Amongst Mathematicians

Author : Elena Nardi
Publisher : Springer Science & Business Media
Page : 349 pages
File Size : 55,9 Mb
Release : 2008
Category : Education
ISBN : 9780387371412

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Amongst Mathematicians by Elena Nardi Pdf

This book offers a unique perspective on ways in which mathematicians: perceive their students' learning; teach; reflect on their teaching practice. Elena Nardi achieves this by employing two fictional, yet entirely data-grounded, characters to create a conversation on these important issues. The construction of these characters is based on large bodies of data including intense focused group interviews with mathematicians and extensive analyses of students' written work, collected and analyzed over a substantial period.

Author : Elena Nardi
Publisher : Springer Science & Business Media
Page : 349 pages
File Size : 42,5 Mb
Release : 2007-11-19
Category : Education
ISBN : 9780387371436

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Amongst Mathematicians by Elena Nardi Pdf

This book offers a unique perspective on ways in which mathematicians: perceive their students' learning; teach; reflect on their teaching practice. Elena Nardi achieves this by employing two fictional, yet entirely data-grounded, characters to create a conversation on these important issues. The construction of these characters is based on large bodies of data including intense focused group interviews with mathematicians and extensive analyses of students' written work, collected and analyzed over a substantial period.

Author : Norma B. Goethe,Philip Beeley,David Rabouin
Publisher : Springer
Page : 210 pages
File Size : 40,5 Mb
Release : 2015-04-20
Category : Science
ISBN : 9789401796644

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G.W. Leibniz, Interrelations between Mathematics and Philosophy by Norma B. Goethe,Philip Beeley,David Rabouin Pdf

Up to now there have been scarcely any publications on Leibniz dedicated to investigating the interrelations between philosophy and mathematics in his thought. In part this is due to the previously restricted textual basis of editions such as those produced by Gerhardt. Through recent volumes of the scientific letters and mathematical papers series of the Academy Edition scholars have obtained a much richer textual basis on which to conduct their studies - material which allows readers to see interconnections between his philosophical and mathematical ideas which have not previously been manifested. The present book draws extensively from this recently published material. The contributors are among the best in their fields. Their commissioned papers cover thematically salient aspects of the various ways in which philosophy and mathematics informed each other in Leibniz's thought.

Author : Sepideh Stewart
Publisher : Springer Nature
Page : 286 pages
File Size : 40,6 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9783031342950

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Mathematicians’ Reflections on Teaching by Sepideh Stewart Pdf

Author : Regional Research Conference on Mathematical Methods in Nonlinear Wave Propagation
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 49,9 Mb
Release : 2005
Category : Nonlinear theories
ISBN : 9780821833490

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Mathematical Studies in Nonlinear Wave Propagation by Regional Research Conference on Mathematical Methods in Nonlinear Wave Propagation Pdf

Lively discussions and stimulating research were part of a five-day conference on Mathematical Methods in Nonlinear Wave Propagation sponsored by the NSF and CBMS. This volume is a collection of lectures and papers stemming from that event. Leading experts present dynamical systems and chaos, scattering and spectral theory, nonlinear wave equations, optimal control, optical waveguide design, and numerical simulation. The book is suitable for a diverse audience of mathematical specialists interested in fiber optic communications and other nonlinear phenomena. It is also suitable for engineers and other scientists interested in the mathematics of nonlinear wave propagation.

Author : Astrid Hilbert,Elisa Mastrogiacomo,Sonia Mazzucchi,Barbara Rüdiger,Stefania Ugolini
Publisher : Springer Nature
Page : 390 pages
File Size : 47,7 Mb
Release : 2023-04-02
Category : Mathematics
ISBN : 9783031140310

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Quantum and Stochastic Mathematical Physics by Astrid Hilbert,Elisa Mastrogiacomo,Sonia Mazzucchi,Barbara Rüdiger,Stefania Ugolini Pdf

Sergio Albeverio gave important contributions to many fields ranging from Physics to Mathematics, while creating new research areas from their interplay. Some of them are presented in this Volume that grew out of the Random Transformations and Invariance in Stochastic Dynamics Workshop held in Verona in 2019. To understand the theory of thermo- and fluid-dynamics, statistical mechanics, quantum mechanics and quantum field theory, Albeverio and his collaborators developed stochastic theories having strong interplays with operator theory and functional analysis. His contribution to the theory of (non Gaussian)-SPDEs, the related theory of (pseudo-)differential operators, and ergodic theory had several impacts to solve problems related, among other topics, to thermo- and fluid dynamics. His scientific works in the theory of interacting particles and its extension to configuration spaces lead, e.g., to the solution of open problems in statistical mechanics and quantum field theory. Together with Raphael Hoegh Krohn he introduced the theory of infinite dimensional Dirichlet forms, which nowadays is used in many different contexts, and new methods in the theory of Feynman path integration. He did not fear to further develop different methods in Mathematics, like, e.g., the theory of non-standard analysis and p-adic numbers.

