Constructivism In Mathematics Vol 1
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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.
Radical Constructivism In Mathematics Education
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Author : E. von Glasersfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-06-30
Radical Constructivism In Mathematics Education written by E. von 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 1991-06-30 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.
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.
Beyond Constructivism
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Author : Richard A. Lesh
language : en
Publisher: Psychology Press
Release Date : 2003
Beyond Constructivism written by Richard A. Lesh and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Education categories.
First Published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.
Radical Constructivism
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Author : Ernst von Glasersfeld
language : en
Publisher: Routledge
Release Date : 2013-08-06
Radical Constructivism written by Ernst von Glasersfeld and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-06 with Education categories.
First Published in 1995. In the past decade or two, the most important theoretical perspective to emerge in mathematics education has been that of constructivism. This burst onto the international scene at the controversial Eleventh International Conference on the Psychology of Mathematics Education in Montreal in the summer of 1987. No one there will forget von Glasersfeld's authoritative plenary presentation on radical constructivism, and his replies to critics. Ironically, the conference, at which attacks on radical constructivism were perhaps intended to expose fatally its weaknesses, served as a platform from which the theory was launched to widespread international acceptance and approbation. Radical constructivism is a theory of knowing that provides a pragmatic approach to questions about reality, truth, language and human understanding. It breaks with the philosophical tradition and proposes a conception of knowledge that focuses on experiential fit rather than metaphysical truth. It claims to be a useful approach, not the revelation of a timeless world. The ten chapters of this book present different facets in an elegantly written and thoroughly argued account of this epistemological position, providing a profound analysis of its central concepts.
Constructivist Views On The Teaching And Learning Of Mathematics
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Author : Robert Benjamin Davis
language : en
Publisher:
Release Date : 1990
Constructivist Views On The Teaching And Learning Of Mathematics written by Robert Benjamin Davis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Education categories.
Constructivist views on the teaching and learning of mathematics (Journal for research in mathematics education).
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.
Key Works In Radical Constructivism
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Author : Ernst von Glasersfeld
language : en
Publisher: Brill / Sense
Release Date : 2007
Key Works In Radical Constructivism written by Ernst von Glasersfeld and has been published by Brill / Sense this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Constructivism (Education) categories.
Key Works on Radical Constructivism brings together a number of essays by Ernst von Glasersfeld that illustrate the application of a radical constructivist way of thinking in the areas of education, language, theory of knowledge, and the analysis of a few concepts that are indispensable in almost everything we think and do. Ernst von Glasersfeld's work opens a window on how we know what we know. The present work grew out of a desire to make more accessible this line of thought, to highlight its originality and consistency, and to illustrate its fecundity in the domains of cognition and learning. The first three parts of this book contain texts by Glasersfeld that outline the constructivist approach and explicate the frequently drastic reconceptualizations he has suggested. Both the last part and the postscript consist of commentaries by Edith Ackermann, Jacques Désautels, Gérard Fourez, Leslie P. Steffe and Kenneth Tobin, scholars in the fields that Glasersfeld has been concerned with. They examine a number of critical aspects pertaining to (radical) constructivism's current and future development, often tracing out paths that warrant further exploration and reflection, in particular concerning the sociopolitical dimension of knowledge. Key Works on Radical Constructivism is intended as a reference book for researchers, educators, and students of education--and for anyone interested in grasping, or deepening their grasp of, radical constructivism's tenets, ambitions and concerns. Readers will discover in this collection of firsthand contributions the contours of a bold, contemporary debate about a most compelling current of thought.
Constructivism
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Author : Catherine Twomey Fosnot
language : en
Publisher: Teachers College Press
Release Date : 2013-09-18
Constructivism written by Catherine Twomey Fosnot and has been published by Teachers College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-18 with Education categories.
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
Social Constructivism As A Philosophy Of Mathematics
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Author : Paul Ernest
language : en
Publisher: State University of New York Press
Release Date : 1997-11-20
Social Constructivism As A Philosophy Of Mathematics written by Paul Ernest and has been published by State University of New York Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-20 with Philosophy categories.
Proposing social constructivism as a novel philosophy of mathematics, this book is inspired by current work in sociology of knowledge and social studies of science. It extends the ideas of social constructivism to the philosophy of mathematics, developing a whole set of new notions. The outcome is a powerful critique of traditional absolutist conceptions of mathematics, as well as of the field of philosophy of mathematics itself. Proposed are a reconceptualization of the philosophy of mathematics and a new set of adequacy criteria. The book offers novel analyses of the important but under-recognized contributions of Wittgenstein and Lakatos to the philosophy of mathematics. Building on their ideas, it develops a theory of mathematical knowledge and its relation to the social context. It offers an original theory of mathematical knowledge based on the concept of conversation, and develops the rhetoric of mathematics to account for proof in mathematics. Another novel feature is the account of the social construction of subjective knowledge, which relates the learning of mathematics to philosophy of mathematics via the development of the individual mathematician. It concludes by considering the values of mathematics and its social responsibility.