A. Lesh
language : en
Publisher: Routledge
Release Date : 2003-05-01
Beyond Constructivism written by Richard A. Lesh and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-01 with Education categories.
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.
Radical Constructivism In Mathematics Education
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Author : E. Glasersfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Radical Constructivism In Mathematics Education written by E. Glasersfeld 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 2006-04-11 with Education categories.
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 : Paul Ernest
language : en
Publisher: SUNY Press
Release Date : 1998-01-01
Social Constructivism As A Philosophy Of Mathematics written by Paul Ernest and has been published by SUNY Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Philosophy categories.
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.
Constructivism In Mathematics
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Author : Anne S. Troelstra
language : en
Publisher:
Release Date : 1988
Constructivism In Mathematics written by Anne S. Troelstra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
Volume 2 Cases And Perspectives
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Author : M. Kathleen Heid
language : en
Publisher: IAP
Release Date : 2008-07-01
Volume 2 Cases And Perspectives written by M. Kathleen Heid and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-01 with Mathematics categories.
(Published in Co-operation with the National Council of Teacher of Mathematics) According to NCTM's Principles and Standards for School Mathematics, "Technology is essential in teaching and learning of mathematics; it influences the mathematics that is taught and it enhances students' learning." How does research inform this clarion call for technology in mathematics teaching and learning? In response to the need to craft appropriate roles for technology in school mathematics new technological approaches have been applied to the teaching and learning of mathematics, and these approaches have been examined by researchers world-wide. The second volume has a dual focus: cases and perspectives. It features descriptive cases that provide accounts of the development of technology-intensive curriculum and tools. In these cases the writers describe and analyze various roles that research played in their development work and ways in which research, curriculum development, and tool development can inform each other. These thoughtful descriptions and analyses provide documentation of how this process can and does occur. The remaining chapters in the second volume address research related issues and perspectives on the use of technology in the teaching and learning of mathematics. The lessons learned from the research presented in these volumes are lessons about teaching and learning that can be applied more broadly than solely in technological settings.
Constructivism In Mathematics
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Author : A. S. Troelstra
language : en
Publisher:
Release Date : 1988
Constructivism In Mathematics written by A. S. Troelstra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Intuitionistic mathematics categories.