Author : Heinz Steinbring
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 47,9 Mb
Release : 2006-03-30
Category : Education
ISBN : 9780387242538

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The Construction of New Mathematical Knowledge in Classroom Interaction by Heinz Steinbring Pdf

Mathematics is generally considered as the only science where knowledge is uni form, universal, and free from contradictions. „Mathematics is a social product - a 'net of norms', as Wittgenstein writes. In contrast to other institutions - traffic rules, legal systems or table manners -, which are often internally contradictory and are hardly ever unrestrictedly accepted, mathematics is distinguished by coherence and consensus. Although mathematics is presumably the discipline, which is the most differentiated internally, the corpus of mathematical knowledge constitutes a coher ent whole. The consistency of mathematics cannot be proved, yet, so far, no contra dictions were found that would question the uniformity of mathematics" (Heintz, 2000, p. 11). The coherence of mathematical knowledge is closely related to the kind of pro fessional communication that research mathematicians hold about mathematical knowledge. In an extensive study, Bettina Heintz (Heintz 2000) proposed that the historical development of formal mathematical proof was, in fact, a means of estab lishing a communicable „code of conduct" which helped mathematicians make themselves understood in relation to the truth of mathematical statements in a co ordinated and unequivocal way.

Author : Nélia Amado,Susana Carreira,Keith Jones
Publisher : Springer
Page : 579 pages
File Size : 45,8 Mb
Release : 2018-11-30
Category : Education
ISBN : 9783319998619

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Broadening the Scope of Research on Mathematical Problem Solving by Nélia Amado,Susana Carreira,Keith Jones Pdf

The innovative volume seeks to broaden the scope of research on mathematical problem solving in different educational environments. It brings together contributions not only from leading researchers, but also highlights collaborations with younger researchers to broadly explore mathematical problem-solving across many fields: mathematics education, psychology of education, technology education, mathematics popularization, and more. The volume’s three major themes—technology, creativity, and affect—represent key issues that are crucially embedded in the activity of problem solving in mathematics teaching and learning, both within the school setting and beyond the school. Through the book’s new pedagogical perspectives on these themes, it advances the field of research towards a more comprehensive approach on mathematical problem solving. Broadening the Scope of Research on Mathematical Problem Solving will prove to be a valuable resource for researchers and teachers interested in mathematical problem solving, as well as researchers and teachers interested in technology, creativity, and affect.

Author : Alan Bishop,M.A. (Ken) Clements,Christine Keitel-Kreidt,Jeremy Kilpatrick,Colette Laborde
Publisher : Springer Science & Business Media
Page : 1336 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Education
ISBN : 9789400914650

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International Handbook of Mathematics Education by Alan Bishop,M.A. (Ken) Clements,Christine Keitel-Kreidt,Jeremy Kilpatrick,Colette Laborde Pdf

ALAN J. BISHOP Monash University, Clayton, Victoria, Australia RATIONALE Mathematics Education is becoming a well-documented field with many books, journals and international conferences focusing on a variety of aspects relating to theory, research and practice. That documentation also reflects the fact that the field has expanded enormously in the last twenty years. At the 8th International Congress on Mathematics Education (ICME) in Seville, Spain, for example, there were 26 specialist Working Groups and 26 special ist Topic Groups, as well as a host of other group activities. In 1950 the 'Commission Internationale pour I 'Etude et l' Amelioration de l'Enseignement des Mathematiques' (CIEAEM) was formed and twenty years ago another active group, the 'International Group for the Psychology of Mathematics Education' (PME), began at the third ICME at Karlsruhe in 1976. Since then several other specialist groups have been formed, and are also active through regular conferences and publications, as documented in Edward Jacobsen's Chapter 34 in this volume.

Author : H. Christiansen,A.G. Howson,M. Otte
Publisher : Springer Science & Business Media
Page : 375 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Education
ISBN : 9789400945043

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Perspectives on Mathematics Education by H. Christiansen,A.G. Howson,M. Otte Pdf

BACOMET cannot be evaluated solely on the basis of its publications. It is important then that the reader, with only this volume on which to judge both the BACOMET activities and its major outcome to date, should know some thing of what preceded this book's publication. For it is the story of how a group of educators, mainly tutors of student-teachers of mathematics, com mitted themselves to a continuing period of work and self-education. The concept of BACOMET developed during a series of meetings held in 1978-79 between the three editors, Bent Christiansen, Geoffrey Howson and Michael Otte, at which we expressed our concern about the contributions from mathematics education as a discipline to teacher education, both as we observed it and as we participated in it. The short time which was at the teacher-educator's disposal, allied to the limited knowledge and experience of the students on which one had to build, raised puzzling problems concerning priorities and emphases. The recognition that these problems were shared by educators from many different countries was matched by the fact that it would be fruitless to attempt to search for an internationally (or even nationally) acceptable solution to our problems. Different contexts and traditions rule this out.

