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Author: Paul Ernest Publisher: SUNY Press ISBN: 9780791435878 Category : Philosophy Languages : en Pages : 336
Book Description
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.
Author: Paul Ernest Publisher: SUNY Press ISBN: 9780791435878 Category : Philosophy Languages : en Pages : 336
Book Description
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.
Author: Paul Ernest Publisher: SUNY Press ISBN: 9780791435885 Category : Philosophy Languages : en Pages : 338
Book Description
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.
Author: Paul Ernest Publisher: State University of New York Press ISBN: 1438402112 Category : Philosophy Languages : en Pages : 334
Book Description
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.
Author: Paul Ernest Publisher: Springer ISBN: 3319405691 Category : Education Languages : en Pages : 33
Book Description
This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.
Author: A.S. Troelstra Publisher: Elsevier Science ISBN: 9780444702661 Category : Mathematics Languages : en Pages : 355
Book Description
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.
Author: Michael Matthews Publisher: Springer Science & Business Media ISBN: 940115032X Category : Science Languages : en Pages : 241
Book Description
Constructivism is one of the most influential theories in contemporary education and learning theory. It has had great influence in science education. The papers in this collection represent, arguably, the most sustained examination of the theoretical and philosophical foundations of constructivism yet published. Topics covered include: orthodox epistemology and the philosophical traditions of constructivism; the relationship of epistemology to learning theory; the connection between philosophy and pedagogy in constructivist practice; the difference between radical and social constructivism, and an appraisal of their epistemology; the strengths and weaknesses of the Strong Programme in the sociology of science and implications for science education. The book contains an extensive bibliography. Contributors include philosophers of science, philosophers of education, science educators, and cognitive scientists. The book is noteworthy for bringing this diverse range of disciplines together in the examination of a central educational topic.
Author: David Sepkoski Publisher: Routledge ISBN: 1136768688 Category : Mathematics Languages : en Pages : 186
Book Description
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.
Author: Ernst von Glasersfeld Publisher: Routledge ISBN: 1135716056 Category : Education Languages : en Pages : 230
Book Description
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.
Author: Bonnie Gold Publisher: MAA ISBN: 9780883855676 Category : Mathematics Languages : en Pages : 392
Book Description
Sixteen original essays exploring recent developments in the philosophy of mathematics, written in a way mathematicians will understand.
Author: Barbara Jaworski Publisher: Psychology Press ISBN: 9780750703734 Category : Education Languages : en Pages : 254
Book Description
The author charts her developing ideas as she undertakes a several-year-long inquiry into an investigative, constructivist approach to mathematics teaching. She presents an account of constructivism as a philosophy of knowledge and learning, provides a rationale for the research methods she employs, and details case studies in the teaching and thinking of three teachers. The research took place in the UK before the introduction of the National Curriculum. Annotation copyright by Book News, Inc., Portland, OR
Author: Paul Ernest
Author: Paul Ernest
Author: Paul Ernest
Author: Paul Ernest
Author: Paul Ernest
Author: A.S. Troelstra
Author: Michael Matthews
Author: David Sepkoski
Author: Ernst von Glasersfeld
Author: Bonnie Gold
Author: Barbara Jaworski