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.
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.
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.
Download or read book What s Happening in Math Class Reconstructing professional identities written by and published by . This book was released on 1996 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
Download or read book Investigating Mathematics Teaching written by Barbara Jaworski and published by Psychology Press. This book was released on 1994 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
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.
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.
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.
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.
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 529 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
Download or read book The Foundational Debate written by Werner DePauli-Schimanovich and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constructibility and complexity play central roles in recent research in computer science, mathematics and physics. For example, scientists are investigating the complexity of computer programs, constructive proofs in mathematics and the randomness of physical processes. But there are different approaches to the explication of these concepts. This volume presents important research on the state of this discussion, especially as it refers to quantum mechanics. This `foundational debate' in computer science, mathematics and physics was already fully developed in 1930 in the Vienna Circle. A special section is devoted to its real founder Hans Hahn, referring to his contribution to the history and philosophy of science. The documentation section presents articles on the early Philipp Frank and on the Vienna Circle in exile. Reviews cover important recent literature on logical empiricism and related topics.
Download or read book Philosophy of Mathematics written by and published by Elsevier. This book was released on 2009-07-08 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics.-Comprehensive coverage of all main theories in the philosophy of mathematics-Clearly written expositions of fundamental ideas and concepts-Definitive discussions by leading researchers in the field-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included
Download or read book Project Based Learning in the Math Classroom written by Chris Fancher and published by Routledge. This book was released on 2021-10-03 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Project-Based Learning in the Math Classroom explains how to keep inquiry at the heart of mathematics teaching and helps teachers build students' abilities to be true mathematicians. This book outlines basic teaching strategies, such as questioning and exploration of concepts. It also provides advanced strategies for teachers who are already implementing inquiry-based methods. Project-Based Learning in the Math Classroom includes practical advice about strategies the authors have used in their own classrooms, and each chapter features strategies that can be implemented immediately. Teaching in a project-based environment means using great teaching practices. The authors impart strategies that assist teachers in planning standards-based lessons, encouraging wonder and curiosity, providing a safe environment where failure occurs, and giving students opportunities for revision and reflection. Grades 6-10
Download or read book Logical Approaches to Computational Barriers written by Arnold Beckmann and published by Springer. This book was released on 2006-06-29 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, June/July 2006. The book presents 31 revised full papers together with 30 invited papers, including papers corresponding to 8 plenary talks and 6 special sessions on proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and Gödel centenary: Gödel's legacy for computability.
Download or read book Symbolizing Modeling and Tool Use in Mathematics Education written by K.P Gravemeijer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the option of building on symbolizing, modeling and tool use as personally meaningful activities of students. It discusses the dimension of setting: varying from the study of informal, spontaneous activity of students, to an explicit focus on instructional design, and goals and effects of instruction; and the dimension of the theoretical framework of the researcher: varying from constructivism, to activity theory, cognitive psychology and instructional-design theory.