Author : Anonim
Publisher : BRILL
Page : 241 pages
File Size : 44,7 Mb
Release : 2009-01-01
Category : Education
ISBN : 9789460910319

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Mathematical Action & Structures of Noticing by Anonim Pdf

John Mason has been a prominent figure in the research field of mathematics education for several decades. His principal focus has been thinking about mathematical problems, supporting those who wish to foster and sustain their own thinking and the thinking of others.

Author : Paul Ernest
Publisher : Routledge
Page : 296 pages
File Size : 46,7 Mb
Release : 2012-10-12
Category : Education
ISBN : 9781136364792

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Constructing Mathematical Knowledge by Paul Ernest Pdf

First published in 1994. This book and its companion volume, Mathematics, Education and Philosophy: An International Perspective are edited collections. Instead of the sharply focused concerns of the research monograph, the books offer a panorama of complementary and forward-looking perspectives. They illustrate the breadth of theoretical and philosophical perspectives that can fruitfully be brough to bear on the mathematics and education. The empathise of this book is on epistemological issues, encompassing multiple perspectives on the learning of mathematics, as well as broader philosophical reflections on the genesis of knowledge. It explores constructivist and social theories of learning and discusses the rile of the computer in light of these theories.

Author : Gila Hanna,Michael de Villiers
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 52,5 Mb
Release : 2012-06-14
Category : Education
ISBN : 9789400721296

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Proof and Proving in Mathematics Education by Gila Hanna,Michael de Villiers Pdf

*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.

Author : Rolf Biehler,Michael Liebendörfer,Ghislaine Gueudet,Chris Rasmussen,Carl Winsløw
Publisher : Springer Nature
Page : 723 pages
File Size : 40,9 Mb
Release : 2023-01-01
Category : Education
ISBN : 9783031141751

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Practice-Oriented Research in Tertiary Mathematics Education by Rolf Biehler,Michael Liebendörfer,Ghislaine Gueudet,Chris Rasmussen,Carl Winsløw Pdf

This edited volume presents a broad range of original practice-oriented research studies about tertiary mathematics education. These are based on current theoretical frameworks and on established and innovative empirical research methods. It provides a relevant overview of current research, along with being a valuable resource for researchers in tertiary mathematics education, including novices in the field. Its practice orientation research makes it attractive to university mathematics teachers interested in getting access to current ideas and results, including theory-based and empirically evaluated teaching and learning innovations. The content of the book is spread over 5 sections: The secondary-tertiary transition; University students' mathematical practices and mathematical inquiry; Research on teaching and curriculum design; University students’ mathematical inquiry and Mathematics for non-specialists.

Author : National Research Council,Commission on Physical Sciences, Mathematics, and Applications,Committee on Strengthening the Linkages Between the Sciences and the Mathematical Sciences
Publisher : National Academies Press
Page : 134 pages
File Size : 42,6 Mb
Release : 2000-05-05
Category : Mathematics
ISBN : 9780309069472

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences by National Research Council,Commission on Physical Sciences, Mathematics, and Applications,Committee on Strengthening the Linkages Between the Sciences and the Mathematical Sciences Pdf

Over three hundred years ago, Galileo is reported to have said, "The laws of nature are written in the language of mathematics." Often mathematics and science go hand in hand, with one helping develop and improve the other. Discoveries in science, for example, open up new advances in statistics, computer science, operations research, and pure and applied mathematics which in turn enabled new practical technologies and advanced entirely new frontiers of science. Despite the interdependency that exists between these two disciplines, cooperation and collaboration between mathematical scientists and scientists have only occurred by chance. To encourage new collaboration between the mathematical sciences and other fields and to sustain present collaboration, the National Research Council (NRC) formed a committee representing a broad cross-section of scientists from academia, federal government laboratories, and industry. The goal of the committee was to examine the mechanisms for strengthening interdisciplinary research between mathematical sciences and the sciences, with a strong focus on suggesting the most effective mechanisms of collaboration. Strengthening the Linkages Between the Sciences and the Mathematical Sciences provides the findings and recommendations of the committee as well as case studies of cross-discipline collaboration, the workshop agenda, and federal agencies that provide funding for such collaboration.